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Full text of "A general history of the science and practice of music"




mM 



NOT TO BE TAKEN 

From the Library 



BRARY OF 
WELLESLEY COLLEGE 




PRESENTED BY 

LADY HUGGINS 



lO^r:^'; 



GENERAL HISTORY 



OF THE 



SCIENCE AND PRACTICE 



OF 



MUSIC, 



BY 



SIR JOHN HAWKINS. 



A NEW EDITION, 
WITH THE AUTHOR'S POSTHUMOUS NOTES. 



VOL. I. 



LONDON : 

NOVELLO, EWER & CO., i, BERNERS STREET (W.), And 35, POULTRY (E.G.) 

NEW YORK, J. L. PETERS, 843, BROADWAY. 

1875- 



NOVILLLO, EWER AND CO., 

TYPOGRAPHICAL MUSIC AND GENERAL PRINTERS, 

I, BERNERS STREET, LONDON. 

\ 8 137 



LIFE OF 



SIK JOHN HAWKINS 



COMPILED FKOJI 



ORIGINAL SOURCES. 



SIR JOHN HAWKINS, the friend and executor of 
Dr. Johnson, and a descendant of the Sir John Hawkins 
who commanded the Victory, and one of the four divi- 
sions of the fleet, as vice-admiral, at the destruction of 
the Spanish armada, was born in 1719. His fathei", an 
architect and surveyor, at first brought his son up to his 
own profession, but eventually bound him to an attorney, 
' a hard taskmaster and a penurious housekeeper.' At 
the expiration of the usual temi, the clerk became a 
solicitor, and by unremitting assiduity, united to the most 
inflexible probity, he, imfdended, established himself in a 
respectable business, while by his character and acquire- 
ments he gained admission into the company of men emi- 
nent for their accomplishments and intellectual attain- 
ments. He w^as an original member of the Madi-igal 
Society, and at the age of thirty was selected by Mr. 
(afterwards Dr.) Johnson as one of the nine who formed 
his Thursday-evening Club in Ivy-lane ; a most flatter- 
ing distinction, which confinned his literary habits, and 
powerfully influenced his future pursuits when, not many 
years after, he relinquished his profession. 

In 1753, Mr. Hawkins married Sidney, the second 
daughter of Peter Storer, Esq., with whom he received 
an. independent fortune, which was greatly augmented in 
1759 by the death of his wife's brother. He then retired 
from all professional avocations, giving up his business to 
his clerk, Mr. Clark, who subsequently became chamber- 
lain of the city of London. With this increase of wealth 
is connected an anecdote of far too honorable a nature to be 
omitted here. The brother of Mrs. Hawkins made a will, 
giving her the whole of his fortune, except a legacy of 
£500 to a sister from whom he had become alienated, 
and communicated the fact to Mr. and Mrs. Hawkins, 
who, by representing the injustice of this act, and by 
adding entreaty to argument, prevailed on him to make 
a more equitable distribution of his property, and an equal 
division was the consequence. ' We lost by this (says 
Miss Hawkins, her father's biographer) more than £1,000 
a-year; but our gain is inestimable, and we can ride 
through a manor gone from us with exultation.' 

Upon retiring from the law, Mr. Hawkins purchased a 
house at Twickenham, intending to dedicate his future 



life to literary labour and the enjoyment of select society. 
But in 1771 he was inserted in the commission of the 
peace for the county of Middlesex, and immediately be- 
came a most active magistrate. Here his independent 
spirit and charitable disposition were manifested. Acting 
as a magistrate, he at first refused the customary fees ; 
but finding that this generous mode of proceeding rather 
increased the litigious disposition of the people in his 
neighbourhood, he altered his plan, took what was his 
due, but kept the amount in a separate purse, and at fixed 
periods consigned it to the clergyman of his parish, to be 
distributed at his discretion. 

Being about this time led, by the defective state of the 
Highways, to consider the laws respecting them, and their 
deficiencies, he determined to revise them, and accord- 
ingly drew up a scheme for an Act of Parliament, to con- 
solidate the several former statutes, and to add such other 
regulations as appeared to him necessary. His ideas on 
this subject he published in 1763, in an 8vo. volume en- 
tituled ' Observations on the state of Highways, and on 
the Laws for amending and keeping them in repair;' 
subjoining a draught of the Act before-mentioned. This 
very bill was afterwards introduced into the House of 
Commons, and passing through the usual forms, became 
the Act under which all the Highways in the kingdom 
were for many years regulated, and which forms the 
nucleus of the statutes now in force. 

Some time after this, a cause as important in its nature, 
if not so extensive in its influence, induced him again to 
exert himself in the service of the public. The Corporation 
of London, finding it necessary to rebuild the gaol of New- 
gate, at an expense, according to their own estimates, of 
£40,000, had applied to Parliament, by a bill brought in 
by their own members, to throw the onus of two-thirds of 
the outlay on the County of Middlesex. This the Magis- 
trates of the County thought fit to resist, and accordingly 
a vigorous opposition was commenced under the conduct 
of Mr. Hawkins, who drew a petition accompanied by a 
case, which was printed and distributed among the mem- 
bers of both Houses of Parliament. This memorial be- 
came the subject of a day's discussion in the House of 
Lords, and in the Commons produced such an effect, that 



IV. 



LIFE OF SIR JOHN HAAVKINS. 



the City of London, by their own members, moved for 
leave to withdraw the bill. 

He was, in 1765, elected chairman of the Middlesex 
(juarter-sessions. 

Not long after this event, the rector and officers of the 
parish of St. Andrew's, Holborn, in which he was then a 
resident, solicited his assistance in opposing an attempt of 
the Corporation of London, to carry out a design whicli 
was fraught with injury to their interests. The City 
had projected opening a street from Blackfriars-bridge 
(then lately built) across the bottom of Holborn-hill, 
and as much fiu-ther northward as tliey might think 
proper. In the execution of this scheme, they had con- 
templated, among other changes, the bestowal of the Fleet 
prison (an intolerable nuisance) on their neighbours, the 
parishioners of St. Andrew's, by its removal to the spot 
on which Ely House then stood. They had accordingly 
entered into a treaty with the then bishop of Ely, and 
wei-e exerting all their influence to drive a bill through 
the House of Commons, which should confirm that con- 
tract, and enable the bishop to alienate the inheritance. 
The inhabitants of the neighbourhood, together with the 
earl of Winchelsea, the ground landlord, reasonably 
alarmed at this project, determined to oppose it through- 
out, and to this end applied to Mr. Hawkins for his aid. 
He accordingly drew two petitions, one in behalf of the 
rector and chm-chwardens, and the other in that of lord 
"Winchelsea, with a case for each, containing the reasons 
on which they rested their opposition. These, like his 
previous endeavours, were successful, and the application 
of the City of London failed. For this assistance, the 
parish not content with returning him their thanks, de- 
termined to expend £30 in the purchase of a silver cup 
to be presented to him, a resolution which was shortly 
afterwards carried into effect. During this time his 
literary reputation had become so highly established, that 
the University of Oxford, meditating a re-publication of 
Sir Thomas Hanraer's Shakespeare, in 6 vols. 4to, with 
additional notes, applied to him to furnish them. This he 
accordingly did, and on the issue of the work, received 
from the University a copy as a present — a favor the 
more to be esteemed as but six copies of the impression 
were thus given. Of these the King received one, the 
Queen another, the King of Denmark a tliird, and Mr. 
Hawkins a fourth. To whom the other two were pre- 
sented is now not known. In 1770, a charge was de- 
livered by him, in his capacity of Chairman of the Quarter 
Sessions, to the grand jury of Middlesex, which, at their 
general i-equest, was printed and published. During the 
years of which we have been speaking, popular dis- 
content had occasionally risen high, and in the execution 
of his duty as a magistrate Mr. Hawkins had more than 
once been called into service of great personal danger ; 
but his was not a character to shrink from peril in a good 
cause, and when the riots at Brentford broke out, as they 
did with great violence on various occasions, he and some of 
bis brethren presenting themselves on the spot, effectually 
suppressed the tumult by their resolute demeanour. 



When, too, the rising of the Spitalfields weavers took 
place, the Middlesex magistrates, and he at their head, 
attended at JNIoorfields, the scene of the disturbances, 
with a party of the Guards, and succeeded by their firm- 
ness and conduct in dispersing the mob, and repressing 
an outbreak which at one time seemed to threaten for- 
midable results. 

Having thus, on many occasions, given proofs of his 
courage, loyalty, and ability, he in 1772 received from his 
Majesty, George III., the honor of knighthood. 

A fresh edition of Shakespeare being contemplated by 
Dr. Johnson and INIr. Stevens in 1773, he was, for the 
second time, requested to furnish notes to that author, 
which he accordingly did. 

In 1775, the year in which it was determined to com 
mence the disastrous American war, it being thought 
proper to carry up an address from the county of Mid- 
dlesex to the King on the occasion, the magistrates, at 
his instance, voted one which he drew up, and had the 
honor of presenting to his Majesty in the October of 
that year. 

It may not be out of place to notice here, an assertion 
made by Boswell in his Life of Johnson, vol. i. p. 168, 
that ' upon occasion of presenting an address to the 
King, he (Hawkins) accepted the usual offer of knight- 
hood.' Without remarking on the spirit which has evi- 
dently actuated Boswell whenever he has spoken of Sir 
John, it is enough to state that no address whatever was 
presented in 1772 (the year in which he was knighted), 
or for some years previously ; and, moreover, that there 
is strong reason to believe that the address of 1775, men- 
tioned above (which was presented exactly three years 
after the date of his knighthood), was the only one in 
which he ever was concerned. Be this last as it maj', the 
fact above mentioned sufficiently disproves the allegation. 
Even, however, if the honor had been attained as Boswell 
describes, it would have mattered little ; for that he was 
not imworthy of it may be gathered from the fact, that 
the Earl of Rochford (then one of the Secretaries of 
State), when presenting him to the King for knighthood, 
took occasion to describe him as the best magistrate 
in the kingdom. 

In the memorable year 1780, an order from the Privy 
Council having been issued through the Secretary of 
State's office, requiring the Middlesex magistrates to 
assemble for the preservation of the public peace, he and 
some others met early in the morning of Monday, the 
5th of June, and continued sitting at Hicks's Hall, their 
Sessions House, till late in the evening. On the following 
day they did likewise ; but at night, instead of returning 
to their own homes, they determined to form parties of 
two each, and thus to distribute themselves in those 
places where mischief was to be apprehended. This re- 
solution was taken in consequence of the prevalence of a 
report that the mob intended to attack the houses of Lord 
North and of other members of the Administration, and 
also that of Lord Mansfield. As Sir John bad long 
been honored with the friendship of the latter, he fixed 



LIFE OF SIR JOHN HAWKINS. 



V. 



upon him as the object of his attention, and accordingly 
proceeded to his house, accompanied by a brother magis- 
trate who resided in the neighbourhood. On their ar- 
rival they found Lord Mansfield writing to the Secretary 
of War for a party of the Guards, and the interval between 
the despatch of the application and the arrival of the 
troops was spent in conferences with his Lordship and 
the Archbishop of York (his neighbour), on the plan to 
be adopted. On Lord Mansfield's asking Sir John his in- 
tentions, he answered that his design was to place the men 
behind the piers which divided the windows, and to hold 
them in readiness to fire on the mob directly the demon- 
strations of the rioters rendered such an act necessary. 
To this, however. Lord Mansfield objected, from a dislike 
to bloodshed, and on the arrival of the troops, declined to 
take them into the house, sending them to the vestry 
at Bloomsbury, to remain there, in readiness to act, if 
their services should be reqiiired. As it appeared he did 
not wish to retain the magistrates, they retired, having 
arranged that Sir John should remain at the house of his 
colleague in Southampton-row, close by, till 12 p.m., at 
which time he intended, if all remained quiet, to return 
to his own home, as his Lordship would still have one 
magistrate in his immediate vicinity in case of any emer- 
gency. In Southampton-row he accordingly staid till 
past midnight, when, no disturbance having occurred at 
Lord Mansfield's, and a messenger arriving from North- 
umberland House to say that it was beset, and that the 
Duke had sent for Sir John, he proceeded thither.* On 
his arrival there, he found that a considerable mob was 
assembled in front of the house, but that no assaidt had 
yet been attempted. Proper precautions were imme- 
diately taken for its defence, and in order that the pro- 
jected measures might be duly carried out, in the event 
of an outbreak, the Duke pressed Sir John to stay there 
the remainder of the night, which he accordingly con- 
sented to do. He was, howerer, very near paying 
dearly for his conduct, for, notwithstanding the lateness 
of the hour at which he entered Northumberland House, 
he had been recognised by the mob, who were heard to 
menace him with their vengeance. This threat they evi- 
dently intended to carry out, for on his return to his 
house in Queen's-square, Westminster, he discovered that 
it had been marked with a red cross, the symbol by which 
during that period the rioters devoted property to de- 
struction. Being, fortunately for him, fully aware of the 
meaning of the sign, he immediately saw the necessity of 
erasing it. This, however, was no easy matter, for, from 
the crowds of people who had assembled in all parts of the 
town, there was great danger of any attempt to efface it 
being at once discovered. Placing himself, however, 
with his back against the wall, in the careless way in 
which an indifferent spectator might be supposed to stand, 

* It was afterwards discovered that there had been aii error in the 
message which he received. It had really been sent from Lord North's, 
in Downing-street, and not the Duke of Northumberland's. The simi- 
larity in the names probably originated the mistake, which might be 
farther confirmed by the fact that the Duke, as Lord Lieutenant of the 
«ounty, was a likely object of attack, at a time when every magistrate 
was favored with the detestation of the populace. 



he passed his hand, in which was a handkerchief, behind 
him, and thus succeeded in totally obliterating the ill- 
omened symbol. Fortunately, his having done so was un- 
noticed ; the mark was not renewed, and his house escaped 
the destruction which, the following night, overtook all 
others similarly distinguished. 

' When these tumults had in some measure subsided, 
it became necessary to bring to trial many persons who, 
by their participation in them, had become involved in 
the guilt of high treason ; and it was therefore im- 
perative that the grand jury of Middlesex, to whom 
the indictments were to be presented, should be in- 
structed in the state of the law as bearing upon the 
offence in question. A message, at the instance of the 
Attorney-General, was accordingly sent to Sir John, 
desiring him to deliver, at the then ensuing session, 
a charge to the grand jury, explanatory of the duties 
required of them. This desire, at the moment it was 
made, was sufficiently embarrassing, for he was away 
from home, and consequently at a distance from the books 
he wished to consult ; and, moreover, he had but forty- 
eight hours in which to prepare his address. Notwith- 
slanding these disadvantages, he, however, constructed a 
charge which on its delivery was highly commended, and 
which the grand jury, after passing a vote of thanks to 
him for its 'learning and eloquence,' desirea to have 
printed and published. 

I But to return to the narrative of his youth ; from 
which this digression has been made in order to relate 
uninterruptedly the incidents of his magisterial career. 
Very early in life he cultivated music as the solace of 
his severer occupations — the recreation of his leisure 
hours. It was the society of the eminent that young 
Hawkins courted, and in the practice of the classical 
music of his day that he took delight. Immyns, and 
through him Dr. Pepusch, were his earliest musical 
associates. His daughter records an interesting anecdote 
of his acquaintance with Handel. She says : — 

" Were I to attempt enumerating my father's musical 
friendships, I should copy, a second time, the greater 
part of the last volume of his History of Music ; I will, 
however, record what I have heard and known of those 
between whom and himself this powerful union subsisted. 
Handel had done him the honor frequently to try his new 
productions in his young ear ; and my father calling on 
him one morning to pay him a visit of respect, he made 
him sit down, and listen to the air of See the conquering 
Hero comes, concluding with the question, ' How do you 
like it ? ' my father answering, ' Not so well as some 
things I have heard of yours;' he rejoined, 'Nor I 
neither ; but, young man, you will live to see that a 
greater favorite with the people than my other fine 
things.' 

He was an original member of the 'Madrigal Society,' 
founded by the former in 1741. With Stanley he en- 
gaged in 1742, in the joint publication of some Canzonets 
of which Hawkins furnished the greater portion of the 
words, while Stanley composed the music. 



VI. 



LIFE OF SIR JOHN HAWKINS. 



Young men, accomplished in music, frequently find it 
an excellent introduction to company which otherwise 
they would hardly reach, and a recommendation to 
patrons by whom their legal or mercantile abilities might 
be overlooked. And so young Hawkins found : his Can- 
zonets were sung and encored at Vauxhall, Ranelagh, 
and other places. The author of 'Who'll buy a heart?' 
was enquired after: amongst others, a Mr. Hare, a 
brewer, and musical amateur, who had often met Hawkins 
at Mr. Stanley's, invited him to his house. At Mr. 
Hare's he met his future father-in-law, Mr. Storer, who 
being a practitioner in a high grade of the law, but de- 
clining into years, found in the young amateur of music, 
first a valuable assistant, and afterwards a welcome hus- 
band for his daughter, and sharer of his opulence. 

Some time previous to the publication of the Canzonets 
mentioned above, he had been well known in the literary 
world as the author of various contributions to the ' Gen- 
tleman's Magazine,' and other periodicals of similar de- 
scription. These, being mostly anonymous, are now, 
of course, not easily traced. This much, however, is 
known : that they were not confined to any one subject, 
but embraced many different topics, and that they 
comprised both prose and poetry. A copy of verses to 
Mr. John Stanley, inserted in the Daily Advertiser for 
Feb. 21, 1741, and bearing date Feb. 19, 1740, is sup- 
posed to have been the earliest of his productions now 
known. But it was not only to the lighter occupation of 
literature that his attention was directed ; for when, in 
the eventful year of 1745, the young Pretender published 
his manifesto, an answer to it, written by Mr. Hawkins, 
was widely circulated and read ; and a series of papers 
on the same subject, furnished to the magazines and 
newspapers of the day, attested his attachment to the 
House of Hanover. His conduct, indeed, at this critical 
period, attracted the notice of the Duke of Newcastle, 
who wished to bring him into public life — 'which at- 
tempt,' says a friend and contemporary of Sir .John's, in 
writing to his son, ' was frustrated by your father's 
predilection for a studious life, and from a reserved 
disposition.' Nor was this the only occasion on which 
the honor was offered him, for in the same letter, 
dated Feb. 4, 1796, the correspondent, Mr. T. Gwatkin, 
of Eign, near Hereford, says — 'When the noise was 
' loud about Wilkes and liberty, Sir John's conduct as 
' a magistrate, and his subsequent charges, met with 
'the approbation of the Duke of Northumberland, the 

* Lord Lieutenant for the county of Middlesex, who 
' wished to introduce him into Parliament. I strongly 
' urged him to accept the offer : my arguments made some 
' impression ; but he was then deeply engaged in the 
' History of Music ; besides he was, as I could easily 
' collect from repeated conversations — although both from 

* habit and theoretical reasoning entirely attached to the 
' House of Hanover — jealous of his own personal in- 

* dependence. If, merely from personal interest, he could 
' have been returned for a county or city, I believe he 
'would have had no objection; but although be was a 



' friend to the Administration, he did not choose to come 
' into Parliament under the auspices of any minister. 
' An offer was made him of placing you and your brother 
' upon the foundation of King's Scholars at Westminster, 
' and I pressed him to accept it, from the examples of 
' Lord Mansfield and other great men who were upon 
' the foundation, yet from the same principle of inde- 
' pendence he rejected it.' 

This letter, which certainly gives great insight into Sir 
John's character, v/ould not have been quoted so much 
at length, did it not furnish the best possible refutation of 
the stigma cast upon him by Boswell — that, in his inter- 
course with Johnson, he betrayed an unworthy spirit of 
subserviency. Of this, however, it will be requisite to 
speak hereafter. 

The motive that induced him to decline the offer of the 
presentation, was the feeling that the intention of the 
founder would be violated, if those who were in a position 
to pay for the education of their children, placed them on 
a foundation designed exclusively for ' poor scholars.' 

In 1760, being in possession of some authentic and in- 
teresting documents relating to the author, he published 
an edition of Walton's ' Complete Angler,' with the 
second part by Cotton. To the original work he added 
notes, and wrote a life of Walton appending one of 
Cotton by the well-known Mr. W. Oldys : and that no 
means of making the work attractive might be neglected, 
he embellished it with cuts, designed by Wade, and 
engraved by Ryland, which are even at this time, when 
art has so much advanced, remarkable for their elegance. 
Of this work, three editions were sold off" before the year 
1784, when he published a fourth. For this, he had revised 
the life of Walton, and the notes throughout the work, 
and made large additions to both, while he re-wrote the 
life of Cotton in order to compress it, retaining, however, 
every fact respecting him mentioned in the former im- 
pressions, and subjoining several more. After his death, 
a fifth edition was published by his eldest son, Avho 
inserted the last corrections and additions found in Sir 
John's papers. 

About the year 1770, the Academy ot Ancient Music 
finding that, owing to the increase in the number of 
places of public amusement, and the consequent enlarged 
demands for eminent performers, their subscription 
of two guineas and a half was not sufficient to carry 
out the plan they had adopted, were obliged to solicit 
farther assistance. To this end ]\Ir. Hawkins, then a 
member, drew up and published a pamphlet entitled 
' An Account of the institution and progress of the 
' Academy of Ancient Music, with a comparative view of 
'the Music of the past and present times.' This was 
published in octavo in 1770, but without any author's 
name. 

Hawkins had long been a member of all the best con- 
certs in London ; and when circumstances permitted him 
to make his own house a central point of assembly, the 
first musical men of the day flocked with pleasure to 
Austin Friars. Drs. Cooke and Boyce were among his 



LIFE OF SIR JOHN HAWKINS. 



Vll. 



intimate friends ; and Bartleman, then a boy, his protege. 
He collected all the standard compositions of his own 
day, and of former times, and pnrchased, after the death 
of their owner, Dr. Pepusch's invaluable collection of 
theoretical treatises.* The idea of becoming the historian 
of the art he cultivated with so much ardour, is said to 
have been first suggested to him by the celebrated Horace 
Walpole : and when the inheritance of his brother-in- 
law rendered him independent of any involuntary labour, 
he seriously applied himself to the task. Of itself it was 
no easy one, and the multiplied demands which the 
duties of an active and presiding magistrate made upon 
his time considerably prolonged its duration. In this, as 
in all his other literary labours, his daughter, together 
with his sons, afforded the assistance of amanuensis, col- 
lator, and corrector of tlie press. In collecting his ma- 
terials Sir John Hawkins was indefatigable — 

' Nil actum reputans, si quid supcresset agendum.' 

lie corresponded with every one from whom information 
could be hoped, and amongst others Avith Dr. Gostling, 
of Canterbury,! from whose collections and recollections 
he obtained much curious matter that no other person 
could have furnished. Correspondence led to personal 
intimacy, and Sir John visited Mr. Gostling at Canter- 
bury in 1772 and the following year. He also, in 1772, 
resided a considerable time in Oxford, making extracts 
from MSS. in the Bodleian and other libraries, and ac- 
companied by an artist from London to copy the portraits 
in the Music School. 

In 177G he published, in 5 vols. 4to, his ' History of 
IMusic,' a work upon which he had been engaged for 
the space of sixteen years. Three years before, he 
had obtained permission to dedicate his book to George 
III. ; and he now presented it to his Majesty at Buck- 
ingham House, during a long audience granted for the 
purpose. The King, no doubt, appreciated the work 
as it deserved, and the University of Oxford showed 
their estimation of it by offering to confer on the author 
the deo-ree of Doctor in Law, which he had reasons for de- 
clining ; but that learned body paid him the compliment 
of requesting his porti-ait, which now hangs in the Music 
School. 

In this delitrhtful book, authorities haA-^ been consulted 
and brought together from various libraries and museums, 
with a diligence in research, and a solicitude almost affec- 
tionate in their collection and arrangement, forming 
together a mass of the most curious and entertaining 

* This collection, when his History of JIusic was published, Sir Jolin 
gave to the British Museum, and thus preserved it from tlie fate which 
attended the rest of his library. 

t The Rev. William Gostling, Minor Canon of Canterbury Cathedral, 
■was the son of that Mr. Gostling for whom Purcell wrote his celebrated 
antliem, ' They that go down to the sea in ships,' and of whom Charles 
II. said, ' You may talk of your nightingales and sky-larks, but I have 
a Gosling shall beat them all.' Combining his own knowledge to the 
information derived from his father, Mr. Gostling was a living de- 
pository of musical history and anecdote back nearly to the middle 
of the seventeenth century. 



information upon a subject the most enchanting. No 
pains have been spared to render the work complete. It 
bears evidence of being a labour of love ; of being one of 
those tasks, which are none to the compiler, — but a 
delight. The evident pleasure he takes in his work, 
reflects itself upon the reader ; rendering it light and 
agreeable, — nothing wearisome, however long and minute. 
There is evidence of toil, but the perusal is not toilsome ; 
for the author's toil is so willingly undertaken, and so cn- 
joyingly pursued, that the effect upon the reader is un- 
alloyed enjoyment. No amount of care has been deemed 
too much ; and the reader feels grateful for being spared 
the trouble of seeking, while he luxuriously profits by the 
result. He sits in liis arm-chair, comfortably ruminating 
the stores of knowledge which have been cidled for him 
from various wide-spread sources, by patient, worthy Sir 
John ; who, — the beauty of it is, — has evidently had as 
much gratification in gathering the materials for the feast, 
as the reader finds from the feast itself. Besides the in- 
formation contained in the book, there is abundance of 
amusing reading. It was a favorite with Charles Lamb, 
who, though no musical authority, was an eminent lite- 
rary one, of unsurpassed refined taste and high judgment. 
In the shape of notes, there is a fund of anecdote, and a 
large amoimt of incidental miscellaneous matter, scattered 
through the work, that pleasantly relieve the graver main 
theme. Anything entertaining, that can by possibility be 
linked on to the subject of music, is easily and chattily 
introduced ; as though the author and his reader were 
indulging in a cheerful gossip by the way. We have, in 
quaint succession, such things as that romantic love- 
passage of Giuffredo Rudello, the troubadour poet ; or 
that wondrous account of the Moorish Admirable Crichton, 
Alpharabius, — which is like a page out of the ' Arabian 
Nights ;' or that naive detail of bluff King Harry's fancy 
for my Lord Cardinal's minstrels, and of his setting oft' 
with them for a certain nobleman's house where Avas 
a shrine to which he had vowed a pilgrimage, and where 
he spent the night in dancing to the sound of the min- 
strels' playing. 

Sir John had no prototype of his great work. The 
design, as the execution, was entirely his own ; and when 
the large extent, and various nature of his materials are 
considered, the plan will be allowed to have been devised 
with considerable ability. 

It is not an unusual, and at first sight appears not an 
imreasonable prejudice, to suppose that, in order to 
qualify a man to write upon any art, he shoidd be a pro- 
fessor of, or at least have been regularly educated to, the 
art of which he treats. A lawyer seems as little qualified 
to write a history of Music, as a composer Avould be 
to expound the nature of Uses and Trusts, or a violin 
player to explain the principles of Architectural beauty. 
To write on the practical department of an art certainly 
requires experience and information which an artist alone 
can acquire ; and had Sir John Hawkins publislied a new 
book of instructions for the organ or violoncello, he would 
probably have subjected himself to being deservedly ac- 



Vlll. 



LIFE OF SIR JOHN HAWKINS. 



cused of presumption. The theory of an art, even, can 
hardly be satisfactorily explained, except by one who has 
that intimate familiarity with its practice and its nomen- 
clature which is rarely, if ever, attained by an amateur. 
But with the historian the case is different : it is to be 
presumed that a man who voluntarily dedicates years of 
labour to collect from all quarters the scattered records of 
an art, must be, on the one hand, himself attached to it, 
and familiar with its practice, in a degree amply sufficient 
to secure him against the danger of misinterpreting any 
technical or conventional phrases ; while, on the other 
hand, the habits of research, the knowledge of languages, 
and the various literar}' acquirements requisite for the 
liistorian, are but seldom to be found united in the mere 
artist. Captain Cook used to say that the best weather- 
glass in the world would be made by the amalgamation 
(or, as he called it, stewing down together) of a sailor 
and a shepherd : for the one spent his whole life in 
studying the prognostics of wind and rain, and the other 
those of sunshine and rain. So the beau ideal of a his- 



torian of music would be found in a man who united irr 
his own person the composer, performer, linguist, and 
philosopher, together with the leisure and studious habits 
of the man of letters. But if we cannot find this phoenix, 
if we must rest contented either with the artist or the 
student, the balance of qualification is highly in favour of 
the latter. Sir John Hawkins, however, was made to 
feel the weight of the prejudice we have alluded to : in 
immediate competition with his History of Music, another 
work imder the same title was published by Dr. Burney. 
The public did not even compare the respective merits of 
the works : they eagerly purchased the professor's history, 
while that of the amateur was left luiasked for, or sneered 
at, on the publisher's counter. 

The fate of the work, however, was decided at last, like 
that of many more important things, by a trifle, a word, 
a pun. A pun condemned Sir John Hawkins's sixteen 
years' labour to long obscurity and obli\ ion. Some wag 
wrote the following catcl), which Dr. Callcott set to 
music : — 



N.B. — Leave out the Bars between + + till the ?>xA Voice comes in, tlien '^o on. 




m^i 



^i 



^Se3 



i=^^?=^^^^ 



o 



3 



e^E 



Have you Sir John Haw-kins' hist'ry, some folks think it quite a myst'ry, Sir John Hawkins, 



iS^li 



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4 



ggS^f^E 



'^: 



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=tfE 



Mu - sic fiird his won-d'rous brain, how d'ye like him is it pliun, how d'ye like him, how d'ye 



Both I've read, and must a - grce that Bur-ney"s his-t'ry pleas- cs me, 



i 



Burney's 



r P- 



E^?=?^ 



^^MHi^^ 



Sir John Hawlcins, 



^-^ 



Sir John HaMkins, 



=^= 



like him, how d'ye like him, how d'ye like him, 



how d'ye like him. 



=PE 



;^i 



Sir John 



how d'^■e 



^=eE 



■=3 » — - ^ — p 
7- 7 - 7 ^^ 






^E 






hist'ry. 



Bur-ney's his-t'ry, Bumey's liis-t'ry, Burney's liis-t'ry, Burney's his-t'ry, Bunicy's 



P 






/7 \ +-•- 

-h- 



-tt- 






P 



Hawkins, Sir John Hawkins, Sir John Hawkins, some folks think it quite 

/Ts -f- 



i;z=;?-=^ 



y-"=7=^^/ — V- 



-/■ — /^ — C- 



^E 



a myst'ry. 



3 



like him, how d'ye like him, how d'ye like him, how d'ye like 

^ + ^_ 

— I- 



him, is 



it plain. 



f^=f=S^^^=?=^=^^^ 



his- fry, Burney's his- fry, Burney's his- Vvy, 



3=3==1S; 



1 



Bur - ncy 's his - f rj' pleas - es me. 

I. W. Callcott, B.M. 



Bmn /lis history was straightway in every one's mouth ; the impression in the profoundest depths of a damp cellar, 

and the bookseller, if he did not literally follow the as an article never likely to be called for ; so that now 

adrice, actually ' wasted,' as the term is, or sold for liardly a copj' can be prociu'ed undamaged by damp and, 

waste paper some hundred copies, and buried the rest of mildew. It has been for some time, however, rising — is 



LIFE OF SIR JOHN HAWKINS. 



IX, 



rising — and the more it is read and known, the more 
it will rise in public estimation and demand. 

It may not, however, be generally known that Barney's 
History, which was more successful at the time, was not 
begun till many years after this, nor till its author had 
been allowed constant and unrestrained access to the 
materials collected by Sir John for his work. Moreover, 
the first volume only of Bumey's History was published 
simultaneously with Sir John's complete work, while the 
remaining three followed at intervals of two years between 
each volume. 

The unfair competition, all things considered, of Dr. 
Burney, and the prejudices it engendered, rendered it 
scarcely surprising that Sir John's History of Music did 
not even furnish a pair of carriage horses to its author ; 
who had often declared that if, in a pecuniary point of 
view, he obtained that trifling reward of his sixteen years' 
labour he should be well satisfied. 

Which of the rival histories is intrinsically the better, 
and consequently the more calculated to secure an en- 
during meed of approbation, has been carefully con- 
sidered ; and the result is, the re-production of Sir John 
Hawkins's valuable work. The great progress which 
has been made in the art since that period, as well as the 
consequent increase in the number of accomplished mu- 
sicians, formed the turning-point in favor of this decision. 

When it is considered that the science of Music is one 
that has pervaded all time, and been to a greater or less 
extent the common property of all nations, it is evident 
that one who could hope to succeed in recording its 
history, must bring to his undertaking a competent know- 
ledge of both ancient and modern languages; an ac- 
quaintance with history critically exact with regard to its 
period-s and their peculiarities ; and a familiarity with 
blackletter and obsolete signs and abbreviations, sufficient 
to discover and decipher any documents relating to the 
art which might be recorded in them. To this were to be 
added a careful assiduity — which, unscared by its details, 
and undeterred by its intricacies, should follow the art 
in its progress through centuries extending from Jubal 
down to Handel; — a laborious zeal, which might know 
neither fatigue nor rest, in investigating not only the pro- 
perties of the science itself, but likewise all circumstances 
respecting the subject which might in any way, however 
remotely, relate to it; — a keen, discriminating action, 
which should unhesitatingly and accurately determine 
authenticities and affix dates ; — and, finally, a judicious 
method, which should first arrange and systematize the 
knowledge acquired, and then present it in the clearest 
form to the contemplation of the world. Sir John 
Hawkins united in himself most of these qualities in an 
eminent degree. 

In the month of December, 1783, Dr. Johnson, with 
whom he had for many years been on terms of great 
friendship, sent for him, and imparting to him that he 
had discovered in himself symptoms of dropsy, declared 
his desire of making a will, and his wish that Sir John 
should be one of his executors. On his consenting, the 



Doctor entered into an account of his circumstances, and 
mentioned the disposition he intended to make of his 
effects. Of this matter Boswell has thought fit to say- 
' that by assiduous attendance upon Johnson in his last 
illness, he (Hawkins) obtained the post of one of his 
executors.' 

Now the impression created by this statement on the 
mind of a person not acquainted with the facts would be, 
firstly, that up to the period mentioned, the acquaintance 
between the Doctor and Sir John had been slight, and 
secondly, that the attention paid by the latter to his 
dying friend proceeded from an unworthy motive. With 
regard, then, to the former portion of the insinuation, it 
may be sufficient to state that the acquaintance between 
them had subsisted for more than thirty years, and that 
up to a comparatively recent period, there were those 
living who had been in the habit of frequently meeting 
Johnson at Hawkins's house, and who could testify to the 
closeness of their intimacy. To the latter, we have the- 
whole tenor of Sir John's life to oppose; and it is not 
very probable that he, who from a scruple which the 
world may consider overstrained, but must admit to be 
honorable, had used, and successfully used, all his ener- 
gies to dissuade another who was bent on enriching him, 
from carrying his intentions into effect ; who had, froni 
a spirit of independence, twice declined a seat in Parlia- 
ment, then a much greater object of ambition than now ; 
and who, as a matter of conscience, had preferred de- 
fraying the expense of his sons' education at one public 
school to accepting a free presentation for them to ano- 
ther ; — it is not likely, we say, that the man who had 
acted in this way, would stoop to the moral degradation 
imputed to him. To these general facts, indeed, his 
vindication might well be left ; but there are others of 
a more particular nature. In the first place, then, the 
conversation in which Dr. Johnson engaged Sir John to 
be his executor, took place in December, 1783 ; and about 
the middle of 1 784 he was ' so well recovered from all 
his ailments' that ' both himself and his friends hoped 
that he had some years to live.' Thus it appears that, 
far from the appointment being the effect of anything 
that occiuTed in his last illness, it in fact, preceded it ;, 
for although the will was not executed till December,. 
1784, all the arrangements had been made the year before 
In the second place, it is established by the testimony of one 
of Sir John's sons, that Johnson had for many years been 
accustomed to consult him on all important matters, and 
more especially those connected with business ; and in 
the third, it can be stated on the same authority, that 
' the office had been wholly unsolicited by words or 
actions.' 

To take, however, Boswell's assertion as it stands — 
if it really be the case that Johnson was moved to select 
Sir John as he describes, it argues a weakness on the 
great Doctor's part which Boswell, as his friend, would 
have done well to conceal ; a weakness, by the way, the 
supposition of which is far from being borne out by his 
choice of the co-executors. Dr. William Scott (afterwards 



X. 



LIFE OF SIR JOHN HAWKINS. 



Lord Stowell) and Sir Joshua Reynolds. If it be not so, 
and Johnson, in the full enjoyment of his usual strength 
of mind, deliberately preferred Hawkins to Boswell, 
[and liliic dice lacriim.cE~\ the inference is obvious that 
he selected the person in whom he had the greatest con- 
fidence. Neither is Boswell's assertion coiTect, that in 
consequence of his appointment as an executoi-, the 
booksellers of London employed him to publish an 
edition of Johnson's works and to write his life. The 
.fact is, that a number of slanders and calumnies had 
been propagated against Johnson during his life, and he 
was apprehensive that many more would be circulated 
after his decease. With this impression on his mind, 
he frequently, in the many interviews which took place 
between the friends during the last year of his life, com- 
mitted in express terms, ' the care of his fame ' to Sir John. 
It was, therefore, to this injunction, and not to a contract 
with the booksellers, that the life of Johnson and edition 
of his works, published by Hawkins in 1787, owed its 
existence. 

He had scarce entered upon his task when his own 
library, that dearest pride and most cherished worldly 
good of a literary man — a labour which it had been the 
toil and deliglit of more than thirty years to collect, and 
which comprised among its books, prints and drawings, 
many articles that no money could replace — was de- 
stroyed by fire, at the time his house in Queen Square, 
Westminster, was burnt down. The blow was a severe 
one, but the sufferer was never heard to murmur or com- 
plain, and as soon as he was settled in another habitation, 
he sought in renewed study the solace of his misfortune. 

In 1787 he closed his literary career, by publishing his 
Ife of Johnson and edition of his works. Immediately on 
its appearance, it was virulently attacked by Boswell and 
others ; but the author was repeatedly accosted in the 
streets by utter sti"angers, who thanked him for the 
amusement and information he afforded them. No one 
can doubt that there existed, at the time of its publica- 
tion, many causes, totally irrespective of the merits of the 
book, which may account for its being so violently de- 
cried. In the first place, he who imdertakes to give 
to the world accounts of his contemporaries invariably 
runs the risk of incurring great animosity : and the more 
candidly and impartially he performs his task, the greater 
is his danger in this respect ; for while the friends of the 
deceased consider that his virtues and amiable qualities 
are not sufficiently enlarged upon, those who disliked 
him, on the other hand, determine that his failings have 
been too much glossed over. This was eminently the 
case with Johnson : there can be no question that his 
strong sense, his wonderful acquirements, and his gigantic 
intellect, had excited the unbounded admiration and se- 
cured the enduring love of many; but it is equally cer- 
tain that his dictatorial spirit and his boorish manner, 
■under which some had personally smarted, had created 
liim enemies in an equal proportion. With Hawkins's 
■work, then, both parties were dissatisfied — the one, that 
ihe representation given of him fell so far short of their 



extravagant idea of his perfection, tlie other that it ex- 
ceeded what they considered his deserts. Again, there 
were, no doubt, others who had pleased their imaginations 
with the hope, that the slight acquaintance they misht 
have with Johnson, would induce the Avriter of his life to 
hand them down to posterity as the friends of the great 
Lexicographer, and who, having travelled through the 
biography without attaining the ' wished-for consum- 
mation ' of seeing their 'names in print,' were not 
inclined to view with very favorable eyes the labours of 
his historian. Another, and the not least bitter class, was 
comjiosed of those who, sufficiently aware of the extent o^ 
Johnson's reputation, had conceived the design of pro- 
fiting by his celebrity. Of these projected biographers 
the number was not small, and it cannot be supposed that 
they could be other than hostile to a work which, by 
superseding the necessity for a second, defeated their hope 
of fame or emolument, whichever might be their object. 

Before concluding this narration, it may be allowable to 
remark, that while few persons have been, both during life 
and after death, so rancorously attacked as Sir John Haw- 
kins, none have come out of an ordeal so severe as that to 
which his reputation has been exposed, more thoroughly 
unscathed than he has done. Some of the most probable 
causes of his being so vir\ilently assailed, have been stated 
above : but there are doubtless others ; and the one whicli 
drew upon him the enmity of Stevens is too important to be 
omitted. It appears that an inexplicable coolnesshadarisei. 
between Garrick and Hawkins, who had formerly been on 
very intimate terms, and on some accidental circumstances 
leading the latter to investigate the soin-ce of this, it was 
discovered, on irrefragable evidence, that Stevens had 
made mischief between the two. With this he was taxed 
by Sir John ; and unable, to refute the impeachment, was 
by him ejected from his house. This, Stevens was not 
likely to forgive ; more especially as he must have been 
conscious that he had been detected in another act of most 
disgraceful nature. A day or two before the intended 
presentation of the address of 1775, mentioned above, 
he had called on Sir John. A manuscript cojiy of the 
address lay on the table in the room into which he was 
shown. This after his departure was missed and was 
never foimd again. On the publication of the St. James's 
Chronicle, the paper with which Stevens was connected, 
a copy of the missing address was found inserted, with 
an account of its presentation. Now it so happened that, 
owing to some accident, the reception of the address by 
the king had been postponed, and that at the time the 
public were reading this accoimt, the address had not 
yet been presented at all. The address too, only existed 
in manuscript, and in Sir John's possession : inider these 
circumstances there can be no doubt that Stevens had 
purloined the copy, trusting that the address would be 
presented at the time proposed, which was anterior to 
the publication of his paper, and that on its appearanc-:- 
in the St. James's Chronicle, it would be supposed that 
he had received it from some person about the Court. 
The accidental delay had however defeated this by- 



LIFE OP SIR JOHN HAWKINS. 



x: 



pothesis ; and, with the other circumstances, fixed the 
guilt of the theft upon him. 

As another instance of Mr. Stevens's mode of pro- 
cedure, the following is subjoined : — 

0, Bridge-street, Westminster, April 3, 1853. 
My Dear Sir, — I enclose you the anecdote which I pro- 
mised. Any information in relation to your edition of 
Hawkins that I am able to afford, shall be cheerfully con- 
tributed in aid of so spirited and useful a publication. 

Most traly yours, W. AYRTON. 
To Sir. J. Alfred Novello. 

Hawlcins's History and George Stevens. 

" When Hawkins's History of Jlusic was ready for printing, 
Ste\'ens — who contributed to it much of the literary portion — 
that is, the literary facts and the result of his research — went 
to Thomas Payne (' Old, honest Tom Payne, of the Mews- 
gate'), and strongly recommended him to purchase the work, 
at the price of 500 guineas, extolling it as exhibiting great 
learning, and abounding in interesting detail. 

" The week after the work appeared, a letter was published 
in the St. James's Evening Post, attacking it with great vio- 
lence. Stevens, in Payne's shop, entered on the subject of the 
letter, condemning in strong terms the injustice and violence 
of the critique. Shortly after, a second attack appeared in 
the same journal, and Stevens, at his usual — almost daily — 
visit to the Mews-gate, where many of the literati used 
to assemble and converse, again expressed his sui-prise and 
disgust at the continuance of such wanton hostility, saying, 
' It is a most unfair and most malignant enemy who writes 
in the St. James's Evening Post.' ' Yes,' said Mr. Payne, 
*it is most malignant and unjust; and I have the best 
proofs, Mr. Stevens, that you are the author of those letters, 
and I never wish to see your face again in this place ! ' 

" Stevens never after repeated his visits ; but wishing to 
meet, as usual, his friend, the Rev. Mr. Cracherode, used to 
walk on the side opposite Payne's shop at the time when Cra- 
cherode generally called there, in order to enjoy his almost 
daily literary chat with him.* 

" The foregoing I had from Mr. Thomas Payne, who suc- 
ceeded his father in the business, which he removed to Pall 
Mall. The account was given to me, in nearly the same words, 
by Mr. Evans, bookseller in Pall Mall, who had been a shop- 
man of the elder Payne ; and this has been confinned by 
IMr. Henry Foss, who, on the death of the second' T. Payne, 
carried on the business, in partnership with Mr. John Thomas 
Payne, in Pall Mall. 

" I have a clear recollection of Sir J. Hawkins, who was a 
constant dropper-in at my father's house, James-street, Buck- 
ingham-gate. He was generally thought somewhat austere ; 
but to me, as a child, he was gentle and kind. After the des- 
truction, by fire, 6f his house in Queen-square, Westminster, 
and of his curious library, he resided in the Broad Sanctuary, 
close to the Abbey ; which house was recently pulled down, 
to make way for the improvements in that quarter. 

" W. A." 

* Mr. Cracherode (qy. Dr. ?) lived at No. 24, Queen-square, West- 
minster, and at Clapham; was a man of large fortune, and possessed 
one of tte finest libraries then existing, v/hich, at his deatii, was pur- 
chased by the British Museum, for £14,000. 



Ail this was surely sufficient to make Stevens rejoice 
in the opportunity of assailing Hawkins, and to induce 
him to use any means to injure one who had such just 
reason to regard him with contempt. 

Where Boswell and Stevens led, others have been found 
to follow ; but it may be remarked that their assaults con- 
sist more of violent expressions of opinion, than of records 
of facts calculated to affect his personal or literary fame. 
The terms of friendship, indeed, on which he stood 
with those who were the best men of the day, both as 
regards high character and literary attainment, form the 
surest criterion of the estimation in which he was held 
by those persons whose good opinion was most to he 
valued. 

Sir John Hawkins had always been a pious man : as 
advancing years brought him nearer and nearer to the 
event which no care can avoid, he became more and 
more attentive to the duties of religion, and to devotional 
and theological studies, to which he latterly dedicated 
every hour which some imperative duty did not claim. 
On the morning of the 14th of May, 1789, he was 
attacked, while away from home, by a paralytic affection : 
he immediately returned and was carried up to bed, 
but rallied so far in the course of the day as to get up 
again to receive an old friend who had promised to 
visit him in the evening : he was however again seized, 
and was compelled to return to his bed from which he 
never again rose, for his malady becoming aggravated 
by apoplectic symptoms, put a period to his life on the 
2lst of May, just one week from the date of his first 
attack. 

He left behind him — to use the Avords of Chalmers — 
'A high reputation for abilities and integrity, united with 
the well-earned character of an active and resolute magis- 
trate, an affectionate husband and father, a firm and zealous 
friend, a loyal subject, and a sincere Christian, and rich 
in the friendship and esteem of very many of the first 
characters for rank, worth, and abilities, of the age in 
which he lived.' 

He was buried in the cloisters of Westminster Abbey, 
in the North Walk, under a stone which, by his express 
direction, hears no more than tlie following inscription : — 

J. H. 

Obiit XXI Maii, mdcclxxxix, 

iEtatis Lxx. 

His wife, who survived him four years, is buried in the 

same grave. 

He left two sons, John Sidney and Henry, and one 
daughter, Letitia Matilda ; all, but especially the latter, 
well known in the literary world. Miss Hawkins's novels 
evince talent ; while the cause of virtue, usefulness, and 
right feeling has never found a more zealous, and but 
seldom, very seldom, a more efficient advocate. 

By this summary of the circumstances which marked 
Sir John Hawkins's life, one of the great ends of 
Bioo-raphy is achieved : serving to stimulate men by a 
worthy example ; and showing, that, however contem- 
poraneous meanness, envy, or detraction, may cause full 



xu. 



LIFE or SIR JOHN HAWKINS. 



justice to be delayed, it cannot prevent eventual honor 
from accruing to one who steadfastly maintains his 
virtuous integrity. It supplies a. pregnant instance of 
the unfailing comfort of conscious rectitude, beneath 
unfounded aspersion and venomous assault. It inspires 
a consoling reliance upon ultimate equitable estimate, 
however long deferred. It furnishes a sustaining moni- 
tion, that patient desert, whatever may be the amount 
of injurious misapprehension it chances temporarily to 
encountei", is sure in the end to triumph, and to secure to 
itself a genuine though tardily-yielded acknowledgement. 
The paltry malice, and base tricks, of such men as 
Boswell and Stevens, in their endeavour to degrade an 
honorable gentleman in the eyes of the world, — to obtain 
an undervaluing and false opinion of him, — and to pro- 
cure the failure of his productions, would not have been 
recorded here ; were it not that there are times when 
such candour of revelation is absolutely needful. No 



occasion could be more fitting than this, when relating 
Sir Jolin's biography, and re-printing his great work. 
Not only was it requisite in justification, — to rescue a 
worthy, honest name from unmerited imputation, and 
to reclaim his literary efforts from unfair slight; but it was 
proper, in order to show how xmiformly the machinations 
of such insidious maligners, after a period of apparent 
success in jirevailing against the object of their attack, 
are sure to recoil upon their devisers' own heads, when 
the verdict of the world shall at last adjudge the cause, 
in a clearer knowledge of the truth. 

Posterity awards honoring repute and distinction to 
Sir John Hawkins, as an excellent upright man, in his 
private character ; and testifies value for his literary 
capacity, by giving the palm to his admirable History 
over the one which claims to be its rival, — a fact proved 
from the present demand for this re-print of the work 
here offered to the Public. 



ANNOUNCEMENT. 



In the present a^^e, when public attention is so exten- 
sively directed towards the study and practice of Music, 
it has been thought that a new edition of Sir John 
Hawkins's valuable Histoi-y of the Science and Practice 
o£ Music would prove peculiarly acceptable, as being by 
far the best history of the Art extant. 

The whole of the original Text has been printed in its 
integrity, together with the Illustrations of Instruments 
(for which more than 200 Woodcuts have been engraved), 
the Musical Examples, and the Fac-similes of Old 
Manuscripts. 

The form adopted, super-royal 8vo., has the advantage 
of bringing much more matter under the eye at one view, 
and in point of economy the 2722 pages of the Quarto 
are comprised in 1016 pages. The paging has been con- 
tinued from the beginning to the end, as more simple for 
reference, and to enable those who like such information 
in one volume, to bind it in that form ; but provision has 
been made, by adding a second title after page 486, to 
divide the work into two volumes, an arrangement which 
may generally be preferable. 

The Medallion Portraits of Musical Composers, which 
were in the Quarto edition, have been printed in a sepa- 
rate volume ; these may be purchased optionally, and 
thus decrease the price of the History to those with whom 
economy must be a consideration. They consist of up- 
wards of sixty portraits, printed from the original coppei*- 
plates engraved for the 1776 edition; to which has been 
added a portrait of Sir John Hawkins himself from the 
painting in the Oxford Music School, through the 
courtesy of the surviving members of his family. All the 
additional manusci'ipt notes which adorn the Author's 
own copy left to the British Museum, are inserted (by per- 
mission of the authorities; in the edition now presented 
to the public : it may therefore be considered what a new 
edition edited by Sir John Hawkins himself would have 



been ; the additions in text or notes are distinguished by 
being printed in italics. 

To ensure the careful reproduction of matter of such 
varied character, the assistance of many correctors has 
been secured. The general correction of the press was 
confided to Mrs. Cowden Clarke, but the pages also 
passed under the eye of the musician, the mathe- 
matician, and the classical linguist. In these depart- 
ments, various portions have had the care of Mr. Edward 
Holmes, Mr. Josiah Pittman, Mr. W. H. Monk, and Mr. 
Burford G. H. Gibsone, with occasional suggestions from 
other well-wishers ; and the whole work, such ad- 
vantage as might be derived from the Publisher's printing 
experience. 

There has been added a Memoir of the Author, com- 
piled from original sources, which will be read with in- 
terest ; but it is anticipated that the most valuable 
addition to the book will be found in the carefully-made 
general and other Indexes. The large subject of a 
History of Music, embracing heterogeneous matter and 
the result of wide research, makes it a storehouse to 
which a definite clue is required in giving ready access. 
The Indexes have been going on cotemporaneously with 
the printing of the book ; and Mrs. Cowden Clarke's ex- 
perience derived from her Concordance to Shakespeare, 
fitted her especially for the task of their compilation. 
A table of parallel books, chapters, and pages has been 
added, to render the new Indexes available for those who 
possess the Quarto edition. 

In concluding these brief but necessary words of ex- 
planation, the warmest thanks are offered to the editorial 
friends above specified, as also to those kind supporters 
who have subscribed for the work during its periodical 
issue by the Public's, and their obedient servant, 



69, Dean Street, SoJio, London. 
August, 1833. 



TuE Publisher. 



AUTHOR'S DEDICATION AND PREFACE. 



To GEORGE THE THIRD, King of Great Britain, &c., a Prince not 
more distinguished by his patronage of those elegant arts whicli 
exalt humanity and administer to the imaginative faculties the 
purest delights, than honoured and beloved for his regal and private 
virtues, the following History is, with all due reverence and gratitude, 
dedicated by him who esteems it equally an honour and a felicity to 
subscribe himself His Majesty's faithful and devoted subject and 
servant, The Author. 

A History of Music by any but a professor of the science, may 
possibly be looked on as a bold understaklng ; and it may appear not a 
little strange that one, who is perhaps better known to the world as 
occupying a public station than as a writer, should choose to be the 
author of a work of this kind, and for which the course of his studies 
can hardly be supposed to have in any degree qualified him. 

In justification of the attempt, and to account for this seeming in- 
consistency, the reader is to know, that the author having entertained 
an early love of music, and having in his more advanced age not only 
become sensible of its worth, but arrived at a full conviction that it was 
intended by the Almighty for the delight and edification of his rational 
creatures, had formed a design of some such work as this many years 
ago, but saw reason to defer the execution thereof to a future period. 

About the year 1759, he found himself in a situation that left his 
employments, his studies, and his amusements in a great measure to 
his own choice ; and having in a course of years been as industrious in 
making collections for the purpose as could well consist with the ex- 
ercise of a laborious profession, he, with a copious fund of materials, 
began the work: but before any considerable progress could be made 
therein, he was interrupted by a call to preside in the magistracy of the 
county of his residence, which, though unsolicited on his part, he could 
not decline without betraying an indifference to the interests of society, 
and the preservation of public order, or such an aversion to the occupations 
of an active life, as in few cases is excusable, and in many reproachful. 

Determining, however, to avail himself of those intervals of leisure 
which the stated recesses from the exercise of his office afforded, and 
which seemed too precious to be wasted either in sloth and indolence, or 
those fashionable recreations and amusements, to which he was ever 
disposed to prefer the pursuit of literature, he re-assumed his work ; and 
with the blessing of health, scarcely interrupted for a series of years, 
has been able to present it to the world in the condition in which it now 
comes forth. 

What the reader is to expect from it, and as the fruit of many years 
study and labour, is the history of a science deservedly ranked among 
those, which, in contradistinction to the manual arts, and others of lower 
importance, have long been dignified with the characteristic of liberal ; 
and as the utility of Music is presupposed in the very attempt to trace 
its progress, an enumeration of its various excellencies will scarcely be 
thought necessary ; the rather perhaps as its praises, and the power it 
exercises over the human mind, have been celebrated by the ablest 
panegyrists. i 

Farther than the circumstances attending the peculiar situation of the 
author and the work may be allowed to entitle him to it, the favour or 
indulgence, or whatever else it is the practice of writers to crave of the 
public, is not here sued for, either on the ground of want of leisure, 
inadvertence, or other pretences ; for this reason, that there can be no 
valid excuse for a publication wittingly imperfect; and it is but a sorry 
compliment that an author makes to his reader, when he tenders him 
a work less worthy regard than it was in his power to make it. 

To be short, the ensuing volumes are the produce of sixteen years 
labour, and are compiled from materials which were not collected in 
double that time. The motives to the undertaking were genuine, and 
the prosecution of it has been as animated as the love of the art, and 
a total blindness to lucrative views, could render it. And perhaps the 
best excuse the author can make for the defects and errors that may be 
found to have escaped him, must be drawn from the novelty of his 
subject, the variety of his matter, and the necessity he was under of 
marking out himself the road which he was to travel. 

It may perhaps be objected that music is a mere recreation, and an 
amusement for vacant hours, conducing but little to the benefit of 
mankind, and therefore to be numbered among those vanities which it 
is wisdcmi to contemn. To this it may be answered, that, as a source 
of intellectual pleasure, music has greatly the advantage of most other 
recreations ; and as to the other branch of the objection, let it be 
remembered that all our desires, all our pursuits, our occupations, and 
enjoyments are vain. What are stately palaces, beautiful and extensive 
gardens, costly furniture, sculptures, and pictures, but vanities ? and 
yet there are few men so vain as that they had rather be without than 
possess them. Nay, if these be denied us, where are we to seek for 
amusements, — for relief from the cares, the anxieties and troubles of life ; 
how support ourselves in solitude, or under the pressure of affliction, — 
or how preserve that equanimity, which is necessary to keep us in good 
humour with ourselves and mankind ? As to the abuses of this excellent 
gift, enough it is presumed is said in the ensuing work by way of caution 
against them, and even to demonstrate that as there is no science or 
faculty whatever that more improves the tempers of men, rendering 
them grave, discreet, mild, and placid, so is there none that affords 
greater scope for folly, impertinence, and affectation. 

The end proposed in this undertaking is the investigation of the 
principles, and a deduction of the progress of a science, which, though 
intimately connected with civil life, has scarce ever been so well under- 
stood by the generality, as to be thought a fit subject, not to say of 
criticism, hut of sober discussion: instead of exercising the powers of 
reason, it has in general engaged only that faculty of the mind, which. 



for want of abetter word to express it by, we call Taste; and which 
alone, and without some principle to direct and controul it, must ever 
be deemed a capricious arbiter. Another end of this work is the settling 
music upon somewhat like a footing of equality with those, which, for 
other reasons than that, like music, they contribute to the delight of 
mankind, are termed the sister arts ; to reprobate the vulgar notion that 
its ultimate end is merely to excite mirth ; and, above all, to demonstrate 
that its principles are founded in certain general and universal laws, into 
which all that we discover in the material world, of harmony, symmetry, 
proportion, and order, seems to be resolvable. 

The method pursued for these purposes will be found to consist in an 
explanation of fundamental doctrines, and a narration of important 
events and historical facts, in a chronological series, ivith such occasional 
remarks and evidences, as might serve to illustrate the one and authen- 
ticate the other. With these are intermixed a variety of musical compo- 
sitions, tending as well to exemplify that diversity of style which is 
common both to music and speech or written language, as to manifest 
the gradual improvements in the art of combining musical sounds. The 
materials which have furnished this intelligence must necessarily be 
supposed to be very miscellaneous in their nature, and abundant in 
quantity : to speak alone of the treatises for the purpose, the author may 
with no less propriety than truth assert, that the selection of them was 
an exercise of deep skill, the result of much erudition, and the effect of 
great labour, as having been for a great part of his life the employment of 
that excellent theorist in the science. Dr. Pepusch. These have been 
accumulating and encreasing for a series of years past : for others of a 
different kind, recourse has been had to the Bodleian library and the 
college libraries in both universities ; to that in the music-school at Ox- 
ford ; to the British Museum, and to the public libraries and repositories 
of records and public papers in London and Westminster; and, for the 
purpose of ascertaining facts by dates, to cemeteries and other places of 
sepulture ; and to him that shall object that these sources are inadequate 
to the end of such an undertaking as this, it may be answered, that he 
knows not the riches of this country. 

A correspondence with learned foreigners, and such communications 
from abroad as suit with the liberal sentiments and disposition of the 
present age, together with a great variety of oral intelligence respecting 
persons and facts yet remembered, have contributed in some degree 
to the melioration of the work, and to justify the title it bears of a 
General History; which yet it may be thought would have been more 
properly its due, had the plan of the work been more extensive, and 
comprehended the state of music in coimtries where the approaches to 
refinement have yet been but small. 

It must be confessed that in some instances, particularly in the dis- 
cussion of the first i)rinciples of morality, and the origin of human 
manners, the researches of learned men have been extended to nations, 
or tribes of people, among whom the simple dictates of nature seemed to 
be the only rule of action ; but the subjects here treated of are science, 
and the scientific practice of music: now the best music of barbarians 
is said to be hideous and antonishing sounds.* Of what importance 
then can it be to enquire into a practice that has not its foundation in 
science or system, or to know what are the sounds that most delight a 
Hottentot, a wild American, or even a more refined Chinese ? 

For the style, it will be found to be uniformly narratory ; as little 
encumbered with technical terms, and as free from didactic forms of 
speech, as could consist with the design of explaining doctrines and 
systems ; and it may also be said that care has been taken not to degrade 
the work by the use of fantastical phrases and modes of expression, 
that, comparatively speaking, were invented yesterday, and will die 
to-morrow ; these make no part of any language, they conduce nothing 
to information, and are in truth nonsense sublimated. 

For the insertions of biographical memoirs and characters of eminent 
musicians, it may be given as a reason, that, having benefited mankind 
by their studies, it is but just that their memories should live: Cicero, 
after Demosthenes, says that ■' bona fama propria possessiodefunctorum;" 
and for bestowing it on men of this faculty, we have the authority of that 
scripture which exhorts us to praise " such as found out musical tunes, 
and recited verses in writing. "+ Besides which it may be observed, that 
in various instances the lives of the professors of arts are in some sort 
a history of the arts themselves. For digressions from his subject, the 
insertion of anecdotes that have but a remote relation to it, or that 
describe ancient modes or customs of living, the author has less to say; 
these must be left to the judgment of his readers, who cannot be supposed 
to be unanimous in their opinions about them. 

It remains now that due acknowledgment be made of the assistance 
with which the author has been favoured and honoured in the course of 
his work ; but as this cannot be done without an enumeration of names, 
for which he has obtained no permission, he is necessitated to declare 
his sense of the obligation in general terms, with this exception, that 
having need of assistance in the correction of the music plates, he was 
in sundry instances eased of that trouble by the kind offices of one, who 
is both an honour to his profession and his country, Dr. William Boyce ; 
and of the difliculty of decyphering, as it were, and rendering in modern 
characters the compositions of greatest antiquity amongst those which 
he found it necessary to insert, by the learning and ingenuity of Dr. 
Cooke, of Westminster Abbey, Mr. ^larmaduke Overend, organist of 
Isleworth in Middlesex, and Mr. John Stafford Smith, of the royal chapel. 

* Characteristics, vol. I. page 242. t Ecclesiasticus, chap. xliv. verse 5. 



Hatton Garden, 

26th Any., 17"G. 



PRELIMINAEY DISCOUESE. 



The powers of the imagination, with great appearance 
of reason, are said to hold a middle place between the 
organs of bodily sense and the faculties of moral per- 
ception ; the subjects on which they are severally exer- 
cised are common to the senses of seeing and hearing, tlie 
office of which is simply perception ; all pleasure thence 
arising being referred to the imagination. 

The arts which administer to the imaginative faculty 
the greatest delight, are confessedly poetry, painting, and 
music ; the two former exhibiting to the mind by their 
respective media, either natural or artificial,* the resem- 
blances of whatever in the works of nature is compre- 
hended under the general division of great, new, and 
beautiful ; the latter as operating upon the mind by the 
power of that harmony which results from the concord of 
sounds, and exciting in the mind those ideas which cor- 
respond wdth our tenderest and most delightful affections. 

These, it must be observed, constitute one source of 
pleasure ; but each of the above arts may in a different 
degree be said to afford another, namely, that which con- 
sists in a comparison of the images by them severally and 
occasionally excited in the mind, with their architypes ; 
thus, for instance, in poetry, in comparing a description 
with the thing described ; in painting, a landscape and 
the scene represented by it, or a portrait and its original ; 
and in music, where imitation is intended, as in the songs 
of birds, or in the expression of those various inflexions 
of the voice which accompany passion or exclamation, 
weeping, laughing, and other of the human affections, the 
sound and the thina: signified. 

It is easy to discover that the pleasures above described 
are of two distinct kinds, — the one original and absolute, 
the other relative ; for the one we can give no reason 
other than the will of God, who in the formation of the 
universe and the organization of our bodies, has esta- 
blished such a relation as is discoverable between man 
and his works ; the other is to be accounted for by that 
love of truth which is implanted in the human mind.f 
In poetry and painting therefore we speak, and with pro- 
priety, of absolute and relative beauty ; as also of music 
merely imitative ; for as to harmony, it is evident that 

* The natural media seem to consist only in colour and figure, and 
refer solely to painting : the artificial are words, which are symbols by 
compact of ideas, as are also, in a limited sense, musical sounds, including 
in the term the accident of time or duration. 

+ In this sentiment liberty has been taken to difTer from Mr. Harris, 
who with his usual accuracy, has analysed this principle of the human 
mind in the following note on a passage in the second of his Three cele- 
brated Treatises : — 

' That there is an eminent delight in this very recognition itself, abstract 
' from any thing pleasing in the subject recognised, is evident from 
' hence — that, in all the mimetic arts, we can be highly charmed with 
'imitations, at whose originals in nature we are shocked and terrified. 
' Such, for instance, as dead bodies, wild beasts, and the like. 

'The cause assigned for this, seems to be of the following kind : we 
' have a joy, not only in the sanity and perfection, but also in the just and 
' natural energies of our several limbs and faculties. And hence, among 
' others, the joy in reasoning, as being the energy of that principal faculty, 
' our intellect or understanding. This joy extends, not only to the wise, 
' but to the multitude. For all men have an aversion to ignorance and 
' error ; and in some degree, however moderate, are glad to learn and to 
inform themselves. 

' Hence therefore the delight arising from these imitations ; as we are 

• enabled in each of them to exercise the reasoning faculty ; and, by com- 
' paring the copy with the architype in our miiids, to infer that this 
'is such a thing, and that another; a fact remarkable among children, 

* even in their first and earliest days." 



the attribute of relation belongs not to it, as will appear 
by a comparison of each with the others. J 

With regard to poetry, it may be said to resemble 
painting in many respects, as in the description of ex- 
ternal objects, and the works of nature ; and so far it 
must be considered as an imitative art ; but its greatest 
excellence seems to be its power of exhibiting the in- 
ternal constitution of man, and of making us acquainted 
Avith characters, mannei's, and sentiments, and working 
upon the passions of terror, pity, and various others. 
Painting is professedly an imitative art ; for, setting aside 
the harmony of colouring, and the delineation of beautiful 
forms, the pleasure we receive from it, great as it is, con- 
sists in the truth of the representation. 

But in music there is little beyond itself to which we 
need, or indeed can, refer to heighten its charms. If v.c 
investigate the principles of harmony, we learn that they 
are general and ixniversal ; and of harmony itself, that 
the proportions in which it consists are to be found in 
those material forms, which are beheld with the greatest 
pleasure, the sphere, the cube, and the cone, for instance, 
and constitute what we call symmetry, beauty, and regu- 
larity ; but the imagination receives no additional delight; 
our reason is exercised in the operation, and that faculty 
alone is thereby gratified. In short, there are few things 
in nature which music is capable of imitating, and those 
are of a kind so uninteresting, that we may venture to 
pronounce, that as its principles are founded in geome- 
trical truth, and seem to result from some general .ind 
universal law of nature, so its excellence is intrinsic, 
absolute, and inherent, and, in short, resolvable only into 
His will, who has ordered all things in number, weight, 
and measure. § 

Seeing therefore that music has its foundation in nature, 

I Nevertheless there have not been wanting those, who, not contem- 
plating the intrinsic excellence of harmony, have resolved the eflicacy of 
music into the power of imitation ; and to gratify such, subjects have 
been introduced into practice, that to injudicious ears have afforded no 
small delight ; such, for instance, as the noise of thunder, the roaring of 
the winds, the shouts and acclamations of multitudes, the waitings of 
grief and anguish in the human mind ; the song of the cuckow, the 
whooting of the screech-owl, the cackling of the hen, the notes of singing- 
birds, not excepting those of the lark and nightingale. Attempts also 
have been made to imitate motion by musical sounds; and some have 
undertaken in like manner to relate histories, and to describe the various 
seasons of the year. Thus, for example, Froberger, organist to the 
emperor Ferdinand III. is said to have in an allemand represented the 
passage of Count Thurn over the Rhine, and the danger he and his army 
ivere in, by twenty-six cataracts or falls in notes. See page 627. 
Kuhnau, another celebrated musician, composed six sonatas, entitled 
Biblische Historien, wherein, as it is said, is a lively representation in 
musical notes of David manfully combating Goliah. Page 663, in note. 
Buxtehude of Lubec also composed suites of lessons for the harpsichord, 
representing the nature of the planets. Page S51. Vivaldi, in two books 
of concertos has striven to describe the four seasons of the year. Page 837. 
Geminiani has translated a whole episode of Tasso's Jerusalem into 
musical notes. Page 916. And Mr. Handel himsflf, in his Israel in 
Egypt, has undertaken to represent two of the ten plagues of Egypt by 
notes, intended to imitate the buzzing of flies and the hopping of frogs. 

But these powers of imitation, admitting them to exist in all the 
various instances above enumerated, constitute but a very small part of 
the excellence of music ; wherefore we cannot but applaud that shrewd 
answer of Agesilaus, king of Sparta, recorded in Plutarch, to one who re- 
quested him to hear a man sing that could imitate the nightingale, 
' I have heard the nightingale herself.' The truth is, that imitation be- 
longs more properly to the arts of poetry and painting than to music ; for 
which reason Mr. Harris has not scrupled to pronounce of musical imita- 
tion, that at best it is but an imperfect thing. See his Discourse on 
Music, Painting, and Poetry, page 69. 

§ 'Wisdom, xi. 20. 



PRELIMINARY DISCOURSE. 



XV. 



••md that reason recognizes what the sense approves, what 
wonder is it, that in all ages, and even by the least en- 
lightened of mankind, its efficacy should be acknow- 
ledged ; or that, as well by those who are capable of 
reason and reflection, as those who seek for no other 
gratifications than what are obvious to the senses, it 
should be considered as a genuine and natural source of 
<lelight ? The wonder is, that less of that curiosity, which 
leads men to enquire into the history and progress of arts, 
and their gradual advances towards perfection, has been 
exercised in the instance now before us, than in any other 
of equal importance. 

If we take a view of those authors who have written on 
music, we shall find them comprehended under three 
classes, consisting of those who have resolved the prin- 
ciples of the science into certain mathematical propor- 
tions ; of others who hare treated it systematically, and 
with a view to practice ; and of a third, who, considering 
sound as a branch of physics, have from various pheno- 
mena explained the manner in which it is generated and 
communicated to the auditory faculty. But to whom we 
are indebted for the gradual improvements of the art, at 
what periods it flourished, what checks and obstructions 
it has at times met with, who have been its patrons or its 
enemies, what have been the characteristics of its most 
eminent professors, few are able to tell. Nor has the 
knowledge of its precepts been communicated in such 
a manner as to enable any but such as have devoted 
themselves to the study of the science to understand 
them. Hence it is that men of learning have been 
betrayed into numberless errors respecting music ; and 
when they have presumed to talk about it, have dis- 
covered the ofrossest ignorance. When Strada, in the 
person of Claudian, recites the fable of the Nightingale 
and the Lyrist, how does his invention labour to describe 
the contest, and how does he err in the confusion of the 
terms melody and harmony ; and in giving to music 
either attributes that belong not to it, or which are its 
least excellence ! and what is his whole poem but a vain 
attempt to excite ideas for which no correspondent words 
are to be found in any language ? Nor does he, who talks 
of the genius of the woi-ld, of the first beauty, and of uni- 
versal harmony, symmetry, and order, the sublime author 
of the Characteristics, discover much knowledge of his 
subject, when after asserting with the utmost confidence 
that the ancients were acquainted with parts and sym- 
phony, he makes it the test of a good judge in music 
' that he understand a fiddle.'* 

Sir William Temple speaking of music in his Essay 
upon the ancient and modern Learning, has betrayed his 
ignorance of the subject in a comparison of the modern 
music with the ancient ; wherein, notwithstanding that 
Palestrina, Bird, and Gibbons lived in the same century 
with himself, and that the writings of Shakespeare and 
the Paradise Lost were then extant, he scruples not to 
assert that ' the science is wholly lost in the woi-ld, and 
' that in the room of music and poetry we have nothing 
' left but fiddling and rhyming.' 

Mr. Dryden, in those two admirable poems, Alexander's 
Feast, and his lesser Ode for St. Cecilia's day, and in his 
Elegy on the death of Purcell, with great judgment gives 
to the several instruments mentioned by him their proper 
attributes ; and recurring perhaps to the numerous com- 
mon places in his memory respecting music, has described 
its effects in adequate terms ; but when in the prefaces to 
his operas he speaks of recitative, of song, and the com- 
parative merit of the Italian, the French, and the English 
composers, his notions are so vague and indeterminate, as 
to convince us that he was not master of his subject, and 
does little else than talk by rote. 

* Vide Characteristics, Vol. III., pa^e 2(13, in note 269. 



Mr. Addison, in those singularly humorous papers in 
the Spectator, intended to ridicule the Italian opera, is- 
necessitated to speak of music, but he does it in such terms 
as plainly indicate that he had no judgment of his own 
to direct him. In the paper. Numb. 18, the highest en- 
comium he can vouchsafe music is, that it is an agreeable 
entertainment ; and a little after he complains of our fond- 
ness for the foreign music, not caring whether it be Italian, 
French, or High Dutch, by which latter we may suppose 
the author meant the music of Mynheer Hendel, as he 
calls him. 

In another paper, viz. Numb. 29, the same person 
delivers these sentiments at large respecting Recitative : — 
' However the Italian method of acting in Recitativo 
' might appear at first hearing, I cannot but think it more 
'just than that Avhich prevailed in our English Opera 
' before this innovation ; the Transition from an air to 
' Recitative Musick being more natural than the passing 
' from a Song to plain and ordinary Sjjeaking, which was 
' the common Method in PurcelVs operas. 

' The only Fault I find in our present Practice, is the 
' making use of the Italian Recitativo with English words. 

' To go to the Bottom of this Matter, I must observe that 
' the Tone, or, as the French call it, the Accent of every 
' Nation in their ordinary Speech is altogether different 
' from that of every other People, as we may see even in 
' the Welsh and Scotch, who border so near upon us. By 
' the Tone or Accent I do not mean the Pronunciation of 
' each particular Word, but the Sound of the whole Sen- 
* fence. Thus it is very common for an English gentle- 
' man, when he hears a French Tragedy, to complain that 
' the Actors all of them speak in a Tone ; and therefore he 
' very wisely prefers his own countrymen, not considering 
' that a Foreigner complains of the same Tone in an 
' English Actor. 

' For this Reason, the Recitative Music in every Lan- 
' guage should be as different as the Tone or Accent of 
' each Language; for otherwise what may properly ex- 
' press a Passion in one Language, will not do it in 
' another. Every one that has been long in Italy knows 
' very well that the Cadences in the Recitativo bear a 
' remote Affinity to the Tone of their Voices in ordinary 
' Conversation ; or, to speak more properly, are only tlie 
' Accents of their Language made more Musical and 
' Tuneful. 

' Thus the Notes of Interrogation or Admiration in the 
'Italian Musick (if one may so call them), which re- 
' semble their Accents in Discourse on such Occasions, 
' are not unlike the ordinary Tones of an English Voice 
' when we are angi-y ; insomuch that I have often seen our 
' Audiences extremely mistaken as to what has been 
' doing upon the Stage, and expecting to see the Hero 
' knock down his Messenger when he has been asking 
' him a question ; or fancying that he quarrels with his 
' Friend when he only bids him Good-morrow. 

' For this reason the Italian artists cannot agree witli 
' our English musicians in admiring Purcell's Composi- 
' tions, and thinking his Tunes so wonderfully adapted 
' to his words, because both Nations do not always ex- 
' press the same Passions by the same Sounds. 

' I am therefore humbly of opinion that an English 
' Composer should not follow the Italian Recitative toO' 
' servilely, but make use of many gentle Deviations from 
' it in Compliance with his own Native Language. He 
' may copy out of it all the lulling Softness and Dying 
' Falls (as Shakespeare calls them), but should still re- 
' member that he ought to accommodate himself to an 
' English Audience, and by humouring the Tone of our 
' Voices in ordinary Conversation, have the same Regard 
' to the Accent of his own Language, as those Persons 
' had to theirs whom he professes to imitate. It is ob- 



XVI. 



PRELIMINARY DISCOURSE. 



^ served that several of the singing Birds of ovir own 
Country learn to sweeten their Voices, and mellow the 

• Harshness of their natural Notes by practising under 
' those that come from warmer Climates. In the same 
' manner I would allow the Italian Opera to lend our 
' English Musick as much as may grace and soften it, but 

• never entirely to annihilate and destroy it. Let the 
' Infusion be as strong as you please, but still let the 
^ Subject Matter of it be English. 

' A Composer should fit his Musick to the Genius of 
' the People, and consider that the Delicacy of Hearing 
' and Taste of Harmony has been formed upon those 
' Sounds which every Country abounds with. In short, 

• that musick is of a relative Nature, and what is Harmony 
' to one Ear may be Dissonance to another.' 

Whoever reflects on these sentiments must be inclined 
to question as well the goodness of the author's ear as his 
knowledge of subject. The principle on which his rea- 
soning is founded, is clearly that the powers of music are 
local ; deriving their efficacy from habit, custom, and 
whatever else we are to imderstand by the genius of 
a people ; a position as repugnant to reason and ex- 
perience as that which concludes his disquisition, viz., 
that ' what is harmony to one ear may be dissonance to 
' another; ' whence as a corollary it must necessarily follow, 
that the same harmony or the same succession of sounds 
may produce different effects on different persons ; and 
that one may be excited to mirth by an air that has 
drawn tears from another. 

A late writer, in a strain of criticism not less erroneous 
than affectedly refined, forgetting the energy of harmony, 
independent of the adventitious circumstances of loudness 
or softness that accompany the utterance of it ; or per- 
haps not knowing that certain modulations or combina- 
tions of sounds have a necessary tendency to inspire 
grand and sublime sentiments, such, for instance, as we 
hear in the Exaltabo of Palestrina, the Hosanna of 
Gibbons, the opening of tlie first concerto of Corelli, and 
many of Mr. Handel's anthems, ascribes to the bursts, as 
he calls them, of Boranello,* and the symphonies of 
Yeomellif the power of dilating, agitating, and rousing 
the soul like the paintings of Timomachus and Aristides,t 
whose works by the way no man living ever saw, and of 
whose very names we should be ignorant, did they not 
occur, the one in Pliny, the other in some of the epigrams 
in the Greek Anthologia. 

In a manner widely different do those poets and philo- 
sophers treat music, who, being susceptible of its charms, 
and considering it as worthy the most abstract specula- 
tion, have made themselves acquainted with its principles. 
Milton, whenever he speaks of the subject, and there are 
many passages in the Paradise Lost and his other poems 
where he has taken occasion to introduce it, besides 
exjjressing an enthusiastic fondness for music, talks the 
language of a master. 

His ideas of the joint efficacy of music and poetry, and 
of the nature of harmony, are manifested in the following 
well-known passage : — 

And ever against eating cares 

Lap mc in soft Lydian aires ; 

MaiTied to immortal verse, 

Such as the meeting soul may pierce 

In notes, with many a winding bout 

Of linked sweetness long drawn out, 

With wanton heed, and giddy cunning, 

The melting voice through mazes running ; 

Untwisting all the chains, that tye 

The hidden soul of harmony. 

* i. e. Buranello, a disciple of Lotti. 

+ Nicola lomelli, a celebrated coiuposer now living at Naples. 
t See an Inquiry into the Beauties of Painting by Daniel Webb, Esq. 
Svo. 1769, page 167. 



Cathedral music and choral service he describes in 
terms that sufficiently declare his abilities to judge of it, 
and its effects on his own mind : — 

There let the pealing organ blow, 

To the fuU-voic'd choir below, 

In service high, and anthems clear, 

As may with sweetness through mine eai 

Dissolve me into extasies, 

And bring all heav'n before mine eyes. 

The following sonnet, addressed to his friend Mr. 
Henry Lawes, points out one of the great excellencies in 
the composition of music to words : — 

Harry, whose tuneful and weli-mcasur'd song 
First taught our English music how to span 
Words with just note and accent, not to scan 
With Midas' ears, committing short and long ; 
Thy worth and skill exempt thee from the throng, 
With praise enough for envy to look wan ; 
To after-age thou shalt be writ the man, 
That with smooth air could humour best our tongue. 
Thou honoiu''st verse, and verse must lend her wing 
To honour thee, the priest of Phoebus' choir, 
That tun'st their happiest lines in hymn or stor}'. 
Dante shall give Fame leave to set thee higher 
Than his Casella, whom he, woo'd to sing, 
Met in the milder shades of Purgatory. 

His sonnet to Mr. Lawrence Hjde conveys his sense of 
the delights of a musical evening : — 

Lawrence, of virtuous father virtuous son. 

Now that the fields are dank, and ways are mire, 
Where shall we sometimes meet, and by the fire 

Help waste a sullen day ; what may be won 

From the hard season gaining ? time will run 
On smoother, till Favonius re-inspire 
Tlie frozen earth ; and clothe in fresh attire 

The lilie and the rose, that neither sow'd nor spun. 

What neat repast shall feast us, light and choice, 

Of Attic taste, with wine ; whence we may i-ise 

To hear tlie lute well toucht, or artful voice 

Warble immortal notes and Tuscan air '? 

He, who of those delights can judge, and spare 

To intei-pose them oft is not unwise. 

And in his tractate on Education, he recommends the 
practice of music in terms that bespeak his skill in the 
science. 'The interim of unsweating themselves regu- 
' larly, and convenient rest before meat, may both with 
' profit and delight be taken up in recreating and coni- 
' posing their travail'd spirits with the solemn and divine 
' harmonies of musick heard or learnt ; either while the 
'skilful organist plies his grave and fancied descant, in 
' lofty fugues, or the whole symphony with artful and un- 
' imaginable touches adorn and grace the well studied 
' chords of some choice composer ; sometimes the lute, or 
' soft organ-stop waiting on elegant voices either to 
' religious, martial, or civil ditties ; which, if wise men and 
' prophets be not extremely out, have a great power over 
' dispositions and manners, to smooth and make them 
"^ gentle from rustic harshness and distempered passions.' 

Lord Bacon, in his Natural History, has given a great 
variety of experiments touching music, that shew him to 
have been not barely a philosopher, an enquirer into the 
phenomena of sound, but a master of the science of har- 
mony, and very intimately acquainted with the precepts 
of musical composition. 

That we have so few instances of this kind is greatly to 
be wondered at, seeing that in poetry and painting the 
case is far otherwise : in the course of a classical education 
men acquire not only a taste of the beauties of the Greek 
and Roman poets, but a nice and discriminating faculty, 
that enables them to discern their excellencies and defects ; 
and in painting, an attentive perusal of the works of 
eminent artists, aided by a sound judgment, will go near 



PRELIMINARY DISCOURSE. 



XVll. 



to form the character of a connoisseur, and render the 
possessor of it susceptible of all that delight which the art 
IS capable of affording ; and this we see exemplified in 
numberless instances, where persons imskilled in the 
practice of painting become enabled to distinguish hands, 
to compare styles, and to mark the beauties of composi- 
tion, character, drawing, and colouring, with a degree of 
accuracy and precision equal to that of masters. But few, 
except the masters of the science, are possessed of know- 
ledge sufficient to enable them to discourse with propriety 
on music ; nor indeed do many attend to that which is 
its greatest excellence, its influence on the human mind, 
or those irresistable charms which render the passions 
subservient to the power of well modulated sounds, and 
inspire the mind with the most exalted sentiments. One 
admires a fine voice, another a delicate touch, another 
what he calls a brilliant finger ; and many are pleased 
with that music which appears most difficult in the 
execution, and in judging of their own feelings, mistake 
wonder for delight. 

To remove the numberless prejudices respecting music, 
which those only entertain who are ignorant of the 
science, or are mistaken in its nature and end ; to point 
out its various excellencies, and to assert its dignity, 
as a science worthy the exercise of our rational as well as 
audible faculties, the only effectual way seems to be to in- 
vestigate its principles, as founded in general and invari- 
able laws, and to trace the improvements therein which 
have resulted from the accumulated studies and experience 
of a long succession of ages, such a detail is necessary to 
reduce the science to a certainty, and to furnish a ground 
for criticism ; and may be considered as a branch of 
literary history, of the deficiency whereof Lord Bacon has 
declared his sentiments in the following emphatical terms : 

* History is Natural, Civil, Ecclesiastical, and Literary ; 
' whereof the three first I allow as extant, the fourth I 
' note as deficient. For no man hath propounded to him- 
' self the general state of learning to be described and 
'represented from age to age, as many have done the 
' works of nature, and the state civil and ecclesiastical ; 
' without which the history of the world seemeth to 
' me to be as the statue of Polyphemus with his eye out, 
' that part being wanting which doth most shew the spirit 
' and life of the person. And yet I am not ignorant, that 

* in divers particular sciences, as of the jurisconsults, the 
' mathematicians, the rhetoricians, the philosophers, there 
' are set down some small memorials of the schools, 

* authors, and books ; and so likewise some barren relations 
'touching the invention of arts or usages. 

' But a just story of learning, containing the antiquities 
' and originals, of knowledges and their sects, their inven- 
' tions, their traditions, their diverse administrations and 
' managings, their flourishings, their oppositions, decays, 
' depressions, oblivions, removes, with the causes and 
' occasions of them, and all other events concerning 
' learning, throughout the ages of the world, I may truly 
'affirm to be wanting.'* 

If anything can be necessary to enforce arguments so 
weighty as are contained in the above passage ; it must 
be instances of error, resulting from the want of that 
intelligence which it is the business of history to commu- 
nicate ; and it is greatly to be lamented that music affords 
more examples of this kind than perhaps any science 
whatever : for, not to remark on those uncertain and con- 
tradictoi-y accounts which are given of the discovery of 
the consonances, some writers attributing it to Pytha- 
goras, others to Diodes, that relation of the fact which 
gained most credit with mankind, as deriving its 



las 



authority from the Pythagorean school, is demonstratably 
* Of the advancement of Learning, book II. 



false and erroneous.f Again, as to the invention of sym- 
phoniac harmony, or, as we now call it, music in parts, 
many ascribe it to the ancients, and say that it was in use 
among the Greeks, though no evidence of the fact can be 
drawn from their writings now extant. Others assert it 
to be a modern improvement, but to whom it is due no 
one has yet been able to discover. 

As to the modern system, there is the irrefragable evi- 
dence of his own writings extant, though not in print, 
that it was settled by Guido Aretinus, a Benedictine 
monk of the monastery of Pomposa in Tuscany, who 
flourished about the year 1028; yet this fact, which is 
also related as an important event in the Annales Ecclesi- 
astici of Cardinal Baronius, has been rendered doubtful 
by an assertion of a writer now living, Signor Martinelli, 
that one of the same name and place, Fra Guittone 
d'Arezzo, an Italian poet of great eminence, and who 
lived about two himdred years after, adjusted that musical 
scale by which we now sing ; J and further that the same 
Fra Guittone was the inventor of counterpoint. Again, 
those who give the invention of the modern system, and 
the application thereto of the syllables used in solmisation 
to the true author, ascribe also to him the invention of 
music in consonance, and also of the Clavicembalum or 
harpsichord; whereas the harpsichord is an improvement 
of the Clavicitherium, an instrument known in England 
in Gower's time by the name of the Citole, fromCisxELLA, 
a little chest. Another writer asserts, on what authority 
we are not told, that counterpoint, which implies music in 
consonance, was invented by John of Dunstable, who 
flourished anno 1400 ; and another, § mistaking the name, 
attributes it to St. Dunstan, archbishop of Canterbury. 
Mr. Marpourg of Berlin, a person now living, has taken 
up this relation, groundless as it is, and in a book of his 
writing, entitled 'Traite dela Fugue et du Counterpoint,' 
has done little less than assert that St. Dunstan invented 
counterpoint, by reducing into order the rules for compo- 
sition in four parts, and not a few give credit to his 
testimony.il 

Again we are told, that whereas the Greeks signified 
the several sounds in their scale by the letters of their 
alphabet, or by characters derived from them, Guido in- 
vented a more compendious method of notation by ])oints 
stationed on a stave of five lines, and occupying both the 
lines and the spaces. This assertion is true but in part ; 
for the stave, and that of many lines, was in use near half 
a century before Guido was born ; and all that can be 
ascribed to him is the placing points as well in the spaces 

t Vide infra, page 10, et seq. 

t ' Fra Guittone d'Arezzo, celebre per i suoi scritta sopra la musica, 
' inventore del contrappunto, e dal quale furono fissati i tuoni, che pre- 
' sentemente si cantano.' Lettere familiari e critiche di Vincenzio Mar- 
tinelli, Londra, 1758. Prefazione, page viii. This person had undertaken 
to write a history of music. See his letters above cited, page 164, con- 
taining an apology for his not having published it. 

Of this Fra Guittone an account may be seen in the Istoria della Vol- 
gar Poesia of Crescimbeni, lib. II. page 84. He flourished about 12.'iO, 
and is celebrated among the best of the ancient Tuscan poets. In the 
same work, lib. III. page 176, is a sonnet of his writing ; and in Mr. 
Baretti's History of the Italian Tongue, prefixed to his Italian library, 
page ix. is a fable of Fra Guittone, which Baretti says may be taken for 
a composition of yesterday. 

§ Wolfgang Caspar Printz, in his History of Music, written in the Ger- 
man language, and published at Dresden in the year 1690, who has 
given a relation purporting that ' In the year of our Lord, 940, Dunstan, 
otherwise Dunstaphus, an Englishman, being very young, betook him- 
' self to tlie study of music, and thereby acquired immortal fame. He 
' was the first that composed songs of different parts, that is to say, Bass, 
' Tenor, Descant, and Vagant or Alt,' page 104, sect. 23. The whole re- 
lation is an error, arising from a mistaken sense of a passage in the 
Prseceptiones Musices Poeticje of Johannes Nucius, a writer on music in 
the year 1613. Vide infra, page 176 in note, 274 in note, 651 in note. 

II ' Dunstan, Archeveque de Canterbory, qui vivoit dans le dixieme 
' si^cle, a tofijours eu I'honneur d'avoir commence, ainsi que d'avoir 
' fraye le chemm aux autres, II redigea en ordre les regies de la com- 
' position a quartre parties, et par la donna une nouvelle 6poque a la 
' musique.' Partie II. page vi. 



xvm. 



PRELIMINARY DISCOURSE. 



as on the lines, which it must be owned is an ingenious 
and useful contrivance. 

To assist the memory and facilitate the practice of sol- 
misation, it is also said that Guido made use of the left 
hand, giving to the top of the thumb the note Tam ut, 
to the joint below it A re, to the next B mi, and so on, 
placing the highest note of his system, E la, at the ex- 
tremity of the hand, viz., the tip of the middle finger ; 
but nothing of this kind is to be found, or indeed is men- 
tioned, or even hinted at, in any of his writings, and 
we may therefore conclude that the whole is an invention 
of some other person. 

Little less confusion attends the relations extant re- 
specting the invention of the Cantus Mensurabilis, and 
those marks or characters used to signify the several 
lengths or durations of notes. The vulgar tale is, that 
John de Muris, a Norman, and a doctor of the Sorbonne 
about the year 1330, invented eight musical characters, 
namely, the Maxima, or as we call it, the Large, the 
Long, the Breve, Semibreve, Minim, Semiminim or 
Crotchet, Chroma or Quaver, and the Semichroma, 
assigning to each a several length in respect of time 
or duration.* Now upon the face of the relation there is 
great reason to conclude, that in the original institution 
of the Cantus Mensurabilis, the semibreve was the 
shortest note ; but there is undeniable evidence that as 
well the minim as the notes in succession after it, were of 
comparatively late invention. 

But this is not all ; De Muris was not a Norman, but 
an Englishman : he was not the inventor of the Cantus 
Mensurabilis : not he, but a person of the name of 
Franco, a scholastic, as he is called, of Liege, about the 
middle of the eleventh century invented certain characters 
to signify the duration of sounds,! that is to say, the four 
first above mentioned. 

Another prevailing error respecting music has got pos- 
session of the minds of many people, viz., that those sin- 
gularly sweet and pathetic melodies with which the Scots 
music abounds, were introduced into it by David Rizzio, 
an Italian musician, and a favourite of Mary, queen of 
Scots ; the reverse is the truth of the matter, and that by 
the testimony of the Italians themselves; the Scots tunes 
are the genuine produce of Scotland ; those of greatest 
merit among them are compositions of a king of that 
country ; and of these some of the most celebrated madri- 
gals of one of the greatest of the Italian composers are 
avowed imitations.! 

Again, few are sufficiently acquainted with the history 
of the science, and in particular how long the several 
musical instruments now known by us have been in use, 
to prevent being imposed on by pretended new inventions : 
the harp of iEolus, as it is called, on which so much has 
been lately said and written, was constructed by Kircher 
above a century ago, and is accurately described in his 
Musurgia ; as is also the perpendicular harpsichord, and 
an instrument so contrived as to produce sound by the 
friction of wheels, from which the modern lyrichord is 
manifestly taken. The new system, as it is called, of the 
flute abec, proposed about forty years ago by the younger 
Stanesby, is in truth the old and original system of that 
instrument, and is to be found in Mersennus ; and the 
clarinet, an instrument unknown in England till within 
these last twenty years, was invented by John Christo- 
pher Denner, a wind musical instrument maker of Leipsic 
above a century ago. § 

* Nicola Vicentino, a writer of the sixteenth century, with some de- 
gree of infrenuity, attempts to shew that these characters are but ('.if- 
ferent modifications of the round and square b, which had been introduced 
into Guido's scale for another purpose. 

t Vide infra, pages 217, 221, 253. 

X Vide infra, page 5G3. 

§ Vide infra, page 651. 



Farther, it has for the honour of this our native country 
been said of Purcell, that his music was very different 
from the Italian ; that it was entirely English, that it was 
masculine.il Against the two first of these assertions we 
have his own testimony in the preface to one of his works, 
wherein he says that he has endeavoured at a just imita- 
tion of the most famed Italian masters, with a view, as he 
adds, to bring the gravity and seriousness of that sort of 
music into vogue.H As to the third, the judicious peruser 
of his compositions will find that they are ever suited 
to the occasion, and are equally calculated to excite 
tender, and robust or manly affections. 

Lastly, of the many who at this time profess to love 
music, few are acquainted with the characters, and even 
the names of those many eminent persons celebrated for 
their skill and great attainments in the science, and who 
flourished under the patronage of the greatest potentates, 
previous to the commencement of the present century ; 
and, with respect to those of our own country, it is true 
there is scarce a boy in any of the choirs in the kingdom 
but knows that Tallis and Bird composed anthems, and 
Child, Batten, Rogers, and Aldrich services ; but of their 
compositions at large, and in what particulars they ex- 
celled, even their teachers are ignorant. 

Under a thorough conviction of the benefits that must 
result from the kind of intelligence here recommended, 
attempts have been made at different periods to trace the 
rise and progress of music in a course of historical narra- 
tion ; and letit not be deemed an invidious oftice, if those 
defects in the attempts of others are pointed out, which 
alone can justify the present undertaking. 

In the Menagiana, tome I. page 303, mention is made 
of a canon of Tours of the name of Ouvard, who wrote 
a history of music : Mattheson, in his Volkommenen 
Capellmeister, takes notice of this work, and says that it 
comes down to the end of the seventeenth century, and is 
perhaps extant in MS. in some library at Paris. But the 
first attempt of this kind in print is a treatise of Johannes 
Albertus Bannius, ' De Musicae origine, progressu et 
' denique studio bene instituendo,' published in 1637, in 
octavo. 

Next to this, in point of time, is the History of Music 
of Wolfgang Caspar Printz, chapel-master and director of 
the choir of the church of Sorau, printed at Dresden 
in the year 1690, in a small quarto volume, with the title 
of ' Historiche Beschreibung der Edelen Singund Kling- 
' ktmst.' Neither of the two latter works can be considered 
as a history of the science ; the first of them is a very 
small volume, and the othei not a large one, containing 
little more than a list of writers on music disposed in 
chronological order. 

The appendix of Dr. Wallis to his edition of Ptolemy, 
published in 1682, though not a history of the science, 
contains many historical particulars respecting music, 
besides that in sundry instances it renders intelligible the 
doctrines of the ancient writers. It is written with great 
accuracy and perspicuity, and abounds with instances of 
that acuteness and penetration for which the author is 
celebrated. 

In 1683, the Sieur Gabriel Guillainne Nivers, organist 
of the chapel of Lewis XIV. published ' Dissertation 
' sur le Chant Gregorien,' a small octavo volume, but in 
effect a history of ecclesiastical music, with a relation of 
the many corruptions it has undergone. In it are many 
curious passages relating to the subject, extracted from 
the fathers and the ritualists, with the observations of the 
author, who appears to have been a learned man in his 
profession. 

II Granger's Biographical History of England, as it is called, vol. II., 
part II., class X. tit. musicians, art. Henricus Pubcell. 

% Vide infra, page 7-H. 



PRELIMINARY DISCOURSE. 



XIX. 



In 1695 Gio. Andrea Angelini Bontempi, of Perugia, 
published in a thin volume a work of some merit, entitled 

* Historia Musica.' Berardi mentions a work of one 
Pietro Arragona, a Florentine, entitled ' Istoria Armonica, ' 
but Brossard doubts the existence of it.* 

A history of the pontifical chapel, and of the college of 
singers thereto belonging, is contained in a work entitled 
' Osservazioni per ben regolare il Coro de i Cantori della 
' Cappella Pontiticia, tanto nelle Funzioni ordinarie che 
' straordinarie,' by Andrea Adami da Bolsena, Maestro 
della Cappella Pontificia, published at Rome in 1711, in 
a quarto volume. In this book are many curious 
particulars. 

Tliere is also extant in two volumes duodecimo, but 
divided into four, a book entitled ' Histoire de la Musique 
' et de ses Effets,' printed first at Paris in 1715, and 
afterwards at Amsterdam in 1725. The materials for 
this publication were certain papers found in the study of 
the Abbe Bourdelot, and others of his nephew Bonnet 
Bourdelot, physician to the king of France, the letters of 
the Abbe Raguenet and others, on the comparative merits 
of the Italian and French opera and music, together with 
sundry other papers on the same subject. The publisher 
was Bonnet, a nephew of the Abbe Bourdelot; 

and the best that can be said of the work is, that the whole 
is a confused jumble of intelligence and controversy ; and, 
saving that it contains some curious memoirs of Lully, 
and a few other of the French musicians, has very little 
claim to attention. 

About the year 1730, Mr. Peter Prelleur, an able 
musician and organist, published a work entitled ' The 
' modern Music-master, containing an introduction to 

* singing, and instructions for most of the instruments in 
' use.' At the end of this book is a brief history of music, 
in which are sundry particulars worth noting : it has no 
name to it, but was nevertheless compiled by the above 
person. 

John Godfrey Walther, a professor of music, and or- 
ganist of the church of St. Peter and Paul at Weimar, 
published in 1732 a musical Lexicon or Bibliotheque, 
wherein is a great variety of information respecting music 
and musicians of all countries and ages. Mattheson of 
Hamburg, in his ' Critica Musica,' his ' Orchestre,' and 
a work entitled ' Volkommenen Capellmeister,' i.e. the 
perfect Chapelmaster, has brought together many parti- 
culars of the like kind ; but the want of method renders 
these compositions, in an historical view, of little use. 

In the year 1740, an ingenious young man of the name 
of Grassineau,t published a Dictionary of Music in one 
octavo volume, with a recommendation of the work by 
Dr. Pepusch, Dr. Greene, and Mr. Galliard. The book 
had the appearance of a learned woi-k, and all men won- 
dered who the author could be : it seems he had been an 
amanuensis of the former of these persons." The founda- 
tion of this dictionary is a translation of that of Sebastian 
Brossard ; the additions include all the musical articles 
contained in the two volumes of Chambers's Dictionary, 
with perhaps a few hints and emendations furnished by 
Dr. Pepusch. The book nevertheless abounds with 
errors, and, though a useful and entertaining publication, 
is not to be relied on. 

In 1756, Fr. Wilhelm Marpourg, a musician of Berlin, 
published in a thin quarto volume, ' Trait6 de la Fugue et 
' duContrepoint,' thesecondpart whereof is a brief history 
of counterpoint and fugue. The same person is also the 
author of a work entitled ' Critische Einleitung in die 

* Geschichte und Lehrsake der alten und neuen Musick,' 
printed at Berlin in 1759. It is part of a larger work, 
and the remainder is not yet published. 

* Catalogue of writers on music at the end of his ' Dictionnaire de 
' Musique,' octavo, page 369. 

t See an account of him page 30, in the notes. 



The ' Storia della Musica' of Padre Martini of Bologna, 
of which as yet only two volumes have been published, 
and those at the distance of thirteen years from each 
other, is a learned and curious work ; but the great study 
and labour bestowed by the author in compiling it, make 
us despair of ever seeing it completed. 

The ' Histoire generate, critique, et philologique de la 
'Musique,' of Mons. De Blainville, printed at Paris in 
1767. in a thin quarto volume, has very little pretence to 
the title it bears : like some other works of the kind, it is 
diffuse where it ought to be succinct, and brief where one 
would wish to find it copious. 

A character very different is due to a work in two 
volumes, quarto, entitled ' De Cantu et Musica sacra, 
' a prima Ecclesise iEtate usque ad prjesens Tempus ; 
' Auctore Martino Gerberto, Monasterii et Congregationis 

* Sancti Blasii in Silva Nigra Abbate, Sacrique Romani 
' Imperii Princeps. Typis San-Blasianis, 1774.' In this 
most valuable work the author has with great learning, 
judgment, and candour, given the history of ecclesiastical 
music ; and the author of the present work felicitates 
himself on finding his sentiments on the subject, particu- 
larly of the church composers, and the corruptions of the 
church style, confirmed by the testimony of so able 
a writer. He is farther happy to see that without any 
communication with this illustrious dignitary, and without 
having perused his book, by the help of materials, which 
this country alone has furnished, he has been able to 
pursue a similar track of narration, and to relate and 
authenticate many facts contained therein. J 

At the beginning of this present year 1776, the musical 
world were favoured with the first volume of a work en- 
titled ' A General History of Music from the earliest 
' Ages to the present Period, with a Dissertation on the 
' Music of the Ancients, by Charles Burney, Mus. D., 
' F. R. S.' The author in the proposals for his sub- 
scription has given assurances of the publication of 
a second, which we doubt not he will make good. 

From those who have thus taken upon them to trace 
the rise and progress of music in a course of historical de- 
duction, we pass to others who appear to have made col- 
lections for the like purpose, but were defeated in their 
intentions of benefiting the science by their labours. 

And first Anthony Wood, who himself was a proficient 
in music, and entertained an enthusiastic fondness for the 
art, had it seems meditated a history of musicians, a work 
which his curiosity and unwearied industry rendered him 
very fit for : to this end he made a collection of memoirs, 
which is extant, in his own hand-writing, among the 
manuscripts in the Ashmolean Museum ; and in the 
printed catalogue thereof is thus numbered and described: 

* 8568. 106. Some materials toward a history of the lives 
' and compositions of all English musicians ; drawn up 
' according to alphabetical order in 210 pages by A. W.' 
Of these materials he seems to have availed himself in 
the Fasti Oxonienses, wherein are contained a great 
number of memoirs of eminent English musicians, equally 
curious and satisfactory, the perusal whereof in the origi- 
nal MS. has contributed to render this work somewhat 
less imperfect than it must have been without such infor- 
mation as they afford. 

Dr. Henry Aldrich, dean of Christ Church, an excellent 
scholar, and of such skill in music, that he holds a place 
among the most eminent of our English church musicians, 
had formed a design of a history of music on a most ex- 
tensive plan. His papers in the library of Christ Church 
college, Oxford, have been carefully perused : among 
them are a great number of loose notes, hints, and memo- 

t The fact is, that the fifth volume of this work was printed off in 
July in the present year, and the former ones in succession in the years 
preceding, and the two volumes of the Abbot Gerbert's work came 
to hand in the month immediately following. 



XX. 



PRELIMINARY DISCOURSE. 



randa relating to music and the professors of the science ; 
in the collection whereof, he seems to have pursued the 
course recommended by Brossard in the catalogue of 
writers on music at the end of his Dictionnaire de 
Musique, page 367 ; but among a great multitude of 
papers in his own hand-writing, there are none to be 
found from whence it can with certainty be concluded 
that he had made any progress in the work. 

Nicola Francesco Haym, a musician, and a man of 
some literature, published, above forty years ago, pro- 
posals containing the plan of a history of music written 
by himself, but, meeting with little encouragement, he 
desisted from his design of printing it. 

Much intelligence respecting music might have been 
hoped for from the abilities and industry of Ashmole, Dr. 
Hooke, and Sir William Petty, the two former of whom 
had been choristers, the one in the cathedral of Litchfield, 
the other of Christ Church, Oxford : the last of the 
three was professor of music at Gresham college ; but 
these persons abandoning the faculty in which they had 
been instituted, betook themselves to studies of a different 
kind : Ashmole, at first a solicitor in Chancery, became 
an antiquary, a herald, a virtuoso, a naturalist, and an 
Hermetic philosopher : Hooke took to the study of 
natural philosophy, mechanics, and architecture, and 
attained to great skill in all :* and Petty, choosing the 
better part, laid the fovmdation of an immense estate by 
a various exertion of his very great talents, and was 
successively a physician, a mathematician, a mechanic, 
a projector, a contractor with the government, and an 
improver of land. 

Enough it is presumed has been said to prove the 
utility, and even the necessity, in order to a competent 
knowledge of the science, of a History of Music, in the 
deduction whereof the first object that piesents itself to 
view is the system of the ancient Greeks, adjusted, it 
must be confessed, with great art and ingenuity, but 
labouring under many defects, which, if we are not 
greatly deceived, are remedied in that of the moderns. 
Of the origin of this system we have such authentic intel- 
ligence as leaves little room to doubt that it was invented 
by Pythagoras, a name sufficiently known and revered, 
and the subsequent deduction of the progress of the 
science, involving in it the names and improvements o ' 
men well known, such as Philolaus, Archytas of Tarentum, 
Aristoxenus, Euclid, Nicomachus, Ptolemy, and many 

* It is said by Anthony Wood of Dr. Hooke, that, heinf; at West- 
minster-school, he lodfjed and dieted in the house of Mr. Busby, the 
master, and that there, of his own accord, he learned to play twenty 
lessons on the organ, and invented thirty several ways of flying. 
Athen. Oxon. vol. II. col. 1039. The latter of these facts must stand on 
the authority of the relator, or rather his authors. Dr. Busby and the 
great Dr. Wilkins of Wadhani college ; but the former is rendered 
highly probable by the following anecdote respecting Dr. Busby, the 
communication whereof we owe to Dr. Wetenhall, one of Busby's 
scholars, and afterwards bishop of Cork and Ross, viz. : that 'the first 
' organ he ever saw or heard was in his, Dr. Busby's house ; and that tlie 
'same was kept for sacred use, and that even when it was interdicted.' 
Dedication of a treatise entitled ' Of Gifts and Offices in the public 
'Worship of God, by Edward Wetenhall, D.D., Chanter of Christ 
'Church, Dublin, 8vo. 1679.' That he was also eminently skilled in 
architecture, may be inferred from an assertion of Dr. Ward, in his life 
of Sir Christopher Wren, among the Gresham professors, viz. : that he 
greatly assisted Sir Christopher in re-building the public edifices. Wood 
goes so far as to say that Hooke designed New Bedlam, Montague- 
house, the College of Physicians, and the pillar on Fish-street Hill ; but 
the erection of the latter of these edifices is ascribed to Sir Christopher 
Wren. As to Montague-house and the College of Physicians, there are 
In Moxon's Mechanic Exercises, under the head of Bricklayer's Work, 
intimations that they were both designed by Hooke ; and Strype, in his 
edition of Stowe's Survey of London, speaking of Aske's hospital at 
Hoxton, says it was built after a modern design of Dr. Hooke. 

Of this latter person it may be said, that he was perhaps one of the 
greatest proficients in the art of thriving of bis time : by places, by 
projects, and by grants, some to himself, and others to his wife, he 
acquired estates, real and personal, to the annual amount of £15,000, to 
the accumulation of which wealth we may well suppose that the virtue 
of parsimony contributed not a little, and the rather as he suffered a 
natural daughter of his to be an actress on the stage under Sir William 
D'Avenant at the Duke's theatre in Dorset-Garden. 



others, may truly be called history, as being founded in 
truth ; and the utility and certainty of their relations will 
teach us to distinguish between fact and fable. 

It is much to be lamented that the greater part of 
what we believe touching music, is founded on no 
better authority than the fictions of poets and mytho- 
logists, whose relations are in most instances merely 
typical and figurative ; such must the stories of Orpheus 
and Amphion appear to be, as having no foundation in 
truth, but being calculated solely for the purpose of 
moral instruction. 

And with regard to facts themselves, a distinction is to 
be made, between such as are in their own nature in- 
teresting, and those that tend only to gratify an idle 
curiosity : to instance in the latter, what satisfaction does 
the mind receive from the recital of the names of those 
who are said to have increased the chords of the primitive 
lyre from four to seven, Chorebus, Hyagnis, and Ter- 
pander ; or when we are told that Olympus invented the 
enarmonic genus, as also the Harmatian mood ; or that 
EuTuolpus and Melampus were excellent musicians, and 
Pronomus, Antigenides, and Lamia celebrated players on 
the flute ? In all these instances, where there are no 
circimistances that constitute a character, and familiarize 
to us the person spoken of, we naturally enquire who he 
is ; and, for want of farther information, become in- 
different as to what is recorded of him. 

Mr. Wollaston has a remark upon the nature of 
fafiie that seems to illustrate the above observation, and 
indeed goes far beyond the case here put, inasmuch as 
the persons by him spoken of, are become wellknown 
characters : his words are these : ' When it is said that 
' Julius Caesar subdued Gaul, beat Pompey, changed the 
' Roman commonwealth into a monarchy, &c. it is the 
' same thing as to say, the conquerer of Pompey was 
' Cassar ; that is, Ceesar and the conqueror of Pompey are 
' the same thing ; and Caesar is as nmch known by one 
' designation as the other. The amount then is only 
• this : that the conqueror of Pompey conquered Pompey ; 
' or somebody conquered Pompey ; or rather, since 
'Pompey is as little known as Caesar, somebody con- 
' quered somebody. 'f 

That memorials of persons, who at this distance of time 
must appear thus indifferent to us, should be transmitted 
down to posterity, together with those events that make a 
part of musical history, is not to be wondered at; and 
Plutarch could never have recorded the facts mentioned 
by him in his Dialogue on Music, had he not also given 
the names of those persons to whom they are severally 
ascribed ; and if they now appear uninteresting we may 
reject them. But the case is far otherwise with respect 
to what is told us of the marvellous power and efficacy of 
the ancient music. Aristoxenus expressly asserts that 
the foundation of ingenuous manners, and a regular and 
decent discharge of the offices of civil life, are laid in a 
musical education ; and Plutarch, speaking of the educa- 
tion of Achilles, and relating that the most wise Chiron 
was careful to instruct him in music, says, that whoever 
shall in his youth addict himself to the study of music, if 
he be properly instructed therein, shall not fail to applaud 
and practise that which is noble and generous, and detest 
and shun their contraries : music teaching those that 
pursue it to observe decorum, temperance, and regularity; 
for which reason he adds, that in those cities which were 
governed by the best laws, the greatest care was taken 
that their youth should be taught music. Plato, in his 
treatise De Legibus, lib. II., insists largely on the utility 
of this practice; and Polybius, lib. IV., cap. iii., scruples 
not to attribute the misfortunes of the Cynetheaus, a 
peopile od" Arcadia, and that general corruption of their 

t KeligioD of Nature delineated, page 117. 



PRELIMINARY DISCOURSE. 



XXI. 



manners, by him described, to the neglect of the disci- 
pline and exercise of music ; which he says the ancient 
Arcadians were so industrious to cultivate, that they in- 
corporated it into, and made it the very essence of, their 
government ; obliging not their children only, but the 
young men till they attained the age of thirty, to persist 
in the study and practice of it. Innumerable also are 
the passages in the ancient writers on harmonics wherein 
the power of determining the minds of men to virtue or 
vice is ascribed to music with as little doubt of its efficacy 
in this respect, as if the human mind was possessed of no 
such power as the will, or was totally divested of those 
passions, inclinations, and habits, which constitute a 
moral character. 

Now, forasmuch as we at this day are incapable of dis- 
covering any such power as is here attributed to mere 
musical sounds, we seem to be warranted in withholding 
our assent to these relations, till the evidence on which 
they are grounded becomes more particular and explicit ; 
or it shall be shown that they are not, what some men 
conceive them to be, hyperbolical forms of speech, in 
which the literal is as far from the true sense, as it is in 
the stories of the effects of music on inanimate beings. If 
indeed by music we are to understand musical sounds 
jointly operating with poetry, for this reason that music is 
ever spoken of by the ancients as inseparably united with 
poetry ; and farther, because we are told that the ancient 
poets, for instance, Demodocus, Thaletas of Crete, Pindar, 
and others, not only composed the words, but also the 
music to their odes and poeans, and sang them to the 
lyre ; a degree of efficacy must be allowed it, propor- 
tioned to the advantages which it could not but derive 
from such an union.* But here a difficulty will arise, 
which, though it does not destroy the credit of these re- 
ports, as they stand on the footing of other historical 
facts, would incline us to suspect that the music here 
spoken of was of a kind very different from what it is in 
general conceived to be, and that for the following reason. 

We know by experience that there is no necessary con- 
nection between music and poetry ; and such as are com- 

* Quintilian has elegantly expressed his sense of the joint eificacy of 
music and poetry in the following passage : ' Nanique et voce et 
'niodulatione grandia elat^, jucunda dulciter, moderata leniter canit, 
' totaque arte consentit cum eorum, qua; dicuntur, affectibus.' Inst. 
Orat. lib. I. cap. x. 

But, notwithstanding this observation, which, as far as it goes, must 
he allowed to be just, the powers of music will be found inadequate to 
the expression of many of those sentiments in poetry which are com- 
prehended in the ideas of the beautiful and the sublime ; such, for 
instance, as these : — 

Where glowing embers round the room 
Teach light to counterfeit a gloom. 

Where I may oft outwatch the bear. 
With thrice gr at Hermes, and unsphere 
The spirit of Plato to unfold 
What worlds or what vast regions hold 
The immortal mind. 

Sentiments that defy the utmost powers of music to suit them with 
correspondent sounds. 

Nor will it be found that the melody or the cadence of sounds are 
either of them so peculiarly appropriated to particular passions or 
descriptions, as to rank the faculty of expression among tlie principal 
excellencies of music. And in proof of this assertion some examples 
might be given that would stagger an intidel in these matters. The late 
Dr. Brown, when he had written his ode entitled the Cure of Saul, for the 
music to it made a selection from the works of the most celebrated 
composers, of such favourite movements as he thought would best 
express the sense of the words ; in particular he took the saraband in 
the eighth sonata of Corelli's second opera for a solo air; and that most 
divine movement in Purcell's ' O give thanks,' ' Remember me, O Lord,' 
for a chorus ; and any stranger would have thought that the music had 
been originally composed to the words : the music to that admired song 
in Samson, ' Return, O God of hosts,' was taken from an Italian 
cantata of Mr. Handel, composed in his youth ; as vras also the music to 
the other, ' Then long eternity,' in the same oratorio : farther, the chorus 
in Alexander's Feast, 'Let old Timotheus yield the prize," saving the 
addition of one of the interior parts, was originally an Italian trio ; as 
was also that in the II Penseroso, ' These pleasures melancholy give.' 
Finally, a great part of the music to Mr. Dryden's lesser ode for 
St. Cecilia's Day was originally composed by Mr. Handel for an opera 
enlitii^Q Alceste, written by Dr. SmoUet, but never performed. 



petent judges of either, know also that though the powers 
of each are in some instances concurrent, each is a sepa- 
rate and distinct language. The poet affects the passions 
by images excited in the mind, or by the forcible im- 
pression of moral sentiments ; the musician by sounds 
either simple and harmonical only in succession, or com- 
bined : these the mind, from its particular constitution, 
supposing it endued with that sense which is the perfec- 
tion of the auditory faculty, without referring to any other 
subject or mediimi, recognizes as the language of nature ; 
and the affections of joy, grief, and a thousand nameless 
sensations, become subservient to their call. 

As the powers of music and poetry are thus different, 
it necessarily follows that they may exist independently of 
each other ; and the instances are as numerous of poets 
incapable of articulating musical sounds, as of musicians 
unpossessed of a talent for poetry. 

If then the poets of the ancients were only such as to 
the harmony of their verse, were capable of joining that of 
music, by composing musical airs, and also singing them, 
and that to an audience grounded and well instructed in 
music, what can we suppose the music of their odes to 
have been ? Perhaps little else than bare recitation ; not 
in true musical intervals, but with such inflections of the 
voice as accompany speech when calculated to make a 
forcible impression on the hearers. 

As to the relations of the effects of music in former 
ages on the passions of men, and of its provoking them to 
acts of desperation, it may be said that they afford no 
greater proofs of its influence on the passions than 
modern history is capable of furnishing, t But there are 

t Vide infra, pages 118, 119 ; and Plutarch relates that Antigenides, the 
tibicinist, playing before Alexander the Great, in a measure of time 
distinguished by the name of the Harmatian mood, enflamed the hero to 
such a degree, that, leaping from his seat, and drawing his sword, he in 
a frenzy of courage assailed those who were nearest him. In Orat II. 
De Fortun. vel Virtut. Alexandr. Magn. 

To these instances may be opposed the following, which modem 
history affords. The first is related of Ericus, king of Denmark, 
surnamed the Good, who reigned about 1130, and is to the following 
purport. When Ericus was returned into his kingdom, and held the 
yearly assembly, he was greatly pleased with the industry both of his 
soldiers and artificers. Among other of his attendants was a musician, 
who asserted that by the power of his art he was able to excite in men 
whatsoever affections he thought proper ; and to make the sad cheerful, 
the cheerful sad, the angry placid, and such as were pleased discontented, 
and even drive them into a raging madness ; and the more he insisted 
on his abilities the greater was the king's desire to try them. The artist 
now began to repent his having thus magnified his talent, foreseeing the 
danger of making such experiments on a king, and he was afraid that if 
he failed in the performance of what he had undertaken, he should be 
esteemed a liar ; he therefore entreated all who had any influence over 
the king to endeavour to divert him from his intention to make proof of 
his art ; but all without effect, for the more desirous he was to evade the 
trial of his skill, the more the king insisted on it. When the musician 
perceived that he could not be excused, he begged that all weapons 
capable of doing mischief might be removed, and took care that some 
persons should be placed out of the hearing of the Cithara, who might 
be called in to his assistance, and were, if necessity required it, to 
snatch the instrument from his hands, and break it on liis head. Every 
thing being thus prepared, the citharist began to make proof of his art 
on the king, who sat with some few about liim in an open hall ; first, by 
a grave mode, he threw a certain melancholy into the minds of the 
auditors ; but, changing it into one more cheerful, he converted their 
sadness into mirth that almost incited his bearers to dancing ; then 
varying his modulation, on the sudden he inspired the king with fury 
and indignation, which he continued to work up in him till it was easy 
to see he was approaching to frenzy. The sign was then given for those 
who were in waiting to enter ; they first broke the Cithara according to 
their directions, and then seized on the king ; but such was his strength, 
that he killed some of them with his fist; being afterwards overwhelmed 
with several beds, his fury became pacified, and, recovering his reason, 
he was grievously afflicted that he had turned liis wrath against his 
friends. Saxo Grammaticus, in Hist. Danicse, edit. Basil, lib. XII. 
page 113. The same author adds, that he broke open the doors of a 
chamber, and, snatching up a sword, ran four men through the body ; 
and that when he returned to his senses he made a pilgrimage to 
Jerusalem as an expiation of his crime. Olaus Magnus, who tells the 
same story, says that he afterwards died in the island of Cyprus. Vide 
Olaus Magnus, in Hist. Gent. Sept. lib. XV. cap. xxviii. and Krantzius, 
in Chron. Regn. Daniae, Suecise, et Norvegiae. 

Hieronymus Magius gives the following relation of a fact recent in 
memory in the year 1.564: Cardinal Hippolyto de Medicis, being a legate 
in the army at Pannonia, the troops being about to engage, upon 
sounding the alarm by the trumpets and drums, was so enflamed with a 
martial ardour, that, girding on his sword, he mounted his horse, and 
could not be restrained from charging the enemy at the head of those 



XXll. 



PRELIMINARY DISCOURSE. 



others that stagger human belief, and leave us in doubt 
whether to give or refuse credit to them; such, for in- 
stance, are the stories of the cure of diseases, namely, the 
sciatica, epilepsy, fevers, the bites of vipers, and even 
pestilences, by the power of harmony. 

What an implicit assent has been given to the reports 
of the sovereign efficacy of music in the cure of the 
frenzy occasioned by the bite of the Tarantula ! Baglivi, 
an eminent physician, a native of Apulia, the country 
where the Tarantula, a kind of spider, is produced, has 
given the natural history of this supposed noxious insect, 
and a variety of cases of persons rendered frantic by its 
bite, and restored to sanity and the use of their reason ; 
and in Kircher's Musurgia we have the very air or tune 
by which the cure is said to be effected. Sir Thomas 
Brown, that industrious exploder of vulgar errors, has let 
this, perhaps the most egregious of any that he has ani- 
madverted on. pass as a fact not to be controverted ; and 
Dr. Mead has strengthened the belief of it by his reasoning 
on the nature of poisons. After all the whole comes out 
to be a fable, an imposture calculated to deceive the cre- 
dulous, and serve the ends of designing people inhabiting 
the country.* 

The natural tendency of these reflections is to draw on 
a comparison of the ancient with modern music ; which 
latter, as it pretends to no such miraculous powers, has 
been thought by the ignorant to be so greatly inferior to 
the former, as scarce to deserve the name. In like manner 
do they judge of the characters of men, and the state of 
human manners at remote periods, when they compare 
the events of ancient history, the actions of heroes, and 
the wisdom of legislators, with those of modern times, 
inferring from thence a depravity in mankind, of which 
not the least trace is discernible. 

This mistaken notion seems to be but the necessary 
consequence of that system of education which directs the 
attention of young minds to the discoveries and trans- 
actions of the more early times ; assigning, as the rule of 
civil policy, and the standard of moral perfection and ex- 
cellence in arts, the conduct, the lives, and works of men 
whose greatest achievements are only wonderful as they 
were rare ; whose valour was Drutality, and whose policy 
was in general fraud, or at best craft ; and whose inven- 
tions and discoveries have in numberless instances been 
superseded by those of later times. To these, which we 
may call classical prejudices, we are to impute those nu- 
merous and reiterated complaints which we meet with of 
the degeneracy of modern times ; and when they are 
once imbibed, complaints of the declension of some arts, 
and of the loss of others, as also of the corruption of 
manners, appear to be but of course. Whether, therefore, 
our reverence for antiquity has not been carried too far 
both as to matters of science and morality, comprehending 
in the latter the virtue of justice, and the qualities of per- 
sonal courage, general benevolence, and refined humanity, 
of which the examples are not less numerous and con- 
spicuous in modern than in ancient history, is a question 
well worthy consideration. f 

whose duty it was to make the onset. Var. Lect. seu Miscell. 
Venet. 1564, lib. IV. cap. xiii. 

And, lastly, it is related, that at the celebration of the marriage of the 
duke of Joyeuse, a gentleman was so transported with the music of 
Claude le Jeune, performed at that solemnity, that he seized his sword, 
and swore that, unless prevented, he must fight with some one present ; 
but that a sudden change in the music calmed him. Bayle, art. 
GoUDiMEL, in not. Vide infra, page 434. 

* Vide infra, page 639, in note. 

+ In a book, which few readers at this day think worth looking into. 
Dr. Hakewill's .\pologie for the Power and Providence of God, are the 
following sentiments touching the reverence due to antiquity : ' Antiquity 
' I unfeignedly honour and reverence ; but why I should reverence the 
' rust and refuse, the dross and dregs, the warts and wens thereof I am 

'yet to seek. As in the little, so in the great world, reason will tell 

' you that old age or antiquity is to be accounted by the fartlier distance 
' from the beginning, and the nearer approach to the end ; and as grey 



Of the loss of many arts, that contribute as well to the 
benefit as delight of mankind, much has been said; and 
there is extant a large volume, written in Latin by Guido 
Pancirollus, a lawyer of Padua, entitled ' De rebus memo- 
' rabilibus deperditis et noviter inventis,' which has not 
escaped censure for the mistakes and peurilities with 
which it abounds, the tendency thereof being to shew that 
many arts known to the ancients are either totally lost, or 
so greatly depraved, that they can scarcely be said to 
have an existence among us.| In this book, which has 
proved a plentiful source of intelligence to such as have 
laboured to depreciate all modern attainments, it is 
roundly asserted of music, which was anciently a science, 
that there are not the least footsteps remaining : and far- 
ther, that the Cardinal of Ferrara, by whom it is supposed 
is meant Hippolyto de Este, the patron of Vicentino, took 
great pains to recover it, but all to no j)urpose.§ 

Such as seem to have adopted the opinion of Pancirol- 
lus with respect to music, for example, Dr. Pepusch, and 

' beards are for wisdom and judgment to be preferred before young green 
' heads, because they have more experience in affairs ; so likewise for the 
' same cause the present times are to be preferred before the infancy or 
' youth of the world, we having the history and practice of former ages 

' to inform us, which they wanted. In disgracing the present times 

'you disgrace antiquity properly so called.' Book V. page 13.3. 

Farther to this purpose the learned and sagacious Sir Thomas Brown 
delivers his sentiments in the following terms : ' The mortalest enemy 
' unto knowledge, and that which hath done the greatest execution upon 
' truth, hath been a peremptory adhesion unto authority ; and more 
' especially the establishing of our belief upon the dictates of antiquity. 
' For, (as every capacity may observe) most men of a^jes present, so 
' superstitiously do look upon ages past, that the authorities of the one 
' exceed the reasons of the ether : whose persons indeed being far 
' removed from our times, their works, which seldom with us pass 
' uncontroled, either by contemporaries, or immediate successors, are 
' now become out of the distance of envies : and the farther removed 
' from present times, are conceived to approach the nearer unto truth 
' itself. Now hereby methinks we manifestly delude ourselves, and 
' widely walk out of the track of truth. 

' For, first, men hereby impose a thraldom on their times, which the 
' ingenuity of no age should endure, or indeed the presumption of any 
' did ever yet enjoin. Thus Hippocrates, about two thousand years ago, 
'conceived it no injustice either to examine or refute the doctrines of 
'his predecessors: Galen the like, and Aristotle the most of any. Yet 
'did not any of these conceive themselves infallible, or set down their 
' dictates as verities irrefragable ; but when they either deliver their 
' own inventions, or reject other men's opinions, they proceed with 
'judgment and ingenuity : estahHsliing their assertions, not only with 
'great solidity, but submitting them also unto the correction of future 
' discovery. 

' Secondly, men that adore times past, consider not that those times 
' were once present, that is, as our own are at this instant ; and we 
'ourselves unto those to come, as they unto us at present: as we rely 
'on them, even so will those on us, and magnify us hereafter, who 
'at present condemn ourselves. Which very absurdity is daily com- 
' mitted amongst us, even in the esteem and censure of our own times. 
' And, to speak impartially, old men, from whom we should expect the 
' greatest example of wisdom, do most exceed in this point of folly j 
' commending the dayes of their youth, which they scarce remember, at 
' least well understood not ; extolling those times their younger years 
'have heard their fathers condemn, and condemning those times the 
' gray heads of their posterity shall commend. And thus is it the 
' humour of many heads to extol the dayes of their fore-fathers, and 
' declaim against the wickedness of times present. Which, notwith- 
' standing tliey cannot handsomely do, without the borrowed help and 
' satyrs of times past, condemning the vices of their own times, by the 
' expressions of vices in times whicli they commend; which cannot but 
' argue the community of vice in both. Horace, therefore, Juvenal, 
' and Persius were no prophets, although their lines did seem to 
' iiidigitate and point at our times. There is a certain list of vices 
' committed in all ages, and declaimed against by all authors, which will 
' last as long as humane nature; which, digested into common places, 
' may serve fur any theme, and never be out of date until Dooms day.' 
Enquiries into Vulgar and Common Errours, Book I. Chap. vi. 

t Of the many instances of arts or inventions lost, or in a state of 
depravity at this time, there are very few, if any, of which evidence can 
be found, or at least that have not been succeeded by others tending to 
the same purpose, and of far greater utility. To instance in a few 
particulars, instead of the papyrus of the ancients, prepared from the 
leaves of a certain buUrush, we have the paper of the modems; in the 
room of their specular stones, glass; and of clepsydras, instruments 
that measured time by the dropping of water, or the falling of sand, 
clocks and watches. As to the art of staining or painting glass, which 
ceased to he practised about the Riformation, and has almost ever since 
been deplored as a lost invention, it is effected by chemical means, and 
is at this day in as great perfection as ever. Vide Chambers's Diet, 
voce Glass. Anecdotes of Painting in England by Mr. Horace Walpole, 
vol. II. page 15. 

§ A like attempt was made in France in the year 1570, by the 
establishment of an academy under the direction of Jean Antoine Baif 



PRELIMINARY DISCOURSE. 



XXI 11. 



a few of his disciples, have asserted as an instance in 
support of it, that the chromatic and enarmonic genera 
are now neither practised nor accurately known. Farther 
they add, that of the various modes of the ancients, only 
two are remaining, viz., those which answer to the keys 
A and C ; for, say they, the ancients took the tones and 
semitones in order as they naturally arise in the diapason 
system, and, without any dislocation of either, considered 
the progression from any fundamental chord as a mode 
or key, and formed their melodies accordingly. 

With regard to the enarmonic genus, it will in the 
ensuing work be shewn that the ancients themselves 
suffered it to grow into disuse by reason of its intricacy ; 
and therefore it cannot so properly be said to have been 
lost, as that it is rejected, and the rather as we are assured 
that Salinas and others have accurately determined it :* 
of the chromatic as much seems to have been retained as 
is necessary to the perfection of the diatonic ; and as to 
the modes, it will also be shewn that there never was, nor 
can there in nature be more, or any other than tlie two 
abovementioned ; and consequently that in this respect 
music has sustained no injury at all. 

The loss of arts is a plausible topic of declamation, but 
the possibility of such a calamity by other means than 
a second deluge, or the interposition of any less powerful 
agent than God himself, is a matter of doubt ; and when 
appearances every where around us favour the opinion of 
our improvement not only in literature, but in the sciences 
and all the manual arts, it is wonderful that the contrary 
notion should ever have got footing among mankind. 

As to the general prejudices in behalf of antiquity, 
it has been hinted above that a reason for them is to 
be found in that implicit belief which the course of 
modern education disposes us to entertain of the superior 
virtue, wisdom, and ingenuity of those, who in all these 
instances we are taught to look on as patterns the most 
worthy of imitation ; but it can never be deemed an ex- 
cuse for some writers for complimenting nations less en- 
lightened than ourselves with the possession or enjoyment 
of arts which it is pretended we have lost ; as they do 
when they magnify the attainments of nations compara- 
tively barbarous, and making those countries on which 
the beams of knowledge can scarcely be said to have yet 
dawned the theatres of virtue and the schools of science, 
recommend them as fit exemplars for our imitation. 

Of this class of authors, Sir William Temple and Isaac 
Vossius seem to be the chief; the one a statesman retired 
from business, an ingenious writer, but possessed of little 
learning, other than what he acquired in his later years, 
and which it is suspected was not drawn from the purest 
sources ; the other a man of great erudition, but little 
judgment, the weakness whereof he manifested in a 
childish credulity, and a disposition to believe things in- 
credible. These men, upon little better evidence than 
the reports of travellers, and the relations of missionaries, 
who might have purposes of their own to serve, have 
celebrated the policy, the morality, and the learning of 
the Chinese, and done little less than proposed them as 
examples of all that is excellent in human nature. f 

and Joachim Theobalde de Courville, but through envy, as it is said, 
the design failed. Mersennus in Quest, et Explic. in Genesin. art. XV. 
pag. 1683. Walth. Musicalisches Lexicon, voce Academie Rotale 
DE MusiauE. 

* Vide infra, page 39. 

+ As an instance of their superior skill in the science of medicine, he 
says tliat their physicians pretend that they are able, not only to tell by 
the pulse how many hours or days a sick man can last, but how many 
years a man in perfect seeming health may live, in case of no accident 
or violence. Essay of Heroic Virtue, sect. II. 

The following summary of Cliinese knowledge may serve to show 
how well they are entitled to the exaggerated encomiums of such 
writers. They carry their history back to many ages before the time of 
the creation. Hearne's Duct. Historic. vcjI. I. page 16. Their notion of 
an eclipse is, that there is in heaven a dragon of an immense bigness, 
ready at all times to eat up the sun or moon, which he likes best ; when 



The topics insisted on by Sir William Temple, in that 
part of his Essay on Heroic Virtue, where he takes occa- 
sion to speak of the Chinese, are their wisdom, their 
knowledge, their wit, their learning, ingenuity, and 
civility, on which he bestows the most extravagant 
encomiums. 

Vossius is more particular, and says that ' the Chinese 
' deplore the loss of their music, the superior merit 
' whereof may be inferred from the relics of it yet re- 
* maining, which are so excellent, that for their perfection 
' in the art, the Chinese may impose silence on all 
Europe.' Farther he says of their pantomimes, or 
theatrical representations by mute persons, in which the 
sentiments are expressed by gesticulations, and even 
nods, that ' these declare their skill in the rythmus, which 
' is the soul of music. '+ Elsewhere he takes occasion to 
celebrate this people for their skill on the tibia, and 
bestows on their performance the following enthusiastic 
encomium : ' The tibia, by far to be preferred to the 
' stringed instruments of every kind, is now silenced, so 
' that, excepting the Chinese, who alone excel on it, 
' scarce any are to be found that are able to please even 
' an ordinary hearer. '§ 

Another writer is more particular, and gives us for his- 
tory this nonsense ; thatFou-Hi, the first of the emperors 
and legislators of China, delivered the precepts of music, 
and having invented fishing, composed a song for those 
who exercised the art ; and to banish all impurity from 
the heart, made a lyre with strings of silk : and farther 
that Chin-Nong, a succeeding emperor, celebrated the 
fertility of the earth in songs of his own composing, and 
made a beautiful lyre and a guitar enriched with precious 
stones, which produced a noble harmony, curbed the 
passions, and elevated many to virtue and heavenly 
truth. II 

These are the opinions of men who have acquired nc 
small reputation in the world of letters ; and therefore 
that error might not derive a sanction from authority, it 
seemed necessary to enquire into the evidence in support 
of them ; of what sort it is, the passage above cited may 
serve to show. It remains now to make the comparison 
above proposed of the modern with the ancient music. 

The method hitherto pursued by those writers who 
have attempted to draw a parallel between the ancient 
and modern music, has been to bring together into one 
point of view the testimonies in favour of the former, and 
to strengthen them by their own suffrages, which upon 
examination will be found to amovmt to just nothing ; for 
these testimonies being no more than verbal declarations 
or descriptions, every reader is at liberty to supply 
them by ideas of his own ; ideas which can only have 
been excited by that music which he has actually heard, 

an eclipse of either happens, they suppose he has got the planet between 
his teeth, and, to make him quit his hold, they beat drums and brass 
kettles. Le Comte's Memoirs of China, edit. 1738, page 70, 488. In the 
judgment of Cassini, and other great astronomers, they err in their 
accounts of sundry conjunctions of the planets; in some of them not 
less than live hundred years. Jenkin on the Reasonableness and 
Certainty of the Christian Religion, vol. I. page 339. They are so little 
skilled in mechanics, that they took a watch, brought into their country 
by a Jesuit, for an animal. They are strangers to the use of etters as 
the elements of words; and have even at this day no alphabet. Ibid. 
Moreover they pretend to be the inventors of music, notwithstanding 
that in the opinion of Father Le Comte they have nothing among them, 
that deserves the name. See his Memoirs, page 214. 

Of their propensity to fraud and deceit in their dealings, there are 
abundant examples in Le Comte and Lord Anson's voyage ; and of their 
morality and civil policy, which are so highly extolled, any one may 
judge, when he is told that in Pekin and other large cities there is an 
officer, whose duty it is every morning to destroy the numerous infants 
that have been exposed in the streets in the preceding night. Mod. 
Univ. Hist. fol. vol. I. page 175. 

I De poemat. cant, et vlrib. Rythmi, page 95. 
§ Ibid, page 107. 

II Extraits des Hist. Chinois, published by Mons. Goguet, page 567, 572. 
Dissert, on the Union, &c. of Poetry and Music, ] age 167. 



XXIV. 



PRELIMINARY DISCOURSE. 



or at least perused and contemplated. An instance 
borrowed from the practice of some critics in painting, 
may possibly illustrate this sentiment : the works of 
Apelles, Parrhasius, Zeuxis, and Protogenes, together 
with those of other artists less known, such as Bularchus, 
Euphranor, Timanthes, Polygnotus, Polycletes, and 
Aristides, all famous painters, have been celebrated in 
terms of high applause by Aristotle, Philostratus, Pliny, 
and the poets ; and those who attend to their descriptions 
of them, associate to each subject ideas of excellence as 
perfect as their imaginations can suggest, which can only 
be derived from such works of later artists as they have 
seen ; in like manner as we assist the descriptions of 
Helen in Homer, and of Eve in Milton, with ideas of 
female beauty, grace, and elegance, drawn from our own 
observation :* the result of such a comparison in the case 
of painting, has frequently been a determination to the 
prejudice of modern artists ; and the works of Raphael, 
Domenichino, and Guido have been condemned as not 
answering to those characters of sublime and beautiful, 
which are given to the productions of the ancient artists. f 
In like manner to speak of music, we can form ideas of 
the perfection of harmony and melody, and of the gene- 
ral effect resulting from the artful combination of musical 
sounds, from that music alone which we have actually 
heard ; and when we read of the music of Timotheus or 
Antigenides, we must either resemble it to that of the most 
excellent of the modern artists, or forbear to judge about 
it ; and if in the comparison such critics as Isaac Vossius, 
Sir William Temple, and some others, reject the music of 
the moderns as unworthy of attention or notice, how 
egregiously are they deceived, and what do they but 
forego the substance for the shadow ? 

Other writers have taken a different course, and endea- 
voured to prove the inferiority of the modern music to the 
ancient, by a comparison of the powers of each in de- 
priving men of the exercise of their rational faculties, 
and by impelling them to acts of violence. To these it 
may be said, that, admitting such a power in music, it 
seems to be common in some degree to that of all ages 
and countries, even the most savage ; but the fact is, that 
these effects are adventitious, and in all the instances 
produced will be found to have followed from some pre- 
disposition of the mind of the hearer, or peculiar coinci- 
dence of circumstances, for that in truth music pretends 
not to the power of working miracles, nor is it the more 
to be esteemed for exciting men to frenzy. Those who 
contemplate it in a philosophical and rational manner, and 
attend to its genuine operation on the human affections, 
are abundantly satisfied of its efficacy, when they dis- 
cover that it has a tendency to exhilarate the mind, to 
calm the passions, to assuage the pangs of affliction, t to 

• Mr. Harris to this purpose has given his sentiments in the following 
judicious observation : ' When we read in Milton of Eve, that 

' Grace was in all her steps, heav'n in her eye, 

' In ev'ry gesture dignity and love ; 
' we have an image not of that Eve which Milton conceived, but of such 
' an Eve only as every one by his own proper genius is able to rei)resent 
' from reflecting on those ideas which he has annexed to those several 
' sounds. The greater part in the mean time have never perhaps 
' bestowed one accurate thought upon what Grace, Heaven, Love, and 
'Dignity mean; or ever enriched the mind with ideas of beauty, or 
' asked whence they are to be acquired, and by what proportiims they 
' are constituted. On the contrary, when we view Eve as painted by an 
'able painter, we labour under no such difficulty; because we have 
' exhibited before us the better conceptions of an artist, the genuine 
' ideas of perhaps a Titian or a Raphael.' Disc, on Music, Painting, 
and Poetry, page 77, in not. 

t Vide Inquiry into the Beauties of Painting, by Daniel Webb, Esq. 
passim. 

I To this purpose we meet in Procopius with the following affecting 
relation, viz : that Geliraer, king of the Vandals, being at war with tlie 
emperor Justinian, and having been driven to the mountains by 
Belisarius, his general, and reduced to great straits, was advised in a 
letter by a friend of his named Pbaras to make terms with ttie enemy ; 
but in the greatness of his spirit disdaining submission, he returned 



assist devotion, and to inspire the mind with the most 
noble and exalted sentiments. 

Others, despairing of the evidence of facts, have re- 
course to argument, contending that the same superiority 
with respect to music is to be yielded to the ancients as 
we allow them in the arts that afford delight to the ima- 
gination ; poetry, eloquence, and sculpture, for instance, 
of which, say they, their works bear luculent testimony. 
To this it may be answered, that the evidence of works 
or productions now existing is irrefragable, but in a ques- 
tion of this kind there is no reasoning by analogy ; and 
farther, that in the case of music, proof of the superiority 
of the ancients is not only wanting, but the weight of the 
argument lies on the other side ; for where are those pro- 
ductions of the ancients that must decide the question ? 
Lost, it will be said, in the general wreck of literature and 
the arts. If so, they cease to be evidence. Appeal we 
then to those remaining monuments that exhibit to us 
the forms of their instruments, of which the lyre and the 
tibia are the most celebrated ; and that these are greatly 
excelled by the instruments of the moderns will not bear 
a question. As to the lyre, considered as a musical 
instrument, it is a very artless invention, consisting 
merely of a few chords of equal length but unequal ten- 
sions, in such a situation, and so disposed, as, without any 
contrivance, to prolong or reverberate the sound, to vi- 
brate in the empty air. The tibia, allowing it the per- 
fection to which the flute of the moderns is arrived, could 
at best be but an imperfect instrument ;§ and yet we are 
told it was in such estimation among the ancients, that at 
Corinth the sum of three, some say seven, talents was 
given by Ismenias, a musician, for a flute. 

But a weightier argument in favour of modern music, 
at least so far as regards the improvements jn theory and 
practice that necessarily result from the investigation of 
new principles and the discovery of new combinations, 
may be drawn from the natural course and order of 
things, which is ever towards perfection, as is seen in 
other sciences, physics and mathematics, for instance ; so 
that of music it may be said, that the discoveries of one 
cige have served but as a foundation for improvements in 
the next; the consequence whereof is, that the fund of 
harmony is ever increasing. What advantages must 
accrue to music from this circumstance, may be discerned 
if we inquire a little into those powers which are chiefly 
exercised in practical composition. The art of invention 
is made one of the heads among the precepts of rhetoric, 
to which music in this and sundry instances bears a near 

this answer : ' Ouod mihi consilium dedisti, magnam habeo tibi gratiam, 
' ut etiam hosti injusto serviam ; id ver6 mihi intolerandum videtur. 
' Si Deus faveret, repetere, poenas ah eo vellem, qui a me nunquam nee 
' facto violatus nee verbo, bello, cujus nulla est causa legitima, praetex- 
'tum prsbuit, meque in hunc statum redegit, accito, nescio unde, 
' immissoque Belisario. Non improbabile esse sclat, passurum ipsura, 
'tanquam hominem ac principem, eorum aliquid, unde abhorrit. 
' Nequit ultra progredi stylus, auferente mentem calamitate, qua? me 
' eircumvenit. Vale, amice Phara, et mihi quod te oro, citharam, panem 
' unum ac spongiam mitte.' Procopius Caesariensis de Bello Vandalico, 
vol. I. lib. II. cap. vi. page 240, edit. Paris, 1662, which we thus render: 
I esteem it a great kindness that you vouchsafe me your advice, recom- 
mending a submission to my enemy, unjust as he has been to me, but 
tlie thought thereof is intolerable. If it please God I am prepared to 
suffer the worst from him, who having never been injured by me, has 
found a pretext fora war, for which no justifiable reason can be assigned ; 
and has let loose upon me Belisarius, who has reduced me to this 
extremity. Let him know that he is a man, and, though a prince, that 
he is not beyond the reach of misfortune. I can proceed no farther, 
the calamities which surround me depriving me of my reason. Farewell 
ray friend Pharas, and send to me a harp, a loaf of bread, and a sponge. 
The historian adds, that the harj) was to console him in his affliction, 
the loaf to satisfy his hunger, he not having seen bread for a long time, 
and the sponge to dry up his tears. 

§ The imperfection of the flute consists in the impossibility of 
attempering its tones, there being no rule or canon by which it can l)e 
tuned ; to which we may add, that the tones in the upper octave are as 
dissimilar, in respect of sound, as those of the human voice in those 
persons who have what is called the falsetto. In the flute at'^ec t>-« 
dilference is discernible in the double shake, which is made on a nota 
that divides the two systems of the natural and artincial tones. 



PRELIMINARY DISCOURSE. 



XXV. 



resemblance; the end of persuasion, or affecting the 
passions, being common to both. This faculty consists 
in the enumeration of common places, which are revolved 
over in the mind, and requires both an ample store of 
knowledge in the subject upon which it is exercised, and 
a power of applying that knowledge as occasion may re- 
quire. It differs from memory in this respect, that 
whereas memory does but recall to the mind the images 
or remembrance of things as they were first perceived, the 
faculty of invention divides complex ideas into those 
whereof they are composed, and recommends them again 
after different fashions, thereby creating variety of new 
objects and conceptions. Now, the greater the fund of 
knowledge above spoken of is, the greater is the source 
from whence the invention of the artist or composer is 
supplied; and the benefits thereof are seen in new com 
binations and phrases, capable of variety and permutation 
without end. And thus much must serve at present 
touching the comparative merits of the ancient and 
modern music. 

In tracing the progress of music, it will be observed, 
that it naturally divides itself into the two branches of 
speculation and practice, and that each of these requires 
a distinct and separate consideration.* Of the dignity 
and importance of the former, Ptolemy, lib. I. cap ii. has 
delivered his sentiments to the following purpose : ' It is 
' in all things the business of contemplation and science 

* to show that the works of nature, well regulated as they 
' are, were constituted according to reason, and to answer 
' some end ; and that nothing has been done by her 
' without consideration, or as it were by chance ; more 
' especially in those that are deemed the finest of her 
' works, as participating of reason in the greatest degree, 

* the senses of sight and hearing.' And Sir Isaac Newton, 
speaking of the examination of those ratios that afford 
pleasure to the eye in architectural designs, says it tends 
to exemplify the simplicity in all the works of the 
Creator. And farther he gives it as his opinion, ' that 

■ some general laws of the Creator prevail with respect to 
' the agreeable or unpleasing affections of all our senses. 'f 
By practical music we are to understand the art of com- 
position as founded in the laws of harmony, and deriving 
its grace, elegance, and power of affecting the passions 
from the genius and invention of the artist or composer ; 
in the exercise of which faculty it may be observed, that 
the precepts for combining and associating sounds are as 
it were the syntax of his art, and are drawn out of it, as 
the rules of grammar are from speech. J 

In musical history the several events most worthy of 
attention seem to be those of the first establishment of a 
system, the introduction of music into the church service, 
the rise of dramatic music ; under these several heads all 
that intelligence which to us is the most interesting may 
be comprehended. As touching the first, it is certain 
that we owe it to the Greeks, and there is nothing that at 
this distance of time can be superadded to the relations of 
the ancient writers on the subject; nor can it be safe to 
deviate, either in respect of form or manner, from the ac- 

* There are but few instances of musicians that have been eminently 
distinguished for skill both in the theory and practice of music, Zarlino, 
Tartini, and Rameau excepted. The two branches of the science have 
certainly no connection with each other, as may be gathered from the 
following sentiment of an ingenious writer on the subject : ' The delights 
' of practical music enter the ear without acquainting the understanding 
' from what proportions they arise, or even so much as that proportion 
' is the cause of them : this the philosopher observes from reason and 
'experience, and the mechanic must be taught, for the framing 
' instruments ; but the practiser has no necessity to study, except he 
'desires the learning as well as the pleasure of his art.' Proposal to 
perform Music in perfect and mathematical Proportions, by Tho. Salmon, 
4to. Lond. I(i88. 

t Vide infra, page 410, in note. 

t ' The art by which language should be regulated, viz. Grammar, is of 
' much later invention than languages themselves, being adapted to what 

■ was already in being, rather than the rule of making it so.' Bishop 
Wilkins's Essay towards a real Character, page 19. 



counts from them transmitted to us of the original consti- 
tution of the lyre, or of the invention and successive pro- 
gress of a musical scale; much less can we be warranted 
in speaking of the ancient practice, and the more abstruse 
parts of the science, namely, the genera and the modes, 
in any other terms than themselves make use of. Were 
a liberty to do otherwise allowed, the same mischief would 
follow that attends the multiplication of the copies of a 
manuscript, or a translation through the medium of divers 
languages, where a new sense may be imposed upon the 
text by different transcribers and translators in succession, 
till the meaning of the original becomes totally obscured. 

Vitruvius, in his treatise De Architectura, has a chapter 
on music, wherein he laments the want of words in the 
Roman language equivalent to the Greek musical terms ; 
the same difficulty is experienced in a greater or less de- 
gree by all who take occasion to speak of the ancient 
music, whether of the Hebrews or the Greeks. The 
English translators of the Bible were necessitated to 
render the words TIJ^ Kinnor and ^J)1^ Gnugab, by 
harp and organ ; and a translator of musical appellatives 
will in many instances be reduced to as great difficulty 
as the Laplander, who in rendering a passage in the 
Canticles, ' He looketh forth at the windows, shewing 
himself at the lattice,' could find no nearer a resemblance 
to a lattice than a snow-shoe, a thing like a racket used 
in the game of tennis, and translated it accordingly. 

The complaint of Vitruvius above mentioned furnishes 
an occasion of enquiry into the state of music among the 
Romans ; and this will appear, even in their most flourish- 
ing condition, to have been, both in theory and practice, 
very low, there being no author to be found till after the 
destruction of the commonwealth who has written on the 
subject; and of those that lived in the time of Augustus 
and afterwards, the number is so small, and, if we except 
Boetius, their writings are so inconsiderable, as scarce 
to deserve notice. Vitruvius wrote not professedly on 
music ; all that he says of it is contained in the third, 
fourth, and fifth chapters of the third book of his treatise 
l)e Architectura; wherein laying down the rules for the 
construction of theatres, he speaks of harmony in general 
terms, and afterwards of certain hollow vessels disposed 
in niches for the purpose of reverberating the voice of the 
singers or actors ; and thence takes occasion to mention 
the genera of the ancients, which he illustrates by 
a scale or diagram, composed, as he says, by Aristoxenus 
himself, though it does not occur in the valuable edition 
of that author published by Meibomius. In the same 
work, lib. X. cap. ii. entitled De Hydraulicis, he de- 
scribes the hydraulic organ of the ancients, but in such 
terms, that no one has been able satisfactorily to ascertain 
either its figure or the use of its parts. 

Of Censorinus, Macrobius, Martianus Cappella, and 
Cassiodorus, it was never pretended that they had made 
any new discoveries, or contributed in the least to the 
improvement of music. Boetius indeed with great in- 
dustry and judgment, collected the sense of the ancient 
Greek writers on Harmonics, and from the several works 
of Aristoxenus, Euclid, Nicomachus, Alypius, Ptolemy, 
and others whose discourses are now lost, compiled his 
most excellent treatise De Musica. In this he delivers 
the doctrines of the author above mentioned, illustrated 
by numerical calculations and diagrams of bis own in- 
vention ; therein manifesting a tiiorough knowledge of 
the subject. Hence, and because of his great accuracy 
and precision, this work of Boetius, notwithstanding it 
contains little that can be said to be new, has ever been 
looked upon as a valuable repository of musical erudition. § 

§ The works of Boetius were published in a folio volume at Venice, in 
the year 1499, and at Basil by Glareanus, in 1.570. In the treatise De 
Musica are sundry diagrams invented by the editor, which tend greatly 
to the illustration of his author. 



XXVI. 



PRELIMINARY DISCOURSE. 



Long before the time of Boetius, the enurmonic and chro- 
matic genera had grown into disuse ; the diatonic genus 
only remaining, the musical characters were greatly re- 
duced in number ; and the notation of music became so 
simple, that the Romans were able to represent the whole 
series of sounds contained in the system of a double 
octave, or the bisdiapason, by fifteen characters ; re- 
jecting therefore the characters used by the Greeks for 
the purpose, they assumed the first fifteen letters of their 
own alphabet ; and this is the only improvement or in- 
novation in music that we know of that can be ascribed 
to the Romans. 

As to the practice of music, it seems to have been 
carried to no very great degree of perfection by the 
Romans ; the tibia and the lyre seem to have been the 
only instruments in use among them ; and on these 
there were no performers of such distinguislied merit as 
to render them worthy the notice of posterity, which 
perhaps is the reason that the names of but few of them 
are recorded. 

Caspar Bartholinus has written a treatise ' De Tibiis 
' veterum et earum antique usu,' in which he has brought 
together a great variety of intelligence respecting the 
flutes of the ancients : in this tract is a chapter entitled 
' Tibia in Ludis Spectaculis atque Comediis,' wherein the 
author takes occasion to speak of the tibiae pares et im- 
pares, and also of the tibiae dextra et sinistrae, used in 
the representation of the comedies of Terence, which he 
illustrates by plates representing the forms of them 
severally, as also the manner of inflating them, taken 
from coins and other authentic memorials. In particular 
he gives an engraving from a manuscript in the Vatican 
library, of a scene in an ancient comedy, in which a 
tibicinist is delineated standing on the stage, and blowing 
on two equal flutes : what relation his mvisic has to the 
action we are to seek. He also gives from a marble at 
Rome the figure of a man with an inflected horn near 
him, thus inscribed, m. iulius victor ex collegio liti- 

CINUM CORNICINUM. 

It appears from a passage in Valerius Maximus, that 
there was at Rome a college of tibicinists or players on 
the flute, who we may suppose were favoured with some 
special privileges and immunities. These seem to have 
been a distinct order of musicians from the former, at 
least there are sundry inscriptions in Gruter purporting 
that there was at Rome a college comprehending both 
tibicinists and fidicinists ; which latter seem to have been 
no other than lyrists, a kind of musicians of less account 
among the Romans than the players on their favourite 
instrument the flute. Valerius Maximus, lib. II. cap. v. 
relates of the tibicinists that they were wont to play on 
their instrument in the forum, with their heads covered, 
and in party-coloured garments. 

That the tibicinists were greatly indulged by the 
Romans, may be inferred from the nature of their office, 
wliich required their attendance at triumphs, at sacrifices, 
and indeed all public solemnities ; at least the sense of 
their importance and usefulness to the state is the only 
reason that can be suggested for their intemperance, and 
that insolence for which they were remarkable, and which 
both Livy and Valerius Maximus have recorded in a 
narration to the following purpose. ' The censors had 

* refused to permit the tibicines to eat in the temple of 
' Jupiter, a privilege which they claimed as founded on 
' ancient custom ; whereupon the tibicines withdrew to 
' Tibur, a town in the neighbourhood of Rome, now 

* Tivoli. As the tibicines were necesssary attendants on 
' the sacrifices, the magistrates were at a loss how to per- 
' form those solemnities in their absence ; the senate 
' therefore stnt embassadors to the Tiburtines, requesting 
' them to deliver them up as officers of the state who had 



' fled from their duty : at first persuasions were tried, but 
' these proving ineffectual, the Tiburtines had recourse to 
' stratagem ; they appointed a public feast, and inviting 
' the tibicines to assist at it, plied them with wine till they 
' became intoxicated, and, while they were asleep, put 
' them into carts, which conveyed them to Rome. The 
' next day, having in some degree recovered their reason, 
' the tibicines were prevailed on to stay in the city, and 
' were not only restored to the privilege of eating in the 
' temple, but were permitted annually to celebrate the 
' day of their return, though attended with circumstances 
' so infamous to their office, by processions in which the 
' most licentious excesses were allowed.'* 

The secession of the tibicinists was in the consulate of 
Caius Junius Bubulcus and Quintus iEmilius Barbula: 
that is to say in the year of the world 3640, three hun- 
dred and eight years before Christ ; and serves to shew 
tlie extreme licentiousness of Roman manners at that 
period, as also the low state of their music, when the best 
instruments they could find to celebrate the praises of 
their deities were a few sorry pipes, little better than 
those which now serve as playthings for children. 

But, leaving the tibicines and their pipes to their ad- 
mirers, if we proceed to enquire into the state of music 
among the Romans at any given period of their history, 
we shall find that, as a science, they held it in small esti- 
mation. And to this fact Cornelius Nepos bears the 
fullest testimony; for, relating in his life of Epaminondas 
that he could dance, play on the harp and flute, he adds, 
that in Greece these accomplishments were greatly es- 
teemed, but by the Romans they were little regarded. 
And Cicero, in his Tusculan Questions, lib. I. cap. i. to 
the same purpose, observes that the ancient Romans, ad- 
dicting themselves to the study of ethics and politics, left 
music and the politer arts to the Greeks. Farther we 
may venture to assert, that neither their religious solemni- 
ties, nor their triumphs, their shows or theatrical repre- 
sentations, splendid as they were, contributed in the least 
to the improvement of music either in theory or practice : 
to say the truth, they seemed scarcely to have considered 
it as a subject of speculation ; and it was not until it re- 
ceived a sanction from the primitive fathers of the church, 
that the science began to recover its ancient dignity. 

The introduction of music into the service of the church 
affords ample scope for reflection, and comprehends in its 
history a great part of what we know of modern music. 
All that need be mentioned in this place respecting that 
important event is, that after the example of the Jews, 
and upon the authority of sundry passages in scripture, 
and more especially in compliance with the exhortation 
of St. Paul in his Epistles, St. Basil, St. Ambrose, and 
St. Chrysostom about the middle of the fourth century in- 
stituted antiphonal singing in their respective churches of 
Cesarea in Cappadocia, Milan, and Constantinople. St. 
Ambrose, who must be supposed to have been eminently 
skilled in the science, prescribed a formula of singing in 
a series of melodies called the ecclesiastical tones, appa- 
rently borrowed from the modes of the ancient Greeks; 
these, as constituted by him, were in number only four, 
and are meant when we speak of the Cantus Ambrosianus ; 
but St. Gregory, near two centuries after, increased them 
to eight. The same father drew up a number of precepts 
respecting the limits of the melodies, the fundamental 
note, and the succession of tones and semitones in each ; 
and, with a view to the establishment of a settled and 
uniform musical science, that would apply to all the 
several offices at that time used in divine worship, founded 
and endowed a school for the instruction of youth in the 

» Livy, lib. IX. cap. xxx. See also Valerius Maximus, lib. II. cap. v. 
The same story is related by Ovid, Fasti, lib. VI., who adds that the 
thirteenth day of June was celebrated as the anniversary. 



PRELIMINARY DISCOURSE. 



XXVll. 



rudiments of music, as contained in this formula, which 
was distinguished by the appellation of the Cantus Ec- 
clesiasticus, and in later times by that of the Cantus 
Gregorianus. 

Before this time music had ceased to be a subject of 
speculation: Ptolemy was the last of the philosophers 
that had written professedly on it ; and though it may be 
said that his three books of Harmonics, as also those of 
Aristoxenus, Euclid, Nichomachus, AristidesQuintilianus, 
and others, being extant, music was in a way of improve- 
ment from the studies of men no less disposed to think 
and reflect than themselves ; yet the fact is, that among 
the Romans the science not only had made no 
progress at all, but even before the dissolution of the 
commonwealth, with them it seemed to be extinct. Nor 
let the supposition be thought groundless, that during 
some of the succeeding ages the books, the very reposito- 
ries of what we call musical science, might be lost ; the 
history of the lower empire furnishing an instance, the 
more remarkable, as it relates to their own, the Roman 
civil law, which proves at least the possibility of such a 
misfortune.* 

To these causes, and the zeal of the fathers above men- 
tioned, and more especially of St. Gregory, to disseminate 
its precepts, it is to be ascribed that the cultivation of 
music became the peculiar care of the clergy. But here a 
distinction is to be noted between the study and practice 
of the science ; for we find that at the time of the institu- 
tion of the Cantus Ambrosianus, an order of clergy was 
also established, whose employment it was to perform 
such parts of the service as were required to be sung. 
These were called Psalmistae ; and though by Bellarmine 
and a few other writers they are confounded with the 
Lectors, yet were they by the canonists accounted a sepa- 
rate and distinct order. The reason for their institution 
was, that whereas in the apostolical age the whole con- 
gregation sang in divine service, and great confusion and 
disorder followed therefrom, it was found necessary to 
settle what the church calls a regular and decent song, 
which, as it was framed by rule, and founded in the prin- 
ciples of harmony, required skill in the performance; and 
accordingly we find a canon of the council of Laodicea 
held as early as the beginning of the fourth century, for- 
bidding all except the canonical singers, that is to say, 
those who were stationed in the Ambo, where the singing- 
desk was placed, and who sang out of a book or parch- 
ment, to join in the psalms, hymns, and other parts of 
musical divine service. We may well suppose that this 
order of men were endowed with all the requisites for the 
discharge of their function, and that the peculiar form 
which the council of Carthage directs to be used for the 
ordination of Psalmistae or singers, f was in effect a recog- 
nition of their skill and abilities. 

The order of men above mentioned can be considered 
in no other view than as mere practical musicians, the 
principal object of whose attention was to make themselves 
acquainted with the songs of the church, and to utter 
them with that decency and gravity, and in such a 
manner as tended most to edification. From the frequent 
repetition of the same offices it must be supposed that in 
general they sang by rote ; at least we have no better 
reason to assign than that they must have so done, for the 
establishment of a school by St. Gregory for the instruc- 
tion of youth in the Cantus Ecclesiasticus, as reformed by 
himself, and for that sedulous attention to their improve- 
ment in it which he manifested in smidry instances. 

At the same time that we applaud the zeal of this 
father of the church, we cannot but wonder at that of his 
predecessors, which is not more apparent in their com- 

* See the relation of the discovery of the Litera Pisana at page 180. 
t See page 106, in note. 



mendations of music, as associated with religious worship, 
than in their severe censures of that which was calculated 
for private recreation. As to the songs of the stage m 
the ages immediately succeeding the Christian era, we 
know little more of them than in general that they were 
suited to the corrupt manners of the times ; and these, by 
reason of their lewdness, and perhaps impiety of sentiment, 
might be a just subject of reprehension ; but against 
the music, the sounds to which they were uttered, or the 
particular instruments that assisted the voice in singing 
them, an objection can scarce be thought of; and yet so 
frequent and so bitter are the invectives of the primitive 
fathers, namely, Clemens Alexandrinus, TertuUian, St. 
Cyprian, Lactantius, Epiphanius, Gregory Nazianzen. 
and of St. Basil, St. Augustine, and St. Chrysostom, who 
were lovers and promoters of the practice of music, against 
wicked measures and effeminate melodies, the noise of 
flutes, cymbals, harps, and other instruments of deceit, 
seducing the hearers to intemperance, and even idolatry, 
that if credit be given to their opinions of the nature and 
tendency of secular music, we must be inclined to believe, 
as they in good earnest profess to have done, that it was 
an invention of the Devil. 

The cultivation of music as a science was the employ- 
ment of a set of men, in whom all the learning of the 
times may then be said to have centered ; these were the 
regular clergy, of such of whom as flourished in the 
eleventh century afterwards, it must in justice be said, 
that what they wanted in knowledge, they made up in 
industry ; and that those frequent bai-barisms which occur 
in their writings, were in no small degree atoned for by 
the clearness and precision I with which on every occasion 
they delivered their sentiments. Nor was the conciseness 
and method of the monkish treatises on music a less 
recommendation of them than their perspicuity : they 
consisted either of such maxims as were deemed of greatest 
importance in the study of the science, or of familiar 
colloquies between a master and his disciple, in which in 
an orderly course of gradation, first the elements, and 
then the precepts of the art were delivered and illustrated. 
To enumerate the instances of this kind which have 
occurred in the course of this work, would be an endless 
task ; let it suffice to say that the Histoire Litteraire de 
France, and the Memoirs of Bale, Pits, and the Bibliotheca 
of Tanner abound with references to a variety of manu- 
script tracts deposited in the public and other libraries, 
that abundantly prove the mode of musical instruction to 
have been such as is above described. 

Before the period above spoken of, music had for very 
good reasons been admitted into the number of the 
liberal sciences ; and accordingly in the scholastic division 
of the arts into the trivium and quadrivium, it held a place 
in the latter : nevertheless, till the Greek literature began 
to revive in Europe, saving the summary of harmonics 
contained in the treatise De Musica of Boetius, the 
students in that faculty had scarce any source of in- 
telligence ; and to this it must be attributed that in none 
of the many tracts written by the monks of those times, 
and afterwards by the professors or scholastics as they 
were called, do we meet with any of those profound dis- 
quisitions on harmony and the proportions which resolve 
the principles of music into geometry • nor any of those 
nice calculations and comparisons of ratios, or subtile 
distinctions between the consonances of one kind and 
those of another, which abound in the writings of the 
ancient Greeks ; so that were we to judge from the many 

t These qualities seem to be but the necessary result of the old scho- 
lastic method of institution, in which logic made a considerable part, and 
are in no instance more manifest than in the ancient forms of judicial 
proceedings, such as writs and pleadings ; of which Sir Matthew Hale, 
in his History of the law, chap. 7, remarks that they were very short, but 
very clear and conspicuous, orderly digested, pithy, clear, and rational. 
The same may he said in general of the more ancient statutes. 



XXVlll. 



PRELIMINARY DISCOURSE. 



discourses written during that dark period, and bearing 
the titles of Micrologus, Metrologus, and others of the 
like import, we should conclude that the science of har- 
monics had scarce any existence among mankind. Nor 
could any great advantage result from the writings of 
Boetius, seeing that there wanted light to read by ; and 
this was not obtained till Franchinus introduced it, by 
procuring translations of those authors from whose 
writings Boetius had compiled his work. 

That the studies of the monkish musicians must have 
been confined to the Cantus Gregorianus is evident from 
this consideration, that they were strangers to music of 
every other kind; an assertion which will be the more 
readily credited when we are told that till the middle of 
the eleventh century rythmic or mensurable music was 
not known. Their method of teaching it was by the 
monochord, without which they had no method of deter- 
mining the progression of tones and semitones in the 
octave, nor consequently of measuring by the voice any 
of the intervals contained in it. 

The reformation of the scale by Guido Aretinus, and 
more especially his invention of a method of singing by 
certain syllables adapted to the notes, facilitated the 
practice of singing to such a degree, that, as himself 
relates, the boys of his monastery were rendered capable 
in a month's time of singing in a regular and orderly 
succession the several intervals with the utmost accuracy 
and precision.* We are told, though not by himself, that 
he also by an ingenious contrivance transferred the notes 
of his scale to the left hand, making a several joint of 
each of the fingers the position of a note. Whether this 
invention is to be ascribed to him or not, it is pretty cer- 
tain that it followed soon after the reformation of the 
scale, and that it gave rise to a distinction of music into 
manual and tonal, the first comprehending the precepts of 
singing by the syllables, the other the Cantus Ecclesias- 
ticus, as instituted in tlie formula of St. Gregory. 

At this time the world were strangers to what we call 
rythmic music, the practice of singing, and thereby of as- 
sociating music with poetry, which till then had universally 
])revailed, rendering any such invention unnecessary. 
Nevertheless, there were some writers who had enter- 
tained an idea of transferring the prosody of poetry to 
music ; and a few scattered hints of this kind, which 
occur in the writings of St. Augustine and our countryman 
Bede on the subject of metre, suggested the formation of a 
system of metrical laws, such as would not only enable 
music to subsist of itself, but aid the powers of melody 
with that force and energy which it is observed to derive 
from the regular commixture and interchange of long and 
short quantities. 

This improvement was effected in the institution of 
what is called the Cantus Mensurabilis ; a branch of 
musical science which subjected the duration of musical 
sounds to rule and measure, by assigning to those of the 
slowest progression certain given portions of time, and to 
the next in succession a less, in a regular gradation, and 
which tauglit a method of signifying by characters, varying 
in form and colour, the radical notes, with their several 
ramifications, terminating in those of the smallest value, 
i. e. of the shortest duration. 

An invention of this kind was all that could then be 
thought wanting to the perfection of instrumental music ; 
and from this period we may observe that it began to 
flourish : it is true that the state of the mechanic arts was 
then very low, and that the instruments in common use 
were so rudely constructed, as to be scarcely capable of 
yielding musical sounds. Bartholomeus, in his book De 
Proprietatibus Rerum, in an enumeration of the musical 
instruments of his time, has described the flute as made of 
the boughs of an elder-tree hollowed; and an instrument 

• Vide infra, page IGl. 



called the Symphonia, as made of a hollow tree, cJos'^d 
in leather on either side, which he says is beaten of 
minstrels with sticks, and that ' by accord of hyghe and 
lowe thereof comyth full swete notes.' And again, de- 
scribing the Psalterium or Sawtrie, he says it differs from 
the harp, for that it is made of an hollow tree, and that 
* the sowne comyth upward, the strynges being smytte 
downwarde ; whereas in the harpe the hollownesse of the 
tre is byneathe.' These descriptions, and others of the 
like kind which are elsewhere to be met with, are evi- 
dence of the inartificial construction of musical instru- 
ments in those days, and leave it a question what kind of 
harp or other instrument that could be on which King 
Alfred had attained to such a degree of excellence as to 
rival the musicians of his time. 

Nevertheless it appears that there were certain instru- 
ments, perhaps not in common use, better calculated to 
produce melody than those above-mentioned, namely, 
those of the viol kind ; the specific difference between 
which and other stringed instruments is, that in the 
former the sound is produced by the action of a plectrum 
or bow of hair on the strings : of these the mention is not 
only express, but frequent in Chaucer, by the names of 
the Fithel, Getron, Ribible, and other appellations, clearly 
synonymous : the invention of this class of instruments is 
by some, who make the viol the prototype of it, ascribed 
to the French ; but there are other writers who derive 
the viol itself from the Arabian Rebab, from whence 
perhaps Ribible and Rebec, the use whereof it is said the 
Christians learned from the Saracens in the time of the 
Crusades ; but it is more probable, by reason of its 
antiquity, that it was brought into Spain by the Moors. 

To ascertain the degree of perfection to which the 
practice of instrumental music had attained at any period 
before the sixteenth century, would be very difficult. 
The Provencal songs, as being mere vocal compositions, 
afford no ground on which a conjecture might be formed : 
and as to their popular tunes, the airs of the Musars ana 
Violers, besides that they seem to have been mere melodies, 
for the most part the effusions of fancy, and not regulated 
by harmonical precepts, the impression of them can hardly 
be supposed to have been either deep or lasting , and 
this may be the chief reason that the knowledge of them 
has not reached posterity. 

That the practice of instrumental music was become 
familiar with such persons of both sexes as had received 
the benefit of a good education, is clearly intimated by 
the old poets. Not only the Squire, but the Clerk, 
Absolon, in Chaucer, are by him described, the one as 
floyting, i. e. fluting all the day, the other as playing 
songs on a small Ribible, and elsewhere on the Geterne;t 
and in the Confessio Amantis of Gower, fol. 178, b. is 
a plain intimation that the Citole, an instrument nearly 
resembling the virginal, was in his time the recreation of 
well educated young women. J 

We are also told by Boccace, in his Account of the 
Plague at Florence in 1348, that the ladies and gentlemen 
who retired from that city, and are relators of the several 
stories contained in his Decameron, among other re- 
creations in the intervals of their discourses, intermixed 
music ; and that sundry of the persons whose names he 
mentions played on the lute and the viol. They also 
danced to the music of the Cornamusa or bagpipe, an in- 
strument which we may infer to have been held in but 
ordinary estimation from this circumstance, that it is put 
into the hands of Tindarus, a domestic of one of the 
ladies ; besides that Chaucer in characterising his Miller 
says, 

' A baggepipe well couth he blowe and soune.' 

+ See the character of the Squire among the Prologues to the Canter- 
bury Tales, as also the Milier's Tale passinr.. 

I Vide infra, page 206. 



PRELIMINARY DISCOURSE. 



XXIX. 



Of vocal concerts, as they stood about the year 1550, 
or perhaps earlier, a judgment may be formed from the 
madrigals of that time, which abound witli all the graces 
of harmony. Concerts of instruments alone seem to be 
of later invention, at least there is no clear evidence of 
the form in which they existed, other than treatises and 
compositions for concerts of viols called Fantasias, few 
whereof were published till thirty years after.* 

Gio. Maria Artusi, an ecclesiastic of Bologna, and 
a writer on music about the year 1600, describes the con- 
certs of his time as abounding in sweetness of harmony, 
and consisting of cornets, trumpets, violins, viols, harps, 
lutes, flutes, and harpsichords : these, as also organs, 
regals, and guitars, are enumerated in the catalogue of 
instruments prefixed to the opera, L'Orfeo, composed by 
Claudio Monteverde, and represented at Mantua in 1607. 
Tom Coryat speaks also of a performance at Venice, 
chiefly of instrumental music, which he protests he would 
have travelled a hundred miles on foot to hear, but with- 
out any such particular description as can enable us to 
compare it with the concerts of more modern times. 

As touching the theory of the science, it has above been 
said to have consisted in manual, tonal, and mensurable 
music, with this farther remark, that, as it was included 
in the very nature of tlieir profession, and besides required 
some degree of literature, the great cultivators of it were 
the regular clergy. These men contented themselves 
with that small portion of knowledge which was to be 
attained by the perusal of Boetius, Cassiodorus, Guido, 
and a few others, who wrote in the Latin tongue ; the 
little they knew they freely communicated ; and it was 
not till the beginning of the fourteenth century that men 
began to suspect that the science was capable of farther 
improvement. 

About this time Johannes De Muris improved the 
Cantus Mensurabilis, by reducing it to form and de- 
monstrating that the measures thereof, like the ratios of 
the consonances, were founded in number and proportion : 
from the rules laid down by him in a treatise entitled 
Practica Mensurabilis Cantus, are derived the dis- 
tinctions of duple and triple proportion, as ftiey respect 
the duration of sounds, with all the various modifications 
thereof. On this tract Prosdocimus Beldimandis wrote 
a commentary, and farther illustrated the doctrines con- 
tained therein in sundry discourses on the subjects of 
plain and mensurable music. It appears that both these 
persons were philosophers at large, and eminently skilled 
in the mathematics ; and the liberal manner in which 
they wrote on music, treating it as a subject of deep 
speculation, was an inducement with many learned men, 
who lived under no ecclesiastical rule, to enter into an 
investigation of its principles. Some of these assumed 
the character of professors of the science, and undertook 
by public lectures to disseminate its principles. The 
most eminent of these persons were Marchettus of Padua, 
Johannes Tinctor, Gulielmus Garnerius, and Antonius 
Suarcialupus, to whom we may add Politian, whose skill 
in music is manifested in a discourse De Musica, contained 
m his Panepistemon or Praelectiones, extant in print. 
But notwithstanding the pains thus taken to revive the 
science, the improvement of it went on very slowly ; 
whatever advances were made in the practice, the theo- 
retical topics of disquisition were soon exhausted, and the 
science of harmonics may be said to have been for some 
ages at a stand. 

At length the beams of learning began to dawn on the 

* The earliest of which we can speak with certainty, is a treatise 
in folio by Thomas a Santa Maria, a Spanish Dominican, publislied at 
Valladoliil in 1570. entitled ' Arte de tanner fantasia jiara teola, visuela, 
' y todo instrumendo de tres o quatro ordenes.' which carries the an- 
ticiuity of concerts for Viols, and those compositions called Fantasias, 
back to that time, but leaves us at a loss as to other instrumental concerts. 



western empire : the city of Constantinople had been the 
seat of literature for some ages, but the sack of it by the 
Turks in the year 1453, had driven a great number of 
learned Greeks thence, who bringing with them an im- 
mense treasure of manuscripts, took refuge in Italy. 
Being settled there, they opened their stores, took 
possession of the public schools, and became the pro- 
fessors and teachers of the mathematical and other 
sciences, and indeed of philosophy, eloquence, and 
literature in general, in all the great cities. Of the many 
valuable books of Harmonics that are known to have been 
written by the mathematicians and other ancient Greeks, 
some have escaped that fate which learning is sure to 
experience from the ravages of conquest, f and the con- 
tents of these being made public, the principles of the 
science began to be known and understood by manj^, 
who till then were scarcely sensible that it had any 
principles at all. 

This communication of intelligence was very propitious 
to music, as it determined many persons to the study of 
the science of harmony. The tonal laws and the Cantus 
Mensurabilis were left to those whose duty it was to 
understand them ; the ratios of sounds, and the nature of 
consonance were considered as essentials in music, and 
the investigation of these was the chief pursuit of such as 
were sensible of the value of that kind of learning. 

Of the many who had profited in this new science, as 
it may be called, one was Franchinus Gafflirius, a native 
of Lodi, who having quitted the tuition of a Carmelite 
monk, who had been his instructor, became soon dis- 
tinguished for skill in those theoretic principles, the 
knowledge whereof he had derived from an attendance 
on the Greek teachers. And having procured copies of 
the treatises on harmonics of Aristides Quintilianus, 
Ptolemy, Manuel Bryennius, and Bacchius senior, he 
caused them to be translated into Latin ; and, besides 
discharging the duty of a public professor of music in the 
several cities of Italy, became the revivor of musical 
erudition ; and that as well posterity, as those of his own 
time, might profit by his labours, he digested the sub- 
stance of his lectures into distinct treatises, and gave them 
to the world. 

The writings of Franchinus, as they were replete with 
learning drawn from the genuine source of antiquity, and 
contained the clearest demonstrations of the principles of 
harmony, were so generally studied, that music began 
now to assume the character of a secular profession. The 
precepts therein delivered afforded a greater latitude to 
the inventive faculty tlian the tonal laws allowed of; and 
emancipating the science from the bondage thereof, many 
who had no relation to the church set themselves to frame 
compositions for its service, in which the powers both of 
harmony and melody were united. And hence we may 
at least with a show of probability date the origin of an 
office that yet subsists in the choral establishments of 
Italy, namely, that of Maestro di Cappella ; the duty 
whereof seems uniformly to have been not only tliat the 
person appointed to it should as precentor regulate the 
choir, but also adapt to music the offices performed both 
on ordinary and solemn occasions. Of the dignity and 
importance of the office of Maestro di Capella a judgment 
may be formed from this circumstance, that the persons 
elected to it for some centuries past appear to have been 
of distinguished eminence ;t and of its necessity and 
utility no stronger argument can be offered, than that 

t Laurus Quirinus of Venice was told by Cardinal Ruthen that 
upwards of one hnndred and twenty thousand volumes were destroyed. 
Hody, de Grajcis illustr. lib. II. cap. i. 

X Andrea Adami l?olsena, in the historical preface to liis ' Osservazioni 
' per ben regolareil Coro de i Cantori della Capella Pontificia,' asserts ^hat 
anciently in the college of pontifical singers the maestro di cappella was r> 
bishop. 



XXX. 



PKELIMINARY DISCOURSE. 



among the Germans, to whom the knowledge of music 
was very soon communicated after its revival in Italy, the 
office was recognized by the appointment of a director of 
the choir in the principal churches of all the provinces 
and cities. The same sense of the importance of this 
office appears to have been entertained by the protestants, 
who at the time of the Reformation we find to have been 
no less sedulous in the cultivation of music with a view 
to religious worship, than the church that had established 
it. It is true that Calvin was for some time in doubt 
whether to adopt the solemn choral service, or that plain 
metrical psalmody which is recommended by St. Paul to 
the Colossians, as an incentive to such mirth as was con- 
sistent with the Christian profession, and at length deter- 
mined on the latter. 

But Luther, who was excellently skilled in music, con- 
sidered it not merely as a relief under trouble and anxiety, 
but as the voice of praise, and as having a tendency to 
excite and encourage devout affections, besides that he 
had translated into the German language the Te Deum, 
and composed sundry hymns, as also tunes to some of the 
German psalms,* he, with the approbation of Melancthon, 
received into his church a solemn service, which included 
anthems, hymns, and certain sweet motets, of which he 
speaks very feelingly, and of music in general he gives 
his opinion in these words : ' Scimus musicam da;mo- 
nibus etiam invisam et intolerabilem esse.'f That the 
office of a chapel-master was recognized by the pro- 
testants in the manner above mentioned is hardly to be 
doubted, seeing that it was exercised at Bavaria by 
Ludovicus Senfelius, a disciple of Henry Isaac, and an 
intimate friend and correspondent of Luther, + and sub- 
sists in Germany to this day. 

For the reasons above assigned, we may without scruple 
attribute to Franchinus a share of that merit which is 
ascribed to the revivers of Literature in the fifteenth cen- 
tury; and the rather as his writings, and the several 
translations of ancient treatises on harmonics which he 
procured to be made, furnished the students in the science 
with such a copious fund of information, as enabled them 
not only to reason justly on its principles, but to extend 
the narrow bounds of harmony, and lay a foundation for 
those improvements which it has been the felicity of later 
times to experience. And it is not a groundless suppo- 
sition that the reputation of his writings was a powerful 
incentive to the publication of those numerous discourses 
on music of which the ensuing work contains a detail. 
Indeed so general was the propensity in the professors of 
the science in Italy, and in Germany more especially, to 
the compilation of musical institutes, dialogues, and dis- 
courses in various forms, that the science was for some 
time rather hurt by the repetition of the same precepts, 
than benefited by any intelligence that could in strictness 
be said to be new. The writings of Zarlino and Salinas 
are replete with erudition ; the same, though in a less 
eminent degree, may be said of those of Glareanus and 
the elder Galilei ; but of the generality of the Introduc- 
tions, the Enchiridions, and the Erotomata published in 
Italy and Germany from about the year 1550 to the 
middle of the next century, the perspicuity of them is 
their best praise. 

* Melchior Adamus, in his life of Luther, has inserted a letter from 
him to Spalatinus, written anno 1524, wherein he says he is looking 
out for poets to translate the whole of the Psalms into the German 
tongue, and requests of Spalatinus his assistance therein. This was some 
years before Marot translated the Psalms into French. 

t In an epistle to Senfelius, Musicus, cited by Dr. Wetenhall from 
Sethus Calvisius, in his Gifts and Offices in the public worship of God, 
page 434, but without reference to any work of Calvisius. This epistle, 
wherever it is, and the above cited passage, are also noticed by Butler in 
his Principles of Music, page 115. Dr. Wetenhall applies this passage to 
the music of our church, and on the authority thereof pronounces it to be 
such as no Devil can stand against. 

J Sonxe niotetts of his composition are extant in the Dodecachordon 
of Glareanus. 



As the revival of the theory of music is to be ascribed 
to the Italians, so also are those improvements in the 
practice of it that have brought it to the state of perfec- 
tion in which we behold it at this day. It is true that in 
the practice of particular instruments the masters of other 
countries have been eminently distinguished, as namely, 
those of Germany for skill on the organ ; the French for 
the lute and harpsichord ; and we are indebted for many 
valuable discoveries touching the nature and properties of 
sound, of consonance and dissonance, the method of con- 
structing the various kinds of musical instruments, and, 
above all, for a nice and accurate investigation of the 
principles of harmonics, to the learning and industry of 
Mersennus, a Frenchman ; but in the science of compo- 
sition the musicians of Italy have uniformly been the 
instructors of all Europe. 

To relate the subsequent instances of improvement in 
music, or to enumerate the many persons of distinguished 
eminence that have excelled in the theory and practice 
thereof, would be to anticipate that information, which it 
is the end of history to communicate ; and to animadvert 
on the numberless defects of the ancient music, may seem 
unnecessary, seeing that as well the paucity as the 
structure of the ancient instruments affords abundant 
evidence of a great disproportion between their practice 
and their theory ; it is nevertheless worthy of remark, 
that they who were so skilful and accurate in the in- 
vention of characters and symbols, the types not only of 
things, but of images or ideas, as the Greeks are allowed 
to have been, have, in the instance of music, manifested 
a great want of that faculty, inasmuch as there is not to 
be found in any of the characters in the ancient musical 
notation, the least analogy or relation between the sign 
and the sound or thing signified ; a perfection so obvious 
in the practice of the moderns, that we contemplate it 
with astonishment, there being no possible arrangement 
or disposition of musical sounds, nor no series or succession 
of equal or unequal, similar or dissimilar measures, but 
may with the greatest accuracy be described by the stave 
of Guido, and the forms of notes with their adjuncts, as 
directed by the rules of the Cantus Mensurabilis ; in- 
somuch that the modern system of notation, compre- 
hending in it the types or symbols of things, and not of 
notions or ideas, may be said to possess all the advantages 
of a real character. 

To celebrate formally the praises of music in a work, 
the design whereof is to display its excellencies, may seem 
unnecessary ; and the rather, as it has from the infancy 
of the world, with historians, orators, and poets, been 
a subject of panegyric : besides the power and effect of 
musical sounds to assuage grief and awaken the mind to 
the enjoyment of its faculties, is acknowledged by the 
most intelligent of mankind ; and, were it necessary, to 
prove that the love of music is implanted in us, and not 
the effect of refinement, examples thereof might be pro- 
duced from the practice of those, who, from their par- 
ticular situation of country, or circumstances of life, are 
presumed to approach nearly to that state in which the 
natural and genuine suggestions of the will are supposed 
to be most clearly discernible. To say nothing of the 
Turks, who are avowed enemies of literature, or of the 
Chinese, who, as has been shewn, notwithstanding all 
that is asserted of them, are so circumstanced, as seem- 
ingly never to be able to attain to any degree of ex- 
cellence, nations the most savage and barbarous profess 
to admit music into their solemnities, such as they are, 
their rejoicings, their triumphs for victories, the meetings 
of their tribes, their feasts and their marriages ; and to 
use it for their recreation and private solace. § St. Chry- 

§ Father Lafitau, in his Moeurs des Sauvages, tome II. page 21.3, et seq. 
has given a full description of the festal solemnities, accompanied with 
music, of the Iroquois, Hnrons, and other tribes of American savages i 



PRELIMINARY DISCOURSE. 



XXXI. 



sostoin, in his Homily on psalm xli. estimates the im- 
portance of music by its universality, and, in a strain of 
simplicity, corresponding with the manners of the times 
in which he lived, says that human nature is so delighted 
with canticles and poems, that by them infants at the 
breast when they are froward or in pain, are lulled to 
rest ; that travellers in the heat of noon, driving their 
beasts, such as are occupied in rural labours, as treading 
or pressing grapes, or bringing home the vintage ; and 
even mariners labouring at the oar, as also women at 
their distaff, deceive the time, and mitigate the severity 
of their labour by songs adapted to their several employ- 
ments or peculiar conditions. Clearchus relates that at 
Lesbos the people had a song which they sung while 
they were grinding corn, and for that reason called 
tTTifivXiov ; and Thales affirms that he had heard a female 
slave of that country singing it, turning a mill : it began 

* Mole pistrinum mole, nam et Pittacus molit rex magnse 
' Mitylenas,' and alluded to the practice of that king, who 
was used to grind corn with a hand-mill, esteeming it a 
healthy exercise. 

Other writers go farther, and affect to discern the prin- 
ciples of music not only in the songs, but the occupations 
and exercises of artificers and even labourers ; one of 
these in a vein of enthusiasm, perhaps more humorous 
and singular than persuasive, says, ' What shall I speak 
' of that pettie and counterfeit music which carters make 

* with their whips, hempknockers with their beetels, 
' spinners with their wheels, barbers with their aizzer.^, 
' smithes with their hammers ? where methinkes the 

* master-smith with his treble hammer sings deskant 
' whilest the greater buz upon the plainsong : who doth 
' not straitwaies imagin upon musick when he hears his 
' maids either at the woolhurdle or the milking pail? good 
' God, what distinct intention and remission is there of 
' their strokes ? what orderly dividing of their straines ? 
' what artificial pitching of their stops ? ' * 

and in the Royal Commentaries of Peru, book II. chap. xiv. the author, 
Garcilasso de la Vega, besides informing us that their fabulous songs 
were innumerable, and carried in them the evidence of a savage spirit, 
speaks thus particularly of their music : ' In musick they arrived to a 
' certain harmony, in wfiich the Indians of Colla did more particularly 
' excell, having been the inventors of a certain pipe made of canes glued 
' together, every one of which having a ditTerent note of higher and lower, 
' in the manner of organs, made a pleasing musick by the dissonancy of 
' sounds, the treble, tenor and basse exactly corresponding and answering 
' each to other ; with these pipes they often plaid in concert, and made 
' tolerable musick, though they wanted the quavers, semiquavers, aires, 
' and many voices, which perfect the harmony amongst us. They had 
' also other pipes, which were flutes with four or five stops, like the pipes 
' of shepherds ; with these they played not in consort, but singly, and 
' tuned them to sonnets, which they composed in metre, the subject of 
' which was love, and the passions which arise from the favours or dis- 
' pleasures of a mistress. These musicians were Indians trained up in 
'that art for divertisement of the Incas, and the Curacas, who were his 
' nobles, which, as rustical and barbarous as it was, it was not common, 
' but acquired with great industry and study. 

• Every song was set to its proper tune ; for two songs of different sub- 
'jects could not correspond with the same aire, by reason that the music 
' which the gallant made on his flute, was designed to-«xpress the satis- 
' faction or discontent of his mind, which were not so intelligible perhaps 
' by the words, as by the melancholy or chearfulness of the tune which he 
' plaid. A certain Spaniard one night late encountered an Indian woman 
' in the streets of Cozco, and would have brought her back to his lodgings ; 
' but she cryed out, " For God's sake. Sir, let me go, for that pipe which 
"you hear in yonder tower calls me with great passion, and I cannot 
" refuse the summons, for love constrains me to go, that I may be his wife, 
" and he my husband." 

' The songs which they composed of their wars and grand atchievements 
' were never set to the aires of their flutes, being too grave and serious to 
' be intermixed with the pleasures and softnesses of love ; for those were 
' oiiely sung at their principal festivals, when they commemorated their 
' victories or triumphs. When I came from Peru, which was in the year 
' 1560, there were then five Indians residing at Cozco, who were great 
' masters on the flute, and could play readily by book any tune that was 
' laid before them ; they belonged to one Juan Rodriguez, who lived at a 
• village called Labos, not far from the city : and now at this time, being 
'the year 1G02, 'tis reported that the Indians are so well improved in 
' musick, that it was a common thing for a man to sound divers kinds of 
'instruments ; but vocal musick was not so usual in my time, perhaps 
' because they did not much practise their voices, though the mongrils, 
' cr such as came of a mixture of Spanish and Indian blood, bad the 
' faculty to sing with a tunable and a sweet voice.' 

* The Praise of Musicke, 8vo. printed anno 1586, at Oxford, for Joseph 



But besides the pleasure that men derive from music, 
this satisfaction arises from the study of it, that its prin- 
ciples are founded in the very frame and constitution of 
the universe, and are as clearly demonstrable as mathe- 
matical truth and certainty can render them ; and in this 
respect music may be said to have an advantage over 
many sciences and faculties in the pursuit whereof the 
attention of mankind has at diiferent periods been deeply 
engaged. To say nothing of school divinity, which, hap- 
pily for the world, has given place to rational theology, 
what can be said of law in general, other than that it is 
mere human invention? a fabric of science erected it is 
true on the basis of a few uncontrovertible principles of 
morality, and of that which we call natural justice, but so 
accommodated to particular circumstances, to the genius, 
situation, temper, and capacities of those who are the 
objects of it, as that what is permitted and encouraged in 
one country, poligamy, for instance, shall be punished in 
another. In some constitutions a diflference of sex shall 
aggravate the guilt of the same offence ; and custom and 
usage shall preserve the inheritance of the parent for the 
benefit of the eldest of his male descendants with the same 
pretence to justice as the law of nature and reason distri- 
butes it among them all. Finally, what shall we say to 
that system of jurisprudence, which, being allowed to be 
imperfect, craves the aid of equity to regulate its operation, 
and mitigate its rigours ? or of those glosses and comments 
which in the civil and canon law are of little less authority 
than the laws themselves? 

As to medicine, setting aside the knowledge of the 
human frame, and the uses of its constitutent parts, a 
noble subject of speculation it must be confessed, the 
wiser part of men, rejecting theory as vain and de- 
lusive, resolve the whole of the science into observation 
and practice ; thereby confessing that its principles are 
either very few, or so void of certainty, as not with safety 
to be relied on. 

Of other liberal arts, such as grammar, logic, and rhe- 
toric, it must be allowed that they are of singular use ; 
but, as being the mere inventions of men, and at best 
auxiliaries to other arts or faculties, they are in their 
nature subordinate, and in that respect do but resemble 
the art of memory, which all men know to be founded on 
principles not existing in nature, but assumed by our- 
selves ; widely differing from those which are the basis as 
well of musical as mathematical science. 

From this view of the comparative excellence of music, 
and its pre-eminence over many other sciences and facul- 
ties, we become convinced of the stability of its prin- 
ciples, and are therefore at a loss for the reasons wh)', in 
these later times at least, novelty in music should be its 
best recommendation ; or that the love of variety should so 
possess the generality of hearers, as almost to leave it a 
question whether or no it has any principles at all. 

To satisfy these doubts, it may be sufficient to observe 
that the principles of harmony allow, as it is fit they 
should, great scope for the exercise of the invention ; and 
though few pretend to skill in the arts without being in 
some degree or other possessed of it, yet as all tl.j imagin- 
ative arts presuppose a disposition in mankind to receive 
their impressions, all claim a right, and many the ability, 
to judge of works of invention and fancy. 

The epic poet, trusting that the mind of his reader is 
co-extensive with his own, endeavours to excite in him the 
ideas of sublimity and beauty ; the dramatic writer hopes 
to move the affections of his audience to terror and pity 
by the representation of actions, the reflection on which 

Barnes, but conjectured to have been written by Dr. John Case, page 76. 
Of this person there is a curious account in Athen. Oxon. col. 299. 
Thomas Ravenscroft, in the Apologie prefixed to his discourse on the 
true charactering of music, published in 1614, cites it as a work of Dr. 
Case, whom he styles a ' Meecenas of musicke.' 



XXXll. 



PRELIMINARY DISCOURSE. 



nspired his mind with those passions ; and the painter, 
giving form to those ideas of grace, greatness, and cha- 
racter which occupy his mind, or selecting the beauties of 
nature, and transferring them to canvas, or at other 
times contenting himself with simple imitation, in all 
these exercises of imagination and art, expects from the 
judgment of the well-informed connoisseur the approba- 
tion of his work. 

Now in the several instances above adduced, notwith- 
standing the concessions made to them, we may discern 
in the generality of men the want of that sense to which 
the appeal is made ; for, with respect to the epic poem, 
few are endowed with an imagination sufficiently capa- 
cious to discover its beauties ; and as to dramatic repre- 
sentation, the most favourite of all public entertainments, 
although all men pretend to be judges of nature, and the 
cant of theatres has persuaded most that they are so, few 
are acquainted with her operations in the various in- 
stances exhibited on the stage, or know with any kind of 
certainty in what manner the actor is to speak, what 
tones or inflections of the voice are appropriated to differ- 
ent passions, or what are the proper gesticulations to express 
or accompany the sentiment which he is to utter. How 
many individuals among those numerous audiences, who 
for a series of years past have affected to admire our great 
dramatic poet, may we suppose capable of discerning his 
sense, delivered in a style of dialogue very little resem- 
bling that of the present day, or of relishing those high 
philosophical sentiments with which his compositions and 
those of Milton abound?* The answer must be, very few. 
Even humour, a talent which lies level with the observa- 
tion of the many, is not alike intelligible to all ; and 
some are disgusted with those delineations of low manners, 
however just and natural, that afford delight to others, as 
exhibiting to view the human mind in the simplicity of 
nature, and free from those restraints which are imposed 
on it by education and refinement. 

The painter, in like manner, submitting his work to the 
public censure, shall find for one that will applaud the 
grandeur of the design, the fineness of the composition, or 
tlie correctness of the drawing, a hundred that would have 
dispensed with all these excellencies for a greater glare of 
colouring, and attitudes suited to their own ideas of grace 
and elegance. 

The case is the same in sculpture and architecture ; to 
speak of the first : — In Roubiliac's statue of Mr. Handel 
at Vauxhall, few are struck with the ease and gracefulness 
of the attitude, the dignity of the figure, the artful dispo- 
sition of the drapery, or the manly plumpness and rotun- 
dity of the limbs, but all admire how naturally the slipper 
depends from the left foot. In works of architecture we 
look for elegance joined with stability ; for symmetry, 
harmony of parts, and a judicious and beautiful arrange- 
ment of pleasing forms ; but to these a vulgar eye is blind ; 
whatever is great or massy, it rejects as heavy and clumsy. 
Such judges as these prefer for its lightness a Chinese to 
a Palladian bridge ; and are pleased with a diagonal view 
of the towers at the west end of St. Paul's cathedral, 
for the same reason as they are with a bird cage. 

Finally, with respect to music, it must necessarily be, 
that the operation of its intrinsic powers can extend no 

* The masque of Comus, written for the entertainment of a noble 
family, and a company of chosen spectators, which within these few 
years was introduced on the public stage, may seem to contradict this 
obsi-rvation, for this reason, that although the sentiments contained in 
it are well known to be drawn from the Platonic, the sublimest of all 
philosophy ; and the imagery has an immediate and uniform reference to 
the fictions of mythology, it afforded great entertainment to the upper 
gallery ; and the performance gave rise to sundry meetings for the 
purpose of drinking and singing, some of which were dignified with 
the name of Comus's Court. Nevertheless it may be supposed that the 
mirth of the enchanter and his crew were more sensibly felt by the mul- 
titude than the charms of divine philosophy, which the author endeavours 
to display, or the reliance on divine providence, which it is the end of the 
poem to inculcate. 



farther than to those whom nature has endowed with the 
faculty which it is calculated to delight; and that a pri- 
vation of that sense, which, superadded to the hearing, is 
ultimately affected by the harmony of musical sounds, 
must disable many, and, as some compute, not fewer 
than nine out of ten, from receiving that gratification in 
music which others experience. Such hearers as these are 
insensible of its charms, which yet they labour to per- 
suade themselves are very powerful; but finding little 
effect from them, they seek for that gratification in novelty 
which novelty will not afford ; and hence arises that in- 
cessant demand for variety which has induced some to 
imagine that music is in its very nature as mutable as 
fashion itself. It may be sufficient in this place to have 
pointed out the reasons or causes of this erroneous opinion 
of the nature and end of music, the effects and operation 
thereof will be the subject of future disquisition. 

In the interim it must he confessed that there is some- 
what humiliating in a discrimination of mankind, that 
tends to exclude the greater number of them from the en- 
joyment of those elegant and refined pleasures which the 
works of genius and invention afford ; but this condition 
of human nature is ca]iable of proof, and is justified by 
that partial dispensation of those faculties and endow- 
ments which we are taught to consider as blessings, and 
which no one without impiety can censure. Seeing this 
to be the case, it may be asked how it comes to pass that 
a sense of what is true, just, elegant, and beautiful in any 
of the above-mentioned arts, exists as it does at this day ? 
or that there are any works of genius which men with one 
common consent profess to applaud and admire as the 
standards of perfection ? To this it may be answered, that 
although the right of private judgment is in some degree 
exercised by all, it is controuled by the few ; and it is the 
uniform testimony of men of discernment alone that 
stamps a character on the productions of genius, and 
consigns them either to oblivion or immortality. 

It is beside the purpose of the present discourse to 
enter into a minute investigation of any particular branch 
of the science of which this work is the history ; what is 
here proposed is the communication of that intelligence 
which seemed but the prerequisite to the understanding 
of what will be hereafter said on the subject. This was 
the inducement to the above observations on Taste, and 
the motives that influence it ; and this must be the 
apology for a further examen, a pretty free one it may 
be said, of those musical entertainments, and that kind 
of musical performance which the public are at present 
most diposed to favour. 

The present great source of musical delight throughout 
Europe is the opera, or, as the French call it, the musical 
tragedy, concerning which it is to be known, that, if 
regard be due to the opinions of some writers, who are 
yet no friends to this entertainment, it is a revival of the 
old Roman tragedy ; and it seems that the inventors of 
the modern recitative, Jacopo Peri and Guilio Caccini, 
wished to have it thought so; forasmuch as they pro- 
fessed in this species of musical intonation to imitate the 
practice of the ancients, remarking with great accuracy 
the several modes of pronunciation, and the notes and 
accents proper to express grief, joy, and the other affec- 
tions of the human mind ; but by what exemplars they 
regulated their imitation we are no where told : and it 
is to be conjectured that those general directions for pro- 
nunciation, which are to be found in many discourses on 
the subject of oratory, were the chief sources whence 
their intelligence was derived. 

In what other respects the musical representations of 
the ancients and moderns bear a resemblance to each 
other it is not necessary here to enquire ; it may suffice 
to say of the modern opera, that by the sober and judicious 



PRELIMINARY DISCOURSE, 



XXXUl. 



part of mankind it has ever been considered as the mere 
offspring of hixury ; and those who have examined it 
with a critical eye, scruple not to pronounce that it is of 
all entertainments the most unnatural and absurd. To 
descend to particulars in proof of this assertion, would be 
but to repeat arguments which have already been urged, 
with little success it is true, but with great force of reason, 
aided by all the powers of wit and humour. 

The principal objections against the opera are summed 
up by an author, who, though a professed lover of music, 
has shown his candour in describing the genuine effect of 
representations of this kind on an unprejudiced ear. The 
person here spoken of is Mons. St. Evremond, and the 
following are his sentiments : — 

' I am no great admirer of comedies in music,* such as 
now-a days are in request. I confess I am not dis- 
pleased with their magnificence ; the machines have 
something that is surprising ; the musick, in some 
places, is charming, the whole together is wondei'ful : 
but it must be granted me also, that this wonderful is 
very tedious ; for where the mind has so little to do, 
there the senses must of necessity languish. After the 
first pleasiu'e that surprize gives us, the eyes are taken 
up, and at length grow weary of being continally fixed 
upon the same object. In the beginning of the consorts 
we observe the justness of the concords ; and amidst all 
the varieties that unite to make the sweetness of the 
harmony, nothing escapes us. But 'tis not long before 
the instruments stun us, and the musick is nothing else to 
our ears but a confused sound that suffers nothing to be 
distinguished. Now how is it possible to avoid being tired 
with the Recitative, which has neither the charm of 
singing, nor the agreeable energy of speech ? The soul 
fatigued by a long attention, wherein it finds nothing to 
affect it, seeks some relief within itself ; and the mind, 
which in vain expected to be entertained with the show, 
either gives way to idle musing, or is dissatisfied that it 
has nothing to employ it. In a word the fatigue is so 
universal, that every one wishes himself out of the house, 
and the only comfort that is left to the poor spectators, 
is the hopes that the show will soon be over. 

' The reason why, commonly, I soon grow weary at 
operas is, that I never yet saw any which appeared not 
to me despicable, both as to the contrivance of the 
subject, and the poetry. Now it is in vain to charm 
the ears, or gratify the eyes, if the mind be not satisfied ; 
for my soul being in better intelligence with my mind 
than with my senses, struggles against the impressions 
which it may receive, or at least does not give an 
agreeable consent to them, without which even the most 
delightful objects can never aftbrd me any great pleasure. 
An extravagance, set off with music, dances, machines, 
and line scenes, is a pompous piece of folly, but 'tis still 
a folly. Tho' the embroidery is rich, yet \he ground it 
is wrought upon is such wretched stuff, that it offends 
the sight. 

' There is another thing in operas so contrary to nature, 
that I cannot be reconciled to it, and that is the singing 
of the whole piece, from beginning to end, as if the 
persons represented were ridiculously matched, and had 
agreed to treat in musick both the most common, and 
most important affairs of life. Is it to be imagined that 
a master calls his servant, or sends him on an errand, 
singing ; that one friend imparts a secret to another, 
singing ; that men deliberate in council singing ; that 
orders in time of battle are given singing ; and that men 
are melodiously kill'd with swords and darts. This is 

* The word Comedie in French comprehends every kind of theatrical 

epresentation ; a truer designation of an opera is the term Tragedie en 

Musique ; those of Lully are in general so called in the title-page ; and 

it is plain by the context that the author means not the comic but the 

tragic opera. 



' the downright way to lose the life of representation, 
' which without doubt is preferable to that of harmony ; 
' for harmony ought to be no more than a bare attendant, 
' and the great masters of the stage have introduced it as 
' pleasing, not as necessary, after they have perform'd all 
' that relates to the subject and discourse. Nevertheless 
' our thoughts run more upon the musician than the hero 
' in the opera ; Luigi, Cavallo, and Cesti, are still present 
' to our imagination. The mind not being able to conceive 
' a hero that sings, thinks of the composer that set the 
' scng ; and I don't question but that in the operas at the 
' Palace Royal, Baptist is a hundred times more thought 
' of than Theseus or Cadmus.' f 

Tlie same author, speaking of recitative, particularly 
that of the Venetian onera, savs that it is neither sinsfino- 
nor reciting, t but somewhat unknown to the ancients, 
which may be defined to be an aukward use of music and 
speech, § 

It may perhaps be said that music owes much of its 
late improvement to the theatre, and to that emulation 
which it has a tendency to excite, as well in composers 
as performers ; but who will pretend to say what direction 
the studies of the most eminent musicians of late years 
would have taken, had they been left to themselves ; it 
being most certain that every one of that character has 
two tastes, the one for himself, and the other for the 
public ? Purcell has given a plain indication of his own, 
in a declaration that the gravity and seriousness of the 

+ Works of Mons. St. Evremond, vol. II. page 84, in a letter to 
Villiers, duke of Buckingham. 

t This remark upon examination will be found to be but too true, not- 
withstanding the arguments in favour of recitative, which amount in sub- 
stance to this, that it is a kind of prose in music, that its beauty consists 
in coming near nature, and in improving the natural accents of words by 
more pathetic or emphatical tones. Preface to the opera of Semele by 
Mr. Congreve. Mr. Hughes to the same purpose, delivers these as his 
sentiments : ' The recitative style in composition is founded on that 
' variety of accent whicli pleases in the pronunciation of a good orator, 
' with as little deviation from it as possible, The different tones of the 
' voice in astonishment, joy, sorrow, rage, tenderness, in affirmations, 
'apostrophes, interrogations, and all other varieties of speech, make 
'a sort of natural music which is very agreeable; and this is what is 
' intended to be imitated, with some helps, by the composer, but witliout 
' approaching to what we call a tune or air ; so that it is but a kind of 
' improved elocution.' Preface to Mr. Hughes's Cantatas in the first 
volume of his Poems. 

Upon these several passages it may be remarked, that in the ex- 
pression of the passions nature doth not oflTer musical sounds to the 
human ear ; for though the natural tones of grief and joy, the two 
passions which are most effectually expressed by music, approach nearer 
to musical precision than any other, yet still they are inconcinnous and 
unmusical. Farther, that the sounds of the voice in speech are im- 
musical is asserted by Lord Bacon in the following passage : ' All sounds 
' are either musical sounds, which we call tones, whereunto there may 
' be a harmony ; which sounds are ever equal, as singing, the sounds of 
' stringed and wind instrments, the ringing of bells, &c. ; or immusical 
' sounds, which are ever unequal ; such as the voice in speaking, all 
'whisperings, all voices of beasts and birds, except they be singing birds, 
' all percussions of stones, wood, parchment, skins, as in drums, and 
' infinite others.' Nat. Hist. cent. II. sect. 101. 

The conclusion from these premises must be, that musical sounds do 
not imitate common speech ; and therefore that recitative can in no 
degree be said to be an improvement of elocution. 

But admitting the contrary to be the ease, and that the sounds of speech 
were equally musical with those employed in recitative, the inflexions of 
the voice are too minute to fall in with the division of the scale, allowing 
even the enarraonic diesis, or the comma, the smallest of all sensible 
intervals, to make a part of it ; and of this opinion is Mons. Duclos, who, 
in the Encyclopedia, art. Declamation des anciens, for this reason 
denies the possibility of a notation for speech. 

Upon the whole, the beauties of the recitative style in music consist 
not in the power of imitating the tones, much less the various inflexions 
of the voice in speech, but in the varieties of accent and melody, which 
follow from its not being subject to metrical laws : In short, what has 
been said and insisted on in this discourse of music in general, may be 
applied to recitative, viz., that its mimetic powers are very inconsiderable, 
and that whatever charms it possesses are absolute and inherent. 

§ These observations of St. Evremond respect the musical tragedy, but 
the Italians have also a musical comedy called a Burletta, which has been 
lately introduced into England, and given rise to the distinction in the 
advertisements for subscriptions of first, second, S:c. serious man or 
woman. This entertainment affords additional proof how little music, as 
such, is able to support itself: in the tragic opera it borrows aid from the 
tumidity of the poetry ; in the comic, from the powers of ridicule, t« 
which music has not the least relation. 



XXXIV. 



PRELIMINARY DISCOURSE. 



Italian music were by him thought worthy of imitation : * 
the studies of Stradella, Scarlatti, and Bononcini for their 
own delight were not songs or airs calculated to astonish 
the hearers with the tricks of the singer, but cantatas and 
duets, in which the sweetness of the melody, and the just 
expression of fine poetical sentiments, were their chief 
praise ; or madrigals for four or more voices, wherein the 
vai'ious excellencies of melody and harmony were united, 
so as to leave a lasting impression on the mind. The 
same may be said of Mr. Handel, who, to go no farther, 
has given a specimen of the style he most affected in a 
volume of lessons for the harpsichord, with which no one 
will say that any modern compositions of the kind can 
stand in competition. These, as they were made for the 
practice of an illustrious personage, as happy in an 
exquisite taste and correct judgment as a fine hand, may 
be supposed to be, and were in fact compositions con 
amore. In other instances this great musician com- 
pounded the matter with the public, alternately pursuing 
the suggestions of his fancy, and gratifying a taste which 
he held in con tempt, f 

Whoever is curious to know what that taste could be, to 
which so great a master as Mr. Handel was compelled 
occasionally to conform, in prejudice to his own, will find 
it to have been no other tlian that which is common to 
every promiscuous auditory, with whom it is a notion that 
the right, as some may think, the ability to judge, to 
applaud and condemn, is purchased by the price of ad- 
mittance ; a taste that leads all who possess it to prefer 
light and trivial airs, and such as are easily retained in 
memory, to the finest harmony and modulation ; and to 
be better pleased with the licentious excesses of a singer, 
than the true and just intonation of the sweetest and most 
pathetic melodies, adorned with all the graces and ele- 
gancies that art can suggest. Such critics as these, in 
their judgment of insti'umental performance, uniformly 
determine in favour of whatever is most diflicult in the 
execution, and, like the spectators of a rope-dance, are 
never more delighted than when the artist is in such a 
situation as to render it doubtful whether he shall incur or 
escape disgrace. 

To such a propensity as this, the gratifications whereof 
are of necessity but momentary, leaving no impression 
upon the mind, we may refer the ardent thirst of novelty 
in music, and that almost general reprobation of whatever 
is old, against the sense of the poet: — 

Now, good Cesario, but that piece of song, 
That old and antique song we had last night, 
Methought it did relieve my passion much ; 
More than light airs, and recollected terms 
Of these most brisk and piddy-paced times. 

Twelfth Night, Act II. Scene iv. 

But to account for it is in no small degree difficult : to jus- 
tify it, it is said that there is a natural vicissitude of things, 
and that it were vain to expect that music should be per- 
manent in a world where change seems to predominate. 

But it may here be observed, that there are certain 
laws of nature that are immutable and independent on 
time and place, the precepts of morality and axioms in 
physics for instance ; there never was since the creation a 
time when there did not exist an irreconcileable difference 
between truth and falsehood ; or when two things, each 

* It is worth remarking that the poets, who of all writers seem the 
most sensible of the elficacy of music, appear uniformly to consider it as 
an intellectual, and consequently, a serious pleasure, enfraging not only 
the attention of the ear, but the powers and faculties of the soul. To 
this end, and not for the purpose of exciting mirth, it is in ninnberless 
instances introduced by Shakespeare; and among the poems of Milton 
is one entitled ' At a solemn Music' 

t An intimate friend of Mr. Handel, looking over the score of an opera 
newly composed by him, observed of some of the songs that they were 
excellent. ' You may think so,' says Mr. Handel, ' but it is not to them, 
but to these,' turning to others of a vulgar cast, ' that I trust for the 
success of the opera.' 



equal to the same third, were unequal one to the other; 
or, to carry the argument farther, when consonance and 
dissonance were not as essentially distinguished from each 
other, both in their ratios and by their effects, as they 
are at this day ; or when certain interchanges of colours, 
or forms and arrangements of bodies were less pleasing 
to the eye than the same are now ; from whence it should 
seem that there are some subjects on which this principal 
of mutation does not operate : and, to speak of music 
alone, that, to justify the love of that novelty which seems 
capable of recommending almost any production, some 
other reasons must be resorted to than those above. 

But, declining all farther research into the reason or 
causes of this principle, let us attend to its effects ; and 
these are visible in the almost total ignorance which pre- 
vails of the merits of most of the many excellent artists 
who flourished in the ages preceding our own : of Tye, of 
Redford, Shephard, Douland, Weelkes, Wilbye, Est, 
Bateman, Hilton, and Brewer, we know little more than 
their names ; these men composed volumes which are 
now dispersed and irretrievably lost, yet did their com- 
positions suggest those ideas of the power and efficacy of 
music, and those descriptions of its manifold charms that 
occur in the verses of our best poets. To say that these 
and the compositions of their successors Blow, Pur cell, 
Humphrey, Wise, Weldon, and others, were admired 
merely because they were new, is begging a question that 
will be best decided by a comparison, which some of the 
greatest among the professors of the art at this day would 
shrink from. 

Upwards of two hundred years have elapsed since the 
anthem of Dr. T3'e, ' 1 will exalt thee,' was composed ; 
and near as long a time since Tallis composed the motett 
' O sacrum convivium,' which is now sung as an anthem 
to the words ' I call and cry to thee, O Lord ;' and it is 
comparatively but a few years since Geminiani was heard 
to exclaim in a rapture that the author of it was inspired. J 
Amidst all the varieties of composition in canon, which 
the learning and ingenuity of the ablest musicians have 
produced, that of Bird, composed in the reign of his mis- 
tress Elizabeth, is considered as a model of perfection. 
Dr. Blow's song, ' Go, perjured man,' was composed at the 
command of king Charles the Second, and Purcell's ' Sing 
' all ye Muses,' in the reign of his successor , but no man 
has as yet been bold enough to attempt to rival either of 
these compositions. Nor is there any of the vocal kind, 
consisting of recitative and air, which can stand a com- 
petition with those two cantatas, for so we may venture to 
call them, ' From rosy bowers,' and ' From silent shades.' 

Of poetry, painting, and sculpture, it has been observed 
that they have at different periods flourished and declined ; 
and that there have been times when each of those arts 
has been at greater perfection than now, is to be attributed 
to that vicissitude of things which gave rise to the present 
enquiry, and is implied in an observation of Lord Bacon, 
that in the youth of a state arms do flourish, in its middle 
age learning, and in its decline mechanical arts and 
merchandise. § And if this observation on the various 

X To this testimony we may add that of a foreigner respecting the 
church-music of queen Elizabeth's days, thus recorded by Strype in 
his Annals of tlie Reformation, vol. II. page 314 : — 

'In her (the queen's) passing, (I say) she visited Canterbury; how 
' magnificently she was received and entertained here by archbishop 
' Parker, I have related elsewhere. This I only add, that while she 
'was here, the French ambassador came to her. Who hearing the 
'excellent music in the cathedral church, extolled it up to the sky, 
'and brake out into these words? "O God, I think no prince beside 
" in all Europe ever heard the like, no not our Holy Father the Pope 
" himself." A young gentleman that stood by him replied, " Ah, do you 
"compare our queen to the knave of Rome, or rather prefer him before 
" her 1." Whereat the ambassador was highly angred, and told it to some 
'of the councillors. They bade him be quiet, and take it patiently, 
' for the hoys, said they, with us do so call him ai.d the Roman Anti 
' Christ too.' 

§ Essay of Vicissitude of Things. • 



PRELIMINARY DISCOURSE. 



X!fXV. 



fates of poetry, painting, and sculpture be true, why is it 
to be assumed of music that it is continually improving, 
or that every innovation in it must be for the better ? 
That the music of the church has degenerated and been 
greatly corrupted by an intermixture of the theatric style, 
has long been a subject of complaint ; the Abbat Gerbert 
laments this and other innovations in terms the most 
affecting ; * and indeed the evidence of this corruption 
must be apparent to every one that reflects on the style 
and structure of those compositions for the church that 
are now most celebrated abroad, even those of Pergolesi, 
his masses, for instance, and those of lomelli and Perez, 
have nothino- that distinguishes them but the want of 
action and scenic decoration, from dramatic represent- 
ations : like them they abound in symphony and the 
accompaniment of various instruments, no regard is paid 
to the sense of the words, or care taken to suit it with 
correspondent sounds ; the clauses Kyrie Eleison and 
Christe Eleison, and Miserere mei and Amen are uttered 
in dancing metres ; and the former not seldom in that 
of a minuet or a jig. Even the funeral service of Perez, 
lately published in London, so far as regards the measures 
of the several airs, and the instrumental aids to the voice- 
parts, differs as far from a sacred and solemn composure 
as a burletta does from an opera or musical tragedy. 

From these premises it may be allowed to follow, that 
a retrospect to the musical productions of past ages is no 
such absurdity, as that a curious enquirer need decline it. 
No man scruples to do the like in painting ; the con- 
noisseurs are as free in remarking the excellencies of 
Raphael, Titian, Domenichino, and Guidd, as in com- 
paring succeeding artists with them ; and very con- 
siderable benefits are found to result from this practice : 
our present ignorance with respect to music may betray 
us into a confusion of times and characters, but it is to be 
avoided by an attention to those particular circumstances 
that mark the several periods of its progress, its perfection 
and its decline. 

Of the monkish music, that is to say the Cantus 
Ecclesiasticus, little can be said, other than that it was 
solemn and devout : after the introduction into the church 
of music in consonance, great skill and learning were' 
exercised in the composition of motetts ; but the elaborate 
contexture, and, above all, the affectation of musical and 
arithmetical subtilities in these compositions, as they con- 
duced but little to the ends of divine worship, subjected 
them to censure, and gave rise to a style, which, for its 
simplicity and grandeur many look up to as the perfection 
of ecclesiastical harmony ; and they are not a few who 
think that at the end of the sixteenth century the Romish 
church-music was at its height, as also that with us of the 
reformed church its most flourishing state was during the 
reign of Elizabeth ; though others postpone ij; to the time 
of Charles II. grounding their opinion on the anthems of 
Blow, Humphrey, and Purcell, who received their first 
notions of fine melody from the works of Carissimi, Cesti, 
Stradella, and others of the Italians. 

For the perfection of vocal harmony we must refer to 
a period of about fifty years, commencing at the year 
1560, during which were composed madrigals for private 
recreation in abundance, that are the models of excellence 
m their kind ; and in this species of music the composers 
of our own country appear to be inferior to none. The 
improvement of melody is undoubtedly owing to the 
drama ; and its union with harmony and an assemblage 
of all the graces and elegancies of both we may behold 
in the madrigals of Stradella and Bononcini, and the 
chorusses and anthems of Handel ; and among the com- 
positions for private practice in the duets of Steffani and 
Handel. As to the harmony of instruments, it is the 

" De Cantu et Musica Sacra, torn. II. page 375. 



least praise that can be bestowed on the works of Corelli, 
Geminiani, and Martini, to say that through all the 
vicissitudes and fluctuations of caprice and fancy, they 
retain their primitive power of engaging the affections, 
and recommending themselves to all sober and judicious 
liearers.f 

To music of such acknowledged excellence as this, the 
preference of another kind, merely on the score of its 
novelty, is surely absurd; at least the arguments in 
favour of it seem to be no better than those of Mr. Bayes 
in behalf of what he calls the new way of dramatic 
writing ; which however were not found to be of such 
strength as to withstand the force of that ridicule, which 
which was very seasonably employed in restoring the 
people to their wits. 

The performance on the organ is for the most part un- 
premeditated, as the term Voluntary, which is appro- 
priated to that instrument, imports ; we may therefore 
look on this practice as extemporary composition ; and it 
is not enough to be regretted how much the applauses be- 
stowed on the mere powers of execution have contributed 
to degrade it. Bird and Blow, as organists, are celebrated 
not so much for an exquisite hand, as for their skill, and 
that fulness of harmony which distinguished their per- 
formance, and which this noble instrument alone is cal- 
culated to exhibit. t The canzones of Frescobaldi, Kerl, 
Krieger, and Thiel, and above all, the fugues of Mr. 
Handel, including those in his lessons, shew us what is the 
true organ style, and leave us to lament that the idea of a 
voluntary on the organ is lost in those Capriccios on 
a single stop, which, as well in our parochial as cathedral 
service, follow the psalms. As to what is called a con- 
certo on the organ, it is a kind of composition consisting 
chiefly of solo passages, contrived to display what in 
modern musical phrase is termed a bi-illiant finger ; and 
which, if attended to, will, amidst the clamour of the ac- 
companiment, in fact be found instead of four, to consist 
of but two parts. 

But of all the abuses of instrumental performance, none 
is more injurious to music than the practice of single 
instruments, exemplified in solos and solo concertos, ori- 
ginally intended for private recreation, but which are now 
considered as an essential part of a musical entertainment. 
Music composed for a single instrument, as consisting of 
the mere melody of one part, is less complicated than that 
which is contrived for many : and melody is ever more 
pleasing to an unlearned ear than the harmony of different 
jjarts. The vmiformity of a minuet, consisting of a deter- 
mined number of bars, the emphasis of each whereof 
returns in an orderly succession of measures or times, 
corresponds with some ideas of metrical regularity which 
are common to all minds, and affords a reason for that 

t Of the instrumental music of the present day, notwithstanding the 
learninfi and abilities of many composers, the characteristics of itare 
noise without harmony, exemplified in the frittering of passages into 
notes, requiring such an instantaneous utterance, that thirty-two of 
them are frequently heard in the time which it would take moderately 
to count four ; and of this cast are the Symphonies, Periodical Overtures, 
ftuartettos, Quintettes, and the rest of the trash daily obtruded on the 
world. 

Of solos for the violin, an elegant species of composition, as is evident 
in those most excellent ones of Corelli and Geminiani, and in many of 
those of Le Clair, Carbonelli, Festing, and Tartini, few have of late been 
published that will bear twice hearing ; in general, the sole end of them is 
to display the powers of execution in prejudice to those talents which are 
an artist's greatest praise. 

The lessons for the harpsichord of Mr. Handel, abounding with fugues 
of the finest contexture, and the most pathetic airs, are an inexhaustible 
fund ol delight ; those of the present time have no other tendency than to 
degrade an instrument invented for the elegant recreation of the youtliful 
of the other sex, and to render it what at best it now appears to be, and 
may as truly as emphatically be termed, a tinkling cymbal. 

X Old Mr. Arthur Bedford, chaplain to Aske's Hospital at Hoxton, and 
who died not many years ago, was acquainted with Dr. Blow, and says of 
him that he was reckoned the greatest master in the world for playing 
most gravely and seriously in his voluntaries. The Great Abuse ol 
Musick, by Arthur Bedford, M.A. Lond. 8vo. 1711, page 24S. 



XXXVl. 



PRELIMINARY DISCOURSE. 



deliglit which the ear receives from the pulsatile iiistm- 
ments. Hence it is easy to account for the obtrusion of 
such compositions on the public ear as furnish opportu- 
nities of clisplaying mere manual proficiency in the artist; 
a solo or a concerto on the violin, the violoncello, the 
hautboy, or some other such instrument, does this, and 
i^ives scope for that exercise of a wild and exuberant fancy 
which distinguishes, or rather disgraces, the instrumental 
performance of this day. 

The first essays of this kind were solos for the violin, 
the design whereof was to afl?ect the hearer by the tone of 
the instrument, and those graces of expression which are 
its known characteristic; but it was no sooner found that 
the merit of these compositions was estimated by the diffi- 
culty of performing them, than the plaudits of the auditory 
became an irresistible temptation to every kind of extra- 
vagance. These have been succeeded by compositions of 
a like kind, Ijut framed with a very different view. Solos 
and Concertos, containing passages that carried the melody 
beyond the utmost limits of the scale, indeed so high on 
the instrument, that the notes could not be distinctly arti- 
culated, in violation of a rule that Lord Bacon has laid 
down, that the mean tones of all instruments, as being 
the most sweet, are to be preferred to those at either ex- 
tremity of either the voice or instrument.* The last im- 
provement of licentious practice has been the imitation of 
tones dissimilar to those of the violin, the flute, for in- 
stance, and those that resemble the whistling of birds ; 
and the same tricks are played with the violoncello. To 
what farther lengths these extravagances will be carried, 
time only can discover. 

Amidst that stupor of the auditory faculties, which 
leads to the admiration of whatever is wild and irregular 
in music, a judicious hearer is necessitated to seek for de- 
light in those compositions, which, as owing their present 
existence solely to their merit, must, like the writings of 
the classic authors, be looked on as the standards of per- 

* Nat. Hist. cent. II. sect. 173. The Sylva Sylvarum, or Natural 
History of Lord Bacon, contains a great variety of experiments and 
observations tending to explain tlie propertes of sound and the nature of 
harmony. The following judicious remark may serve as a specimen of 
the author's skill in his subject, and at the same time shew his sentiments 
of harmony, and in what he conceived tlie perfection thereof to consist. 
' The sweetest and best harmony is, when every part or instrument is not 
' lieard by itself, hut a conflation of them all ; which requireth to stand 
' some distance off, even as it is in the mixture of perfumes, or the taking 
' of the smells of several flowers in the air.' Cent. III. sect, 22.5. 



fection ; in the grave and solemn strains of the most cele- 
brated composers for the church, including those of our 
own country, who in the opinion of the best judges are 
inferior to none ; f or in the gayer and more elegant com- 
positions, as well instrumental as vocal, of others con- 
trived for the recreation and solace, in private assemblies 
and select companies, of persons competently skilled in 
the science. 

How far remote that period may be when music of this 
kind shall become the object of the public choice, no one 
can pretend to tell. To speak of music for instruments, 
the modern refinements in practice, and the late improve- 
ments in the powers of execution have placed it beyond 
the reach of view : and it affords but small satisfaction to 
a lover of the art to reflect that the world is in possession 
of such instrumental compositions as those of Corelli, 
Bononcini, Geminiani, and Handel, when not one prin- 
cipal performer in ten has any relish of their excellencies., 
or can be prevailed on to execute them but with such fe 
degree of unfeeling i-apidity as to destroy their effect, and 
utterly to defeat the intention of the author. In such 
kind of performance, wherein not the least regard is paid 
to harmony or expression, we seek in vain for that most 
excellent attribute of music, its power to move the pas- 
sions, without which this divine science must be con- 
sidered in no better a view than as the means of recreation 
to a gaping crowd, insensible of its charms, and ignorant 
of its worth. 

+ Such music as this has been the delight of the wisest men in all ages. 
Luther, who was so great an admirer of music, that he scrupled not as 
a science, to rank it next to theology, which is styled the queen of the 
sciences, was often used to be recreated with the singing of 
motetts. Bishop Williams, while he was lord keeper, chose to retain the 
deanery of Westminster for the sake of the choral service performed there : 
' He was loathe,' says the historian, ' to stir from the seat where he had 
' the command of such exquisite music' And in a more particular man- 
ner the same person speaks of the love which that great prelate bore to 
music, for, says he, ' that God might be praised with a cheerful noise in 
' his sanctuary, he procured the sweetest music both for the organ and 
' voices of all parts that ever was heard in an English quire. In those 
' days that abbey and the Jerusalem Chamber, where he gave entertain- 
' ment, were the volaries of the choicest singers that the land liad bred.' 
Life of the Lord Keeper Williams, by Hackett, Bishop of Litchfield and 
Coventry, page 62, 4G. Milton has been very explicit in declaring what 
kind of music delighted him most, in the verses entitled ' At a solemn 
music' Dr. Busby the master of Westminster-school had an organ, and 
music of the most solemn kind in his house at the time when choral ser- 
vice was throughout the kingdom forbidden to be performed. Vide 
ante, page xxi. in note. 



A 



GENERAL HISTORY 



OF THE 



SCIENCE AND PRACTICE OF MUSIC. 



BOOK I. CHAP. I. 



There is scarce any consideration that affords 
greater occasion to lament the inevitable vicissitude 
of things, than the obscurity in which it involves, 
not onl)^ the history and the real characters, but 
even the discoveries of men. When we consider 
the various pursuits of mankind, that some respect 
merely the interest of individuals, and terminate 
with themselves, while others have for their object 
the investigation of truth, the attainment and com- 
munication of knowledge, or the improvement of 
useful arts ; we applaud the latter, and reckon upon 
the advantages that posterity must derive from them : 
but this it seems is m some degree a fallacious hope ; 
and, notwithstanding the present improved state of 
learning in the world, we have reason to deplore the 
want of what is lost to us, at the same time that 
we rejoice in that portion of knowledge which we 
possess. 

Whoever is inclined to try the truth of this 
observation on the subject of the present work, if 
he does not see cause to acquiesce in it, will at least 
be under great difficulties to satisfy himself how it 
oomes to pass, that seeing what miraculous effects 
have been ascribed to the music of the ancients, we 
know so little concerning it, as not only to be 
ignorant of the use and application of most of their 
instruments, but even in a great measure of their 
system itself. 

To say that in the general deluge of learning, 
when the irruptions of barbarous nations into civi- 
lized countries, the seats and nurseries of science, 
became frequent, music, as holding no sympathy 
with minds actuated by ambition and the lust of 
empire, was necessarily overwhelmed, is not solving 
the difficulty ; for though barbarism might check, ?is 
it did, the growth of this as well as other arts, the 
utter extirpation of it seems to have been as much 
then, as it is now, impossible. That conquest did 
not produce the same effect on the other arts is 
certain ; the architecture, the sculpture, and the 
poetry of ancient Greece and Rome, though they 
withdrew for a time, were yet not lost, but after 
^ retirement of some centuries appeared again. But 
what became of their music is still a question : the 



Pyramids, the Pantheon, the Hei'cules of Glycon, 
the Grecian Venus, the writings of Homer, of Plato, 
of Aristotle, and other ancients, are still in being ; 
but who ever saw, or where are deposited, the com- 
positions of Terpander, Timotheus, or Phrynis ? 
Did the music of these, and many other men whom 
we read of, consist of mere Energy, in the extempo- 
rary prolation, of solitary or accordant sounds ; or 
had they, in those very early ages, any method of 
notation, whereby their ideas of sound, like those of 
other sensible objects, were rendered capable of com- 
munication ? It is hard to conceive that they had 
not, when we reflect on the very great antiquity of 
the invention of letters ; and yet before the time of 
Alypius, who lived a. c. 115, there are no remain- 
ing evidences of any such thing. 

The writers in that famous controversy set on foot 
by Sir William Temple, towards the close of the 
last century, about the comparative excellence of the 
ancient and modern learning, at least those who sided 
with the ancients, seem not to have been aware of the 
difficulty they had to encounter, when they under- 
took, as some of them did, to maintain the superiority 
of the ancient over the modern music, a difficulty 
arising not more from the supposed weight on the 
other side of the argument, than from the want of 
sufficient Data on their own. In the comparison of 
ancient with modern music, it was reasonable to ex- 
pect that the advocates for the former should at least 
have been able to define it ; but Sir William Temple, 
who contends for its superiority, makes no scruple to 
confess his utter incapacity to judge about it : 'What,' 
says he, ' are become of the charms of music, by which 
' men and beasts, fishes, fowls, and serpents were so 

* frequently enchanted, and their very natures changed; 

* by which the passions of men are raised to the greatest 
' height and violence ; and then so suddenly appeased, 
' so as they might be justly said to be turned into 
' lions or lambs, into wolves or into harts, by the 
' powers and charms of this admirable art ? 'Tis 
' agreed of all the learned that the science of music, 
' so admired by the ancients, is wholly lost in the 
' world, and that what we have now is made up of 
' certain notes that fell into the fancy or observation 



HISTORY OF THE SCIENCE 



Book I. 



of a poor friar in chanting his mattins : so as those 
•two divine excellences of music and poetry are 
' grown in a manner to be little more but the one 
'fiddling, and the other rhyming, and are indeed 
' very worthy the ignorance of the friar, and the 
' barbarousness of the Goths that introduced them 
' among us.'* 

Whatever are the powers and charms of this 
admirable art, there needs no further proof than 
the passage above-cited, that the author of it was 
not very susceptible of them ; for either the learned 
of these later times are strangely mistaken, or those 
certain notes, which he speaks so contemptuously of, 
have, under the management of skilful artists, pro- 
duced effects not much less wonderful than those 
attributed to the ancient music. And it is not to be 
imagined but that Sir William Temple, in the course 
of a life spent among foreigners of the first rank, and 
at a time when Europe abounded with excellent mas- 
ters, must have heard such music, as, had he had any 
ear to appeal to, would have convinced him that the art 
had still its charms, and those very potent ones too. 

But, not to follow the example of an author, whose 
zeal for a favorite hypothesis had led him to write on 
a subject he did not imderstand, we will proceed to 
trace the various progress of this art : its progress, it 
is said, for the many accounts of the time of the in- 
vention, as well as of the inventors of music, leave 
us in great uncertainty as to its rise. The authority 
of poets is not very respectable in matters of history ; 
and there is hardly any other for those common 
opinions that we owe the invention of music to 
Orpheus, to Amphion, Linus, and many others ; un- 
less we except that venerable doctor and schoolman, 
Thomas Aquinas, who asserts, that not music alone, 
but every other science, was understood, and that by 
immediate revelation from above, by the first of the 
human race. However, it may not be amiss to men-r 
tion the general opinions as to the invention of music, 
with this remark, that no greater deference is due to 
many of them than is paid to other fables of the 
ancient poets and mythologists. 

There can be no doubt but that vocal music is 
more ancient than instrumental, since mankind were 
endowed with voices before the invention of instru- 
ments ; but the great question is, at what time they 
began to frame a system, and this naturally leads to 
an inquiry into the time of the invention of instru- 
ments ; for if we consider the evanescence of sound 
uttered by the human voice, the notion of a system 
without, is at this day not very intelligible. 

But previous to any such inquiry, we may very 
reasonably be allowed the liberty of conjecture, in 
which if we indulge ourselves, we cannot suppose 
but that an art so suited to our natures, and adapted 
to our organs, as music is, must be nearly as ancient 
as those of Agriculture, Navigation, and numberless 
other inventions, which the necessities of mankind 
suggested, and impelled them to pursue : the desire of 
the conveniences, the comforts, the pleasures of life, 
is a principle little less active than that which leads 

• Essay on ancient and modern learning. 



US to provide for its wants ; and perhaps it might be 
even before they had learned to ' go down to the sea 
in ships ' that men began to ' handle the harp and 
organ,' which it cannot be supposed they could do to 
any other delightful purpose, without some knowledge 
of those harmonical relations and coincidences of 
sound, which are the essence of the art. Such a 
knowledge as this we may easily conceive was soon 
attained by even the earliest inhabitants of the earth. 
The voices of animals, the whistling of the winds, 
the fall of waters, the concussion of bodies of various 
kinds, not to mention the melody of birds, as they 
all contain in them the rudiments of harmony, may 
easily be supposed to have furnished the minds of 
intelligent creatures with such ideas of sound, as 
time, and the accumulated observation of succeeding 
ages, could not fail to improve into a system.^ 

■I- Lucretius supposes that manlcind took their first notions of music 
from the singing of birds : — 

At liquidas avium voces imitarier ore 
Ante fuit multo, quam Ijevia carmina cantu 
Concelebrare homines possent, aureisque juvare. Lib. V. 

And the same poet has in some sort ascertained the origin of wind in- 
struments m the following elegant verses : — 

Et zephyri cava per calamorum sibila primum 

Agresteis docuere cavas inflare cicutas, 

Inde minutatim dulceis didicere querelas, 

Tibia quas fundit digitis pulsata canentum. Ibid. 

Thro' all the woods they heard the charming noise 
Of cliiriping birds, and try'd to frame their voice 
And imitate. Thus birds instructed man, 
And taught them songs before their art began ; 
And whilst soft evening gales blew o'er the plains, 
And shook the sounding reeds, they taught the swains, 
And thus the pipe was fram'd and tuneful reed. Creech. 

Part of the natural song of the blackbird consists of true diatonic in- 
tervals, and is thus to be expressed in musical notes : — 



f 



^mM^^^^=mM 



i 



That of the cuckow is well known to be this : — 



9z 






rp— .^p 



'in ^ 



ZQzrsr 



Cu 



cu, 



Cu 



cu, 



Cu - cu 



And Kircher, Musurg. lib. I. cap. xiy., has given the songs of other 
birds, which with great ingenuity and industry he had investigated, as 
namely that of the nightingale, the quail, the parrot, the cock and hen, 
in the common characters of musical notation. Though that which he 
gives of the common dunghill cock seems to be erroneous, and is thus to 
be expressed : — 



* 



S=S=E 



=?2: 



-t- 



:?: 



And it may be observed that between the dijnghill and bantam cock 
there is a difference, for the latter intonates the following sounds, which 
constitute the interval of a true fifth : — 



t^ 



S=E 



=^- 



-f2- 



-jctz 



The song of the hen at the time of her laying, is thus described by him :— 



■ ^^^^^^^^^^ ^^^m 



and clearly appears to be an intonation of a major sixth. 

The same author asserts that other animals, and even quadrupeds, 
articulate diflerent sounds that have a musical ratio to each other, as an 
instance whereof he mentions an animal produced in America called the 
Pijrilia, or Sloth, of which he gives the following curious account : — 

'Before I speak of his voice I will give a description of this whole 
' animal, which this very year I received from the mouth of father 
' Johannes Torus, procurator of the province of the new kingdom in 
' America, who had some of these animals in his possession, and made 
'several trials of their natures and properties. The figure of this animal 
' is uncommon, they call it Pigritia, on account of the slowness of its 
' motions. It is of the size of a cat, has an ugly countenance, and claws 
' projecting in the likeness of fingers : it has hair on the back part of its 
' head, which covers its neck ; it brushes the very ground with its fat 
' belly. It never rises upon its feet, but moves forward so slowly, that 



Chap. I. 



AND PRACTICE OF MUSIC. 



A reason has already been given to show that the 
notion of a musical system does necessarily pre- 
suppose musical instruments ; it therefore becomes 
necessary to trace the invention of such instruments 
as are distinguished by the simplicity of their con- 
struction, and whose forms anil properties at this 
distance of time are most easily to be conceived of, 
and these clearl}^ seem to be reduced to two, the lyre 
and the pipe. 

The lyre, the most considerable of the two, and the 
prototype of the fidicinal or stringed species, is said 
to have been invented about the year of the world 
2000, by Mercury, who finding on the bank of the 
river Nile a shell-fish of the tortoise kind, which an 
inundation of that river had deposited there, and ob- 
serving that the flesh was already consumed, he took 
up the back shell, and hollowing it, applied strings to 
it ;* though concerning the number ot strings there 
is great controversy, some asserting it to be only 
three, and that the sounds of the two remote were 
acute and grave, and that of the intermediate one 
a mean between those two extremes : that Mercury 
resembled those three chords to as many seasons of 
the year, which were all that the Greeks reckoned, 
namely. Summer, Winter, and Spring, assigning the 
acute to the first, the grave to the second, and the 
mean to the third. 

Others assert that the lyre had four strings ; that 
the interval between the first and fourth was an 
octave ; that the second was a fourth f from the first, 

• it scarce in a continued sjiace advances above the cast of a dart in even 
' fifteen days. No one knows what meat it feeds on, nor are they seen to 
'eat ; they for the most part keep on tlie tops of trees, and are two days 
'ascending and as many in descending. Moreover, nature seems to have 
' furnished them with two kinds of arms or weapons against other beasts 
'and animals their enemies. First their feet, in whicli tliey have such 
' strength, that whatsoever animal they lay hold on they keep it so fast, 
' that it is never after able to free itself from their nails, but it is com- 
' pelled to die through hunger : and the other is, that this beast so greatly 
' affects the men that are coming towards it by its countenance, that in 
' pure compassion they refrain from molesting it, and easily persuade 

• themselves not to be solicitous about that which nature has subjected to 

• so defenceless and miserable a state of body. The above-mentioned 
'father, in order to make a trial of this, procured one of these animals to 
' be brought to the college of our society at Carthagena of the new king- 

< dom, and threw a long pole under its feet, which he immediately grasped 
' so tenaciously, that it would by no means let it go ; the animal thus 
'bound by a voluntary suspension, was placed between two beams, where 
' he stuck thus suspended for forty days together, without either meat, 

< drink, or sleep, having his eyes continually fixed on those that looked 
' on him, whom he affected so with his sorrowful aspect, that there was 
( scarce any one that was not touched with pity for him. Being at length 
' freed from this long suspension, a dog was thrown to him, which he 
•immediately seized with his feet, and forcibly detained for the space of 
' four days, at the end whereof the miserable creature expired, being 
'famished through hunger.' This I had from the mou'^h of the above 
father. 

They add, moreover, fto return to the purpose) that this beast makes no 
noise or cry but in the night, and that with a voice interrupted only by 
the duration of a sigh or semi pause. It perfectly intonates, as learners 
do, the first elements of music, ut, re, mi, fa, sol, la. la, sol, fa. mi, re, ut. 
Ascending and descending through the comtnon intervals of the six 
degrees, insomuch that tlie Spaniards, when they first took possession of 
these coasts, and perceived such a kind of vociferation in the night, 
thought they heard men accustomed to the rules of music. It is called 
by the inhabitants Haul, for no other reason than that it repeats through 
every degree of the interval of a sixth the sound lia, ha, ha, ha, ha, 
ha, &c. 



and the fourth the same distance from the third, and 
that from the second to the third was a tone.| 

Another class of writers contend that the lyre of 
Mercury had seven strings : Nicomachus, a follower 
of Pythagoras, and the chief of them, gives the 
following account of the matter : ' The lyre made 
' of the shell was invented by Mercury, and the 
' knowledge of it, as it was constructed by him of 
' seven strings was transmitted to Orpheus ; Orpheus 
' taught the use of it to Thamyris and Linus, the 
' latter of whom taught it to Hercules, who com- 
' municated it to Amphion the Theban, who built the 
' seven gates of Thebes to the seven strings of the 
' lyre.' The same author proceeds to relate ' that 
' Orpheus was afterward killed by the Thracian 
' women, and that they are reported to have cast his 
' lyre into the sea, which was afterwards thrown up 
' at Antissa, a city of Lesbos : that certain fishers 
' finding it, they brought it to Terpander, who carried 
' it to Egypt, exquisitely improved, and shewing it 
' to the Egyptian priests, assumed to himself the 
' honour of its invention.'§ 

And with respect to the form of the ancient lyre, 
as little agreement is to be found among authors as 
about the number of strings ; the best evidences con- 
cerning it are the representations of that instrument 
in the hands of ancient statues of Apollo, Orpheus, 
and others, on bass reliefs, antique marbles, medals 
and gems ; || but of these it must be confessed that 
they do not all favour the supposition that it was origi- 
nally formed of a tortoise shell ; though on the other 
hand it may be said, that as none of those monuments 
cau pretend to so high an antiquity as the times to 
which we assign the invention of the lyre, they are 
to be considered as exhibitions of that instrument in 
a state of improvement, and therefore are no evidence 
of its original form. Galilei mentions a statue of 
Orpheus in the Palazzo de Medici, made by the 
Cavalier Bandinelli, in the left hand %vhereof is a lyre 
of this figure.^ (No. 1.) He also cites a passage from 
Philostratus, importing that the lyre was made of the 
horns of a goat, from which Hyginius undertook thus 
to delineate it. (No. 2.) 



o 





ha, ha, ha, ha, ha, ha, ha, ha, ha, ha, ha, 

* Nicomachi Harmonices Manualis, lib. II. ex vers. Meibom. p. 29. 

t In this and in all other instances, where the measures of intervals 
are assigned, it is to be observed that they include the two extreme terms, 
in W'hich respect the phrases of music and physic agree ; to this purpose 
a very whimsical but ingenious and learned writer on music and many 
other subjects, in the last century, namely Charles Butler, thus speaks : 
•As physicians say a tertian ague, which yet cometh but every second 
'day, and a quartan, whose access is every thild day, (because they crunt 



' the first fit-day for one) so do musicians call a third, a fourth, and a fifth 
' (which yet are but two, three, and four notes from the ground) because 
' they account the ground itself for one.' Principles of Music, by Charles 
Butler, quarto, London 1036, pag. 52, in not. 

I Boctius de Musica, lib. I. pag. 20. 
§ Nicom. lib. II. pag. 29. 

II Mersennus de Instrumentis Harmonicis, lib. I. pag. 7. Vincentio 
Galilei Dialogo della Musica Antica e Moderna, pag. 125. Athanasiu* 
Kircher Musurgia universalis, lib. H. cap. vi. § iii. 

1 Galilei, 12,9. 



HISTORY OF THE SCIENCE 



Book I. 



Mersennus says that by means of his friends Naude 
and Gaffarel, he had obtained from Rome, and other 
parts of Italy, drawings of sundry ancient instruments 
from coins and marbles ; among many which he has 
given, are these of the lyre ; the first is apparently 
a part of a tortoise shell, the other is part of the head 
with the horns of a bull. 





The above -cited authors mention also a Plectrum, 
of about a span in length, made of the lower joint of 
a goat's leg ; the use whereof was to touch the strings 
of the lyre, as appeared to Galilei by several ancient 
bass-reliefs and other sculptures discovered at Rome 
in his time. 

lurcher has prefixed as a frontispiece to the second 
tome of the Musurgia, a representation of a statue in 
the Matthei garden near Rome, of Apollo standing 
on a circular pedestal, whereon are carved in basso 
relievo a great variety of ancient musical instruments, 
But the most perfect representation of the lyre is 
the instrument in the hand of the above statue, which 
is of the form in which the lyre is most usually de- 
lineated. Vide Musurg. tom. I. pag. 536. * 

The pipe, the original and most simple of wind 
instruments, is said to have been formed of the 
shank-bone of a crane, and the invention thereof is 
ascribed to Apollo, Pan, Orpheus, Linus, and many 
others. Marsyas, or as others say, Silenus, was the 

* Isaac Vossius, a bigotted admirer of the ancients, de Poemat. cant, 
et virib. Rythm. pag. 97, contends that hardly any of these remaining 
monuments of antiquity are in such a state as to warrant any opinion 
touching the form of the ancient lyre. He speaks indeed of two statues 
of Apollo in the garden of his Britannic majesty at London, in the year 
1673, (probably the Privy Garden behind the then palace of Whitehall) 
each holding a lyre ; and as neither of these instruments was then in the 
least mutilated, he considers them as true and perfect representations of 
the ancient cythara or lyre, iji two forms, and has fhus delineated §nd 
described tl]em : — 




A 

B 

C C 

D 



The bridge over which the chords are stretched. 

The chordotopr.ni, from which the chords proceed. 

The echei, made of brass, and affixed to the bridge to encrease the 

sound. 
The bridge as in the former figure. 



first that joined pipes of different lengths together 
with wax ; but Virgil says, 

Pan prim ofi calamos cera conjungere phires 
Instituit.-\ 
forming thereby an instrument, to which Isidore, 
bishop of Seville, gives the name of Pandorium, and 
others that of Syringa and which is frequently repre- 
sented in collections of antiquities.:}: 

As to the instruments of the pulsatile kind, such 
as are the Drum, and many others, they can hardly 
be ranked in the numl)er of musical instruments ; 
inasmuch as the sounds they produce are not re- 
ducible to any system, though the measure and 
duration or succession of those sounds is ; which is 
no more than may be said of many sounds, which yet 
are not deemed musical. 

Such are the accounts that are left us of the in- 
vention of the instruments above-mentioned, which 
it is necessary to make the basis of an enquiry into 
the origin of a system, rather than the Harp, the 
Organ, and many others mentioned in sacred writ, 
whose invention was earlier than the times above 
referred to, because their respective forms are known 
even at this time of day to a tolerable degree of pre- 
cision : a lyre consisting of strings extended over the 
concave of a shell, or a pipe with a few equidistant 
perforations in it, are instruments we can easily con- 
ceive of ; and indeed the many remaining monuments 
of antiquity leave us in very little doubt about them ; 
but there is no medium through which we can deduce 
the fig\ire or construction of any of the instruments 
mentioned either in the Pentateuch, or the less 
ancient payts of sacred history ; and doubtless the 
translators of those passages of the Old Testament, 
where the names of musical instruments occur, 
after due deliberation on the context, found them- 
selves reduced to the necessity of rendering those 
names by such terms as would go the nearest 
to excite a correspondent idea in their readers : 
so that they -yvould be grossly mistaken who should 
imagine that the organ, handled by those of whom 
Jubal is said to have been the father,§ any way re- 
sembled the instrument now known among us by 
that name. 

Those accounts which give the invention of the lyre 
to Mercury, agree also in ascribing to him a system 
adapted to it ; though with respect t;o ^he na(;ure of that 
system, as also to the number of strings of which the 
lyre consisted, there is a great diversity of opinions ; 
and indeed the settling the first of these questions 
would go near to determine the other. Boetius inr 
clines to the opinion that the lyre of Mercury had 
only four strings ; and adds, that the first and the 
fourt.h ^nade a diapason ; that the middle distance 
was a tone, and the extremes a diapente.|| 

Zarlino, following Boetius, adopts his notion of 
a tetrachord, and is more particular in the explana^ 
lion of it;^| his woj-ds are as follows : — 'From the first 
^ string to the second was a diatessaron or a fourth ; 

+ Eclog II. ver. 32. 

X Vide Mcrsen. de Instrum. Harmon, lib. II. pag. 73. 

§ Genesis, chap. iv. ver. 21. 

II Do Musica, lib. I. cap, 20. Bontempi, 4S. 

II Istitutiiini Harmoniche, pag. I'l, 



Chap. II. 



AND PRACTICE OF MUSIC. 



' from the second to the third was a tone ; and from 

* the third to the fourth was a diatessaron ; so that the 
' first with the second, and the third with the fourth, 
' contained a diatessaron ; the first with the third, 

* and the second with the fourth, a diapente or fifth.' 
Admitting all which, it is clear that the first and 
fourth strings must have constituted a diapason. 





1( 

c 
\o/j 




6 Trite 


1 






8 Lychanos 


2 


< 

a- 


/ . 

3 

H 


9 Parhypate Meson 


3 


\ 




12 Parhypate Hypaton 


4 



It is to be observed that the above diagram is used 
by Boetius, and is adopted by Zarlino, Kircher, and 
many other writers ; * but that though the appli- 
cation of the letters C G F C in one edition of 
Boetius, is plainly intended to shew that the strings 
immediately below them were supposed to corres- 
pond with those notes in our system, yet the authors 
who follow Boetius have not ventured to make use 
of them ; and indeed there is great reason to reject 
them ; for in the earlier editions of Boetius de Musica, 
the diagram above given is without letters. It seems 
as if Glareanus, who assisted in the publication of the 
Basil edition of that author, in 1570, thought he 
should make the system more intelligible by the 
addition of those letters ; but there is no ground to 
suppose that the Mercurian lyre, admitting it to con- 
sist of four strings, was so constructed. 

Bontempi, an author of great credit, relying on 
Nicomachus, suspects the relation of Boetius, as to 
the number of the strings of the Mercurian lyre ; and 
farther doubts whether the system of a diapason, as 
it is above made out, did really belong to it or not ; 
and indeed his suspicions seem to be well grounded ; 
for, speaking of this system, he says that none of the 
Greek writers saj^ anything about it, and that the 
notion of its formation seems to be founded on a dis- 
covery made by Pythagoras, who lived about 5CX) 
years before Christ, of which a very particular rela- 
tion will be given in its proper place ; and farther to 
shew how questionable this notion is, he quotes the 
very words of Nicomachus before cited, concluding 
with a modest interposition of his own opinion, which 
is that the lyre of Mercury had three strings only, 
and was thus constituted : — f 

■ G 



Interval of a tone. 



Interval of a hemitone. 



F 



E 



However, notwithstanding the reasons of the above 

* Vide Boetius de Musica, lib. I. cap. 20. Kirclier, MusurRia univer- 
salis, torn. I. hb. ii. cap. 6. Zarlino Istit. Harmon, pag. 73. 75. 
+ Hist. Music, pag. 49. 



author, the received opinion seems to have been that 
the lyre consisted of four strings, tuned to certain 
concordant intervals, which intervals were undoubt- 
edly at first adjusted by the ear ; but nevertheless 
had their foundation in principles which the inventor 
was not aware of, though what that tuning was, is 
another subject of controversy. Succeeding musicians 
are said to have given a name to each of these four 
strings, which names, though they are not expressive 
of the intervals, are to be adopted in our inquiry 
after a system : to tlie first or most grave was given 
the name of Hypate, or principal ; the second was 
called Parhypate, viz., next to Hypate ; the third was 
called Paranete, and the fourtli Nete, which signifies 
lowest ; it is observable here, that it seems to have 
been the practice of the ancients to give the more 
grave tones the uppermost place in the scale, con- 
trary to the moderns, by whom we are to understand 
all who succeeded the grand reformation of music by 
Guido, in the eleventh century, of which there will 
be abundant occasion to speak hereafter. 

The several names above-mentioned, exhibit the 
lyre in a very simple state, viz., as consisting of four 
strings, having names from whence neither terms nor 
intervals can be inferred. 

H Y PATE 

P A R H Y PAT E 

PARA N E T E 

^NETE 



Those who speak of the lyre in the manner above- 
mentioned, seem to imagine that its compass included 
two diatessarons or fourths, which being conjoined, 
extended to a seventh, differing from that of Boetius, 
in that his diatessarons, being separated by a tone, 
took in the extent of an octave, and thereby formed 
a diapason. They proceed to relate farther, that 
Chorebus, the son of Atys, king of Lydia, added 
a fifth string, which he placed between Parhypate 
and Paranete, calling it, from its middle situation, 
Mese ; that Hyagnis, a Phrygian, added a sixth, which 
he placed between Mese and Parhypate ; this string 
he called Lychanos, a word signifying the indieial 
finger, viz., that on the left hand, next the thumb : 
and lastly say these ^witers, Terpander added a 
seventh string, which he placed between IMese and 
Paranete, and called Paramese : the lyre, thus im- 
proved, included a septenary, or system of seven 
terms, disposed in the following order : — 
HYPATE 






-PARHYPATE- 
-LYCHANOS- 
MESE— ^- 



-PARAMESE- 
-PARANETE- 
NETE 



i 



CHAP. II. 

The system-above exhibited was the Heptachord 
Synemmenon of the GreelvS ; it consisted of two 
tetrachords or fourths, conjoined, that is to say, the 
middle term was the end of the one, and the begin- 
ning of the other ; and as the last string was added 



HISTORY OF THE SCIENCE 



Book I. 




1 


Mi 




Fa 




Sol 




4 


La, Mi 






5 


Fa 






6 


Sol 






7 

lb 


La 




by Terpander, the system was distinguished by his 
name, and considered as the second state of the lyre. 
Here then we may discern the foundation of a 
system, viz., a succession of seven sounds, including 
two tetrachords, conjoined, by having the Mese or 
middle term common to both, thus represented by 
Glareanus in his edition of Boetius, lib. i. cap. 20 : — 

Hypate 
Parhypate 
Lychanos 
Mese Synaphe 
Paramese or Trite 
Paranete 



Nete 



The seeming perfection of this system, as also the 
consideration that in musical progression every eighth 
sound is but the replicate of its unison, has served to 
confirm an opinion that there is somewhat mysterious 
in the number seven : to say the truth, for different rea- 
sons an equal degree of perfection has been ascribed 
to almost every other of the digits : the number 
four was greatly reverenced by Pythagoras and his 
disciples, as that of three is at this day by many 
Christians. Seven and nine multiplied into them- 
selves made sixty-three, commonly esteemed the grand 
climacteric of our lives ; the ground of superstitious 
fears in persons of middle age, and the subject of 
much learned disquisition : and there is now extant 
a treatise in folio, intitled, IlysticcB numerorum 
significationis, written by one Peter Bongus, and 
published at Bergamo, in the year 1585 ; the sole 
end whereof is to unfold the mysteries, and explain 
the properties of certain numbers ; and whoever has 
the curiosity to search after so insignificant a work, 
will find that in the judgment of its author this of 
Seven is intitled to a kind of pre-eminence over 
almost every other number. 

Had these opinions of numerical mystery no better 
a foundation than the suffrage of astrologers, they 
would hardly deserve confutation, even though per- 
haps in the case of errors so glaring, to expose is to 
detect them ; but when we find them maintained 
not only by men of sound understandings, but by 
the gravest philosophers, they become matter of 
importance ; at least there is somewhat of curiosity 
in observing the extravagancies of an heated imagin- 
ation, and marking the absurdities that a favourite 
hypothesis will frequently lead men into. 

There is not perhaps a more pregnant instance of 
this kind, or of the misapplication of learned industry, 
than the work above-mentioned ; as a proof whereof 
the following chapter is selected, as well by way of 
specimen of the manner of reasoning usual among 
writers of his class, as to explain the properties of 
the number seven, the only one which we are here 



concerned to enquire about. If the arguments in 
favour of its perfection are not so conclusive as might 
be expected, the reader may rest assured that they 
are some of the best that have yet been adduced for 
the purpose : — - 

' The number Seven,' says this learned author, 
has a wonderful property, for it neither begets nor 
is begotten, as the rest are, by any of the numbers 
witliin ten, wherefore philosophers resemble it to the 
ruler or governor of all things, who neither moves 
nor is moved. Philolaus the Pythagorean, no 
ignoble author, testifies thus, and writes that the 
eternal God is permanent, void of motion, similar 
to himself, and different from others ; and Boetius 
has a passage much to the same purpose. The idea 
of virginity had such a relation to the number 
Seven, that it was also named Pallas ; and the Py- 
thagoreans, initiated in her rites, compare the virgin 
Minerva to that number, seeing she was not born, 
but sprung from the head of Jupiter. God rested 
on the Seventh day, wherefore it is named Sabbath, 
a word signifying rest. The Seventh petition of 
the Lord's Prayer is, deliver us from evil ; because 
the number Seven denotes rest, and all evil being 
removed from man, he rests in good ; and farther, 
the seventh day or sabbath represents death, or 
the rest of the soul from worldly labours. In 
Seven days after Noah entered the ark the flood 
began : in the Apocalypse Seven trumpets are men- 
tioned : Job speaks of the visitation of six tribula- 
tions, which six succeeding days brought on him, 
but on the Seventh no harm could touch the just : 
God blessed only the Seventh day, wherefore the 
number Seven is attributed to the Holy Ghost, 
without whom there is no blessing. This St. John 
proves, when in the Apocalypse he calls the Seven 
horns and the Seven eyes the Seven spirits of God. 
The fever left the son of Regulas, according to St. 
John, at the Seventh hour. Elisha breathed Seven 
times on the dead man. Christ after his resurrection 
feasted with Seven disciples ; and Seven brothers 
were sent to baptise Cornelius. The Seven hairs of 
Sampson ; Seven golden candlesticks : and in Le- 
viticus command was given to sprinkle the blood 
and oil Seven times. The Seven stars in the bear ; 
the Seven principal angels who rule the world 
under God, and have charge of the Seven planets, 
as namely, Horophiel the spirit of Saturn, Anael 
the spirit of Venus, Zachainel of Jupiter, Raphael 
of Mercury, Samael of Mars, Gabriel of the moon, 
and Michael the spirit of the sun. The moon 
changes its form Seven times, and completes its 
course in twenty-eight days, which is the sum of 
the number Seven, and all the numbers under it. 
Josephus writes that a certain river in Syria is dry 
for six days, and full on the Seventh. Farther, the 
great artist did not only dignify the heavens, but he 
also adorned with the number Seven his favourite 
creature man, who has seven inward parts, or bowels, 
stomach, heart, lungs, milt, liver, reins, and bladder ; 
and seven exterior, as head, back, belly, two hands, 
and two feet. There are seven objects of sight, as 
body, distance, figure, magnitude, colour, motion. 



Chap. 1[. 



AND PRACTICE OF MUSIC. 



and rest : and Seven species of colour, taking in the 
two extremes of white and Wack, viz., yellow, sky- 
blue, green, purple, and red. No one can without 
eating live after the Seventh day. Physicians 
reckon ten times Seven years to be the period 
of human life, which Hippocrates divides into 
Seven stages. The ancient lyre, used both by 
Orpheus and Amphion, had only Seven chords, 
answering, as it is said, to the Seven gates of 
Thebes. Every Seventh daughter, no son coming 
between, hath, by virtue of the number Seven as 
I imagine, a great power in easing the pains of 
child-birth : and every Seventh son, no daughter 
coming between, has the power of curing the scurvy 
and leprosy by the bare touch ; so that diseases, 
incurable by physicians, are curable by the virtue 
contained in the number Seven. A right-angled 
triangle is constituted of the sides three, four, five, 
but three and four contain the right angle, which is 
' perfection itself, and therefore their sum seven, 
' must as a number be most perfect. Every active 
' body has three dimensions, length, breadth, and 
' thickness, and these have four extremes, point, line, 

* surface, and solid, and these together make up the 
' number Seven.' 

By such arguments as these do many of the 
musical writers endeavour to excite a mysterious 
reverence for that number which is confessedly the 
limits of a system, as far as it goes, perfect in its 
kind ; in answer to which it may be said, that this 
superstitious regard for certain numbers seems to be 
very deservedly ranked among those vulgar and 
common errors, which it is professedly the end of 
a very learned and justly celebrated publication of 
the last century to refute, wherein it is said, that 
' with respect to any extraordinary power or secret 

* virtue attending the number sixty-three, or any 
' other, a serious reader will hardly find anything 
' that may convince his judgment, or any farther 

* persuade than the lenity of his belief, or pre-judg- 
' ment of reason inclineth.'* 

But to return from this digression : the rudiments 
of the present greater musical system are discernible 
in that of a septenary, adjusted, as we are told, by 
Terpander, in the form above declared ; and as to 
the intervals of which it was constitivted, modern 
authors have not scrupled to assert that they were 
precisely the same as those contained in a double 
diatessaron, according to the present practice ; the 
consequence whereof must be, that each of the two 
tetrachords, of which the above system is supposed 
to have been formed, consisted of a hemitone and 
two tones ; which will be readily conceived by such 
as reflect, that in the passage either upwards or 
downwards from any given note to its fourth, in 
that progression which is most grateful to the ear, 
those intervals must necessarily occur. Persuaded 
of the truth of this supposition, succeeding musicians 
have ventured to apply the modern method of no- 
tation to the terms of the ancients, and are pretty 
well agreed that the term Mese answered to a, or la, 

* Sir Thomas Browne's Enquiry into Vulgar Errors, 173. 




in our scale. Taking this for granted, the system of 
Terpander \vill appear in the following form ; — 

SYSTEM OP TERPANDER. 
E Hypate. 

Hemitone 
F Parhypate 
Tone 
G Lychanos 
Tone 
a Mese 

Hemitone 
Paramese 
Tone 
Paranete 
Tone 
Nete 

But here it is necessary to observe, that though, as 
has been said, it was the practice with the ancients to 
give the grave tones the uppermost, and the more 
acute the lowermost place in their scale, f wliich they 
might very properly do, if, as there is the greatest rea- 
son to believe, their music was solitary, and they were 
stran2:ers to the art of combining sounds in con- 
sonance. Yet the moderns, immediately on the 
making that most important discovery, found it 
necessary to differ from them, and accordingly we 
now place the grave tones at the bottom, and the 
acute at the top of our scale ; | the consequence of 
this diversity has been, that whenever any of the 
modern authors have taken occasion to exhibit the 
whole or any part of the ancient Greek scale, they 
have done it in their own way, placing Hypate at 
the bottom of the diagram ; and this wall be the 
method we shall observe for the future. 

Great confusion has arisen among the writers on 
music, in respect to the order of the several additions 
to the system of Terpander. That it was perfected 
by Pythagoras will be related in due time ; but the 
eagerness of most authors to explain the improve- 
ments made by him, has betrayed them into the error 
of confounding the two systems together, whereby 
they have rendered their accounts unintelligible. 
Boetius has erred in this respect ; and Bontempi, 
a modern Italian, notwithstanding he professes to 
have followed the Greek writers, more particularly 
Nicomachus, has made the same mistake ; for in 
every one of the representations of the improved 
system of Terpander which he has given, is contained 
an exhibition of the Synemmenon or conjunct tetra- 
chord, which before the invention of the Diezeug- 
menon, or disjunct tetrachord, by Pythagoras, could 
have no existence. He indeed confesses as much 
when he admits that the distinction imported by its 
name was rather potential than actual ; or, as we 
perhaps should say, rather contingait than absolute. 

+ Vincentio Galilei, Dialog, della Musica, pag. US. Francisc-us 
Salinas de Musica, lib. iii. cap. 4. 
X Bontemp. 51. 52. 



8 



HISTORY OF THE SCIENCE 



Book I. 



To refute this error it is necessary in some sort to 
adopt it, and proceed after Bontempi to describe 
what he calls the first addition to the system of Ter- 
pander. His words are nearly these : — 

' To the lyre of seven strings, forming a conjunct 
' tetrachord,were added two tetrachords; the most grave 
' was joined to that tetrachord, which for its gravest, 
' or, to use the modern method of position, its lowest 
' sound, hatl Hypate, and the most acute tetrachord 

* was joined to that which for its most acute sound, 
' had Nete : the acuter of these two additional tetra- 

* chords, from its situation named hyperboleon, pro- 

* ceeded from Nete by three other terms, viz., Trite, 

* Paranete, and Nete, to each whereof was given the 
' epithet Hyperboleon, to distinguish them from the 

* sounds denoted by the same names in the primitive 

* septenary. The other of the additional tetrachords, 

* which began from Mese, was called Synemmenon 
'or conjunct, and proceeded likewise by the same 

* terms of Trite, Paranete, and Nete ; and each of 
' these had, for the reason just given, the epithet of 
' Synemmenon, as in the following figure appears :' — 

ADDITION I. to the SYSTEM of TERPANDER. 

■£ TNete h3'perboleon g 
g; Tone 

>^ j Paranete hyperboleon f 
■^ - Hemitone 

Trite hyperboleoif e 



B - 



^Nete 




Lychanos 
2 j Parhypate 
Hypate 



Tone 

Tone 

Tone 

Hemitone 

Tone 

Tone 

Hemitone 



Nete sjniemmenon 
Tone 

Paranete synemmenon 
Tone 

Trite synemmenon 
Hemit. 

Mese 



G 
F 
E 



It is observable in the above scheme, that between 
the Synemmenon tetrachord and that marked B, 
which was originally a part of the system of Terpan- 
der, there is not the least difference : the interval of 
a hemitone between a and b being common to both ; 
of what use then this auxiliary tetrachord was, or how 
it became necessary to distinguish it by the epithet 
Synemmenon or conjoined, from that which as yet 
had never been disjoined, is hard to conceive ; the 
only addition therefore that we consider is that of 
the Hyperboleon tetrachord, which increasd the 
number of terms to ten, as above is shown : how- 
ever, after all, as the lyre thus limited to the compass 
of a musical tenth, reaching from E to g, was not 
commensurate in general to the human voice, a 
farther extension of it was found necessary ; and 
another tetrachord was added to this, which began at 
Hypate in the former sy.stem, and proceeded by 
a repetition of the same terms as that did, with the 
addition of hypaton. This addition begat also a dis- 
tinction in the terms of the tetrachord, to which it 
had been joined ; which, to shew their relation to the 
]\Iese, had each of them the adjunct of meson, and the 



tetrachord to which they belonged was thence called 
the tetrachord meson. This last addition of the te- 
trachord Hypaton increased the number of terms to 
thirteen, in which were included four conjunct tetra- 
chords, the Mese being the seventh from each ex- 
treme, and carried the system down to B ; though to 
show that hypate Hypaton was a hemitone below 
Parhypate or C, the Italians generally denote it by 
the character J]. 

ADDITION II. to the SYSTEM OP 
TERPANDER. 

.0 ^Nete hyperboleon g 
g. Tone 

15 I Paranete hyperboleon f 
^ i Hemitone 

Trite hyperboleon e 
Tone 



Nete 



w 






Tone 



>Mese 



Tone 
Hemitone 



Tone 



"H I Paranete 

2 Trite 

<( 

g I Lychanos meson 
•= < Tone 

2 j Parhypate meson 
H I " Tone 

VHypate meson 
i I Tone 

£ j Lychanos hypaton 
Tone 



Nete synemmenon 

Tone 
Paranete synemmenon c I 

Tone 
Trite synemmenon b | 

Hemitane 
Mese a' 



W 



F 



E 



D 



§ 1 Parh}'pate hypaton C 
■£ I Hemitone 

^ ^Hypate hypaton j-, 

In this diagram also the synemmenon Tetrachord 
is inserted : we forbear to repeat the reasons against 
connecting it with the system of Terpander, with 
which it seems absolutely incompatible, and shall 
hereafter endeavour to shew when and how the in- 
vention of it became necessary, and what particular 
ends it seems calculated to answer. In order to this 
it must be observed, tnat the system, improved even 
to the degree above related,wanted much of perfection : 
it is evident that the lower sound Hypate hypaton, 
or as we should now call it, Btj, was a hemitone 
below C, and that b, which in the order of succession 
upwards was the eighth term, was a whole tone below 
the term next above it, consequently it was a hemi- 
tone short of a complete musical octave or diapason ; 
to remedy this defect, as also for divers other reasons, 
Pythagoras is said to have reverted to the primitive 
system of a septenary, and with admirable sagacity, 
by interposing a tone in the middle of the double tetra- 
chord, to have formed the system of a Diapason or 
Octochord. 

But before we proceed to relate the particulars of 
this and other improvements of Pythagoras in music, 
and the wonderful discovery made by him of the 
proportions of musical sounds, it may be proper to 
take notice of two variations in the septenary, intro- 
duced by a philosopher, and a disciple of Pythagoras, 
named Philolaus ; the one whereof, for ought we can 
discover, seems to have been but very inconsiderable, 
that is to say, no more than an alteration of the term 



Chap. II. 



AND PRACTICE OP MUSIC. 



Mese, which, because that sound was a third distant 
from Nete, he called Trite ; the other consisted in 
an extension of the diatessaron included between the 
Mese and Nete to a diapente, by the insertion of 
a trihemitone between Paramese, or as he termed it, 
Trite and Paranete ; by which the system, though it 
laboured under the inconvenience of an Hiatus, com- 
prehended the interval of a diapason, the extreme 
terms whereof formed a consonance much more 
grateful to the ear than any of those contained in 
that of Terpander. Nicomachus speaks more than 
once of Philolaus, and says that he was the first who 
called that Trite, which before was called Paramese, 
as beino; a diatessaron distant from Nete. But al- 
though it is certain that he was a contemporary of 
Pythagoras, we must suppose that this improvement 
of his to be prior to that of Pythagoras above hinted 
at ; for the latter adopted the appellation of Trite, 
though by restoring the ancient name Paramese, 
which he gave to the inserted tone, he altered the 
situation of it, as will be shown hereafter. 

SYSTEM OF PHILOLAUS. 

-e Nete 

Tone 

Paranete 

Trihemitone 

Trite 
Tone 

Mese 
Tone 

G Lychanos 

Tone 
F Parhypate 

Hemitone 
E Hypate 

The gradual improvements of this system from the 
time of Terpander to that of Philolaus having been 
severally enumerated, and its imperfection noted, we 
are now to speak of those made by Pythagoras. Hia 
regulation of the octave by the insertion of a tone 
has been just hinted, and it will be necessary to be 
more particular ; but previous to this it is requisite 
to mention that discovery of his, which though 
merely accidental, enabled him to investigate the 
ratios of the consonances, and to demonstrate that 
the foundations of musical harmony lay deeper than 
had ever before his time been imagined. 

Of the manner of this discovery Nicomachus has 
given a relation, which Mr. Stanley has inserted in his 
History of Philosophy in nearly the following terms : — 

' Pythagoras being in an intense thought whether 
' he might invent any instrumental help to the ear, 
' solid and infallible, such as the sight hath by a 
■' compass and a rule, and by a Dioptre ; or the touch, 

* or by a balance, or by the invention of measures ; 

* as he passed by a smith's shop by a hapjiy chance 
' he heard the iron hammers striking on the anvil, 
' and rendering sounds most consonant to one another 
' in all combinations except one. He observed in 





them these three concords, the diapason, the diapente, 
and the diatessaron ; but that which was between 
the diatessaron and the diapente he found to be 
a discord in itself, thoug!) otherwise useful for the 
making up of the greater of them, the diapente. 
Apprehending this came to him from God, as 
a most happy thing, he hastened into the shop, and 
by various trials finding the difference of the sounds 
to be according to the weight of the hammers, and 
not according to the force of those who struck, nor 
according to the fashion of the hammers, nor ac- 
cording to the turning of the iron which was in 
beating out : having taken exactly the weight of the 
hammers, he went straightway home, and to one 
beam fastened to the walls, cross from one corner 
of the room to the other, lest any difference might 
arise from thence, or be suspected to arise from the 
properties of several beams, tying four strings of 
the same substance, length, and twist, upon each of 
them he hung a several weight, fastening it at the 
lower end, and making the length of the strings 
altogether equal ; then striking the strings by two 
at a time interchangeably, he found out the afore- 
said concords, each in its own combination ; for 
that which was stretched by the greatest weight, 
in respect of that which was stretched by the least 
weight, he found to sound a Diapason. The greatest 
weight was of twelve pounds, the least of six ; thence 
he determined that the diapason did consist in 
double proportion, which the weights themselves 
did shew. Next he found that the greatest to the 
least but one, which was of eight pounds, sounded 
a Diapente ; whence he inferred this to consist in 
the proportion called Sesquialtera, in which pro- 
portion the weights were to one another ; but unto 
that which was less than itself in weight, yet greater 
than the rest, being of nine pounds, he found it to 
sound a Diatessaron ; and discovered that, propor- 
tionably to the weights, this concord was Sesqui- 
tertia ; which string of nine pounds is naturally 
Sesquialtera to the least ; for nine to six is so, viz., 
Sesquialtera, as the least but one, which is eight, 
was to that which had the weight six, in proportion 
Sesquitertia ; and twelve to eight is Sesquialtera ; 
and that which is in the middle, between Diapente 
and Diatessaron, whereby Diapente exceeds Dia- 
tessaron, is confirmed to be in Sesquioctava propor- 
tion, in which nine is to eight. The system of both 
was called Diapason,* that is both of the Diapente 
and Diatessaron joined together, as duple proportion 
is compounded of Sesquialtera and Sesquitertia ; 
such as are twelve, eight, six, or on the contrary, 
of Diatessaron and Diapente, as duple proportion is 
compounded of Sesquitertia and Sesquialtera, as 
twelve, nine, six, being taken in that order. 

' Applying both his hand and ear to the weights 
which he had hung on, and by them confirming the 
proportion of the relations, he ingeniously trans- 
ferred the common result of the strings upon the 
cross beam to the bridge of an instrument, which he 
called XophoToy(T, Chor-dotonos ; and for stretching 
them proportionably to the weights, he invented 

* i. e. per omnes. 



10 



HISTORY OF THE SCIENCE 



Book I. 



' pegs, by the turning whereof he distended or 
' relaxed them at pleasure. Making use of this 
' foundation as an infallible rule, he extended the 
' experiment to many kinds of instruments, as well 
' pipes and flutes, as those which have strings ; * and 
' he found that this conclusion made by numbers was 
' consonant without variation in all. That sound 
' which proceeded from the number six he named 
' Hypate ; that from eight Mese, being Sesquitertia 
' to the other ; that from nine Paramese, it being one 
' tone more acute, and sesquioctave to the Mese ; that 
' from twelve he termed Nete ; and supplying the 
' middle spaces with proportionable sounds, according 
' to the diatonic genus, he so ordered the octochord 
' with convenient numbers. Duple, Sesquialtera, Ses- 
' quitertia, and the difference of the two last, Sesqui- 
' octava. 

* Thus by a kind of natural necessity he found the 
' progress from the lowest to the highest, according 
' to the diatonic genus ; and from thence he proceeded 
'to declai'e the chromatic and enharmonic kinds.' f 
Hist, of Philosophy, pag. 387. folio edit. 1701. 

* This seems difficult to conceive, for the tuning ofpipep and flutes 
is regulated by the size and distance of the apertures for the emission of 
the wind or breath ; and to these the proportions of six, eight, nine, 
twelve, are in no way whatever applirabie. 

t The result of this discovery is, that consonancy is founded on 
geometrical principles, the contemplaiion \vhere(jf, and the making them 
the test of beauty and harmony, is a pleasure separate and distinct from 
that which we receive by the senses. This geometrical relation of the 
consonances has been farther illustrated by Archimedes, who has de- 
monstrated that the proportions of certain solid bodies are the same with 
those of the musical consonances ; to speak first of the diapason. 

By a corollary from the thirty-fourth proposition of Archimedes it is 
shewn, that the proportion of the octave is as the whole superficies of 
a right cylinder described about a sphere, is to the whole superficies of an 
equilateral cylinder inscribed, that is to say, as 2 is to 1. For the cir- 
cumscribed is to the spheric superficies as 12 is to 8 ; but the spheric is to 
the inscribed as 8 is to 6 ; therefore the circumscribed is to the inscribed 
as 12 is to 6, or 2 to 1. Vide Theorems selected out of Archimedes by 
Andrew Taquet, printed at the end of Whiston's Euclid. 

As to the diatessaron, the proportion of it is precisely the same with 
that which subsists between the superficies of a sphere and the whole 
superficies of a square cylinder inscribed therein, viz., 4 to 3. Ibid. 
Prop, xxxiv. 

But which is admirable, the sesquialteral proportion of the diapente, 
and of the same interval continued, is demonstrated by Tacquet himself, 
by a sphere, a right cylinder, and an equilateral cone thus disposed : — 




His words are these : ' An equilateral cone circumscribed about a 
'sphere, and a right cylinder in like manner circumscribed about the 
'same sphere, and the same sphere itself continue the same proportion; 
' to wit, the sesquialteral, as well as in respect of the solidity as of the 
'whole superficies. 

' For by 32 of this book, the right cylinder G K encompassing the 
' sphere, is to the sphere, as well in respect of solidity, as of the whole 
' superficies, as 3 is to 2, or as G to 4. But by the foregoing, the equilateral 
' cone BAD circumscribed about the sphere, is to the spliere, in both the 
' said respects, as 9 is to 4. Therefore the same cone is to the cylinder, 

• both in respect of solidity and surface, as nine is to six ; wherefore 

• these three bodies, a cone, a cylinder, and sphere, are betwixt them • 
' selves as the numbers 9, 6, 4 ; and consequently continue the sesqui- 
' altera! proportion.' Q. E. D. Prop. xlv. at the conclusion of the 
' Theorems of Archimedes by Tacquet. 

Farther the same author shows, that the same sesquialteral proportion 
holds betwixt an equilateral cone and cylinder circumscribed about the 
same sphere, in respect of their whole surfaces, their simple surfaces, 
their solidities, altitudes, and bases. 

Archimedes was so delighted with the thirty -second of his propositions, 
above referred to, that he left it in charge to his friends to erect on his 



Other writers attribute the discovery of the con- 
sonances to another, named Diodes ; who, say they, 
passing by a potter's shop, chanced to strike his 
stick against some empty vessels which were standing 
there ; that observing the sounds of grave and acute 
resulting from the strokes on vessels of different mag- 
nitudes, he investigated the proportions of music, 
and found them to be as above related ; | notwith- 
standing which testimony, the uniform opinion of 
mankind has been, that we owe this invention to 
Pythagoras ; the result whereof may be conceived 
by means of the following diagram : — 
DIAPASON. 

• "^ s 

DIATESSARON TONE DIATESSAKON 



12 

V 



8 



9 



6 



DIAPENTE 



DIAPENTE 

It is observable that there is nothing in this 
account to authorise the supposition that the lyre 
of Mercury was tuned in any of those proportions 
which this discovery had shewn to be consonant. 
Bontempi, who, as we have hinted before, had his 
doubts about it, says expressly that none of the Greek 
writers assert any such matter ; and Zarlino, though 
he adopts the relation of Boetius, does it in such 
a way as sufficiently shews it stuck with him : we 
may therefore justly suspect that Boetius went too 
far in assigning to the strings of the Mercurian lyre 
the proportions of six, eight, nine, twelve. 

CHAP. III. 

If we consider the amount of this discovery, it 
will appear to be, that certain sounds, which the 
human ear had previously recognised as grateful and 
harmonious, were, by the sagacity of Pythagoras, 
found to have a wonderful relation to each other in 
certain proportions ; that those proportions do really 
subsist between the musical concords above-mentioned 
is demonsti'ated by Ptolemy, and will be shown here- 
after ; but then it has been by experiments of a 
different kind from that of strings distended by 
hammers or other weights in the proportion of six, 
eight, nine, twelve, and such as prove a most 
egregious error in those said to be made by Py- 
thagoras ; so that though his title to the discovery 
of the proportions above-mentioned is not contested ; 
yet that it was the result of the experiment above 
related to have been made by him, is demonstrably 
false. 

For suppose, as will be shown hereafter, that the 
sounds of four strings, in every other respect alike, 
and in length as these numbers, six, eight, nine, 
twelve, will make the intervals above-mentioned, viz., 
a fourth, fifth, and octave ; yet let weights in these 
proportions be hung to strings of equal length and 
thickness, and the intervals between the sounds pro- 
tomb a sphere included in a cylinder, and Tacquet seems to have been 
little less pleased with his improvement on it, for he has given the figure 
referred to in the demonstration of it, in the title page of his Theorems 
selected from Archimedes. 

t Vincent. Galilei, Dial, della Musica, pag. 127. 



Chap. III. 



AND PRACTICE OF MUSIC. 



11 



duced by strings thus distended will be far different 
from those above-mentioned. 

It is said that we owe the detection of this error 
to the penetration and industry of Galileo Galilei, 
whose merits as well as sufferings are sufficiently 
known. He was the sou of a noble Florentine 
named Vincentio Galilei, the author of a most learned 
and valuable work, intitled Dialogo della Musica antica 
e moderna, printed at Florence in 15S1 and 1602 ; 
and also of a tract, intitled Discorso intorno all' Opere 
del Zarlino ; and of his father, who was an admirable 
performer on the lute, learned both the theory and 
practice of music ; in the latter whereof he is said to 
have been such a proficient, as to be able to perform 
to a great degree of excellence on a variety of instru- 
ments ; however, notwithstanding this his propensity 
to music, his chief pursuits were natural philosophy 
and the mathematics. The inquisitiveness of his 
temper leading him to the making experiments, in 
the course thereof he made many noble discoveries ; 
that of the telescope seems to be universally attributed 
to him ; his first essay towards an instrument for 
viewing the planets was an organ pipe with glasses 
fixed therein ; and it was he that first investigated 
those laws of pendulums, which I\Ir. Huygens after- 
wards improved into a regular and consistent theory. 

In a work of the younger Galilei, intitled Discorsi 
6 Dimostrazioni Matematiche intorno, a due nuove 
Scienze, attenenti alia Mecanica, ed i Movimenti 
locali, is contained a detection of that error, which it 
is here proposed to refute. 

It is true some writers refer this discovery to 
Vincentio Galilei ; and first Bontempi says, that in 
his discourse on the works of Zarlino, he affirms, that 
in order ' to find the consonances by weights hung 
' to chords, the weight to produce the diapason 
' ought to be in quadruple proportion ; that to pro- 
' duce the diapente ought to be in dupla sesquiqi;arta ; 
' for the diatessaron in sesquisettima partientenono 

* and for the tone in sesquisettima partiente 64.' * 

Malcolm also, speaking of the discovery of the 
consonances by Pythagoras, makes use of these words : 
' But we have found an error in this account, which 
' Vincenzo Galileo, in his Dialogues of the ancient 

* and modern Music, is, for what I know, the first 
' who observes ; and from him Meibomius repeats it 
' in his notes upon Nicomachus.'f 

Here it may be observed, that this author Malcolm 
has himself been guilty of two mistakes : for first, it 
is not in his notes on Nicomachus, but in those on 
Gaudentius that Meibomius mentions the error now 
imder consideration : and farther, in the passage of 
Meibomius, which Malcolm meant to refer to, the 
discovery is not ascribed to Vincentio Galilei, but to 
Galileo Galilei his son. To take the whole together, 
Gaudentius, speaking of the experiment of Pytha- 
goras, and asserting, that if two equal chords be dis- 
ended by weights in the same proportion to each 
other as the terms of the ratio, containing any inter- 
val, those chords when struck will give that interval. 
Meibomius upon this passage remarks in the follow- 
ing words : ' Mirandum sane, banc experientiam, tot 



• Hist. Music, pag. 54 



t Malcolm on Music, pag. 503. 



' gravissimorum auctorum adsertione confirmatam, 
' nostro primum seculo deprehensam esse falsam. 
' Inventionis gloriam debemus nobilissimo mathema- 
' tico Galileo Galilei, quem vide pag. 100. Tractatus 
' qui inscribitur : Discorsi e Dimostrazioni jMatem- 
' atiche intorno a due nuove Scienze.' | 

But notwithstanding Bontempi has given from the 
elder Galilei a passage which seems to lead to a dis- 
covery of the error of Pythagoras, yet he himself 
acquiesces in the opinion of Meibomius, that the 
honour of a formal refutation of it is due to the 
younger, and is contained in the passage above 
referred to, which translated is as follows : — 

' I stood a long time in doubt concerning the forms 
of consonance, not thinking the reasons commonly 
brought by the learned authors who have hitherto 
w^rote of music sufficiently demonstrative. They 
tell us that the diapason, that is the octave, is con- 
tained by the double ; and that the diapente, which 
we call the fifth, is contained by the sesquialter : 
for if a string, stretched upon the monochord, be 
sounded open, and afterwards placing a bridge 
under the midst of it, its half only be sounded, you 
will hear an eighth ; and if the bridge be placed 
under one third of the string, and you then strike 
the two thirds open, it will sound a fifth, to that of 
the whole string struck when open ; whereupon 
they infer that the eighth is contained between 
two and one, and the fifth between three and two. 
But I do not think we can conclude from hence 
that the double and sesquialteral can naturally 
assign the forms of the diapason and diapente ; and 
my reason for it is this : there are three ways by 
which we may sharpen the tone of a string, viz., bv 
shortening it, by stretching it, or by making it 
thinner : if now, retaining the same tension and 
thickness, we would hear an eighth, we must make 
it shorter by half; i. e., we must first sound the 
whole string, and then its half. But if, keeping the 
same length and thickness, we w'ould have it rise to 
an eighth from its present tone, by stretching it, or 
screwing it higher, it is not sufficient to stretch it 
with a double, but with four times the force : thus, 
if at first it was distended by a weight, suppose of 
one pound, we must hang a four pound weight to 
it, in order to raise its tone to an eighth. And 
lastly, if, keeping the same length and tension, we 
would have a string to sound an eighth, this string 
must be but one fourth of the thickness of tliat 
which it must sound an eighth to.§ And this that 
I say of the eighth, I would have understood of all 
other musical intervals. To give an instance of the 
fifth, if we would produce it by tension, and in order 
thereto hang to the grave string a four-pound 
weight ; we must hang to the acute, not one of six, 
which yet is in sesquialteral proportion to four, viz., 

X Meibom. Not. in Gaudent. pag. 37. 

§ Isaac Vossius says that in this passage the author has erred, and 
with his usual temerity asserts, that ceeteris paribus, the thicker the cliorcl, 
the acuter the sound. De Poemat. Cant, et Viribus Rythnii, pag. 113. 
And this, even tliough he confesses tliat both Des Cartes and Mersennus 
were of opinion with Galilei in this respect. The only appeal in such 
a case as this must be to experiment, and whoever will make one for 
the purpose will lind the converse of this proposition to be true, and 
that, as Galilei has said, chords comparatively thin render acute, and not 
grave sounds. 



12 



HISTOEY OF THE SCIENCE 



Book I. 



' three to two, but one of nine pounds. And to pro- 
' duce tlie above intervals by strings of the same 
' length, but different thickness, the proportion 
' between the grave and the acute string must be 
' that of nine to four. These things being really so 
' in fact, I saw no reason why these sage philosophers 
• should rather constitute the form of the eighth 
' double than qiiadruplo, and that of the fifth rather 
' in sesquialtera than in double sesquiipiarta, &c.' * 
Discorsi e Dimostrazioni Matematiche del Galileo 
Galilei, pag. 75. 

To give yet farther weight to the above objection, 
it may be necessary here briefly to explain a ductrine 
yet unknown to the ancients, viz., that of pendulums, 
between the vibrations whereof, and those of musical 
chords, there is an exact coincidence. 

Sound is produced by the treraulation of the air, 
excited by the insensible vibrations of some elastic, 
sonorous body ; and it has been manifested by re- 
peated experiments, that of musical sounds the acute 
are produced by swift, and the grave by comparatively 
slow vibrations. f A chord distended by a weight or 
otherwise, is, with respect to the vibrations made 
between its two extremities, to be considered as 
a double pendulum, ^ and as subject to the same laws. 

The proportions between the lengths of pendulums, 
and the niuiiber of vibrations made by them, are in 
an inverse duplicate ratio ; so that if the length be 
quadrupled, the vibrations will be subdupled ; on the 
contrary, if the length be subquadupled, the vibra- 
tions will be dupled.§ 

The same proportions hold also with respect to 
a chord, but with this difference, that in the case of 
pendulums the ratios are inverse, the greater length 
giving the fewer vibrations ; whereas in that of 
chords they are direct, the greater tension giving 
the greater number of vibrations : thus if the tensive 
power be as one, if that be quadrupled, the number 
of vibrations is dui)led ; and the sound produced by 
the greater power will be duple in acumen to that 
produced by the lesser. In a word, the same ratios 
that subsist between the vibrations of pendulums and 
their respective lengths, are to be found inversely 
between the vibrations of chords and the powers that 
distend them : what those ratios are, so far as they 

* The reason of these safre philosophers for doing; thus, notwithstanding 
that Galilei could not discover it, seems to be very obvious ; they con- 
stituted the form of the eiRhth double because they found it to arise 
from the division of a chord into two equal parts; and the fifth they 
found to arise from the division of a chord into five parts, three whereof 
struck against the remaining two produced that interval ; therefore they 
assigned to it the sesquialtera proportion, 3 to 2. And certainly there 
needs no better reason for the Pythagorean constitution of the con- 
sonances, than that it is founded in the actual division of a chord ; and 
had the followers of Pythagoras rested the matter there, their tenets 
would have escaped reprehension. 

But they say of him that he produced the consonances by chords of 
equal length and thickness, distended by weights of six, eight, nine, 
and twelve pounds ; Galilei has shewn that this could not be ; and from 
the principles laid down by writers since his time, as also by experiments, 
it most evidently appears, that to produce the consonances, from chords 
thus conditioned, weights must be used of a very different proportion 
from those said to have been taken by Pythagoras. 

As to the proportions, there can be no boubt but that they are as 
above-stated : but the error chargeable on the Pythagoreans is the 
making the discovery of them the result of an experiment, which must 
havfc jeoduced, instead of consonances, dissonances of the most offensive 
kind 

t Treatise on the natural Grounds and Principles of Harmony, by 
William Holder. Passim. 
I Ibid. xi. 43. 
§ Ibid. 16. 



respect the acuteness or gravity of sound, will shortly 
be made appear. 

In order to apply the doctrine of tensive powers 
to the question in debate, it is necessary to state the 
ratios of the several consonances, and those are de- 
monstrated to be as follows, viz., that of the diapente 
3 to 2, and of the diatessaron 4 to 3, that of the dia- 
pason 2 to 1, and that of the tone 9 to 8 ; or in other 
words, a chord being divided into five parts, the sound 
produced at three of these parts will be a diapente 
to that produced at two ; if divided into seven parts, 
four of them will sound a diatessaron against the re- 
maining three ; and if divided into three parts, two 
of them make a diapason against the other one : 
farther, if the chord be divided into seventeen parts, 
nine of them on one side will sound a sesquioctave 
tone to the eight remaining on the other. These are 
principles in harmonics which we may safely assume, 
and the demonstrations may be seen in Ptolemy's 
description of the nature and use of the Harmonic 
Canon. || 

It is equally certain, and is deducible from the 
doctrine of pendulums, that if two chords, of equal 
lengths, A B be so distended as that their vibra- 
tions shall be as three to two, that is, that A shall 
make three vibrations while B is making two, the 
consonance produced by striking them together will 
be a diapente. 

If the vibrations be as four to three, the consonance 
will be a diatessaron. 

If the vibrations be as two to one, the consona»ice 
will be a diapason ; and lastly — 

If the vibrations be as nine to eight, the interval 
will be a sesquioctave tone. 

We are now to enquire what are the degrees of 
tensive power requisite to produce the vibrations 
above-mentioned ; and here we must recur to the 
principle above laid down, that the squares of the 
vibrations of equal chords are to each other as their 
respective tensions : if then we suppose a given sound' 
to be the effect of a tension by a weight of six pounds, 
and would know the weight necessary to produce the 
diapente, which has a ratio to its unison of 3 to 2, 
we must take the .square of those numbers 9 to 4, 
and seek a number that bears the same ratio to six, 
as nine does to four, and this can be no whole number, 
but is thirteen and a half. 

By the same rule we adjust the weight for the 
diatessaron, 4 to 3, which numbers squared are six- 
teen and nine, and as 16 is to 9, so is 10| to 6. 

For the diapason 2 to 1, which numbers squared 
are 4 to 1, the weight must be twenty-four ; so as 4 
is to 1, so is 24 to 6. 

The several weights above adjusted, have a re- 
ference to the unison expressed in the scheme of Py- 
thagoras, by the number six, supposed to result from 
a tension of six pounds. But the sesquioctave tone, 
as it is the difference between the diapente and dia- 
tessaron, takes its ratio from the sound expressed by 

II Mersennus recommends for the purpose of making these experiments, 
the use of two chords rather than one, for this reason, that where one 
only is taken, only one sound can be heard at a time ; whereas when two 
are used, both sounds are heard at the same instant, and thereby the 
consonance is perceii ud. Harmonie universelle, Traitfe des Instrumena, 
Prop. V. 



Chap. III. 



AND PRACTICE OF MUSIC. 



13 



the number eight, as the diapente does from that ex- 
pressed by nine ; in order then to adjust the weight 
for this interval, we miist square those numbers ; and 
as 81 is to 64, so is 13J to 10|. 

Whoever is disposed to prove tlie truth of these 
positions, and doubts the certainty of numerical 
calculation, may have recourse to experiment ; in 
which, however, this caution is to be observed, that 
in the making it the utmost degree of accuracy is 
necessary ; for it should seem that one of the authors 
above-cited failed in an attempt of this sort, which 
is not to be wondered at, if we conaider the nature of 
the subject. 

The author here meant is Bontempi ; who, after 
citing the authority of Vincentio and Galileo Galilei, 
adds, that, ' prompted by curiosity, he made an ex- 

* periment by hanging weights to strings of equal 

* lengths and thickness, the result whereof was, that 
' the first and second strings, having weights of 12 
' and iJ, produced not the diatessaron, but the trihemi- 
' tone ; the first and third 12, 8, not the diapente but 
' tlie ditone ; the first and fourth, 12, 6, not the dia- 
' pason but the tritone ; the second and the third, 9, 8, 
' not the tone, but the defective or incomplete hemi- 
' tone ; the second and fourth, 9, 6, not the diapente, 

* but the semiditone ; and the third and fourth, 8, G, 
' not the diatessaron, l:)ut the distended or excessive 
' tone, as the following figure demonstrates : — * 

TRITONE. 



12 



TRIHEMITONE. HEMITONE incomplete. TONE excessive. 



9 



8 



DITONE. 



iSEMIDITONE. 

But that the proportions of a diatessaron tone and 
diatessaron would result from an experiment made 
by strings of several lengths of twelve, nine, eight, 
six ; or rather by a division of the monochord, ac- 
cording to that rule, is demonstrable. This invention 
of Pythagoras, as it regarded only the proportions or 
ratios of sounds, was applicable to no one system in 

• Egli ^ cosa da restar confuso, e formare un cumulo di maraviglie, 
che questo sperimento, confennato da gravisslmi autori, e teimto tanti 
secoli per veto sia stato finalinente scoperto esser falso da Galileo Galilei, 
sicome riferisce ne' suoi Discorsi e Dimoytrazioni Mathematiche, e Vin- 
cenzo Galilei nel discorso intorno all' opere del Zarlino afferma, che per 
ritrovare co' pesi attaccati alle corde le consonanze de Martelli; per la 
diapason debbono costituirsi i pesi in quadrupla proportione : per la 
diapente, in dupla sesquiqiiarta ; per la diatessaron, in sesqui 7 par- 
tiente 9; e pe'l tuono, in sesqui 7 partjente 64. E noi, spinti dalla 
curiosity messo in opera questo sperimento co' pesi de Martelli, habbiamo 
ritrnvato cheil prime ed il secondo 12, 9, partoriscono non la diatessaron : 
nia il triemituono; il primo ed il terzo, 12, 8, non la diapente; ma il 
ditono; il primo e'l quarto 12, 6, non la diapason; ma il tritono ; 11 
Becondo e'l terzo 9, 8, non il tuono : mal'hemitunno rimesso o mancante ; 
il secondo e'l (Quarto 9, 6, non la diapente : ma il semiditono ; ed il terzo 
e'l quarto 8, 6, non la diatessaron : ma il tuono disteso overo eccedente, 
sicome la ottoposta figura dimostra. Bontempi, pa. 54. 

Ptolemy observes, that it is extremely difficult to find chords perfectly 
fiqual in respect of crassitude, density, and other qualities that determine 
their several sounds ; and farther he says, that the same chord distended 
by the same weight,, will at different times yield different sounds. 
Ptolem. Harmonicor. lib. I. cap. 8. Ex vers. Wallis. Mersenn. Harm, 
universelle. Traite des Instrumens, Prop. iv. So that the success of ex- 
periments for investigating the consonances, by the means of weights 
h\ing to chprds, must be very precarious, and is little to be depended on. 



particular ; however it produced a discovery, which 
enabled him at once to supply a defect in even the 
improved system of Terpander, and lay a foundation 
for that more enlarged one, which is distinguished by 
his name, and has never since his time been capable 
of any substantial improvement. We are here to 
remember that the diapason or octave had been found 
to consist in duple proportion, or in the ratio of 12 
to 6 ; and that the interval between the diatessaron 
twelve, nine, and that other eight, six, viz., nine, 
eight, was a complete tone, or sesquioctave ratio. 
Pythagoras, in consequence of this discovery re- 
curring to the ancient septenary, found that its ex- 
tremes were discordant, and that there wanted but 
little to produce that supremely sweet concord the 
diapason, which the means above had enabled him to 
investigate. Observing farther that in the septenary 
the interval between Mese and Paramese was but 
a hemitone, he immediately interposed between them 
a whole tone, and thereby completed the diapason. 

It must be confessed that some authors have in 
general terms ascribed the addition of an eighth 
string to the heptachord lyre to others ; Boetius 
gives it to Licaon, and Pliny to Simonides ; but 
Nicomachus, from whom the following relation is 
taken, does most expressly attribute it to Pythagoras. 

History has also transmitted to us the bare names 
of sundry persons, by whom at different times the 
strings of the lyre are said to have been encreased 
to eighteen in number ; as Theophrastus, who added 
a ninth ; Hestius, who added a tenth, and so on ;f 
but as to the ratio subsisting between them, or any 
system to which they could be said to be adapted, 
there is a total silence. Indeed we h^ve the greatest 
reason to think that these additions were not made 
in any ratio whatever, but served only to increase 
the variety of sounds |. That innovations were made 
in the heptachord is certain ; and when we are in- 
formed that Timotheus, for his presumption in adding 
to the strings of the ancient lyre, had a fine imposed 
on him by the magistracy, we may fairly conclude 
that those innovations tended rather to the corruption 
than the improvement of music. 

But the case is different with respect to him of 
whom we are now speaking ; the system of Pytha- 
goras had its foundation in nature : the improvement 
of an instrument was not his care ; he was a phi- 
losopher and a musician in the genuine sense of the 
word, and proposed nothing less than the establish- 
ment of a theory to which the practice of succeeding 
ages should be accommodated. His motives for 
attempting it, and in what manner he effected this 
great purpose, shall now be given in the wo^'ds of 
his learned biographer : — 

' Pythagoras, lest the middle sound by conjunction 
* being compared to the two extremes, should render 
' the diatessaron concent both to the Nete and 
' the Hypate ; and that we might have a greater 
' variety, the two extremes making the fullest con- 
' cord each to other, that is to say, a diapason, which 

f Boetius de Musica, lib. ii., cap. 20. Vincen. Galilei, Dial, della 
Musica, pag. 1(6. 

X Nicom. lib. ii. Boet. lib. i., cap. 20. Bont. pag. 71. 



u 



HISTORY OF THE SCIENCE 



Book I. 



consists in duple proportion, inserted an eighth 
sound between the Mese and the Paramese, pLacing 
it from the Mese a whole tone, and from the Para- 
mese a semitone ; so that what was formerly the 
Paramese in the heptachord, is still the third from 
the Nete, both in name and place ; but that now 
inserted is the fourth from the Nete, and hath a 
concent to it of diatessaron, which before the Mese 
had to the Hj'pate : but the tone between them, 
that is the IMese, and the tone inserted, called the 
Paramese, instead of the former, to whichsoever 
tetrachord it be added, whether to that which is 
at the Hypate, being the lower, or to that of the 
Nete, being the higher, will render the concord of 
diapente ; which is either way a system, consisting 
both of the tetrachord itself, and of the additional 
tone : and as the diapente proportion, viz., sesqui^ 
altera, is found to be a system of sesquitertia and 
sesquioctava, the tone therefore is sesquioctava. 
Thus the interval of four chords, and of five, and 
of both conjoined together, called diapason, with 
the tone inserted between the two tetrachords, 
completed the octochord."*' 



SYSTEM OF PYTHAGORAS. 



6 c Nete 

Tone 
d Paranete 
Tone 
c Trite 
Arithmetical Hemitone ^^^^ 

Mean 9 b Paramese 

Tone 



GREAT SYSTEM OF PYTHAGORAS. 




Harmonical 
Meanf 




8 a Mese 

Tone 
G Lychanos 

Tone 
F Parhypate 
Hemitone 
12 E Hypate 



It remains now to enquire what this variation of 
and addition to the septenary led to. Pythagoras 
immediately after he had adjusted his system of the 
octochord in the manner above related, transferred to 
it the additions which had been made to that of Ter- 
pander ; and first he connected with it the tetrachord 
hypaton, which carried the system down to B, and 
placing at the other extremity the hyperboleon 
tetrachord, he continued it up to a a, as is here 
shewn. 

* Stanl. Hist, of Philosophy, pag. 386, from Nicom. lib. i. 

+ The difference between the arithmetical and harmonical division of 
the diapason is explained in a subsequent chapter. But as this division 
is frequently occurring, it may not be improper here to remark in general 
that the numbers 12, 9, 6, express the arithmetical, and 12, 8, 6, the 
Jiarmonical division. 



< 
O 

o 

< 

tB 
H 



■£ /'Nete hyperboleon 

I Tone 

^ I Paranete hyperboleon 

« I Trite hj'perboleon 

Hemitone 
Nete diezcugmenon 
/"« I Tone 

■H I Paranete diezcugmenon 

1 < Tone 

2 I Trite diezcugmenon 
Hemitone 



aa 



e 
d 



s; I 



B 






Paramese 
Mese 



"S I Lychanos meson 

2 I Parhypate meson 
■£ I 



p. 
a 



Hypate meson 
Lychanos hypaton 
Parhypate Itypaton 
^Hj-pate hypaton 



Tone 

Tone 

Tone 

Hemitone 

Tone 

Tone 

Hemitone 



G 
F 
E 
D 
C 
b 



In consequence of the separation of the system of 
the octochord above noted, we see that in the above 
diagram the tetrachord B is separated from the 
tetrachord A by a whole tone : this disunion of the 
one diatessaron from the other, gave rise to the 
epithet of Diezcugmenon or disjunct, whereby the 
former of the two tetrachords is distinguished : we 
are therefore now to look for the invention of that 
other tetrachord, which hitherto has been represented 
as part of a system, to which it could never with any 
propriety be applied. 

No one in the least acquainted with the principles 
of harmony need be told, th^t that relation which 
modern musicians denominate a Tritonus, can have 
no place in any regular series of progression, either 
ascending or descending ; for of the eftects of sounds 
produced at the same instant we are not now speak- 
ing : that such a relation immediately arose from the 
separation of the Diezcugmenon and Meson tetra- 
chords, will appear by observing that in the progression 
upwards through the Meson tetrachord, beginning 
at Parhypate Meson, and proceeding to Paramese, 
that interval which should be a diatessaron, and con- 
sist of two tones and a hemitone, will contain three 
tones, and have for its ultimate sound what in this 
place is to be considered as an excessive fourth.^ 
The consequence of this was, that the lower sound 
coiild never be used as a funda^riental ; and so far the 
system must be said to have been imperfect. To 
remedy this defect in part, collateral or auxiliary 
tetrachord was with great ingenuity constituted, in 
which the sounds followed in the order of hemitone, 
tone, and tone, a succession which a true and perfect 
diatessaron requires. 

t Some writers have given the name of Tritonus to the defective fifth, 
J] f, for this reason, that it is an interval compounded of hemitone, tone, 
tone, and hemitone, the sum whereof is three tones. But in this they 
are mistaken, for the ratios of the tritonus or excessive fourth, and the 
semidiapente or defective fifth are different, the one being 45 to 32, the 
other 64 to 4.5. Vide Mersennus Harmonic, De Dissonantiis, pag. 75. 
Holder on the natural Grounds and Principles of Harmony, pag. 128. 



Chap. III. 



AND PRACTICE OF MUSIC. 



15 




The intervals that compose this system will appear 
upon comparison to be precisely the same with those 
of the tetrachord B, in the conjunct system ; whereas 
between the tetrachord B. in the disjunct system, and 
that at present xmder consideration, this difference is 
apparent ; in the former the distance between a and b 
is a whole tone, in the latter it is a hemitone : if 
therefore this question should be asked, Wherein did 
the merit of the improvements made by Pythagoras 
to the ancient system consist ? the answer would be, 
first, in the invention of the disjunct system, and the 
consequent completion of the octochord ; next in the 
introduction of the octochord into the system of 
Terpander ; and lastly, in such a disposition of the 
disjunct tetrachord as was yet consistent with the 
re-admission of that part of the system which it 
seems to exclude whenever the perfection of the harr 
mony should require it. After what has been said 
it will be needless to add that this collateral tetra- 
chord Avas distinguished by the epithet of Synemr 
menon or conjunct. With these improvements the 
Pythagorean system assumed the following form ; — 

ADDITION to the GREAT SYSTEM of 
PYTHAGORAS. 

aa 



g 
f 



H r. 



ji /-Nete hyperboleon 
I Tone 

^ I Paranete hyperboleon 
^ < _ Tone 

g j Trite hj'perholeon 
« I Hemitone 

Nete diezeugmenon 

Tone 
Paranete diezeugmen. 

Tone 
Trite diezeugmenon 

Hemitone 
Paramese 

Tone 
y'Mese 

Tone 
Lychanos meson 
Tone 
g J Parhyp.'jite meson 
u ! Hemitone 

^ Hypate meson E 

Tone 
Lychanos Jivpaton 
j < Tone 

\i I Parhypate hypaton C 
■£ I Hemitone 

^ Hypate hjT^^o'^ h 

There ^yer^ two reasons that seemed to suggest 



a still farther improvement ; the one was that by the 
separation of the Diezeugmenon and Meson tetra- 
chords there followed an unequal division of the 
system ; for, ascending from Mese to Nete Hyper- 
boleon, the distance was a complete Octave ; whereas 
descending to Hypate Hypaton it was only a Seventh : 
from hence arose another inconvenience, a false rela- 
tion between Hypate Hypaton and Parhypate Meson, 
which though to appearance a fifth, was in truth an 
interval of only two tones and two hemitones, con- 
stituting together the very discordant relation of 
a defective fifth. To supply this defect nothing 
more was required than the addition of a tone at 
the lower extremity of the system. Pythagoras ac- 
cordingly placed another chord at the distance of 
a tone below Hypate Hypaton, which he named 
Proslambanomenos, a word signifying additional or 
superntmierary, it not being includable in the division 
of the system by tetrachords ; and thus was completed 
that system of a Bisdiapason or double octave, which 
the Italians distinguished by the several appellations 
of Systema immutabile, Systema diatonico, Systema 
Pitagorico, and Systema massimo. 

IMMUTABLE SYSTEM OF PYTHAGORAS. 

• /'Nete hyperboleon aa 
S I Tone 

Paranete hyperboleon g 

Tone 
Trite hyperboleon f 

Hemitone 
Nete diezeugmenon e 

Tone 
g I Paranete diezeug. 
'•3 ■{ Tone 

■S I Trite diezeugmenon 
S I Hemitone 

H ^Paramese 

Tone 
<i ^Mese 

5 I Tone 

||] 



Nete synemmenon d^ 

Tone 
Paranete synemmenon c 

Tone 
Trite synemmenon b 

Hemitone 
Mese &' 



A< 






G 

F 



D 



P3 



I 

en 






Nete synemmenon ( 

Tone 
Para,nete synem. 

Tone 
Trite sjTiemmenon 

Hemitone 
Mese 



I 



Lychanos meson G 



Tone 



F 



D 



P£^rhypate meson 

Hemitone 
^ ^Hypate meson E 

i j Tone 

P; I Lychanos hypaton 
%J Tone 

I I Parhypate hypaton C 
^ j Hemitone 

^ ^Hypate hypaton j-| 

Tone 

Proslambanomenos A 



Here it is to be observed, that although in this 
and the preceding scale the Synemmenon tetrachord 
is given at large, yet the generality of writers either 
insert it entire in its place, immediately above the 
Meson tetrachord. placing the Diezeugmenon tetra- 
chord above it, as Kircher in his Musurgia, tom. I, 
lib. III. cap. xiii. or else following perhaps the ex-^' 
ample of Guido, whose reformation of the scale might 
suggest this latter method as the most concise, they 
have borrowed from the synemmenon tetrachord 
one only of its terms. Trite, and inserted it im-^ 
mediately after Mese, with Paramese next above it ; 
thereby leaving it to the imagination to select which 



16 



HISTORY OF THE SCIENCE 



Book I. 



of the two sounds the nature of the progression might 
require ; however, the better to explain its con- 
struction and use, it was here thouglit proper to 
exhibit the synemmenon tetrachord in that detached 
situation which seems most agreeable to its original 
formation.'^ 



CHAP. IV. 

But here it may very naturally be asked what 
were the marks or characters whereby the ancients 
expressed the different positions or powers of their 
jnusical sounds ? An answer to this question may 
be produced from an author of undoubted credit, 
Boetius, and also Alypius, an ancient Greek, of whose 
writings we shall have occasion to speak more par- 
ticularly, and these inform us that the only characters 
in use among the Greeks to denote the sounds in 
music, were the letters of their alphabet, a kind of 
Brachygraphy totally devoid of analogy or re- 
semblance between the sign and the thing signified. 
Boetius de Musica, lib. IV., cap. iii., gives an account 
of the ancient method of notation in the following 
words : — ' The ancient mi;sicians, to avoid the 
' necessity of always writing them at length, invented 
' certain characters to express the names of the chords 

* in their several genera and modes ; this short method 
' was the more eagerly embraced, that in case a mu- 
■ sician should be inclined to adapt music to any poem, 
' he might, by means of these characters, in the same 
' manner as the words of the poem were expressed 
' by letters, express the music, and transmit it to 
' posterity. Out of all these modes we shall only 
' specify the Lydian.' This description of the sounds 
consisted in the different application of the Greek 
letters to each of them ; Boetius proceeds thus : — ' To 

express Proslambanomenos, which may be called 

* Acquisitus, was used Z imperfect, and tau lying t^. 
^ Hypate hypaton, f reversed and F right rjj. 

* Parhypate hypaton, B imperfect T supine, j Hy- 
' paton enarmonios, V supine and V reversed, having 

* a stroke Hypaton chromatice, y, having a line 

* and r reversed, having two lines \ Hypaton dia- 

* tonos, (^ Greek, and digamma » Hypate meson C 

C • P 

'and C, p. Parhypate meson P and C supine JT' 

* Meson enarmonios, 11 Greek and C reversed. ' Me- 



* son chromatice, 11 having a stroke, and C reversed, 

* having a stroke through the middle tj t-^* Meson 

M 

'diatonos, M Greek and 11 drawn open _. Mese, 

I . T^ 

* I and A lying, ^ . Trite synemrppnon, 6 and A 

' supine ^ • Synemmenon enarmonios, H Greek and 

* A lying, with a stroke througl^ the middle ^ • 

♦ MersKiin. Harmon, lib. vi. De Genevilius et Modis, pag. 100. 



' Synemmenon chromatice, H Greek and A reversed 

' with a stroke 4t * Synemmenon diatonos, F and 

N -"^ . w 

' N p . Nete synemmenon, Q, supine and Z, y. Para- 

' mese, Z and F Greek lying Hr. Trite diezeugmenon, 
' E square and F supine y ' Diezeugmenon enarmo- 
' nios, A and F Greek lying reversed y_ . Diezeug- 
' menon chromatice, A with a stroke, and 11 Greek lying 
' reversed with an angular line ^n' Diezeugmenon 
' diatonos, Q. square and Z, y. Nete diezeugmenon. ^ 
'lying and N inverted draw open .^j. Trite hyperbo- 
' leon, F looking downwards to the right, and half A 
'to the left . Hyperboleon enarmonios, T supine 
<and half A to the right supine, -^^^ Hyperboleon 

' chromatice, T supine, having a line and half A to the 

" — > 

' right supine, having a line drawn backward ;^~fil 

'Hyperboleon, diatonos M Greek having an acute, 

M' 
' and F having an acute _ . Nete hyperboleon, I hav- 

' ing an acute, find A lying having an acute also ^ .f 

Here it is to be remarked, that although the above 
passage of Boetius is given, not from any of the 
printed copies of his works, but from a very ancient 
manuscript, which Mr. Selden collated, and is pre- 
fixed to Meibomins's version of Alypius : there 
occur in it some instances of disagreement betwceo 
the verbal description of the character and the cha- 
racter itself; some of these Meibomius in his notes 
has remarked, and others have escaped him ; never- 
theless it was not thought advisable to vary the 
representation which Boetius has given, and there- 
fore the following scheme of the ancient musical 
characters is inserted, as he has delivered it in 
lib. IV. cap. iii. of his book De Musica. 



+ Boetius as he goes along gives the Latin signification of the Greek 
names, which it was thought proper to omit in order to make room for 
an extract from Kircher to the same purpose, wherein the Latin are 
opposed to the Greek names in the order in which they arise in the several 
tetrachords : — 

aa Nete hypejboleon, sive ultima acutarum. 

g Parancte hyperboleon, sive secunda acutarum. 

f Trite hyperboleon, sive tertia acutarum. 

e Nete, sSve ultima disjunctarum. 

d Paranete diezeugmenon, sive secunda cji-'^junc- 
tarum. 

c Trite diezeugmenon, sive tertia di.sjunctarum. 

b Paramese, sive vicina mediis. 

d Nete synemmenon, sive ultima conjunctarum. 

Parancte synfmmeno.n, sive secunda conjunctarum. 

b Trite synemmenon, sive tertia conjunctarum. 

a Mese, id est media. 

G Lychanos meson, sive index mediarum. 

F Parhypate meson, sive secunda mediarum. 

E Hypate meson, sive gravis mediarum. 

D Lychanos hypaton, sive index gravium. 

C Parhypate hypaton, sive secunda gravium 

B Hypate hypaton, sive gravis gravium. 

A Proslambanomenos, sive vox assumpta. 



Tetrachordon 
Neton 

Tetrachordon 
Diezeugm. 

Tetrachordon 
Synemmen. 



Tetrachordon 
Meson 

Tetrachordon 
Hypaton 



Chap. IV 



AND PRACTICE OF xAIUSIC. 



17 



/ j^ Proslambanomcnos 

~Xy Hypate Hypaton 

jjj Parhypate Hypaton 

"V/ Lychanos hyp. enarm. 

^ Lychanos hyp. chrora. 

(kQ Lychanos hyp. diat. 

C Hypate mesoii 

P Parhypate meson 

T|-v Lychanos meson enarm. 

\A Lychanos meson chrom. 




Lychanos meson diaton. 



Paranete diezcuc?. enarm. 



A_. 



^^™j Paranete diezenp^. chroni. 



-^-r Trite synemmenou 

Paranete synem. enarm. 




^ Par 
-G- 



anete diezeus:. diat. 



Nete diezeusTmenon 



f\\^ Paranete synem. chrom. 

JN Paranete synem. diaton. 

Lt- Nete svnem. extenta 
>^^ Nete synem. ultima 
Paramese 



-T-7- Trite hyperboleon 



V 



Paranete hyperb. diaton. 



^J^ Paranete hyperb. chrom. 



V 



jVL Paranete hyperb. diaton. 
\L—^ Nete hyperboleon 



^ 



If 



E Trite diezeu 



gmenon 



There is this remarkable difference between the 
method of notation practised by the ancients, and 
that now in use, that the characters used by the 
former were arbitrary, totally destitute of analogy, 
and no way expressive of those essential properties 
of sound, gravity and acuteness ; which is the more 
to be wondered at, seeing that in the writings of the 
ancients the terms Acumen and Gravitas are per- 
petually occuring, whereas the modern scale is so 
adjusted, that those sounds, which in their own 
nature are comparatively grave or acute, have such 
a situation in it, as does most precisely distinguish 
them according to their several degrees of each ; 
so that the graver sounds have the lowest, and the 
acuter the highest place in our scale. But here it 
may be asked, does this distinction of high and low 
properly belong to sound, or do we not borrow those 
epithets from the scale in which we see them so 
posited ? It should seem that we do not ; for if we 
attend to the formation of sounds by the animal 
organs, we shall find that the more grave are pro- 
duced from the lower part of the larynx, as the 
more acute are from the higher ; so that the diffe- 
rence between the one and the other seems to be 
more than ideal, and to have its foundation in 
nature : the modern musicians seem however to pay 
a greater regard to this diversity than is either 
requisite or proper ; for where is the necessity that 
in a vocal composition such a sentiment as this, 
' They that go down to the sea in ships,' &c. should 
be expressed by such sounds, as for the degree of 
gravity few voices can reach ? much less can we see 
the reasonableness of that precept which directs that 
the words Hell, Heaven, are invariably to be ex- 
pressed, the one by a very grave, and the other by 
a very acute sound. Those who affect to be severely 
critical on the compositions of this later age, allow 
no greater merit to this sort of analogy than is due 
to a pun, and their censure seems to be no more than 
the error will warrant. 



The description above given of the ancient mu- 
sical characters, is derived, through Boetius, from 
Alypius, the most copious and intelligible of all the 
Greek writers on this branch of music : his autho- 
rity, so far as it goes, has been implicitly acquiesced 
in ; and indeed from his testimony there can lye no 
appeal. The reader will naturally expect to be in- 
formed of the method by which the ancients denoted 
the different degrees in the length or duration of 
their musical sounds ; but it seems they were stran- 
gers to music merely instrumental : the lyre, and 
other instruments in use among them, was applied 
in aid of the voice ; and the ode, or hymn, or pean, 
or whatever else the musician sang, determined by 
its measure, and the feet of the verse the length of 
the sound adapted to it, and took away the necessity 
for such marks or characters of distinction in this 
respect as are used by the moderns. Nor need we 
any farther prof)f of this assertion, than the absolute 
silence of the Greek writers as to any method of 
denoting what we now understand by the Time or 
measure of sounds. It is true that those among the 
learned who have undertaken a translation of some 
few remaining fragments of ancient music into 
modern notes, have, in particular instances, ventured 
to render the characters in the original by notes ot 
different lengths ; but it is to be presumed they were 
determined so to do rather by the cadence of the 
verse, than by any rythmical designation observable 
in any of those characters. Mr. Chilmead, the pub- 
lisher of the Oxford edition of Aratus, and of Eratos- 
thenes de Astris, in octavo, 1672, has given at the 
end of it three hymns or odes of a Greek poet named 
Dionysius, with the ancient musical characters, which 
he has rendered by semibreves only ; but Kircher, in 
his Musurgia, tom. I. pag. 541. from a manuscript in 
the library of the monastery of St. Salvator, near 
the gate of Messina, in Sicily, has inserted an ancient 
fragment of Pindar, with the musical notes, which 
he has explained by the different signs of a breve, 

c 



■.8 



HISTORY OF THE SCIENCE 



Book I. 



Bemlbreve, crotchet, and quaver, as understood by us 
moderns. Meibomius also has given from an ancient 
manuscript a Te Deum, with the Greek characters, 
and in modern notes, the former of whicli appear to 
be more simple and less combined than those de- 
scribed by Boetius ; which is the less to be wondered 
at considering that St. Ambrose, who is said to have 
been the author of that hymn,* was consecrated bishop 
of Milan, a. c. ST-i, and Boetius flourished not till 
about the year 500 ; so that there is a period of more 
than one hundred years, during which every kind of 
literature suffered from the rage of conquest that pre- 
vailed throughout all Europe, to induce a suspicion 
that the Greek characters were not transmitted down 
to the time of Boetius uncorrupted. In the trans- 
lation of these musical characters of the above-men- 
tioned Te Deum, Meibomius has made use of the 
breve, the semibreve, and minim : lapon what autho- 
rity those several modes of translation is founded we 
do not pretend to determine ; it seems that nothing 
is wanting to enable us to judge with certainty in 
this matter but a perfect knowledge of the powers of 
the ancient characters, with respect to the sounds 
which they were intended to signify ; and concerning 
these Kircher seems to have entertained no kind of 
doubt : he had access to two manuscripts of great 
antiquity, and his judgment of their authority, and 
the use that may be made of them, he has given 
in the following words : — ' The ancient musical 
' characters were no way similar to those of the 
' moderns ; for they were certain letters, not indeed 
' the pure Greek ones, but those sometimes right, 
' sometimes inverted, and at others mutilated and 
' comi^ounded in various manners, each of which 
' characters answered to one of the chords in the 
' musical system. I laid my hands on two manu- 
' scripts, which by God's mercy, were preserved 

* from the injuries of time, the one in the Vatican 
' library, the other in ours of the Roman college : 
' the author is Alypius ; he, in order to give the 
' harmonical characters of the ancients in great per- 
' fection, has exhibited with wonderful care every 
' tone in the Octodecachord, according to the different 
' genera. He keeps a twofold order in these several 
' characters ; the first as they were used in the Can- 
' tus ; the second as adapted to instruments, differing 

* from the former almost after the same manner as at 
' this day the notes of vocal music do from those 
' characters called by us the Tablature, which are 
' used only in instrumental music. Several writers, 

* not understanding this order of Alypius, have con- 

* sidered this twofold series as a single one : among 
' these are Liardus, and Solomon de Caux, who has 
' followed him, both of whom have given to the 
' world most false and corrupted specimens of ancient 

* music. Alypius wrote an entire volume on the 
' musical characters or notes, which, together with 
' other manuscripts of the old Greek musicians, 

* The Te Deum is commonlj- styled the Song of St. Ambrose, and it 
is sairt that it was composed jointly by him and St. Augustine, upon 
occasion of the baptism of the latter by St. Ambrose. Alliance of 
Divine Offices, by Hamon L'Estrange, folio, 1690, pag. 79. But arch- 
bishop Usher ascribes it to Nicetius, and supposes it not to have been 
composed till about the year 500, which was long after the time of 
Ambrosi- and Augustine. Ibid. 



' remain preserved in the library of the Roman 
' college ; a translation of this volume into the Latin 
' language, I will, with the permission of God, at 
' a convenient opportunity give to the learned world; 
' in the interim I trust I shall do a favour to posterity 
' by exhibiting a specimen of the characters in the 
' order in which they lie in the manuscript, correcting 
' from the interpretations thereto annexed such errors 
' as I found required it.' f 

The specimen, the whole of which seems by his 
account to be taken from Alypius, contains the cha- 
racters through all the fifteen tones in the diatonic 
and chromatic genera in two separate tables. (See 
Apjiendix, Nos. 35 and 36.) 

Kircher gives the following explanation of these 
characters : — 

The top of the plate contains the names of the 
fifteen tones or modes: the side exhibits eighteen 
chords, answering to every tone, and expressed by 
their Greek names, to each of which, the Guidonian 
keys now used by the Latins answer, in the first 
column. To know therefore, for instance, by what 
characters the ancients expressed the Mese in the 
Phrygian tone, we must look in the side for the 
chord Mese, and on the top for Tonus Phrygius, and 
where they meet we shall find the character sought 
for, and so for the rest. 

Having exhibited this key to the ancient charac- 
ters, Kircher gives the fragment of Pindar above- 
mentioned in the Greek notes, and also in those of 
the modern scale, as is represented. (See Appendix, 
No. 37.) 

And the tables (35 and 36) given from him seem 
to have been his authority for rendering the ancient 
characters in modern notes, as shewn in 37. By 
way of illustration he adds, that the Chorus vocalis 
contains the characters written over each word ; 
and that the Chorus instrumentalis, which is nothing 
else but the antistrophe to the former, was played 
according to the strophe, on the cythara or the pipe. 
As the characters agree with those of Alypius, he 
says he has no doubt about their meaning ; and as to 
the time, he is clear that it was given by the measures 
of the syllables, and not by the characters. 

The several variations of the system of music have 
been traced with as much accuracy as the nature of 
the subject will allow of: the improvements made by 
Terpander and others, more especially Pythagoras, 
have been distinctly enumerated, we are therefore 
now to proceed in our narration. 

Pythagoras having, as has been related, investigated 
the proportion of sounds, and extended the narrow 
limits of the ancient system, and also demonstrated, 
not merely the affinity of sounds, but that a harmony, 
analogous to that of music, was to be found in other 
subjects wherein number and proportion were con- 
cerned.; and that the coincidences of sounds were 

+ It seems by this that Alypius had not been published in Kircher's 
time ; and though he here promises to give the world a translation of it, 
there is no other extant than that very correct one of Meibomius. 
Kircher expresses a confidence that by publishing these characters he 
should confer an obligation on the learned world, but the mrnner in 
which he has done it, furnished a ground of censure to jVteibomius. 
which he delivers in very bitter terms in the preface to his e^-ition of 
the Greek writers. 



Chap. IV. 



AND PRACTICE OF MUSIC. 



19 



a physical demonstration of those proportions which 
arithmetic and the higher geometry had till then 
enabled mankind only to specnlate, it followed that 
music from thenceforth became a subject of philo- 
sophical contemplation. Aristotle, by several pas- 
sages in his writings now extant, appears to have 
considered it in this view : it is even said that he 
wrote a treatise professedly on the subject of music, 
but that it is now lost. 

Fabricius has given a catalogue of sundry writers, 
as namely. Jades, Lasus Hermionensis, Mintanor, 
Diodes, Hagiopolites, Agatho, and many others, 
whose works are lost ; and in the writings of Aris- 
toxenus, Nicomachus, Ptolemy, Porphyry, Manuel 
Bryennius, and other ancient authors, we meet with 
the names of Philolaus, Eratosthenes, Archytas of 
Tarentum, and Didymus of Alexandria, who seem 
mostly to have been philosophers ; but as they are 
also enumerated among the scriptores perditi, nothing 
can be said about them. In those early times the 
principles of learning were very slowly disseminated 
among mankind, and it does not appear, that from 
the time of Pythagoras, to that of Aristoxenns, which 
included a period of near three hundred years, the 
music of the ancients underwent any very considerable 
alteration, unless we except that new arrangement 
and subdivision of the parts of the great system, 
which constituted the Genera, and those dissimilar 
progressions from every sound to its diapason, which 
are distinguished by the name of Modes. Of these 
it is necessary now to speak ; and first of the Genera. 

Till the time of Pythagoras, the progression of 
sounds was in that order, which as well the modern 
as the ancient writers term the diatonic, as proceding 
by tones, a progression from the unison to its fourth 
by two tones and a hemitone, which we should now 
express by the syllables do, re, mi, fa, confessedly 
very natural and extremely grateful to the ear ; 
though it seems not so much so as to hinder succeed- 
ing musicians from seeking after other kinds of pro- 
gression ; and accordingly by a different division of 
the integral parts of each of the tetrachords, they 
formed another series of progression, to which, from 
the flexibility of its nature, they gave the epithet of 
Chromatic, from Chroma, a word signifying colour ; 
and to this they added another, which was termed 
enharmonic ; besides this they invented a subvariation 
of each progression, and to distinguish the one from 
the other, they made use of the common logical term 
genus, by which we are to understand, as Kircher 
tells us, tom. I. lib. III. cap. xiii. a certain con- 
Btitution of those sounds that compose a diatessaron, 
or musical fourth ; or, in other words, a certain 
relation which the four chords of any given tetra- 
chord bear to each other. The Genera are elsewhere 
defined, certain kinds of modulation arising from the 
different disposition of the sounds in a tetrachord : 
every Cantus or composition, says Aristoxenus,* is 
either Diatonic, Chromatic, or Enharmonic ; or it 
may be mixed, and include a community of the 
genera. Aristoxenns, for aught now discoverable, 

• Lib, II. pag. 44. ex Vers. Meihom. 



is the first that has written professedly, though 
obscurely, on this part of music. Ptolemy, as he 
is in general the most accurate and methodical of 
all the ancient writers, so is he more copious in his 
explanation of the Genera. Nicomachus has men- 
tioned them, but in a very superficial manner ; and 
as to the latter authors, we are not to wonder if they 
have contented themselves with the bare enumeration 
of them ; since before the times in which the greater 
number of them wrote, the Diatonic was the only one of 
the three genera in common use. Nor does it any where 
appear, that even of the five Species, into which that 
Genus was divided, any more than one, namely, the 
syntonous or intense of Ptolemy, was in general 
estimation. It must be confessed that no part of the 
musical science has so much divided the writers on 
it as this of the genera ; Ptolemy has exhibited no 
fewer than five different systems of generical har- 
mony, and, after all, the doctrine on this subject is 
almost inscrutable : however, the substance of what 
these and other authors have related concerning the 
nature of it, is here, as in its proper place, referred 
to the consideration of such as are desirous to know 
the essential difference between the music of this and 
the more early ages. 

But before this doctrine of the Genera can be 
rendered to any degree intelligible, it is necessary to 
observe, that hitherto we have spoken only of the 
more common and obvious musical intervals, the 
tone and hemitone ; for the system of Pythagoras is 
formed of these only ; and a more minute division of 
it was not till after his time thought on, nevertheless 
it is to be noted, that in order to the completion 
of his system, it was found requisite to institute 
a method of calculation that should as it were resolve 
the intervals into their elements, and adjust the ratios 
of such sounds as were not determinable by the 
division of a chord in the manner herein before - 
mentioned. That division was sufficient, and it 
answered to the greatest degree of mathematic exact- 
ness for ascertaining the ratios of the diatessaron, the 
diapente, and the tone : and, agreeable to what has 
been already laid down concerning the investigation 
of the consonances by Pythagoras, it will most 
evidently appear upon experiment, that if a chord be 
divided into twelve equal parts, six of those parts 
will give an octave to that sound which would have 
been produced by the same chord, if struck before such 
division ; from whence it appears, that the ratio sub- 
sisting between the unison and its octave is duple : 
again, that eight parts of the twelve will give a 
diatessaron, which bears to the unison six a ratio of 
4 to 3 ; and that nine parts, according to the same 
division ; will produce the diapente, which bears to 
the unison six a ratio of 3 to 2 ; and lastly, that the 
sound produced at the ninth part will be distant 
from that at the eighth, and so reciprocally ; a tone, 
in the ratio of 9 to 8, called a Sesquioctave, and 
often the Diezeuctic tone, which furnished the ear 
at least with a common measure for the greater 
intervals. 

But we are to note, that the, system of Pythagoras 
was not completed, till, by the very artful contrivance 



20 



HISTORY OF THE SCIENCE 



Book I. 



of two tetrachoi'ds, to be used alternately, as the 
nature of the melody might require, a division of the 
tone between a and b was effected. By this an 
interval of a Hemitone was introduced into the sys- 
tem, with which no one section of the chord, supposing 
it to be divided into twelve parts, would by any 
means coincide : with great ingenuity therefore did 
Euclid invent that famous division the Sectio Canonis, 
by means whereof not only the positions of the several 
sounds on a supposed chord are precisely ascertained, 
but a method is suggested for bringing out those 
larger numbers, which alone can shew the ratios of 
the smaller intervals, and which therefore make a 
part of every representation that succeeding writers 
have given of the immutable system. 

The Sectio Canonis of Euclid is a kind of appendix 
to his Isagoge, or Introductio Harmonica, containing 
twenty theorems in harmonics. Nevertheless the 
title of Sectio Canonis was by him given to the fol- 
lowing scheme of a supposed chord, divided for the 
purpose of demonstrating the ratios of the several 
intervals thereby discriminated, which scheme is 
inserted at the end of his work. 

SECTIO CANONIS OF EUCLID. 
.-B 



Nete hyperboleon. 

Nete diezeugmenon. 
Nete syneniinenon. 


M- 

N- 


-E 

H 
-Z 


Paranete hyperboleon 
Trite hyperboleon. 


Paramese. 


X- 


-K 


Trite diezeugmenon. 


Mese. 


" 


-D 


* Trite synemmenon. 




K- 


- 


Meson diatonos. 




0- 


- 


Parhypate meson. 


Hypate meson. 


- 


-e 






G- 


_ 


Hypaton diatonos. 



Hypate gravis. 



Proslambanomenos. 



Parhypate hypaton. 



L 



The foregoing canon or scheme of a division is 
introduced by a series of theorems, preparatory to an 
explanation of it, which explanation is contained in 
Theorems XIX and XX ; the first of these refers to 
the immoveable sounds, that is to say, Proslamliano- 
menos, and the other sounds to the left of the line, 



and the latter to the moveable, which are Parhypate, 
and the rest on the right thereof; the sum of which 
two species composed the great or immutable system. 

Theorem XIX directs the adjustment of the canon 
for the Stabiles or immoveable sounds, and that in 
the manner following : — 

' Let the length of the canon be A B, and let it be 
' divided into four equal parts at G D E, therefore 

* B A, as it will be the gravest sound, will be the 
' sonus bombus. Farther, A B is supertertius of G B, 
' therefore G B will sound a diatessaron to A B, 
' towards the acumen, and A B is Proslambanomenos ; 
' wherefore G B will be Hypaton Diatonos. Again, 
' because A B is duple of B D, the former will sound 
'a diapason to the latter, and B D will be Mese. 
' Again, because A B is quadruple of E B, E B will 
' be Nete Hyperboleon ; therefore G B is divided 
' twofold in Z, and G B will be duple of Z B, so as 
' G B will sound to Z B the interval of a diapason, 
' wherefore Z B is Nete Synemmenon. Cut off from 
' D B a third part D H, and D B will be sesquialtera 
' to H B, so as for this reason D B will sound to H B 
' the interval of a diapente, therefore H B will be 
'Nete diezeugmenon. Farther, make H O equal to 
' H B, therefore Q B will sound a diapason to H B, 

* so that B will be Hypate meson. Again, take the 
'third part of 9 B, 6 K, and then 6 B will be 
' sesquialtera to K B, so that K B will be Paramese. 
' Lastly, cut off L K equal to K B, and then L B will 
' be Hypate the most grave, and thus all the immove- 
' able sounds will be taken in the canon.' 

Theorem XX contains the following directions 
respecting the Mobiles or moveable sounds : — 

' Divide E B mco eight parts, of which make E M 
' equal to one, so as M B may be superoctave of E B. 
' And again, divide M B into eight equal parts, and 
' make one of them equal to N M, therefore N B will 
' be a tone more grave than B M, and M B will be a 
' tone graver than BE; so as N B will be Trite 
' hyperboleon, and M B will be Paranete hyperboleon 
' diatonos. Farther, divide N B into three parts, and 
' make N X equal to one of them, so as X B will be 
' supertertius of N B, and the diatessaron will be pro- 
' duced towards the grave, and X B will be Trite 
' diezeugmenon. Again, taking half of X B, make X O 
' equal to it, so as for this reason B will give a 
' diapente to X B, wherefore B will be Parhypate 
' meson ; then make P equal to B, * so as P B 
' will be Parhypate hypaton. Lastly, take the fourth 
' part of G B, G R, and R B will be Meson diatonos.* 

CHAP. V. 

The Sectio Canonis of Euclid, in the judgment of 
the most eminent writers on harmonics, was the first 
essay towards a determination of the ratios by the 
supposed division of a chord ; and, assuming the 
proportions of the diapason, diapente, diatessaron, 

* In the Canon O P is not equal to O B but to O X, and Meibomius, 
■with all his care, has made a mistake, which the following page, to go no 
farther, furnishes the means of rectifying ; for observe, that in the Canon 
of Aristides Quintilianus, which has the numbers to it, Trite diezeug- 
menon, marked X in that of Euclid, is 3888, and Parhypate hypaton 
marked P in that of Euclid also, is 7776, which is just double the former 
number, the consequence whereof is evident. 



Chap. V. 



AND PRACTICE OF MUSIC. 



21 



cliezeuctic tone, and limma, as laid down by the 
Pythagoreans, the division will be found to answer 
to the ratios : yet this does not appear by a bare 
inspection, but can only be proved by an actual 
admeasurement of" the several intervals contained in 
the canon. Now as whatever is geometrically divi- 
sible, is also divisible by numbers, succeeding writers 
in assigning the ratios of the intervals have taken the 
aid of the latter, and have applied the numbers to 
each of the sounds, as they result from a division of 
the canon. How they are brought out will hereafter 
be made appear. 

But here it is necessary to add. that the Sectio 
Canonis of Euclid, perfect in its kind as it may seem, 
is supposed to have received some improvement from 
Aristides Quintilianus, at least with respect to the 
manner of dividing it ; for this we have the testimony 
of Meibomius, who speaks of a canon of Aristides, 
which had been once extant, but was perished, or at 
least was wanting in all the copies of his work : and 
which he his editor had happily restored. The fol- 
lowing is a representation of the Canon, with the 
numbers annexed : — 

-B 



Nete hyperboleon. 
Hyperbol. diatonos. 

Trite hyperboleon. 
Nete diezeugmeuon. 

Nete synemmenon. 
& diezeiigm. diatonos. 
Trite diez. & Syn. diat 

Paramesos. 

Trite synemmenon. 
Mese. 



Meson diatonos. 

Parhypate meson. 
Hypate meson. 

Hypaton diatonos. 

Parhypate hypaton. 
Hypate hypaton. 

Proslambanomenos. 



D. 


2304 


1. 


2592 


m. 
G. 


2916. 
3072. 


F. 


8456 


n. 


3888. 


1. 


4096. 


0. 


4374 


C. 


4608. 



P. 5184. 

q. 6832. 
H. 6144. 

E. 6912. 

- r. 7776. 

- K. 8192. 

A. 9216. * 



• The division of Euclid aprrees with that of Aristides as to the manner 
of obtaining the standing, but differs as to some of the moveable chords, 
for Euclid finds the Trite diezeugmenim, by setting off towards the grave 
a diatessaron from the Trite hyperboleon; he next finds the Parhypate 
meson, by setting off towards the grave a diapente from the Trite diezeug- 
menon, which might be easier found by setting down a diapason from the 
Trite hyperboleon. He also finds the Parhypate hypaton by making O P 



It does not appear whether the numbers were 
originally part of the canon, or whether they were 
inserted by Meibomius. However, from several 
passages in Ptolemy, particularly in Book I. Chap. 10, 
where he demonstrates the ratio of the limma, we 
meet with the number 2048, which is the half of 4096, 
1944, the half of 3888, and others, which shew the 
antiquity of this method of numerical division. 

The following is an explanation of the canon as 
given by Meibomius, in his notes on Aristides Quin- 
tilianus, page 312, et seq. ; — 

' The standing sounds are first set down in the 
' division of the canon, and after them the moveable 
' ones ; we have marked the standing sounds by 
' capital letters, and to these are added the moveable 
* ones. The Hypaton diatonos and the rest are 
' marked by the small letters. They are thus to be 
' taken : — 

' I. Proslambanomenos, A B, which is the whole 
' length of the chord or line. 

' II. Mese, C B, half thereof. 

'III. Nete hyperboleon, D B, the fourth part of 
'the whole chord. 

' IV. Hypaton diatonos, E B, three fourths thereof. 

' V. Nete synemmenon, P B, the said three fourths, 
'E B, divided into two equal parts. 

' VI. Nete diezeugmenon, Gr B, two thirds of half 
' the chord, that is one third of the whole chord ; 
' but this may be perceived by multiplying an half 
' by two thirds, thus, ^ 1 1 5. 

' VII. Hypate meson, H B, two thirds of the whole 
'chord, or tlie two thirds, G B, of the half chord 
' twice set off, which chord therefore we take in the 
' opening of the dividers, and set off twice. 

'VIII. Paramesos,. I B, (one third I H, being 
' taken out of the two thirds H B of the whole chord) 
' is two thirds of two thirds of the whole. 

' IX. Pypate hypaton, K B ; two thirds I B of the 
' two thirds H B twice set off. 

' In order to assume the lesser intervals, the fol- 
' lowing method must be made use of : — 

' I. The 4th part D B of the whole chord being 
' divided into eight equal parts, I set off 1 below 
' D equal to one of those parts, and 1 B will be 
' Paranete hyperboleon. 

' II. Trite hyperboleon m B is assumed in the 
' same manner, viz., by dividing the line 1 B into 
' eight equal parts, and taking 1 m equal to one of 
'them out of 1 A. 

' III. Trite diezeugmenon, and the following 
'moveable sounds, are easily to be assumed in the 
' same manner.' 

Besides the foregoing explanation of the canon, 
Meibomius has given the following, which he calls a 

equal to O X, that is by setting off a diapason towards the grave from the 
Trite diezeugmenon, for he had made O X equal to half X B, and conse- 
quently twice X O P must be equal to X B. And lastly, he finds the 
Meson dlatnnos by setting off a diatessaron towards the acute from the 
Hypaton diatonos, whereas all the four sounds, as wl-U as the other 
moveable ones, are found in Aristides, by a division into eight parts, that 
is by setting offsesquioctave tones. It seems, however, upon the whole, 
that Aristides followed the division of Euclid, but neither of these can 
answer to the Aristoxenian principles, for this reason, that the Sectio 
Canonis both of Euclid and Aristides refer to those arithmetic and har- 
monic ratios, which are discernable in the proportions of Pythagoras, 
whereas Aristoxenus rejected the criterion of ratios, and maintained that 
the measure of intervals was determinable by the sense of hearing only. 



oo 



HISTORY OF THE SCIENCE 



Book I. 



Notable Theorem, and says of it that it is very useful 
in facilitating the section of the canon. 

' The difference between two lines that are to each 

* other in a sesqnitertia ratio, being divided into two 
' equally, will give the eighth part of the greater line. 

C 

A — 1 — I — \ — I — I — i — I — B 
D — i — I — I — I — 1 — E 

' A B is sesquitertia to D E ; C B is the excess of 
' A B above D E, C B divided into two equally will 
^ ' exhibit the eighth part of A B. 

' We shall see the same in the section of our canon. 
' Let the line G B be divided into eight equal parts, 
'I say the part G D thereof will contain two eighth 
' parts ; so that this need only be divided into two 
' equally, as appears by this following demonstration ; 
' for as G B is sesquitertia to D B, that is as 4 to 3, 
'if G B be divided into twice four parts, that is 
' eighths, D B will contain six of those eighths, and 
'consequently D G two eighths, and its half will 

* contain one eighth. Also if F B is to be divided 
' into eight equal parts, its part F 1 need be divided 
' only into two equally, in order to have one eighth 
'part, which I set off from F to n, to find the excess 
' of the tone above F B. The same method may be 
' used in the following ones. 

' Moreover, the Meson diatonos, and the other two 
' moveable chords may also be obtained by the follow- 
' ing method, namely. Meson diatonos, by setting off 

* the part 1 B, twice from B ; Parhypate meson, by 
' setting off the part m B, twice ; Parhypate hypaton, 
' by setting off the part n B, twice. 

' But whatsoever is here shown in lines may, by 
' the ingenuity of the intelligent reader, be easily 
' applied in finding out the numbers.' 

The canon of Aristides Quintilianus, with the 
numbers affixed, supposes the whole chord to con- 
tain 9216 parts, and being struck open, to produce 
the most grave sound of the system, viz., A ; the in- 
terval then of a tone at J], the next sound in suc- 
cession, as being in the proportion of 8 to 9 to A, will 
require that the chord be stopped at 8192 ; and, 
supposing it to answer, we may with the utmost 
propriety say, that the ratio of a tone is as 9216 is 
to 8192, or in other words, that j^ is produced at 
8192 of those parts whereof the chord A contains 
9216 ; and these two numbers will be found to bear 
the same proportion to each other as those of 9 and 
8. Again, for the diapason a, the number is 4608, 
which is just the half of 9216, as 6 is the half of 12 ; 
for the diatessaron D, the number is 6912. which is 
three fourths of 9216 ; and for the diapente E, the 
number is 6144, which is two thirds of 9216. Hence 
It appears that the numbers thus taken for the tone, 
or for the consonances of the diatessaron, and the 
diapente, or their replicates, as often as it may be 
;;hought necessary by the reiteration of an octave, or 
any less system, to extend that of the bisdiapason, 
answer in like manner to the ratios of 9 to 8, 6 to 
12, 12 to 9, and 12 to 8, in the primitive system. 

These proportions we are told will be the result 
of an actual division of a string, which whoever is 



desirous of making the experiment, is hereby enabled 
to try ; though, by the way, it is said by Meibomius 
that for this purpose one of two ells in length will 
be found necessary. Nevertheless, by the help of the 
principles already laid down, namely, that the dia- 
pason has a ratio of 2 to 1, the diapente of 3 to 2, 
the diatessaron of 4 to 3, and the tone of 9 to 8, 
which are to be considered as data that all harmonical 
writers agree in, it is very easy, by means of arith- 
metic alone, to bring out the numbers corresponding 
to the intervals, in the diatonic bisdiapason. Bon- 
tempi has given a very particular relation of the 
process in an account of the method taken by the 
ancients for that purpose ; and immediately after, an 
exhibition of that system with the proper numbers in 
the following scale : — 



5 r2304. 



aa 



f 



3456. Nete synem. 

Tone 
3888. Paranete synem. c 

Tone 
4374. Trite synem. b 

Hemitone 
4608. Mesa a 



d^ p 



m 



G 



Nete hyperb. 

Tone 
Paranete hyperb. 

Tone' 
Trite hyperb. 

Hemitone 
Nete diezeug. 

Tone 
Paranete diezeug. 

Tone 
Trite diezeug. 

Hemitone 
Paramese 

Tone 
Mese 

Tone 
Lychanos meson 

Tone 
Parhypate meson F 

Hemitone 
Ilypate meson E 

Tone 
Lychanos hypat. D 

Tone 
Parhypate hypat. C 

Hemitone 
Hypate hvpaton h 

Tone 
Proslambano. A* 



His description of the process is in these words : 
The numbers affixed to the several chords in the 
system draw their origin from the sesquioctave pro- 
portion, which is the relation that the second chord 
bears to the first ; and, proceeding from the acute 
to the grave, the numbers will be found to be in the 
ratio of subsesquioctave, subsesquitertia, subsesqui- 
altera, and subduple. But to be more particular : — 

' As the third chord was to be the sesquioctave 
of the second, and as the second had not an eighth 
part, the ancients multiplied by 8, and set down the 
number produced thereby : if the fourth chord was 
to be the sesquitertia, they multiplied the numbers 
by 3 ; If it was to be sesquialtera the numbers were 
doubled ; and if by chance there were any fractions, 
they doubled them again to find even numbers, and 
so they went on : but as all these operations belong 
to arithmetic, and of course must be known, there 
is no necessity to explain them farther. 

' However, as all this is different from any practice 

• Bontemp. 97. 



Chap. V. 



AND PRACTICE OF MUSIC. 



23 



'• in the modern music, in order that those who are not 

' perfectly versed in arithmetic may understand the 

' I'oandation of this science, itwiii nut be amiss here to 

' expLain it. You must then know, that as harmonic 

music was subordinate to arithmetic, the ancients 

shewed only the intervals by numbers arising from 

the measures they had found out by experiments 

upon tlie monochord. 

' When they wanted therefore to demonstrate in 

the constitution of the system what chord was either 

' double, or sesquialtera, or sesquitertia, or sesqui- 

octave to another by arithmetical numbers, they 

■ used multiplication, or the doubling of the nimibers, 
in order that they might rise by degrees one above 
the other. They began from the most acute chord, 

■ which is the Nete hyperboleon, going on as far as 
the Trite synemmenon ; which operation is demon- 
strated by the following columns of numbers : — 



aa 

g 

f 

e- 

d 

c 

h 



1 

8 
9 



2 
64 

72 
81 



3 

192 
216 
243 
-256 
288 
324 



576 

648 
729 
768 
864 
972 
-1024 



o 

1152 
1296 
1458 
1536 

1728 
1944 
2048 

2187 



6 

2304 
2592 
2916 
3072 
3456 
3888 
4096 
4374* 



' The method which they used in these multipli- 
cations and reduplications was this ; as g was to be 
sesquioctave of aa, and f sesquioctave of g ; and as 
g had not an eighth part, to find it they multiplied 
aa and g by 8 ; from which multiplication the 
numbers of the second order were produced, and 
they put down 81 sesquioctave of 72. As e was to 
be sesquitertia of aa, and had not a third part, they 
multiplied all the second order by 3 ; from which 
multiplication was produced the third order, and 
there came out the number 256, sesquitertia of 192; 
in like manner d was found to be sesquitertia of g, 
and c of f. 

' As h was to be sesquitertia of e, and had not a 
third part, they multiplied all the third order by 3, 
from which was produced the fourth order, and 
there came out 1024, sesquitertia of 768 ; as b was 
to be sesquialtera of f, there came out fractions, to 
avoid which all the fourth order was doubled, and 
so the fifth order was produced ; and there was the 
number 2187, sesquialtera of 1458. 

' In a word, give me leave to repeat again this 
operation, with common explications for those who 
are quite unacquainted with the rules of arithmetic; 
by multiplying eight times 8 they had 64 for aa ; 
by multiplying nine times 8 they had 72 for g ; and 
adding to 72 the number nine, they had 81 for f. 

* The sesquitertia, which is nothing but the pro- 
portion 4 to 3, constituting the diatessaron from e 
to aa, was produced by giving to aa three times 64, 
which made 192, and to e four times 64, which made 
256. 

' That of d to g was produced by giving to g three 
times the number 72, which made 216 ; and to d 
four times the same, which made 288. 

* Bontenip. 98. 



' That of c to f was produced by giving to g three 
' times 81, which made 243 ; and to c four times the 

* same, which made 324. 

' That of J] to e was produced by giving to e three 
' times 256, which made 768 ; and to Jj four times 
' the same, which made 1024. 

' The sesquialtera, which is nothing but the pro- 
' portion 3 to 2, constituting the diapente from b to f, 
' was produced by giving to f twice 729, which made 
' 1458 ; and to b three times the same, which made 
' 2187. 

' Finally, in order that this kind of numbers might 

* do for the chords of the chromatic and enharmonic 
' genera ; to avoid fractions they doubled all the fifth 
' order, and thereby brought out the sixth ; so that 
' the second order is the produce of the first multi- 
' plied by 8 ; the third order is the produce of the 
' second multiplied by 3 ; the fourth order is the 
' produce of the third multiplied by 3 ; the fifth 
' order is double the fourth, and the sixth double 

* the fifth ; and the numbers of the sixth order are 
' the same as those of the tetrachords Hyperboleon, 
' Diezeugmenon, and Synemmenon, in the foregoing 
' scale. 

' There is besides these the Mese, the number of 
'which is 4608, which is the double of 2304, the 

* number of the Nete hyperboleon, because there is 
' between the one and the other chord the interval of 
' a diapason. 

' The number 5184 of the Lychanos meson is twice 
' the number 2592 of the Paranete hyperboleon, be- 
' cause there is between them the same interval of 
' the diapason ; and so the following numbers towards 
' the grave are double to the numbers belonging to 
' the acute chords, following from the Paranete hyper- 
' boleon in succession ; because there is between them 
' all, in their respective degrees, the usual interval of 
' the diapason. As the sounds of the diatonic genus 
' have their numbers, so likewise have the sounds of 
' the other genera numbers, which are peculiar to 
' them, except the Nete hyperboleon, the Nete die- 

* zeugraenon, the Nete synemmenon, the Paramese, 
' the Mese, the Hypate meson, the Hypate hypaton, 
' and the Proslambanomenos, whose numbers are 
' common to all the genera, as their sounds are 
' fixed. Every thing relating to them may be seen 
' in their respective systems.' 

It is to be remembered, that it was for the purpose 
of explaining the doctrine of the genera that the fore- 
going enquiry into the proportions of the intervals 
was entered into ; this enquiry respected the diatonic 
series only, and the proportions thereby ascertained 
are the diapason, diapente, diatessaron, and tone ; 
besides these, another interval, namely, that whereby 
the diatessaron exceeds the ditone, and which is 
generally supposed to be a semitone, for now we 
shall use the appellation given to it by the Latin 
writers, has been adjusted, and in general shewn to 
have a ratio of 256 to 243. 

But here it is necessary to mention, that the ratio 
of this interval was a subject of great controversy 
with the ancient musicians. What were the senti- 
ments of Pythagoras about it we are nowhere told ; 



'i4 



HISTORY OF THE SCIENCE 



Book I. 



though if it he true that he constituted the diatessaron 
ill tiie ratio of 4 to 3, and made each of the tones 
contained in it sesquioctave, it will follow as a conse- 
quence, that the interval necessary to complete that 
system must have been in the ratio of 256 to 243 : 
this is certain, that Boetius, and the rest of the 
followers of Pythagoras, deny the possibility that 
it can consist in any other : but this is a method of 
deduction by numerical calculation, and the appeal 
is made to our reason, which, in a question of this 
nature, say some, has nothing to do. 

The first who asserted this doctrine, and he has 
done it in terms the most explicit, was Aristoxenus, 
the disciple and successor of Aristotle ; he taught 
that as the ear is the ultimate judge of consonance, 
w'e are able by the sense of hearing alone to de- 
termine the measure both of the consonants and 
dissonants, and that both are to be measured or 
estimated, not by ratios but by intervals.* The 
method he took was this, he considered the diapason 
as consisting of the two systems of a diatessaron and 
diapente; it was easy to discover the difference 
between the two to be a tone, which was soon found, 
allowing the ear to be the judge, to be divisible 
into semitones. These two latter intervals being 
once recognized by the ear, became a common mea- 
sure, and enabled him to determine the magnitude 
of any interval whatever, which he did by various 
additions to, and subductions from, those --bove 
mentioned ; in like manner as is practised .. > the 
singers of our times, w'ho by an instantaneous effort 
of the voice, are able not only to utter a fourth, a 
fifth, a greater or lesser third, a tone, a semitone, and 
the rest, but by habit and practice are rendered 
capable of separating and combining these intervals 
at pleasure, without the assistance of any arithmetical 
process or computation. 

It must be confessed that there seems to be a kind 
of retrogradation in a process which directs the 
admeasurement of a part by the whole, rather than 
of the whole by a part, as this evidently does ; but 
notwithstanding this seeming irregularity, the ad- 
herents to the former method are very numerous. 

The principles on which these two very different 
methods of judging are founded, became the subject 
of great contention ; and might perhaps give rise to 
another question, as extensive in its latitude, as im- 
portant in its consequences, namely, whether the 
understanding or the imagination be the ultimate 
judge of harmony and beauty ; or, in other words, 
what are the peculiar offices of reason and sense in 
subjects common to them both. The consequence of 
this diversity of opinions, so far as it related to music, 
was that, from the time of Aristoxenus the musicians 
of earlier times, according as they adhered to the one 
or the other of these opinions, were denominate 
either Pythagoreans or Aristoxeneans, by which appel- 
Jations the two sects continued for a long time to be 
as much distinguished as those of the Peripatetics 
and Stoics were by their respective names.f 

* Wallis Appendix de Veterum Harmonica, Quarto, pag. 290. 

+ Porphyrii in Ptolcmoei Harmonica Commentarius, Edit. Wallisii, 
pag. isy. 



But it seems that as well against the one as tlie 
other of the positions maintained by the two parties, 
there lay strong objections ; for as to that of Pytha- 
goras, that reason, and not the hearing, is to determine 
of consonance and dissonance, it was erroneous in 
this respect, it accommodated harmonical proportions 
to incongruous intervals ; and as to Aristoxenus, he, 
by rejecting reason, and referring all to sense, ren- 
dered the very fundamentals of the harmonical science 
incapable of demonstration. The several offices of 
reason and sense, by which we are here to under- 
stand the sense of hearing, are very accurately 
discriminated by Ptolemy, who undertook the task 
of reviewing this controversy ; and the method he 
took to reconcile these two militant positions will be 
shewn at large in that extract from his treatise, 
which we mean hereafter to exhibit in its proper 
place ; the only question at present to be discussed, 
is that relating to the measure of the diatessaron. 
That it exceeded two of those tones, one whereof 
constituted the difference between the diapente and 
diatessaron, was agreed by both parties ; but the 
me-asure of this excess was the point in debate : the 
Pythagoreans asserted it to be an interval in the ratio 
of 256 to 243, to which, for want of a better, they 
gave the name of Limma ; the Aristoxeneans, on the 
other hand, contended that it was neither more nor 
less than a semitone. The question then became. 
Whether is the system of a diatessaron compounded 
of two tones and a limma, or of two tones and a 
semitone ? 

Ptolemy has entered into a very minute examin- 
ation of this question ; and though he professes to be, 
as he certainly is, an impartial arbiter between the 
two sects, and is very free in his censures on each ; 
yet has he most irrefragably demonstrated tlie Pytlia- 
gorean tenet to be the true one. The method he has 
taken to do it may be seen in the first book of his 
Harmonics, chap, x., but the following process will 
enable any one to judge of the force of his reasoning. 

Let the number 1536, which it is said is the 
smallest that will serve the purpose, be taken, and 
after that 1728, its sesquioctave, to express a tone ; 
and again, the sesquioctave of 1728, which is 1944, 
for another tone ; the numbers 1536 and 1944 will 
then stand for the ditone. The diatessaron is sesqui- 
tertian, or as 4 to 3, it is therefore necessary to seek 
a number that shall contain four of those parts, of 
which 1536 is three, and this can be no other than 
2048 ; so that the interval whereby the diatessaron 
exceeds the ditone, is in the ratio of 2048 to 1944 ; 
or, in smaller numbers, as 256 to 243. But to judge 
of the magnitude of this interval, let the sesquioctave 
of 1944, 2187 be taken for a third tone ; it will then 
remain to enquire the difference between the two 
ratios 2187 to 2048, and 2048 to 1944, and the 
former will be found the greater ; for 2187 exceeds 
2048 by more than a fifteenth, and by less than a 
fourteenth part ; whereas 2048 exceeds 1944 by more 
than a nineteenth, and by less than an eighteenth ; 
and consequently that which, together with the ditone 
completes the diatessaron, is the lesser part of the 
third tone. 



Chap. VI. 



AND PRACTICE OF MUSIC. 



25 



Salinas calls this demonstration of Ptolemy an 
excellent one, as most undoubtedly it is, and in his 
Treatise de Musica, lib. II., cap. xx., exhibits it in 
the following diagram : — 

DI A TESSA EON. 



-^^ 



GREATER TONE. GREATER TONE. GREATER TONE. 



APOTOME. LIMMA. 
2187 20-18 1941: 



1728 



To this lesser part of the third tone 2048 to 1944, 
or in lesser numbers, 256 to 243, was given the 
name of the Limma of Pythagoras ; though some 
writers, and those of the Pythagorean sect, scrupled 
not to term it a Diesis. The greater part of the tone 
resulting from the above division was termed Apo- 
tome, a word signifying the residue of what remains 
of a line after part has been cut off. 

Salinas, lib. II. cap xx., remarks, that both the 
theoretic and practical musicians among the moderns 
are deceived in thinking that the Apotome of the 
ancients is that interval, which, in such musical in- 
struments as the organ, and others of the like kind, 
is found between J] and b ; or, in other words, that 
the interval between J] and b is greater than that 
between ]-| and c, and than that between b and a ; 
when, says he, the thing is quite the reverse, and may 
be proved by the ear. 

Farther, lib. II. cap. x., he observes of the Limma, 
that as Pythagoras had divided the diapason into two 
diatessarons and a sesquioctave tone, he discovered 
that the diatessaron was capj,ble of a like method of 
division, namely, into twoicontinued tones, and that 
interval which remained after a subtraction of the 
ditone from the diatessaron. And this which he 
calls a semitone, is that which Pto.emy calls the 
semitone accepted and best known ; and of which 
Plato in Timeus makes mention ; when having fd- 
lowed the same proportion, he says that all the duple 
ratios were to be filled up with a sesquitertias and a 
sesquioctave, and all the sesquitertias with sesqui- 
octaves, and the interval 256 to 243. He adds, that 
Cicero mentions this semitone in his book de Uni- 
versitate, as does Boetius in all his divisions ; and 
that there were none of the ancients to whom it was 
not known, for that all the Philosophers ^embraced 
the Pythagorean traditions of music. The same 
author adds, that the Pythagorean Limma was 
esteemed by the Greeks, particularly Bacchius and 
Eryennius, \o be irrational ; and that Plato himself 
dared not to call it a proportion, for the reason, as 
he conceives, that it was n(jt superparticular. 

Hitherto we have spoken of the tone in general 
terms, and as an interval in a sesquioctave ratio, such 
as constitutes the difference between the diatessaron 
and diapente, and it is said that the Pythagoreans 
acknowledged no other ;* it is nevertheless necessary 
to mention that there is a lesser interval, to which 
the appellation of tone is also given ; the ratio 
kvhereof is that of 10 to 9. It is not sufficiently 
dear who it was that first discovered it, but, from 

» Salinas de Musica, lib. II., cap. 17. Boet. lib. IV., cap. 5. 



several passages in the harmonics of Ptolemy,f it 
should seem that Didymus, an ancient musician, 
whom he frequently takes occasion to mention, was 
the first that adjusted its ratio. 

Dr. Wallis, who seems to have founded his opinion 
on that of Salinas, and certainly entertained the 
clearest conceptions of the subject, has demonstrated 
very plainly how both the greater and lesser tone 
are produced ; for assuming the diapente to be in the 
ratio of 3 to 2, or which is the same, the numbers being 
doubled, 6 to 4; by the interposition of the arithmetical 
mean 5, he shows it to contain two intervals, the one 
in the ratio of 6 to 5, the other in that of 5 to 4.| 



DIAPENTE. 



Semiditone 



Ditone 



Sesquialtera. 



The latter of these, which constituted the ditone 
or greater third, subtracted from the diapente, left 
that interval in the ratio of 6 to 5, which by the 
Greeks was called a Trihemitone, and by the Latins 
a deficient, or semi ditone, but by the moderns a 
lesser or flat third. 

The consideration of the semiditone will be here- 
after resumed ; but as to the ditone it had a super- 
particular ratio, and consequently would not, any 
more than the diapente, admit of an equal division. § 
In order therefore to come at one that should be the 
nearest to equality, Dr. Wallis doubled the terms 5, 
4, and thereby produced the numbers 10, 8, which 
have the same ratio. Nothing then was wanting 
but the interposition of the arithmetical mean 9, 



DITONE. 



Greater Tone, j 

8 _ 9 

Sesquioctave | 



Lesser Tone. 
Sesquinonal 



10 



Sesquiquarta. 



I 



and a division was effected which produced the 
greater or sesquioctave tone, 9 to 8, and the lesser or 
sesquinonal tone, 10 to 9.j| 

CHAP. VL 

Having thus adjusted the proportions of the greater 
and lesser tone, it follows next in order to consider 
the several divisions of each, the first and most obvious 
whereof is that of the semitone ; but here two things 
are to be remarked, the one that the adjunct semi, 
though it may seem to express, as it does in most in- 
stances, the half of any given quantity, yet in musical 

+ Lib. II., cap. I.'?, 14. Salinas, lib. II , cap. 17. 

t Wallis, Append, de Yet. Harm, quarto, paj?. 322. 

§ That a superparticular is incapable of an equal di%-ision is clearly 
demonstrated by Hoetius, lib. III., cap. 1, and must be considered as a 
first principle in harmonics. Vide Macrobius in Somnium Scipioiiis, 
lib. II.. cap. 1. 

II Wallis Append, de Vet. Harm, quarto, pag. 323. Salinas de Musica, 
lib. II., cap. 17. 



26 



HISTORY OF THE SCIENCE 



Book T. 



language has a signification the same with deficient 
or incomplete : the other is that although as the lesser 
is always contained in the greater, and consequently 
the tone comprehends the semitone and more, yet the 
semitone is not, nor can be found in, or at least can- 
not be extracted from, or produced by any possible 
division of the tone. The Aristoxeneans, who asserted 
that the diatessaron consisted of two tones and a half, 
had no other way of defining the half tone, than by 
taking the ditone out of the diatessaron, and the 
residue they pronounced to be a hemitone, as it 
nearly is ; and the Pythagoreans, who professed the 
admeasurement and determination of intervals by 
ratios, and not by the ear, were necessitated to pro- 
ceed in the same way ; for after Pythagoras had 
adjusted the diezeutic tone, and found its ratio to be 
sesquioctave, or as 9 to 8, it nowhere appears that he 
or any of his followers proceeded to a division of that 
interval into semitones, and indeed it is not in the 
nature of the thing possible to effect any such division 
of it by equal parts. Ptolemy, who, so far as regards 
the method of defining the intervals by their ratios, 
must be said to have been a Pythagorean, has had 
recourse to this method of subtracting a lesser inter- 
val from a greater for adjusting the proportion of the 
Limma ; for after having assumed that the ratio of 
the diatessaron was sesquitertia, answering to the 
numbers 8 and 6, or which is the same, 4 to 3, he 
measures out three sesquioctave tones, 1536, 1728, 
1944, 2187, and subtracts from them the diatessaron 
2048 to 153G, and thereby leaves a ratio of 2187 to 
2048, which is that of the apotome ; the limma 2048 
to 1944, then remains an adjunct to the two sesqui- 
octave tones 1728 to 1536, and 1944 to 1728 ; and 
the ratio of 2048 to 1536 is 8 to 6, or 4 to 3 ; and 
would we know the ratio of 2048 to 1944, it will be 
found to be 256 to 243, for eight times 256 is 2048, 
and eight times 243 is 1944.* 

And Didymus, who after he had discovered the 
necessity of a distinction of tones into the greater and 
lesser, and found that it required an interval diiferent 
in magnitude from the limma, to complete the dia- 
tessaron, had no way to ascertain the ratio of that 
interval, but by first adjusting that of the ditone ; in 
the doing whereof he also determined that of the 
semitone, for so are we necessitated to call the inter- 
val by which the diatessaron is found to exceed the 
ditone. With respect to this interval, wdiich in the 
judgment of Salinas, is of such importance, that he 
seems to think it the hinge on which the knowledge 
of all instrumental harmony turns ; it seems clearly 
to have taken place of the limma, immediately after 
the discrimination of the greater and lesser tone : 
and there is reason to think it was investigated by 
Didymus in the following manner. First he con- 
sidered the ratio of the diatessaron to be, as has been 
shewn, sesquitertian, or as 8 to 6 ; or, which is the 
same, those nimibers being doubled, 16 to 12. The 
ditone he had demonstrated to be in sesquiquarta 
proportion, as 5 to 4. It remained then to find out 
a number that should contain 5 of these parts, of 

* See the preceding demonstration of the ratio of the Pythagorean 
limma. 



which 12 contained four, and this could be no other 
than 15, and these being set down, demonstrated the 
ratio of the semitone to be 16 to 15. 



DIATESSARON. 



I Ditone | Greater Semitone 

12 1^ . 16 

I Sesquiquarta | Sesquidecimaquinta 



Sesquitertia. 



t 

This interval is also the difference between the 
semiditone 6 to 5, and the sesquioctave tone 9 to 8, 
which, multiplying the extreme numbers by 3, is 
thus demonstrated ; — 



SEMIDITONE. 



Tone 



Greater Semitone j 

15 16 18 

Sesquidecimaquinta | Sesquioctave 



Sesquiquinta, 



t 

But it seems that this interval, so very accurately 
adjusted, did not answer all the combinations of 
which the greater and lesser tones were capable ; nor 
was it adapted to any division of the system, other 
than that which distinguishes the diatonic genus. 
These considerations gave rise to the invention of the 
lesser semitone, an interval so peculiarly appropriated 
to the chromatic genus, that Salinus and Mersennus 
scruple not to call it the Chromatic Diesis ; the 
measure of it is the difference between the ditone 
and semiditone, the former whereof is demonstrated 
to be in sesquiquarta proportion, or as 5 to 4 ; or, 
which is the same, each of those numbers being 
multiplied by 5, 25 to 20, The semiditone is sesqui- 
quinta, that is to say, as 6 to 5 ; or multiplying each 
of those numbers by four, as 24 to 20 ; from a com- 
parison therefore of the semiditone with the ditone, 
it will appear that the difference between them is an 
interval of 25 to 24, the ratio sought, and which is 
the measure of the lesser semitone. 



DITONE 



j Semiditone ) Lesser Semitone 

20 24 

Sesquiquinta ] Sesquivigesimaquarta 



25 



Sesquiquarta 



Salinas remarks that this lesser semitone of 25 to 
24, and the greater one of 16 to 15, compose the 
sesquinonal or lesser, and not the sesquioctave or 
greater tone, between which and the former he 
demonstrates the difference to be a comma, or an 
interval in the ratio of 81 to 80, 

Salinas, IMersennus, and other writers, chiefly 
moderns, speak of a mean semitone in the ratio of 

+ This and most of the diagrams for demonstrating the other intervals 
are taken from Salinas, '.vlio, it is to be remarked, differs from Tnany 
other writers in the order of the numbers of ratios, placing the Sfx:allesJ 
first. 

I Salinas, lib. II. cap. xviii. 

§ Salinas, de Musica, lib. 11 cap. 20 



CUAP. VI. 



AND PRACTICE OF MUSIC. 



27 



loS to 128, which with that greater one of IG to lo, 
completes the sesquioctave tone ; and of another in 
the ratio of 27 to 25, which added to the lesser 
semitone 25 to 24, also makes up the greater or 
sesquioctave tone.*^ Salinas ascribes the invention 
of this latter to Ludovicus Follianus, a very in- 
genious musician of the sixteenth century, of whom 
an account will be hereafter given ; but he says it is 
unfit for harmony : and indeed it does not appear to 
have ever been admitted into practice. Salinas de 
jMusica, lib. III., cap. 7. 

We are now to speak of the Diesis, as being an 
interval less in quantity than a semitone : though it 
is to be remembered that the word as it imports in- 
definitely a Particle, f is of very loose signification, 
and is used to express a great variety of dissimilar 
intervals. Aristotle calls dieses the Elements of 
song, as letters are of speech ; but in this the moderns 
differ from him. Others of the Greek writers, and 
Vitruvius, a Latin, after them, make the diesis to be 
a quarter of a tone, and Salinas less. The Py- 
thagoreans use the word Diesis and Limma in- 
discriminately to express the interval 256 to 243. 
In the subsequent division of the tone into lesser 
parts, the name of diesis has been given sometimes 
to one, and at others to other parts arising from that 
division ; and hence those different definitions which 
we meet with of this interval ; but the general 
opinion touching it is that it is less than a semitone, 
and more than a comma. We will consider it in all 
its variety of significations. 

Boetius, in the third book of his treatise de Musica, 
has related at large the method taken by Philolaus 
the Pythagorean for dividing the tone into nine 
parts, called commas, of which we shall speak more 
particularly hereafter ; according to this division, 
two commas make a diaschisma, and two diaschismata 
a diesis. This is one of the senses in which the term 
diesis is used, but it is not easy to discover the use 
ot this interval, for it does not seem to be adapted 
either to the tetrachord composed of sesquioctave 
tones, or that later one of Didymus, which supposes 
a distinction of a greater and lesser tone ; so that in 
this instance the term seems to be restrained to its 
primitive signification, and to import nothing more 
than a particle ; and Salinas seems to concur in this 
sense of the word when he says that in each of the 
genera of melodies the least interval is called a diesis. 

In other instances we are to understand by it such 
an interval as, together with others, will complete the 
system of a diatessaron. There are required to form 
a diatessaron, or tetrachord in each of the genera, 
tones, semitones, and dieses. In the diatonic genus 
the diesis is clearly that, be it either a semitone, a 
limma, or any other interval, which, together with 
two tones is necessary to complete the tetrachord. 
If with the Pythagoreans we suppose the two tones 
to be sesquioctave, it will follow that the diesis and 
the limma 256 to 2-i3 are one and the same interval ; 
on the other hand, if with Didymus we assign to the 

* Salinas, lib. II. cap. 20, lib. III. cap. 7. Mersen. Harmonic, lib. V. 
De Dissonantii.<, pag. 7. 

t Macrob. in Soran. Scipion. lib. II. cap. 1 



two tones, the different ratios of 10 to 9, and 9 to 8, 
the interval necessary to complete the diatessaron 
will be IG to 15 ; or the difference between the ditone 
in the ratio of 5 to 4, and the diatessaron above 
demonstrated. In short, this suppletory interval, 
whatever it be, is the only one in the diatonic genus, 
to which the appellation of diesis is ever given. 

To the chromatic genus belong two intervals of 
different magnitudes, and the term diesis is common 
to both ; the first of these is that of 25 to 24, men- 
tioned above, and shewn to be the difference between 
the ditone and semiditone, and is what Salinas has 
appropriated to the chromatic genus. Gaudentiiis 
mentions also another species of diesis that occurs in 
this genus, in quantity the third part of a tone,| in 
which he has followed Aristoxenus ; but as all the 
divisions of the Aristoxeneans were regulated by the 
ear, and supposed a division of the tone into equal 
parts, which parts being equal, must necessarily be 
irrational, it would be in vain to seek a numerical 
ratio for the third part of a tone. 

We are now to speak of that other diesis incident 
to the enarmonic genus, to which the term, in the 
opinion of most writers, seems to be appropriated ; § 
for whereas the other diesis obtained that name, only 
as being the smallest interval required in each genas, 
this other is the smallest that any kind of musical 
progression will possibly admit of. Aristides Quin- 
tilianus says, a diesis is as it were a dissolution of the 
voice. II 

According to Boetius, who must everywhere be 
understood to speak the sense of the Pythagoreans, 
the two dieses contained in the tetrachord of the 
enarmonic genus must have been unequal, for he 
makes them to arise from an arithmetical division of 
the limma, 256 to 243. ^ 

Ptolemy has exhibited,** as he has done in each of 
the other genera, a table of the enarmonic genus, 
according to five different musicians, all of whom, 
excepting Aristoxenus, make the dieses to be unequal, 
those of Ptolemy are 24 to 23, and 46 to 45. 

Salinas uses but one enarmonic diesis, which he 
makes to be the difference between the greater semi- 
tone 16 to 15, and the lesser 25 to 24. 



GREATER SEMITONE. 



Lesser Semitone j Diesis 

120 125 128 

I Sesquivigesimaquarta | Supertripartiens 125 | 



S 



esquidecima quinta. 



m 

Which numbers are thus produced, 15 and 16 
each multiplied by 8 will give 120, and 128, for the 
greater semitone ; we are then to seek for a number 
that bears the same ratio to 120, as 25 does to 24, 
which can be no other than 125, so that the ratio of 
the diesis will stand 125 to 128. 

Brossard has applied the term diesis to those signs 

t Ex Vers. Meibom. p-^g. 5. 

§ Boetius lib. II. cap. 23, has given dieses only to the enarmonic. 

II Ex Vers. Meibom. pag. 13. 

ir Boetius, lib. IV. cap. 5. 

** Lib. II. cap. 14. 

tt Salinas, lib II. cap 21. 



28 



HISTORY 01 THE SCIENCE 



Book \. 



or characters used by the moderns to denote the 
several de^irees by which a sound may be elevated 
or depressed above or beneath its natural situation ; 
for the doing whereof he seems to have had no better 
authority than that of the practitioners of his time, 
who perhaps are the only persons entitled to an 
excuse for having given to the sign the name of the 
thing signified. He professes to follow Kircher, 
when he says that there are three sorts of dieses, 
namely, the lesser enarmonic or simple diesis, con- 
taining two commas or about a quarter of a tone ; 
the chromatic or double diesis, containing a lesser 
semitone, or nearly four commas, and the greater 
enarmonic diesis, containing nearly three fourths of 
a tone, or from six to seven commas ; but this defi- 
nition is by much too loose to satisfy a speculative 
musician. 

These are all the intervals that are requisite in the 
constitution of a tetracliord in any of the three 
genera : it may not be improper however to mention 
a division of the tone, invented perhaps rather as an 
essay towards a temperature, than as necessary to the 
perfection of the genera ; namely, that ascribed by 
Boetius, and others to Philolaus, by which the tone 
was made to consist of nine parts or commas. 

The account of this matter given by Boetius is 
long, and rather perplexed; but Glareanus,*^ who 
has been at the pains of extracting from it the history 
of this division, speaks of it thus : ' A tone in a ses- 
' quioctave ratio is divided into a greater and lesser 
' semitone ; the greater was by the Greeks called an 
'apotome, the lesser a limma or diesis, and the 
'difference between these two was a comma. The 
' diesis was again divided into diaschismata, of which 
'it contained two; and the comma into schismata, 
' two whereof made the comma.' The passage, to give 
it at length, is thus : — 

' It is demonstrated by musicians, for good reasons, 
that a tone cannot be divided into two equal parts, 

* because no superparticular ratio, such as is that of a 

* tone, is capable of such a division as Divus Severinus 
'Boetius fully shews in his third book, chap, i., a 
' tone which is in a sesquioctave ratio is divided into 
' a greater and lesser semitone. The Greeks call the 

* greater semitone an apotome, and the lesser a diesis 
'or limma; but the lesser semitone is divided into 
'two diaschismata. The excess whereby a greater 
' semitone is more than a lesser one is called a comma, 
' and this comma is divided into two parts, which are 
'called schismata by Philolaus. This Philolaus, 

* according to Boetius, gives us the definitions of all 
'those parts, A diesis, he says, is that space by 
'which a sesquialteral ratio or diatessaron exceeds 

* two tones ; and a comma is that space whereby 
' a sesquioctave ratio is greater than two dieses, that 
' is than two lesser semitones. A schisma is that 

half of a comma, and a diaschisma is the half of a 
'diesis, that is of a lesser semitone; from which 
'definitions and the following scheme you may easily 
' find out into how many diaschismata, and the other 
' smaller spaces, a tone may be divided, for the same 

* Boetius shews that it can be done many ways in his 

' Dodecachordon, lib. I. cap. x. 



' treatise, lib. Ill, cap. viii., from whence we have 
' taken these descriptions. It is to be observed that 
' the name of diesis is proper in this place ; but when, 
' as the ancients have done, we give it to the enar- 
' monic diaschisma, it is improper : — 

mi 1] 4096 



H 
^ 




O 




^1 


H 


H 


O 


> 


fM 


< 


< 


^ 




U 




O 




i— 1 




P 




O" 




crj 




a 




■J2 





Diaschisma 



Diaschisma 




COMMA 



( Schisma 



( Schisma fa 



Diaschisma 



Diaschisma 



re 



c 4213 

d 4330 
e 4352 
/ 4374 



ff 



91 



4608 



' Let a J] be a tone, \j d, or fa, a lesser semitone, 
or as the Greeks call it, as Boetius witnesseth lib. II, 
cap. xxvii., a limma or diesis, ]j f, or d a, a greater 
semitone, called by the Greeks an apotome, J] c and 
c d, also / g and g a, diaschismata, or the halves of 
a diesis, (Ifs. comma, whose halves d e and e f are 
schismata; but it is necessary for our purpose 
to observe this, let a be Mese, or a la mi re, f 
Trite synemmenon ox fa in \>fa J] mi \^ Paramese 
or mi in b /a J] mi, therefore the note re in a la mi 
re is distant from fa in b fa J] vii by a lesser 
hemitone, and from mi in the same key by a tone ; 
from whence it follows, that the two notes in b fa 
Yj mi, which seem to be of the same key, are farther 
distant from each other than from the extremes or 
neighbouring keys above and below, viz., 7ni from e 
sol fa xd, and/a from a la mi re, for mi and_/a are 
separated from each other by a greater semitone, and 
from the extremes on either side by only a lesser 
semitone, for which reason this theory is not to be 
despised. We must not omit what the same Seve- 
rinus tells us in lib. III., cap. xiv. and xv., to wit, 
that a lesser semitone is not altogether four commas, 
but somewhat more than three ; and that a greater 
semitone is not five commas, but somewhat more 
than four ; from whence it comes to pass that a tone 
exceeds eight commas, but does not quite make up 



nine. 



This of Philolaus is generally deemed the true 
division of the tone, and may serve to prove the 
truth of that position, which all the theoretic writers 
on music seem to agree in, namely, that the sesqui- 
octave tone, as being in a superparticular ratio, is 
incapable of an equal division. But unfortunately 
the numbers made use of by Glareanus do not answer 
to the division, for those for the diesis or limma ]-] d 
4330, 4098 have no such ratio as 256 to 243, which 
is what the limma requires, and that other f a, has. 
and it seems that in his assertion that J] and b are 
farther distant from each other than from c and a. 



Chap. VI. 



AND PRACTICE OF MUSIC. 



231 



respectively, he is mistaken. This is noticed by- 
Salinas, who insists that the converse of the propo- 
sition is the truth. De Musica, lib. II. cap. xx.* 

As to the comma, it appears by the foregoing 
calculation to be in the ratio of 4374 to 4330. 
Nevertheless, Salinas, for the purpose of accommo- 
dating it to practice, has assumed for the comma an 
interval in the ratio of 81 to 80, which is different 
from that of Glareanus and Boetius, but is clearly 
shewn by Salinas to be the difference between the 
greater and lesser tone. Ptolemy looked upon this 
latter comma as an insensible interval, and thought 
that therefore it was a thing indifferent whether the 
sesquioctave or sesquinonal tone held the acutest 
situation in the diatonic tetrachord; but Salinas 
asserts, that though it is the least, it is yet one of the 
sensible intervals, and that by means of an instrument 
which he himself caused to be made at Rome, he was 
enabled to distinguish, and by his ear to judge, of 
the difference between the one and the other of the 
tones. 

Mersennus says that the Pythagoreans had another 
comma, which was in the ratio of 531441 to 524288, 
and was between sesqui Jj and sesqui ■^•, and that 
Christopher Mondore, in a book inscribed by him to 
Margaret, the sister of Henry III. of France, speaks 
of another between sesqui •^, and sesqui -gly-.f As 
to the first, though he does not mention it, it is clear 
that he took the ratio of it from Salinas, who in the 
nineteenth and thirty-first chapters of his fourth book 
speaks very particularly of the Pythagorean comma, 
and says that it is the difference whereby the apotome 
exceeds the limma. 

We have now investigated in a regular progression 
the ratios of the several intervals of the greater and 
lesser tone, the greater and lesser semitone, the 
apotome and limma, the diesis, and the comma ; and 
thereby resolved the tetrachord into its elements. It 
may be worth while to observe the singular beauties 
that arise in the course of this deduction, and how 
wonderfully the lesser intervals spring out of the 
greater ; for the difference between 



The 



f Diapente and "| 
\ Diiitessaron j 



IS 



The 



The 



a sesquioctave tone. 
a sesquinonal tone. 



- is a greater semitone. 



( Ditone and \ . 
\ Greater tone j 
Seniiditone and greater tone, 
and also between the dia- 
( tessaron and ditone, 

(Lesser tone and greater S 
semitone, and also between Vis a lesser semitone, 
the ditone and semiditone, J 
f Greater tone and \ ■ 
\ Lesser tone J 



The 



■is 



a comma. 



The 



( Greater semitone and 1 . 
I Lesser semitone ) 



an enarmonic diesis. 



Salinas remarks much to the same purpose on the 
regular order of the simple consonances in these 
words. • It seems worthy of the greatest observa- 
' tion, that the differences of the simple consonances, 
' each above that which is the next under it, are 
' found to be in the proportions which the first square 
* numbers hereunderwritten bear to those that are the 

* See his sentiment of it pac 25 of the present work. 
t Harmonicor. lit). V. Dissonantiis, pag. 88. 



■ next less to them : to instance in the diapason, the 
' excess above the diapente is the diatessaron, which 

■ is found in the ratio between the first square num- 

■ ber 4, and its next less number 3. The excess of 
' the diapente above the diatessaron is the greater 

tone, which is found in the ratio between the num- 
bers 9 and 8. Again, that of the diatessaron above 
the ditone is the greater semitone, found in the ratio 
16 to 15 ; farther, the excess of the ditone above the 
semiditone is the lesser semiditone 25 to 24. All 
these will appear more clearly in tlie following dis- 
position of the numbers : — 



A 



B C A B 

2 3 4 Diapason Diapente 

6 8 9 Diapente Diatessaron 

12 15 16 Diatessaron Ditone 

20 24 25 Ditone Semiditone 



c 

Diatessaron 
Tone Major 
Semitone majus 
Semitone miims 



' In the above disposition, the last numbers are 
' square, the first longilateral, and the middle ones 
' less than those that are square by unity, but greater 
' than the longilateral ones by as many units as there 
' are numbers of squares above them. The greatest 
' ratios are those between the longilaterals and the 
'squares, the lesser between the longilaterals and 
' middle numbers, and the least or differences those 
' between the squares and the middle ones. Of the 
' ratios the greatest are marked A, the lesser B, and 
Uhe least C.':|: 

Observations of this kind are perpetually occurring 
in the course of harmonical calculations ; and it can- 
not but be a matter of astonishment to an intelligent 
mind to find, that those combinations of musical 
sounds which afford delight to the sense of hearing, 
have such a relation among themselves, and are 
disposed with such order and regularity, that they 
approve themselves also to the understanding, and 
exhibit to the mind a new species of beauty, such as 
is observable in theorems, and will for ever result 
from design, regularity, truth, and order. It is said 
that the senses are arbitrary, and that too in so great 
a des;ree, as to give occasion to a well-known axiom 
that precludes all dispute about them ; but that of 
hearing seems to be an exception ; for what the ear 
recognises to be grateful, the understanding approves 
as true. To enquire farther into the reasons why 
the sense is delighted with harmony and consonance, 
would be vain, since all beyond what we are able to 
discover by numerical calculation is resolvable into 
the will of Him who has ordered all things in 
number, weight, and measure. 

The genera, as has been mentioned, were three ; 
the diatonic, the chromatic, and the enharmonic. 
We are farther to understand a subdivision of these 
into species. Gaudentius expressly says, ' The 
'species or colours of the genera are many,'§ and 
an author of much greater authority, Aristoxenus, 
has particularly enumerated them. According to him 
the diatonic genus had two species, the soft and the 

J De Musica, lib. II. cap. xx. 
§ Ex Vers. Meibom. pag. 5. 



.so 



HISTORY OF THE SCIENCE 



Book. T 



intense ; the chromatic three, the soft, the hemiolian,* 
and tlie tonic ; f as to the enharmonic, it had no 
subdivision. Indeed, the representations of the 
genera and their species, as well by diagrams as in 
words, are almost as numerous as the writers on 
music. Monsieur Brossard has exhibited a view of 
the Aristoxenean division, taken as he says, from 



Vitruvius; and the same is to be met with in an 
English dictionary of music, published in the veuv 
1740, by James Grassineau.ij; 

But this representation is not near so particular 
and accurate, as the Aristoxenean Synopsis of the 
Genera given by Dr. Wallis in the Appendix to his 
edition of Ptolemy, and here inserted : — 



.30 



24 



18 
15 
12 



Enarmonic 
Genus 



Nete 



24 



Paranete 



Lichanos 

3 

Trite 



Paihvpate 
3 



Chromatic Genus 



Soft 



Nete 



Paranete 



LichaiK; 

4 
Trite 



Parhvpate 
4 



Hemiolian 



Nete 



21 



Paranete 



Lichanos 



4'- 

Trite 



Parhvpate 

4 



Toniac 



Nete 



18 



Paranete 



Lichanos 

6 

Trite 



Parhypate 
6 



Diatonic Genus 



Soft 



Nete 



Paranete 



I-ichanos 



Trite 



Parhypate 
6 



Intense 



Nete 



12 



Paranete 



Lichanos 



12 



Trite 



Parhvpate 
6 



30 



24 



18 

15 

12 

9 

6 

3 



In order to imderstand this scheme, we must sup- 
pose the tetrachord hypaton, though any other would 
have served the ]n;rpose as well, divided into thirty 
equal parts : in the primitive division of this system, 
according to the diatonic genus, the stations of the 
two intermediate sounds parhypate and lichanos, for 
it is to be noted that those at the extremities termed 
stabiles, or immovables, were at 6 and 18 ; that is to 
say, the first interval in the tetrachord was 6 parts, 
and each of the other two 12, making together 30 ; 
so that the second interval was the double of the 
first, and the third equal to the second, answering 
precisely to the hemitone, tone, and tone ; this is 
spoken of the intense diatonic, for it is that species 
which the ancients are supposed to have meant when- 
ever they spoke of the diatonic generally. 

The soft diatonic has for its first interval G, for its 
Becond 9, or a hemitone and a quadrantal diesis, or 
three fourths of a tone, and for its third 15, viz., a 
tone and a quadrantal diesis. 

We are now to speak of the chromatic genus, the 
first species whereof, the tonic, had for its first inter- 

• This is but another name for sesqiiialtera, as Andreas Ornithnparcus 
asserts in his Microlo?;us, Hb. II. on tiie authority of Aiilus Gellius. It 
signifies a whole and its half, consequently the sesquialtera ratio in its 
ini'Mest numbers is 3 to 2. 

i Vide Wall. Append, de veter. Harm, quarto, pag. 299. 



val 6, or a hemitone ; for its second also 6, and for 
its third 18, a trihemitone, or tone and a half. 

In the hemiolian chromatic, called also the ses- 
quialteral,§ the first and also the second interval was 
4|, which is a hemiolian or sesquialteral diesis ; and 
the third 21, or a tone, a hemitone, and a quadrantal 
diesis, 

t At the time when the above book was published the world were sur- 
prised ; no such per,«on as James Grassineau being known to it as pos- 
sessed of any great share of musical erudition, and the work offered to 
the public appeared to be the result of great study and skill in the 
science. But the wonder ceased when it came to be known that the 
basis of Grassineau's book was the Dictionaire de Musique of Monsieur 
Sebastian Brossard, of Strasburg; though, to do him justice, Grassineau 
in his preface ingenuously confesses he had made a liberal use of it. For 
the rest of it he stood indebted to Dr. Pepusch, and perhaps, in a small 
degree to the other masters, Dr. Greene and Mr. Galliard, who have 
joined in the recommendation of it. 

Grassineau was an ingenious young man; he understood the Latin 
and French langua.ges, the latter very well, and knew a little of music ; 
he had been clerk to Mr. Godfrey, the chemist in Southampton Street, 
Covent Garden, but being out of employ, he became the amanuensis of 
Dr. Pepusch, and translated for him into English some of the Greek 
harmonicians from the Latin version of Meibomius. The Doctor having 
no farther occasion for him, recommended it to him to translate Brossard's 
dictionary above-mentioned, which he undertook and completed, the 
Doctor furnishing him with many new articles, and with additional mat- 
ter for the enlargement of those contained in Brossard ; and Grassineau's 
dictionary would have been an inestimable present to the musical world, 
had due care been taken in the correction of it, but it abounds with 
errors, and the author is not now living to correct them in a new edition. 

Although the dictionary of Brossard, and this of Grassineau, contain a 
great variety of useful knowledge, it is to be wished that it had been 
communicated to the world in some better form than that of a dictionary ; 
for to speak of the latter, some of the articles contained in it are com 
plete treatises. 

§ Vide previous note in this page. 



CHAr. VIL 



AND PRACTICE OF MUSIC. 



31 



The soft chromatic makes the first and also tlie 
Becond interval a triental diesis, or third part of a 
tone, by assigning to parypate and lichanos, the 
stations of 4 and 18 ; and gives to the third twenty- 
two twelfths of a tone, or, which is the same, twenty- 
two thirtieths of the whole tetrachord, which amount 
to a tone, a hemitone, and a triental diesis. 

In the enharmonic genus, which, in the opinion of 
most authors, had no division into species, the first 
and second intervals, being terminated by 3 and 6, 
were each quadrantal dieses, or three twelfths of 
a tone, and the last a ditone. Of the diesis in 
this genus it is said by Aristoxenus and others, that 
it is the smallest interval that the human voice is 
capable of expressing ; and it is farther to be re- 
marked, that it is ever termed the enarmonic diesis, 
as being appropriated to the enarmonic genus. 

Euclid's account of the genera is not much different 
from this of Aristoxenus. The diatonic, he says, 
proceeds from the acute to the grave by a tone, a 
tone, and a hemitone ; and, on the contrary, from the 
grave to the acute by a hemitone, a tone, and a tone. 
The chromatic from the acute to the grave by a tri- 
hemitone, a hemitone, and a hemitone : and con- 
trary wise, from the grave to the acute by a hemitone, 
a hemitone, and a trihemitone. The enharmonic 
progression, he says, is a descent to the grave by 
a ditone, a diesis, and a diesis ; and an ascent to the 
acumen by a diesis, a diesis, and a ditone. He speaks 
of a commixture of the genera, as namely, the diatonic 
with the chromatic, the diatonic with the enarmonic, 
and the chromatic with the enarmonic. 

He exhibits the bisdiapason according to each of 
the genera, enumerating the several sounds as they 
occur, from Proslambanomenos to Nete hyperboleon, 
and observes that some of them are termed Stantes 
or standing sounds, and others Mobiles or moveable ; 
the meaning of which is no more than that the ex- 
treme sounds of each tetrachord are immoveable, and 
that the difference between the genera consists in 
those several mutations of the intervals, which are 
made by assigning different positions to the two 
intermediate sounds. 

Colour he defines to be a particular division of a 
genus ; and, agreeable to what is said by Aristoxenus, 
he says that of the enarmonic there is one only ; of 
the chromatic three; and of the diatonic two. He 
says farther, that the enharmonic progression is by 
a diesis, a diesis, and incomposite ditone ; that the 
chromatic colours or species are the soft, proceeding 
by two dieses, each being the third part of a tone, 
and an incomposite interval equal to a tone, and its 
third part ; and the sesquialteral, proceeding by a die- 
sis in a sesquialteral ratio to that in the enarmonic, 
another such diesis, and an incomposite interval con- 
Bisting of seven dieses, each equal to a fourth part of 
a tone ; and the tonic by a hemitone, a hemitone, and 
a trihemitone. Of the diatonic he says there are two 
species, namely, the soft and the intense, by some 
called also the syntonous ; the former proceeding by 
a hemitone, an interval of three quadrantal dieses, 
and by another of five such dieses ; and the latter by 
a common division, with its genus, namely, a tone, 
a tone, and a hemitone. 



And here it is to be observed, that these several 
definitions of the genera are taken from some one or 
other of their respective species ; thus, that of the 
tonic chromatic is the same by which the genus itself 
is defined ; and the definition of the syntonous or 
intense diatonic is what is used to denote the genus 
itself. From hence it should seem that of the si^ecies 
some were deemed spurious, or at least that some 
kind of pre-eminence among them, unknown to us, 
occasioned this distinction ; which amounts to no less 
than saying that the soft chromatic is more truly the 
chromatic than either of the other two species of that 
genus ; and that the intense or syntonous diatonic is 
more truly the diatonic than the soft diatonic ; as to 
the enarmonic, it cannot in strictness be said to 
have had any colour or species, for it admits of no 
specific division. 

To demonstrate the intervals in each species by 
numbers, Euclid supposes a division of the tone into 
twelve parts. To the hemitone he gives six, to the 
quadrantal diesis three, and to the triental diesis four ; 
and to the whole diatessaron he assigns thirty. In 
the application of these parts to the several species, 
he says first, that the intervals in the soft chromatic 
are four, four, and twenty-two ; in the sesquialteral 
four and a half, four and a half, and twenty-one ; and 
in the tonic six, six, and eighteen ; in the soft dia- 
tonic six, nine, and fifteen ; and in the syntonous six. 
twelve, and twelve. 

CHAP. VII. 

Aristides Quintilianus, who, in the judgment of 
Dr.Wallis,* seems in this respect to have been an 
Aristoxenean, speaks of the genera and their species 
in the following manner : — ' Genus is a certain di- 
' vision of the tetrachord. There are three genera 

* of modulation, namely, the harmonic, chromatic, 
' and diatonic ; the difference between them consists 
' in the distances of their respective intervals. The 
' harmonic is that genus Avhich abounds in the least 
' intervals, and takes its name from adjoining together. 
' The diatonic is so called becaiase it proceeds by, or 
' abounds in, tones. The chromatic is so termed, 
' because, as that which is between white and black 
' is called Colour, so also that which holds the middle 

* place between the two former genera as this does, 
' is named Chroma. The enarmonic is sung by a 
' diesis, diesis, and an incomposite ditone towards the 
' acute ; and contrarywise towards the grave. The 
' chromatic towards the acute by a hemitone, a hemi- 
' tone, and trihemitone ; and contrarywise towards 

* the grave. The diatonic by a hemitone, a tone, 
' and tone towards the acute : and contrarywise to- 

* wards the grave. The diatonic is the most natural 
' of all, because it may be sung by every one, even 
' by such as are unlearned. The most artificial is 
' the chromatic, for only learned men can modulate 
' it ; but the most accurate is the enharmonic : it is 
' approved of by only the most skilful musicians ; 
' for those who are otherwise look on the diesis as 
' an interval which can by no means be sung, and to 

* Append, dc veter. Ilanii. pag. 318. 



32 



HISTORY OF THE SCIENCE 



Book I 



' these, by reason of the debility of their faculties, 
' the use of this genus is impossil)le. Each of the 

* genera may be modulated both by consecutive 
' sounds and by leaps. IMoreover, modulation is 

* either direct or straightforward, reverting or turn- 
' ing back, or circumcurrent, running up and down : 
' the direct is that which stretches towards the acute 
' from the grave ; the reverting that which is contrary 

* to the former ; and the circumcurrent is that which 
' is changeable, as when we elevate by conjunction, 
' and remit by disjunction. Again, some of tlie 
' genera are divided into species, others not. The 
' enarmonic, because it consists of the smallest 
' dieses, is indivisible. The chromatic may be 

* divided into as many rational intervals as are 
' found between the hemitone and enarmonic diesis ; 
' the third, namely the diatonic, into as many rational 
' intervals as are found between the hemitone and 

* tone ; there are therefore three species of the chro- 

* matic, and two of the diatonic. And, to sum up 
'the whole, these added to the enarmonic make six 
' species of modulation ; the first is distinguished by 
' quadrantal dieses, and is called the enarmonic ; 
' the second by triental dieses, and is called the soft 
' chromatic ; the third by dieses that are sesquialteral 

* to those in the enarmonic, and is therefore called 
' the sesquialteral chromatic. The fourth has a pe- 
' culiar constitution of two hemitones, it is called 
' the tonic chromatic : the fifth consists of an hemi- 
' tone and three dieses, and the five remaining ones, 
' and is called the soft diatonic : the sixth has an 

* hemitone, tone, and tone, and is called the intense 
' diatonic. But that what we have said may be 

* made clear, we shall make the division in the 
' numbers. Let the tetrachord be supposed to con- 

* sist of sixty units, the division of the enarmonic 

* is 6, 6, 48, by a quadrantal diesis, a quadrantal 
' diesis, and a ditone. The division of the soft chro- 

* matic 8, 8, 44, by a triental diesis, a triental diesis, 
' and a trihemitone and triental diesis. The division 
' of the sesquialteral chromatic is 9, 9, 42, by a 
' sesquialteral diesis, a sesquialteral diesis, and a tri- 
' hemitone and quadrantal diesis. The division of 
' the tonic chromatic is 12, 12, 3G, by an hemitone, 
' an hemitone, and a trihemitone. That of the soft 
' diatonic is 12, 18, 30, by a hemitone, and three 

* quadrantal dieses, and five quadrantal dieses. That 
' of the intense diatonic is 12, 24, 24, by a hemitone, 
' a tone, and a tone.'* 

It is observable in this division of Aristides Quin- 
tilianus, that the numbers made use of by him are 
double those used by Euclid ; the reason is, that the 
two dieses in the sesquialteral chromatic are not so 
well defined by four parts and a half of thirty, as by 
9 of 60 ; and it is evident that preserving the pro- 
portions, whether we take the numl)er 30 or 60 for 
the gross content of the tetrachord, the matter is 
just the same. 

Ptolemy, the most copious, and one of the most 
accurate of all the ancient harmonicians, has treated 

* Aristides Quintilianus ex vers. Meib. pag 18, et seq.,in which pas- 
sage it is observable that he sometimes uses the term apiioina, and 
others evapfiovia, to signify the enarmonic genus. 



very largely of the genera ; and has, for the reason 
above given, adopted the number 60 for the measure 
of the tetrachord ; he has represented the Aristox- 
enean constitution of the six species by the following 
proportions : — 

Acute 
Mean 
Grave 



48 
6 
6 


44 

8 
8 


42 
9 
9 


36 
12 
12 


30 
18 
12 


24 
24 
12 


60 


60 


60 


60 


60 


60 


Enar- 
monic 


Chro- 
matic 

son 


Chro- 
matic 
sesqui- 
alteral 


Chro- 
matic 
tonic 


Dia- 
tonic 
soft 


Dia- 
tonic 
intense 



In which proportions he agrees both with Euclid 
and Aristides Quintilianus ; though, for the purpose 
of ascertaining them, he has preferred the numbers 
of the latter to those used by Euclid. 

In chapter xiv. of his second book, Ptolemy has 
given the genera, with each of their several species, 
according to the five different musicians, namely, 
Archytas, f Aristoxenus, Eratosthenes, J Didymus, 
and himself. The sum of his account, omitting the 
division of Aristoxenus, for that is given above, is as 
follows : — 

J Enarmonic 

Chromatic 

Diatonic 

Enarmonic 

Chromatic 

Diatonic 

Enarmonic 

Chromatic 

Diatonic 

In his own division Ptolemy supposes five species 
of the diatonic genus, which, together with the en- 
harmonic, and two species of the chromatic, he thus 
defines : — 

/'Enarmonic 

f Soft 

*• Intense 

^Soft 

Tonic 

Ditonic 

Intense 



Archytas 



Eratosthenes 



Didvmus 



2 8 
2T 


X 


3fi 


X 


s 

4 


4 

— 7 


28 


X 


243 

2irf 


X 


3 2 


4 

— ¥ 


2 8 
2T 


X 


8 

T 


X 


9 

■8 


=i 


40 
39 


X 


30 

3 8 


X 


1 9 
15^ 


4 

— 3^ 


2 


X 


1 


X 


fi 
5 


— 4 

— 3" 


2. '5 6 
24;T 


X 


9 

"8 


X 


9 

"8- 


— 4 

— S' 


3 2 
3 1 


X 


31 

3 


X 


.5 


— 4 

— 3" 


IG 
15 


X 


2r> 

2 4 


X 


6 
'5 


= 1 


1 6 
i5 


X 


10 


X 


9 
8 


— 4 

^ 



Pt 'cmv< 



Chromatic 



Diatonic ^ 



46 
45 


X 


24 
2 3 


X 


5 
4 


— 4 

— S 


28 
27 


X 


1 5 
14 


X 


6 
6 


= ^ 


21 


X 


1 2 
1 1 


X 


7 
"6" 


4 

— 7 


21 
20 


X 


1 


X 


8 

T 


4 

— 3- 


2 8 
2 7 


X 


8 
T 


X 


9 


4 

— S 


2.'-, 6 
24 3^ 


X 


9 


X 


1 


4 

— 3- 


1 fi 


X 


9 

if 


X 


1 

IT 


— 4 

— T 


1 2 
1 1 


X 


1 1 

T7f 


X 


10 


4 



+ There were two of this name, the one of TarLntum, a Pythagorean, 
famous, as Auhis Gellius and others relate, for having constructed an 
automaton in the form of a pipe, i, which had the power of flying to 
a considerable distance; the other a musician of Mitylene. They ate 
both mentioned by Diogenes Laertias, but it is not certain which of the 
two was the author of the division here given. 

t Erathosthenes, a Cyrenean philosopher, and a disciple of Aristo and 
Callimachus, was librarian at Alexandria to Ptolemy Evergetes. Ht 
was for his great learning esteemed a second Plato. An astronomica. 
discourse of his is extant in the Oxford edition of Aratus ; prefixed to 
which is an account of many other books of his writing now lost. He 
is said to have lived to the age of eighty-two ; and, according to Helvicus, 
flourished about th*- Olympiad cxxxviii. that is to say, about two hundred 
and thirty years before Clirist. 

The above-mentioned edition of Aratus is a book not unworthy the 
notice of a learned musician, as containing a short but curious disserta- 
tion De Musica antiqua Graca, by the editor Mr. Edmund Chilmead. 
Aratus was an eminent astronomer and poet, contemporary with Era- 
tosthenes ; and in the Oxford publication is an astronomical poem, which 
it seems St. Paul alludes to in his speech at Athens. Acts xvii. ver. 28. 
'As certain of your own poets have said.' Aratus was a Cilicinn, and 
a countryman of the Apostle. Vide Bentley's Sermons at Boyle'* 
Lecture, Sermon II. 



Ciuv. VII. 



AND PRACTICE OF MUSIC. 



33 



Martianus Capolla gives this explanation of the 
genera : — ' The euarmonic aboinids in small intervals, 
' the diatonic in tones. The chromatic consists wholly 
' of semitones, and is called chromatic, as partaking of 
' the nature of both the others ; for the same reason 
' as we call that affection colour which is included 
' between the extremes of white and black. The 
' enarmonic is modulated towards the acumen, or, as 
' we should now say, ascends by a diesis, diesis, and 
' an incomposite ditone ; the, chromatic by a semi- 
' tone, semitone, and an incomposite trihemitone : 
' and the diatonic, content with larger intervals, 
•' proceeds by a semitone, tone, and tone : we now 
' chiefly use the diatonic' He says farther,—' The 
' possible divisions of the tetrachord are innumerable, 
' but there are six noted ones, one of the enarmonic, 
'three of the chromatic, and two of the diatonic. 

* The first of the chromatic is the soft, the second 
' is the hemiolian, and the third the tonian. The 
' divisions of the diatonic are two, the one soft and 

* the other robust. The enarmonic is distinguished 
' by the quadrantal diesis, the soft chromatic by the 
' triental diesis, and the hemiolian chromatic by the 
'hemiolian diesis, which is equal to an enarmonic 
' diesis and a half, or three eighths of a tone.' * In 

all this Capella is but a copier of Aristides Quin- 
tilianus ; and, in the judgment of his editor Mei- 
bomius, and others, he is both a servile and an 
injudicious one. 
Boetius t has treated the subject of the genera in 
a manner less satisfactory than could have been ex- 
pected from so scientific a musician : he mentions 
nothing of the species, but contents himself with an 
exhibition of the enarmonic, the chromatic, and 
diatonic, in three several diagrams, which are here 
given. He says that the diatonic is somewhat hard, 
but that the chromatic departs from that natural in- 
tension, and becomes somewhat more soft ; and that 
the enarmonic is yet better constituted through the 
five tetrachords. The diatonic progression, he says, 
is by a semitone, tone, and tone ; and that it is called 
diatonic, as proceeding by tones. He adds that the 
chromatic, which takes its name from the word Chroma, 
signifying colour, is, as it were, the first change or in- 
flexion from that kind of intension preserved in the 
diatonic : and is sung by a semitone, a semitone, and 
three semitones;^ and that the enarmonic, which in 
his judgment is the most perfect of all the genera, is 
sung by a diesis and a ditone ; a diesis, he says, is the 
half of a semitone. The following is his division of 
the tetrachord in each of the three genera : — 



C H 11 M A T I C 



Semitone Semitone Three semitones iucomposite 



ENAEMONIC 



Diesis | Diesis | 
^ V— ■■ 



Ditone 



"V 



-.^ 



He is somewhat more particular in his fourth book, 
chap, v., and again in the seventh chapter, for in the 
chromatic tetrachord he makes the semitones to be, 
the one a greater and the other a lesser ; and the 
trihemitone he makes to consist of one greater and 
two lesser semitones. 

TETRACHORD. 

Nete hyper'ooleon Nete hyperboleon Nete hyperbolcon 



O ■$ 
< -3 



o 
c 
o 
H 


2304 
2592 


O en 

So 
2 ^ 

o • 

C u 
O (U 


2304 
2730 


0) 

c 
o 


2304 
291G 


§ 

H 

Is 

X 


Paranete hyp. 
2916 


Paranete hyp. 
291G 


Trite hyperb. 
3072 


Is 

■-H X 


Trite hyperb. 
3072 


•71 

5_ 

X 

'x 

(5 


Paranete hyp. 


Trite hyperb. 
3072 




Nete diezeug. 

DIATONIC 




Nete diezeug. 

CHROMATIC 


Nete dlezeuR. 

ENARMONIC 



DIATONIC 



Semitone 



Tone 



Tone 



"N^- 



* De Nuptiis PhilologiEe et Mercurii, lib. IX. De Generibus Tetra- 
chordorum. 

t Lib. I. cap. xxi. 

t In a dia-jram of Glareanus, representing Boetius's division of the 
chromatic, the last interval is thus defined ; — ' tria semitonia incom- 
posita,' which epithet, as Boetius himself explains it, is not meant to 
signify that the semitones are incomplete, but that the interval con- 
stituted by them is to be considered as an integer, and uncompounded 
like the tone, without regard to its constituent parts. De Mus. lib. I. 
cap. xxiii. 



It is somewhat remarkable that this author has 
said nothing of the colours or species of the genera, 
about which so much is to be met with in Ptolemy 
and other writers, except towards the conclusion of 
his work, where he professes to deliver the sentiments 
of Aristoxenus and Archytas on this head ; but he 
seems rather to reprehend than adopt their opinions, 
for which it seems difficult to assign any reason, 
other than that he was, as his writings abundantly 
prove, a most strenuous assertor of the doctrines of 
Pythagoras. 

'Mcrsennus§ has given a scale of the succession of 
sounds in each of the three genera, as near as it could 
be done, in the characters of modern notation, which 
is here inserted, and may serve to shew how ill the 
division of the tetrachord in the chromatic and enar- 
monic genera agree with the notions at this time 
entertained of harmony, and the natural progression 
of musical sounds. 

§ Harmonic. De Generibus et Modis, pag. 9/. 



34 



HISTORY OF THE SCIENCE 



Book I. 



as 



DIATONIC GENUS. 

Tetrachord. Tetrachord. Tetrachord. 

hypaton. parhypaton. eynemmen. 



Wm 



Tetrachord. 
diezeug. 



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Tetrachord. 
hyperb. ^ 



RE, MI FA SOL LA, MI FA SOL LA, MI FA SOL LA, 



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Other authors there fire, particularly Fraiichinus, 
Vieentino, Viucentio Galilei, and Zarlino, that pro- 
fess to treat of the genera; but it is to be noted 
that all their intelligence is derived from the same 
source, namely, the Avritings of Aristoxenus, Euclid, 
Aristides Quintilianus, and more especially Ptolemy ; 
and therefore we find no other variation among them 
than what seems necessarily to arise from their dif- 
ferent conceptions of the subject. Boetius himself 
can in this respect be considered no other\vise than 
as a modern ; and he himself does not pretend to an 
investigation of the genera, but contents himself with 
a bare repetition of what is to be found in the writings 
of the ancients respecting them : and when it is con- 
sidered that in his time only the diatonic genus was 
in use, the other genera having been rejected for 
their intricacy, and other reasons, long before, it 
must appear next to impossible that he could contri- 
bute much to the explanation of this most abstruse 
part of the science ; and the excessive caution with 
which he delivers his sentiments touching them, 
is a kind of proof of the difficulties he had to 
encounter. 

If this was the case with Boetius, how little is to 
be expected from the writers of later times. In 
short, for information as to the doctrine of the 



genera, we are under an indispensible necessity of 
recurring to the ancients ; and it will be much safer 
to acquiesce in their relations, defective and obscure 
as they are, than to trust to the glosses of modern 
authors, who in general are more likely to mislead 
than direct us : for this reason it has been thought 
proper to reject an infinitude of schemes, diagrams, 
and explanations, which the fertile inventions of the 
moderns have produced to exemplify the constitution 
of the chromatic and enarmonic genera, and that 
from a thorough persuasion that many of them are 
erroneous. 

But it seems the considerations above suggested 
were not sufficient to deter a writer, who flourished 
in the sixteenth century, who, to say the least of him, 
appears to have been one of the ablest theorists of 
modern times, from attempting to develope the 
doctrine of the genera, and deliver it free from those 
difficulties. 

The author here meant is Franciscus Salinas, 
a Spaniard by birth, and who, under all the dis- 
advantages of incurable blindness, applied himself 
with the most astonishing patience and perseverance 
to the study of the theory of music ; and in many 
respects the success of his researches has been equal 
to the degree of his resolution. His svstem of the 



Chap. VII. 



AND PRACTICE OF MUSIC. 



35 



genera is mucli too copious to be inserted here ; it is 
therefore referred to a part of this work reserved for 
an account of liim and bis writings. 

Kircher has given a compendious view of the 
genera,* together with the jiroportions of their com- 
ponent intervals, in the tetraclaord of each genus, by 
the help whereof we are enabled to form an idea of 
those various progressions that constitute the dif- 
ference between the one and the other of them. But 
though he professes to have in his possession, and 
to have perused the manuscripts of Aristoxenus, 
Archytas, Didymus, Eratosthenes, and others,f he 
gives the preference to Ptolemy in respect to his 
division of the genera, and apparently follows the 
elder Galilei, not indeed in the order, but in the 
method of representation. According to him the 
species of the diatonic genus are five, namely, the 
ditonic or Pythagorean, the soft, the syntonous, the 
toniac, and the equable. The following is his defi- 
nition and representation of them severally in their 
order, with his remarks on each : — 

DITONIC or PYTHAGOREAN DIATONIC I. 

* The Pythagorean or ditonic diatonic consists in a 

* progression from the grave to the acute, through the 
' tetrachord, by the interval of a lesser semitone, and 
' two tones, each in the ratio of 8 to 9 ; and con- 

* trary wise from the acute to the grave by two tones 
' and a lesser semitone, as in the following example : — 

o 



6912- 



Sesquioctave tone, 8 to 9 



7776- 

] 

8192- 



Sesquioctave tone, 8 to 9 



-Hypate meson 
-Lychanos hypaton 



Lesser semitone, 243 to 256 



-Parypate hypaton 



-Hypate hypaton 



< 

W 

' This kind of progression is said to have been held 
' in great estimation by the philosophers, particularly 
' Plato and Aristotle, as having a conformity with the 
' composition of the world and with nature itself. 

SOFT DIATONIC II. 

' The second or soft species of the diatonic genus 

* proceeds from the grave to the acute by an interval, 

* in the ratio of 20 to 21 ; the other intervals have 
' a ratio, the one of 9 to 10, and the other of 7 to 8, 
' as is here represented : — 



O 

o 

H 



63 



80 



Sesquiseptima, 7 to 8 
Sesquinona, 9 to 10 



-Hypate meson 
-Lychanos hypaton 



84 



Sesquivigesima, 20 to 21 



-Parypate hypaton 



-Hypate hypaton 



* Musurg. torn. I. lib. III. cap. xiii. 

t Meibomius questions the trutli of this assertion, upon the supposition 
that Archytas, Didymus, and Eratosthenes are to be reckoned among the 
scrjptores perditi. It is true that, excepting a small astronomical tract 
of Eratosthenes, there is nothing of the writing of eitlierof them in print. 
But it is said that in the library of St. Mark, at Venice, there are even now 
a great number of Greek manuscripts that were brought into Italy upon 
the sacking of Constantinople, and among them it is not impossible that 
some tracts of the above-named writers might be found. 



SYNTONOUS DIATONIC III. 

'The third species, distinguished by the epithets 
' syntouum incitatum, or hastened, proceeds from the 
' grave to the acute by an interval in the ratio of 15 
'to 16, or greater semitone, a greater tone 8 to 9, and 
'a lesser 9 to 10; and descends from the acute to the 
' grave by the same intervals. 

Greater terms. 



C 
Q 



I J t(i 40 
g r [^ 48 



-Hypate meson 



Sesquinona, 9 to 10 tone minor 

Lychanos hypaton 

Sesquioctave, S to 9 tone major 

Parypate hypaton 

Sesquiquindecima, 15 to 10 greater semit. 
Hypate hypaton 



TONIAC DIATONIC IV. 

'The toniac, the fourth species of the diatonic 
' genus, supposes such a disposition of the tetrachord 
'as the first and second chords shall include an inter- 
' val of 27 to 28 ; next an interval of 7 to 8, and 
' lastly one of 8 to 9. Thus adjusted it will ascend 
' from the grave to the acute, and on the contrary 
' descend from the acute to the grave, as in the 
' example : — 



O 



Greater terms. 
flGS 






189 



216 



Sesquioctave, 8 to 9 
Sesquiseptima, 7 to 8 



Hypate meson 

Lychanos hypaton 

Parypate hypaton 
Sesquivigesimaseptima, 27 to 28 
224 Hypate hypaton 

EQUABLE DIATONIC V. 

'The fifth and last species of this genus is the 
' equable, proceeding in arithmetical progression from 
' the grave to the acute, by the ratios of 11 to 12, 10 
' to 11, and 9 to 10 ; and contrarywise from the 
' acute to the grave : — 






^ I 






< 



J '^ 

^5 



9 
10 
11 
12 



Sesquinona 



Sesquidecima 



Sesquiundecima 



- Hypate meson 

- Lychanos hypaton 

- Parypate hypaton 

- Hypate hypaton 



' Ptolemy, whose fondness for analogies has already 
' been remarked, resembles the tetrachord thus con- 
' stituted to Theology and Politics.' 

The chromatic genus, in the opinion of this author 
had three species, the ancient, the soft, and the syn- 
tonous, thus severally described by him : — 

ANCIENT CHROMATIC L 

'This species proceeded by two semitones, and 
' a trihemitone, that is to say, it ascended from the 
' grave to the acute, by a lesser semitone ; then by an 
'interval somewhat greater, as being in the rat.'.o of 



3C 



HISTORY OF THE SCIENCE 



Book I. 



' 81 to 76 ; and lastly by an incomplete trihemitone, 
' in tlie ratio of 19 to IG : — 




fGlM 



Hypate meson 



Trihemitone, IG to 19 

7296 Lyclianos liypaton 

Semitone, 7G to 81 

777g Parypate liypaton 

j Lesser semitone, 243 to 256 

I 8192 Hypate liypaton 

SOFT CHROMATIC 11. 

* The chromatic molle was so disposed, as that the 
' lowest chord and the next to it had a ratio of 27 to 
' 28, the second and third 14 to 15, and the third and 
' fourth 5 to G : — 



O 

w 

Q 

<1 



G144: 



Ditone 



777G 
7984 



Diesis 



Diesis 



8192 



Hypate meson 
Lychanos hypaton 
Parypate liypaton 
Hypate hypaton 



ENARMONIC OF PTOLEMY IL 

' The Ptolemaic enarmonic, which was scarce 
' formed before both the chromatic and enarmonic 
' grew into dis-esteem, ascended from the most grave 

• to the next chord by an interval in the ratio of 45 
' to 46, thence by one of 23 to 24, and lastly by one 

* of 4 to 5, which is said to be a true enharmonic 
' ditone : — 



o 

Q 



fios 



126 



Sesquiquinta, 5 to 6 



- Hypate meson 

- Lychanos hypaton 
Sesquiquartadecima, 14 to 15 

135 Parypate hypaton 

Sosquivigesimaseptima, 27 to 28 
140 Hypate hypaton 



!76 



Sesquiquarta, 4 to 5 



Hypate meson 

345 ■ • — Lychanos hypaton 

Sesquivigesima tertia 23 to 24 
360 — — - Parypate hypaton 

Sesquiquadragesimaquinta, 45 to 46 
368 Hypate hypaton 



SYNTONOUS CHROMATIC IIL 

' In the chromatic syntonnm the first and second 
' chords, reckoning from the lowest, were distant by 
' an interval in the proportion of 22 to 21, the second 
' was removed from the third by an interval in the 
' proportion of 12 to 11, and the tliird from the fourth 
' by one of a sesquisexta proportion, which is as 6 to 
' 7, as here is shewn : — 



P 
O 



ree 






84 
88 



Sesquisexta, 6 to 7 
Sesquiundecima, 11 to 12 



Hypate meson 
Lychanos hypaton 



Parypate hypaton 
Sesquivigesima prima, 21 to 22 
Hypate hypaton 

' Of this genus it is said by Macrobius that it was 
' deemed tobe of an effeminate nature, and that it had 
' a tendency to enervate the mind f for which reason 
' the ancients very seldom used it ; Ptolemy resembles 
* this tetrachord to ceconomics.' 

The enarmonic, the third and last in order of the 
genera, seems to have been originally simple or 
undivided into species ; but the refinements of 
Ptolemy led to a variation in the order of the enar- 
monic progression, which formed that species distin- 
o-uished by his name, so that it may be said the 
enarmonic contained two species, the ancient and 
the Ptolemaic. Kircher thus defines it : — 

ANCIENT ENARMONIC L 

'In this species the tetrachord ascended by two 
'dieses, and an incomplete ditone, the several ra- 
'tios whereof were as denoted by the following 
* numbers : — 

» Vide Macrob, in Somn. Scipion Lib. II. cap. iv. 



P^ 

o 
W 
o 

p^ 

H 

Dr. Wallis has treated this subject of the genera 
in a manner worthy of that penetration and sagacity 
for which he is admired. It has been mentioned, 
that of all the ancients Ptolemy has entered the most 
minutely into a discussion of this doctrine ; he has 
delivered the sentiments of many writers, which but 
for him we should scarcely have known, and has 
adjusted the species in such a way as to leave it 
a doubt whether even A.ristoxenus or he be the 
nearest the truth : Dr. Wallis published an edition 
of this valuable author, with a translation and notes 
of his own ; to this work he has added an appendix, 
wherein is contained a very elaborate and judicious 
disquisition on the nature of the ancient music, and 
a comparison of the ancient system with that of the 
moderns. In this he has taken great pains to explain, 
as far as it was possible, the genera : the enarmonic 
and chromatic he gives up, and speaks of as irre- 
coverably lost ; but of the diatonic genus he ex- 
presses himself with great clearness and precision; 
for, after defining, as he does very accurately, the 
several species of the diatonic, he says, that one only 
of them is now in practice ; and, as touching the 
question which of them that one is, he gives the 
opinions of several musicians, together with his own ; 
and lastly shows how very small and inconsiderable 
must have been the difference between those divisions 
that distinguish the species of the diatonic genus. 
His words are nearly these : — 

' It now remains to discuss one point, which we 
'have referred to this place, the genera and their 
* colours or species. We have before said that for 
' many years only one of theni all has been received 
' in practice, and this is by all allowed to be the 
' diatonic ; the enarmonic and all the chromatics, and 
'the other diatonics, being laid aside. But it is 
' matter of dispute whether it is the intense diatonic 
' of Aristoxenus, or the ditonic diatonic of Ptolemy, 



CuAr. VIII. 



AND PRACTICE OF IMUSIC. 



37 



' or the intense diatonic of the same Ptolemy ; that 

* is to say, when we sing a diatessaron from mi or la 
' in the grave towards the acute in the syUables fa 
' SOL la, which express so many intervals, to ascertain 
' the degree of magnitude wliich each of these in- 
' tervals contains. The first opinion is that of Aris- 
' toxenus, who, when he made the diatessaron to 
'consist of two tones and a half, would have the 

* greatest sound fa, to be a hemitone, and the other 
' two SOL la, to be whole tones, which is the intense 
'diatonic of this author.* And in this manner 
' speak all musicians even to this day, at least when 
'they do not profess to speak with nicety. But 
' those who enter more minutely into the matter, 
' will have what is understood by a hemitone to be, 
' not exactly the half of, but somewhat a little less 
' than a tone ; and this is demonstrated by Euclid, 
' who in other respects was an Aristoxenean, though 
' I do not know whether he was the first that did 
' it. Euclid, I say, admitting the principles of the 
' Pythagoreans in estimating the intervals of sounds 
' by ratios ; and admitting also that a tone is in 
'a sesquioctavc ratio, in his harmonic introduction 
' treats of the tones and hemitones in the same 
' manner as do the Aristoxeneans ; yet in his section 
'of the canon he shows that what remains after 
' subtracting two tones from a diatessaron is less than 
'a hemitone, and is called a limma, which is in the 
' ratio of 1^1 ; for if a diatessaron contains two tones 
' and a liaff, then a diapason, which is two diatcssarons 
' and one tone, must contain six tones ; but a diapason, 
' which has a duple ratio, is less than six tones, for 
' a sesquioctavc ratio six times compounded is more 
'than duple ;t a diapason therefore is less than six 
' tones, and a diatessaron less than two tones and 
' a half. 

CHAP. VIII. 

'The next opinion is that of those, who, instead 
of a tone, tone, and hemitone, substitute a tone, 
tone, and limma. And these, if at any time they 
call it a hemitone, would yet have us understand 
them to mean a limma, which differs very little from 
a hemitone, and therefore they will have the syl- 
lable LA to express a limma.and the syllables sol la 
two tones, that is -ffg-Xf Xf=f, and this is the 
ditonic diatonic of Ptolemy, but which was shewn 
by Euclid before Ptolemy; and it was also the 
diatonic of Eratosthenes, as has been said above ; 
and these have been the sentiments of musicians 
almost as low as to our own times. Ptolemy 
himself, though he has given other kinds of diatonic 
genera, does not reject this ; and the rest who have 
spoken of this matter in a different way, did it 
more out of compliance Avith custom, than that they 
adhered to any contrary opinion of their own, as 
Ptolemy himself tells us, lib. I. cap. xvi. And 
' thus Boetius divides the tctrachord, and after him 
* Guido Aretinus, Fabcr Stapulensis, Glarcanus, and 
' others ; it is true, however, that, about the begin- 

* See tlie Synopsis, p. 30, of Dr. Wallis's Appendix, hercin-before 
given. 

t This is excellently demonstrated by Boetius, lib. lU, cap. i. 



' ning of the sixteenth century, Zarlino, and also 
' Kepler, resumed the intense diatonic of Ptolemy, 
'and attempted to bring it into practice ;;{; but for 
' this they were censured by the elder Galileo. § 

' The third opinion, therefore, is that of those 
' who, following Ptolemy, substituted in the place of 
' a hemitone or limma, a sesquidecimaquinta ratio 
' -}-0, which they also call a hemitone ; and for the 
' tones, both which the others had made to be in the 
'ratio f, one they made to be in the ratio \^, so 
' that they compounded the diatessaron by the ratios 
'|-|-X|-X \f=-|-, expressing by the syllable fa the 
'ratio -}-", by sol that of -|, and by la lffM| which 
' is the intense diatonic of Ptolemy, and the diatonic 
'of Didymus, except that he, changing the order, 

nas-p5-x -gr Xg — -J- 

' And as they called -J-S- a greater hemitone, they 
' made the lesser ff, which with -fS- completes the 
'lesser tone, as ttXM X=V' ''^^^ ^^ ^^^^ difference, 
'as they say, between the greater and the lesser 
'third. Mersennus adds two other hemitones, one 
' in the ratio i|4, which with -}-§- completes f the 
' greater tone, and the other l-T-, which with ff also 
'makes up |- the greater tone.'^[ 

The above is an impartial state of the several 
opinions that at different times have prevailed among 
the moderns, touching the preference of one or other 
of the species of the diatonic genus to the rest. 
Dr. Wallis is certainly right in saying, that to the 
time of Boetius, and so on to the end of the sixteenth 
century, the ditonic diatonic of Ptolemy prevailed, 
for so much appears by the writings of those several 
authors ; and as to the latter part of his assertion, it 
is confirmed by the present practice, which is to 
consider the tetrachoi'd as consisting of a sesqui- 
decimaquinta ratio, a tone major, and a tone minor, 
and to this method of division he gives the pre- 
ference ; but he closes his relation with a remark 
that shews of how very little importance all enquiries 
are, which tend to adjust differences too minute for 
a determination by the senses, and cognizable only 
by the maderstanding, and that, too, not till after_ 
a laborious investigation. His words are these : — 

'But as those species which we have mentioned. 
' differ so very little from one another, that the nicest 
' ear can scarcely, if at all, distinguish them, since the 
' ratio -fS- from the ratio of a limma -f^^, as also the 
' ratio of a greater tone % from V° differ only by the 
' ratio |rJ-, which is so small that the ear can with 
'difficulty discriminate between the one and the 
' other of the two tones ; we must therefore judge 
' not so much by our senses, which opinion ought 

t Dr. Wallis has a little mistaken Kepler in this place : it was not the 



9 — 4 



=4 that 



intense diatonic of Ptolemy, but of Didymus -ff X y- X -g- — -j 

he was for resuming. Joann. Keplerus Harm. Mundi, lib. HI. cap. vii. 

§ Galileo did not contend for the ditonic division of the diatonic, but 
for the intense of Aristoxenus, defined in his synopsis of the genera 
herein before given ; the reason whereof was, that he was a lutenist, and 
the performers on that instrument unanimously prefer the Aristoxenean 
division. 

II It may be proper to remark, that in this and other instances of sol' 
misation that occur in the passage now quoting. Dr. Wallis uses the 
method of solmisation by the tetrachords, in which the syllables UT be 
are rejected, and which took place about the year 1050. See Clifford's 
Collection of Divine Services and Anthems, printed in the year 1664. 

f Append, de Vet. Harm. 317, et seq. 



38 



HISTORY OF THE SCIENCE 



Book I, 



'most to be regarded, because the senses wovild 
' without any difficulty admit any of them, but 
' rea*3n greatly favours the last.'^-' 

There is yet another writer, with whose senti- 
ments, and a few observations thereon, we shall con- 
clude our account of the genera ; this was Dr. John 
Christopher Pepusch, a man of no small eminence 
in his profession, and who for many years enjoyed, at 
least in England, the reputation of being the ablest 
theorist of his time. In a letter to Mr. Abraham 
de Moivre, printed in the Philosophical Transactions 
of the year 1746, No. 481, he proposes to throw 
some light upon the obscure subject of the ancient 
species of music ; and after premising that, ac- 
cording to Euclid, the ancient scale must have 
been composed of tones major and limmas, without 
the intervention of tones minor, which in numbers are 
thus to be expressed, -f |^ -| A 2-|fi 1. 1-, he proceeds 
in these words: — 'It was usual among the Greeks to 
' consider a descending as well as an ascending scale, 
' the former proceeding from acute to grave pre- 
' cisely by the same intervals as the latter did from 

* grave to acute. The first sound in each was the 
' proslambanomenos. The not distinguishing these 
' two scales, has led several learned moderns to sup- 
' pose that the Greeks in some centuries took the 
' proslambanomenos to be the lowest note in their 
' system, and in other centuries to be the highest ; but 
' the truth of the matter is, that the proslambano- 
' menos was the lowest or highest note according as 
' they considered the ascending or descending scale. 

* The distinction of these is conducive to the variety 

* and perfection of melody ; but I never yet met 
' with above one piece of music where the composer 
' appeared to have any intelligence of this kind. 
' The composition is about one hundred and fifty 
' or more years old, for four voices, and the words 
' are, — ' Vobis datum est noscere mysterium regni 
" Dei, cseteris autem in parabolis ; ut videntes non 
" videant, et audientes non intelligant.' By the 
' choice of the words the author seems to allude to 
' his having performed something not commonly 
' understood.' The doctor then exhibits an octave 
of the ascending and descending scales of the diatonic 
genus of the ancients, with the names of their several 
sounds, as also the corresponding modern letters, in 
the following form : — 



B 




•g" 


C 


25G 


D 


9 


E 


9 

"8" 


F 


25 G 
¥4 3" 


G 


f 


a 


9 

'S 



Proslambanomenos 


8 

•g" 


S 


Hypate hypaton 


243 
23« 


f 


Parhypate hypaton 


8 
1) 


e 


Lychanos hypaton 


8 
"9 


d 


Hypate meson 


243 

25G 


c 


Parhypate meson 


8 
"9" 


b 


Lychanos meson 


8 
'0 


a 


Mesc 




G 



He observes, that in the octave above given, the 
Proslambanomenos, Hypate hypaton, Hypate meson, 
and Mese, were called Stabiles, from their remaining 
fixed throughout all the genera and species ; and 



• Append, de Vet. Harm. 318. 



that the other four, being the Parhypate hypaton, 
Lychanos hypaton, Parhypate meson, and Lychanos 
meson, were called Mobiles, because they varied 
according to the different species and varieties of 
music. 

He then proceeds to determine the question what 
the genera and species were, in this manner: — *By 
' genus and species M^as understood a division of the 
' diatessaron, containing four sounds, into three in- 
' tervals. The Greeks constituted three genera, 
' known by the names of Enarmonic, Chromatic, 
' and Diatonic. The chromatic was subdivided into 
' three species, and the diatonic into two. The three 
' chromatic species were, the chromaticum molle, the 
' sesquialterum, and the tonifcum. The two diatonic 
' species wore, the diatonicum molle, and the inten- 
' sum ; so that they had six species in all. Some of 
' these are in wse among the moderns, but others arc 
' as yet unknown in theory or practice. 

' I now proceed to define all these species by 
' determining the intervals of which they severally 
* consisted, beginning by the diatonicum intensum as 
' the most easy and familiar. 

' The diatonicum intensum was composed of two 
' tones and a semitone ; but, to speak exactly, it con- 
' sists of a semitone major, a tone minor, and a tone 
' major. This is in daily practice, and we find it 
' accurately defined by Didymus in Ptolemy's Har- 
' monies, published by Dr. Wallis.f 

* The next species is the diatonicum molle, as yet 
' undiscovered, as far as appears to me, by any 
' modern author. Its component intervals are the 
' semitone major, an interval composed of two semi- 
' tones minor, and the complement of these two to 
' the fourth, being an interval equal to a tone major 
' and an enarmonic diesis. 

' The third species is the chromaticum tonireum, 
' its component intervals are a semitone major suc- 
' ceeded by another semitone major, and lastly, the 
' complement of these two to the fourth, commonly 
' called a superfluous tone. 

' The fourth species is the chromaticum sesqui- 
' alterum, which is constituted by the progression of 
' a semitone major, a semitone minor, and a third 
' minor. This is mentioned by Ptolemy as the 

t Dr. Wallis has remarked in the passage ahove cited, that it had long 
been a matter of controversy whether the system of the moderns corres- 
ponded with the intense diatonic of Aristoxenus, the ditonic diatonic of 
Ptolemy, or rather Pythagoras, or the intense of Ptolemy ; and though h% 
seems to incline to the opinion of Zarlino, that tlie music now in use is 
no other than the intense diatonic of Ptolemy, it is far from clear that 
the modems have gone farther than harely to admit in theory and in a 
course of numerical calculation the latter as the most eligible. Salinas, 
lib. III. cap. xiii. contends for an equality of tones, and for the consequent 
necessity of distributing throughout the diapason system those intervals 
by which the greater tones exceed the lesser. 

Bontempi, Hist. Mus. 188. says that that temperament which makes 
the intervals irrrational, is to be looked upon as a divine thing, and 
asserts that nowhere in Italy, nor indeed in Europe, does the practice of 
discriminating between the greater and lesser tone prevail in the tuning 
of the organ, and that the organ of St. Mark's chapel at Venice, where 
he liimself sang for seven years, continued to be tuned without regard to 
this distinction, notwithstanding what Zarlino had written and the efforts 
he made to get it varied. 

The practice has long been in tuning the organ, and such like instru- 
ments, to make the fifths as flat and the thirds as sharp as tlie ear will 
bear, which necessarily induces an inequality in the tones. 

Lastly, Dr. Smith, in his Harmonics, second edition, pag. 33. asserts 
that since the invention of a temperament, the ancient systems of ditonic 
diatonic, intense diatonic, &c., have justly been laid aside. So that after 
so many opinions to the contrary, it may very well be doubted whether 
the diatonicum intensum is in daily practice or not. 



Chap. VIII. 



AND PRACTICE OF MUSIC. 



30 



' cliromatic of Didymus. * Examples among the 
' moderns are frequent. 

' Thp fifth species is the chromaticum moUe. Its 
' intervals are two subsequent semitones minor, and 
' the complements of these two to the fourth, that is 
' an interval compounded of a third minor and an 
' enarmonic diesis. This species I never met with 
' among the moderns. 

* The sixth and last species is the enarmonic. 
' Salinas and others have determined this accurately, f 
' Its intervals are the semitone minor, the enarmonic 

* diesis, and the third major. 

' Examples of four of these species may be found 
' in modern practice. But I do not know of any 
' theorist who ever yet determined what the chro- 

* maticum toniseum of the ancients was ; nor have 
' any of them perceived the analogy between the 
' chromaticum sesquialterum and our modern chro- 
' matic. The enarmonic, so much admired by the 
' ancients, has been little in use among our musicians 
' as yet. As to the diatonicum intensum, it is too 

* obvious to be mistaken.' 

The above-cited letter is very far from being 
what the title of it indicates, an explanation of the 
various genera and species of music among the 
ancients. To say the best of it, it contains very 
little more than is to be met with in almost every 
writer on the subject of ancient music, except that 
seemingly notable discovery, that the ancients made 
use of both an ascending and descending scale, the 
consideration whereof will be presently resumed. 
As to the six species above enumerated, the doctor 
says four are in modern practice, but of these four 
he has thought proper to mention only two, namely, 
the diatonicum intensum, and the chromaticum ses- 
quialterum ; and it is to be wished that he had 
referred to a few of those examples of the four, 
which he says are to be found ; or at least that he 

* Lib. II. cap. xiv. 

t Salinas de Musica, lib. III. cap. viii. 



had mentioned the authors in whose works the latter 
two of them occur ; and the rather, because Dr. 
Wallis asserts that the enarmonic, all the chromatics, 
and all but one of the diatonics, for many years, he 
might have said centuries, have been laid aside. 

As to his assertion that the Greeks made use of 
both an ascending and descending scale, it is to be 
remarked, that there are no notices of any such dis- 
tinction in the writings of any of the Greek har- 
monicians. The ground of it is a composition about 
one hundred and fifty years old, in the year 1746, to 
the words of a verse in the gospel of St. Mark,| so 
obscure, if we consider them as referring to the 
music, that they serve more to excite, than allay 
curiosity ; and Dr. Pepusch could not have wished 
for a fairer opportunity of displaying his learning 
and ingenuity than the solution of this musical 
enigma afforded him. Nay, had ho condescended 
to give this composition in the state he found it, or 
had he barely referred to it, the world would have 
been sensible of the obligation. The only excuse 
that can be alledged for that incommunicative dis- 
position which the whole of this letter betrays, is, 
that the author of it subsisted for many years by 
teaching the precepts of his art to young students, 
and it was not his interest to divulge them. How 
far the composition above-mentioned, which is not 
yet two hundred years old, is an evidence of the 
practice of the ancient Greeks, will not here be in- 
quired into ; but it may gratify the curiosity of the 
reader to be told that the author of it was Costanzo 
Porta, a Franciscan monk, and chapel-master in the 
church of St. Mark, at Ancona, and that it is pub- 
lished at the end of a book printed at Venice in 1600, 
entitled, ' L' Artusi, overo delle Imperfettioni della 
moderna Musica,' written by Giovanni Maria Artusi, 
an ecclesiastic of Bologna, of whom a particular 
account will hereafter be given. As to the com- 
position, it is for four voices, and is as follows : — 

t Chap, iv, ver. 9. 




Mp 



— o- 



=ri3 



<- — h- 



)jji<S A — r 



:t=? 



5 



^ 



Vo 



,his da - turn est 



no - see Mis - te 



n - um no - 



■^ 



-- — 0- 



--^z=.^: 



:i=i: 



^^ 



L^E£ 



-H-l— I- 



iit: 






Vo - bis da - turn est 



no - see Mis - te - 



n - um, no 



see Mia - te - ri 



^: 



^=?= 



T=-M=^-;= 



3^4^ 



Vo 



bis da - turn est 



no - see Mis 




6 V ' -» 



t=P 



^^ 



^=^ 



:t 



^ 



^—T 



-Jr-^ii 



-« — o=?= 



bis da -turn est no -see Mis - te - li-uin, no - see Mia -to - ri • um, 



40 



HISTORY OF THE SCIENCE 



Book I. 




see Mis - te - ri 



^l5=i^^l3:^l 



-um, 






Vo - bis da-tum 



est 



no - see Mis 



te - ri - iim, 



:iL~t:=t; 



^- 



^ 



I — I i — «>- 

--I — ♦ — ;^ — |— 



te 



ri - um. 



Vo 



bis da - turn est no - see IMis 



te 



HE: 



l^^if^si^^^i^H^i^ 



tz; 



— ♦- 



Vo - bis da-tura est 



no -see Mis - te 



n - um, 



n 



•^w 






11 

41 




— t: 



r-iz:]--:. 



:^- 



—tzzszzz 



' -um, Reg - ni De 



l^fp: 



m^m 



Ce - te-ris au-tem in Pa - ra - bo - lis, 



Si 



t:: 



^^eeS 






— 0- 



Ce - te-ris au-tem in Pa 




Reg - ni De 



te-ris au-tem 



_^ 




i 



ft 



^t=it:=|; 



-■ i — 6 — ^ — i A 



:± 



Ut vi - den - tes non 



m 



vi - de 

3S 



Mm 



Ut vi - den - tes non 



vi - de 



ant, 



:=c: 



ant. 



iJ ^ij— 1^ 



Et 



au - di 



!l^E^t"=i 



Et au - di - 



— — 



— 0- 



^ 



1— dd^^-Si--?z^ : 



in Pa - ra - bo - lis. 



Ut 



vi - den 



tes non vi 



"F?T— ^ — 



"N 



zzitzi^EE^ 



i^=r0-=q=z;q: 



-iS — jS- 



in Pa - ra - bo - lis, 



Ut vi - den 



tes non vi 



ite^ 



dc - ant, 
j> — ;?- 



—c- 



de - ant. 



krs 




' " -en - tes. 



li=2 



■ ^-1= 



-0 - 



jg ^gj^ggg 






et au - di - en 




m 



tF= 



;i^ 



—I- 



tz:^^E^ 



en 



tes, 



et au - di - en 



tes non 



tes non 

T- 



3? — '--^—\ — •^-t-4-— ir— ^ — ^— -^ — -A — if' — o— 



in - tel - 

T O 



li - 



LSeI= 



in - tel - ligant, non in - tel - li 









i=gl3^ 



zi-;:~5: 



:fc; 



■^ 



■§ 



Et au - di 



en - tes 



non in - tel 



li - gant. 



non 



e±= 



-4=^-- 



?: 



•n 



E^^ 



-iS-'^ — J-f-ir 



:p=t=tr^ 



in - tel 






Et au - di 



en 



tes 



non in - tel 



li - gant, non 



in - tcl - 



h - 



CiiAr. VIII. 



AND PRACTICE OF MUSIC. 



41 




i^E^^^fe^l 



gant, 



vi - den 



non vi-de - ant, ut vi - den - tes non vi 



de - ant, 






li - gant. 




li - gant. 



?s^^i=i^ili^E^ls^^ 



et au-di - en 



non in - tel 



11 - gant 



gant. 



Artnsl observes upon this composition, which, the 
better to shew the contrivance of it, is here given 
in score, that it is a motet for four voices, and that 
it may be sung two ways, that is to say, first, as the 
cliffs direct tliat are placed nearest to the notes, and 
afterwards turning the top of the book downwards, 
from the right to the left ; taking the extreme cliff 
for a guide in naming the notes ; the consequence 
whereof will be, that the base will become the soprano, 
the tenor the contralto, the contralto the tenor, and 
the soprano the base. Besides this, he says that the 
second time of singing it, b must be assumed for ^., 
and in other instances fa for mi. He concludes with 
a remark upon the words of this motet, that they 
indicate that it is not given to every one to under- 
stand compositions of this kind. 

Upon the example above adduced the remark is 
obvious, that it falls short of proving the use of both 
an ascending and descending scale by the Greek 
harmonicians. In a word, it is evidence of nothing 
more than the antiquity of a kind of composition, of 
which it is probable Costanzo Porta might be the 
inventor, namely that, where the parts are so con- 
trived as to be sung as well backwards as forwards. 
In this he has been followed by Pedro Ccrone, and 
other Spanish musicians, and by our own countryman 
Elway Bevin, and others, who seem to have thought 
that the merit of a musical composition consisted 
more in the intricacy of its construction than in its 
aptitude to produce the genuine and natural effects 



of fine harmony and melody on the mind of an 
unprejudiced hearer. 

From the foregoing representations of the genera, 
the reasons for the early preference of the diatonic 
to the chromatic and enarmonic are clearly deducible; 
but notwithstanding these and the consequent rejec- 
tion of the latter two by Guido and all his followers, 
the ingenuity of a few speculative musicians has 
betrayed them into an opinion that they are yet 
actually existing, and that with the addition of a few 
intervals, occasionally to be interposed among those 
that constitute the diapason, both the chromatic and 
enarmonic genera may be brought into practice. 

The first of these bold assertors was Don Nicola 
Vicentino, an author of whom farther mention will 
hereafter be made. . In a work entitled ' L'Antica 
Musica ridotta alia Moderna Prattica,' published by 
him at Rome in 1555, we find not only the tetra- 
chord divided in such a manner as seemingly to 
answer the generical division of the ancients, but 
compositions actually exhibited, not only in one and 
the other of the genera, but in each of them severally, 
and in all of them conjunctly, and this with such 
a degree of persuasion on his part that he had accur- 
ately defined them, as seems to set all doubt at 
defiance. 

It is true that little less than this was to be 
expected from an author who professes in the very 
title of his book to reduce the ancient music to 
modern practice, but that he has succeeded in his 



42 



HISTORY OF THE SCIENCE 



Book I. 



attempt so few are disposed to believe, that in the 
general estimation of the most skilful professors of 
the science, Vicentino's book has not its fellow for 
musical absurdity.* And of the justice of this 
censure few can entei'tain a doubt, that shall peruse 
the following account of himself and of his studies : — 
' To shew the world that I have not grudged the 
' labour of many years, as well for my own improve- 
' ment, as to be useful to others, in the present work 
' I shall publish all the three genera with their 
' several species and commixtures, and other inven- 

* tions never given to the world by any body; and 
' shall shew in how many ways it is possible to 
' compose variously in the sharp and flat modes : 
' though at present there are some professors of 
' music that blame me for the trouble I take in this 

* kind of learning, not considering the pains that 

* many celebrated philosophers have taken to explain 
' the doctrine of harmonics ; nevertheless I shall not 
' desist from my endeavours to reduce to practice the 
' ancient genera with their several species by the 
' means of voices and instruments ; and if I shall 
' fail in the attempt, I shall at least give such hints 
' to men of genius as may tend to the improve - 

* ment of music. We see by a comparison of the 
' music that we use at present, with that in practice 
' a hundred, nay ten years ago, that the science is 
' much improved ; and I doubt not but that these 
' improvements of mine will appear strange in com- 
' parison with those of our posterity, and the reason 
' is, that improvements are continually making of 
' things already invented, but the invention and be- 
' ginning of every thing is difficult ; therefore I re- 
' joice that God has so far favoured me, that in these 
' days for his honour and glory I am able to sliew 
' my honourable face among the professors of music. 
' It is true that I have studied hard for many years ; 
' and as the divine goodness was pleased to enlighten 
' me, I began this work in the fortieth year of my 
' age, in the year 1550, the jubilee year, in the 
' happy reign of Pope Julius the Third ; since that 
' I have gone on, and by continual study have en- 

' deavoured to enlarge it, and to compose according 
' to the precepts therein contained, as likewise to 
' teach the same to many others, who have made 
' some progress therein, and particularly in this 
' illustrious town of Ferrara, where I dwell at pre- 
' sent, to the inhabitants whereof I have explained 
' both the theory and practice of the art ; and many 
' lords and gentlemen who have heard the sweetness 
' of this harmony have been charmed therewith, and 
' have taken pains to learn the same with exquisite 
' diligence, because it really comprehends what the 
' ancient writers shew. As to the diatonic genus, it 
' was in use in the music sung at public festivals, and 

* in common places, but the chromatic and enarmonic 
' were reserved for the private diversion of lords and 
' princes, who had more refined ears than the vulgar, 
' and were used in celebrating the praises of great 

* persons and heroes. And, not to detract from the 

• This is remarked by Gio Battista Doni, in his treatise entitled 
De Prsstantia Musicae veteris. Florent. 1647, and numberless other 
writers. Kircher, however, seems to entertain a different opinion of it; 
his sentiments are given at length in a subsequent page of this chapter. 



' virtues of the ancient princes, the most excellent 
' prince of Ferrara, Alfonso d' Este, after having very 

* much countenanced me, has with great favour and 
' facility learned the same, and thereby shown to the 
' world the image of a perfect prince ; and he, as he 

* has a most worthy name of eternal glory in arms, 
' so has he acquired immortal honours by his skill in 
' the sciences.'f 

In the prosecution of this his notable design of 
accommodating the ancient music to modern practice, 
Vicentino has exhibited in the characters of modern 
notation a diatonic, a chromatic, and an enarmonic 
fourth and fifth in all their various forms. The 
following is an example of their several varieties, 
taken from the third book of his work above-cited, 
pages 59 a, 59 b, 62 b, et seq. : — 

DIATONIC FOURTHS. 

12 3 



^m' 



EaiE 



z:;s=5z: 



<&- 



6— szr^ 



zsz 



CHROMATIC FOURTHS. 

12 3 



EP 



-^l-=^±^^±=±z 



:0-)j(<& 



ZJ2~ 



ZS 



-fc& — ^ 



o- 



ENARMONIC FOURTHS. 

12 3 



3£ 



?0 — 0- 



35z:2; 



-o 



Zl^^I^ZZ^ 



_s5_si 



:^i=-^- 



DIATONIC FIFTHS. 



M 



I— 



-^=SZ 



:i==2: 



:^=Z5.— 



i 



^=0^=2: 



"t« 


C H R MA T I C 

t 1 


I FIFTHS. 

2 


<5 


4\A 




s> ' 





A- 



:=s:z&s5r-:2zf±z=±: 



:b2— 51 



?e — ♦- 



ENARMONIC FIFTHS. 

1 2 



-O— &- 



mgg-O oife 



■^ 



-0- 



:^ 



^^-« 



zfaifezisr 



M 



M:=^=^^^^^^^ 






Having thus adjusted the several intervals of a 
fourth and fifth in each of the three genera, the 
author proceeds to exhibit certain compositions of his 
own in each of them ; and first we have a motet 
composed by himself, and sung, as he says, in his 

t Iiibro prlmo, cap. iv. 



Chap. VIII. 



AND PKACTICE OF MUSIC. 



43 



church on the day of the resurrection, as a specimen 
of the true chromatic : — - 



-] 



,'11 



iw 



S: 



:=P=i5: 



-g-«- 



'-^^m-"^ 



-AVi 



^^-^^^g gj^____-^^^ ^UU| 



Al-le-lu-ia, Al-lo-lu-ia, Al-le-lu-ia, 



I Al - le - lu - ia, Al - le - lu - ia, Al - le - lu - ia, 



m 



IE? 



^=i==? 



t:±Et 



'W 



:jn P^-^^-^-H^ ^^ F=a ^^ .1 



f 



:4- 



':^^E:±^ 



J^ 



Al-le - lu - ia, Al-le - lu 



Al-le-lu-ia, Al-le-lu - - ia, hac di-es 



-{■-[ 



SII35: 



H — ,»—«>- 



-A 1 



-l=p: 



la, hffic di - es quam 



3C 



itnc:: 




— 



«9 «• 



i^E^^^z^s^^fe M 



-^— -^ ^— -^ ■- — "---^ — '^--- -ii^i — s— y— » -— -* — ■» — :^ — 0-^t /K3 — 1^ 

quam fe - cit do - nii-nus, ha;c di - es quam fe - cit q^LY. ' ' | ~cj [~ y | r y Q "^ H' 



^^^ 

fe-cit ij do - mi-nus, hac di-csquamfe-cit 



3C 



^i^^ 



•& «► 



a^EESES 



j Ij do - mi-nus, quam fe-cit do - mi 



bSr. 



'^iT- 



nus; 



h 



do -minus, quam fe-cit do - mi - nus; Ex-ul - 



ZI--5-: 



-^g-b^r^- 



I- 



P^ 



;i^ 



--0- 



w- 



llfV! 



11 Ex - ul - te-mus et le-temur, ex-ul -te-mus et le - -M-?-— 



te-mus et le - te-mur, ex - ul - te - mus et le 






*:=: 



^^3;^-^=g5^z^£*^^=zrM: 



IPlI - te - mur in ea, et le - te - mur in ea. 



-a-^g — n-^- 



- - te-mur in e - a, et le - te-mur in e - a. 



^1 



3^^ 



^^g~fe 



-m-^- 



-— E§=^ 



"^W 



zsz:. 



Slife?=5== 



3^E2 



"'SV 



Al-le-lu - ia, Al-le-lu - ia, Al-le-lu - ia, 






s ^ 1—1 H <^ / 


^ C" ■• t V Y 


S H<> ftH'*- 


>- 1 ' ■ T ■ ^v- 


nn - 1— 1 ■> P 







Al-le - 


lu-ia, Al-le-lu - ia. 


Al-le-lu - ia, 


-Sj?-- H 


^> 


^ 1— 1 • / 


s 


H+— 


t 





Al-le-lu - ia, Al-le - lu 



ia, hjEc 



^i 



Al-le-lu-ia, Al-le-lu - ia, hrec di-es quam 



gi^E^^^=E 



:±=i-=E 



r'w 



di - es quam fe - cit do - mi - nus, ha2c di - es 



il- 



^t- 






¥*EE£ 



It 



--w^ 



EPs- 



5 C^I 



:2izq=i 



^ 



:=:prr3: 



fe - cit do - mi-nus, hajc di - es, hsec di - es quam 



quam fe - cit do - mi 



-R- 



-m 



- nus ; Ex - ul - te - 






s 



z:i: 



d: 



^ 



S^ 



^ ^ ^ m-^- ^ ^ 



■^=t=±: 



fe - cit do - minus, quam fe - cit do - mi - nus ; 



-n- 



--^l 



"H-TT 



"W^ 



-m 



- - mus et le - te-mur, ex-ul - te-mus et le - te 



Ex-ul - te-mus et le - te-mur, ex-ul - te-mus et le - 



E3E 



W- 



.-^^ig' ^-ziz— 



43 



m 



te-mur in e - a, et le - temur in e - a. 



- - mur in e - a, et le - te-mur in e - a. 

Alleluia. 
As an example of the enarmonic, he gives the fol- 
lowing, which is the beginning of a madrigal in four 
parts : — 



S 



In I So-av' e dol-c'ar-do-re ij 



rqzxzr: 



-«— « — "»- 



-a- 



3z±i 



^i^ 



r.^i#2iiir?±if^z=±: 



= izrtzrlizrl^si^izgzrr 



che fra piante sos-pi- ri, che fra pi - an - te sos-pi-ri 



f:=F=t:=p:^iE^^^^^:^E^^E^=^ 



41 



^EFg ^±i?-^ ^-J^ = 



SZI^-i-^ 



=t 



ztEE 



So - av' e dol » c'ar - do - re ij che fra piante sos-pi - ri ij 




So-av' e dol - c'ar - do -re ij 



che fra piante sos-pi - ri ij 



Eii; 



^^4: 



iSE^^^^E^^; 



3=3E5El-EiE 



--Rz:b2= 



So-av' e doWar do - re ij 



- .> »-^^tr— ( - 



NJ-^pl=i=^ 



-| ? T 



che fra piante sos - pi - ri - plan 



Note. — Vicentlno has not been pflrticular in explaining the use of the points over many of the notes in this and the following examples of th« 
enarmonic ; but from the practice of Salinas and other writers it ia presumed that the point is intended to denote the enarmonic diesis as defined in 
:lic foregoing representations of that genus. 



44: 



HISTORY OF THE SCIENCE 



Book I. 



And as a proof of the practicability of nniting all 
the genera in one composition, he exhibits the fol- 
lovring madrigal for four voices, which he says may 
be sung in five ways, that is to say, as diatonic, as 
chromatic, as chromatic and enarmonic, as diatonic 
and chromatic, and lastly as diatonic, chromatic, and 
enarmonic : — 



i fe^?--"^""?-?^^— -^-^^-*- 



^^fefei^EtE' 



t|:=E=s: 



m. 



-O } 

— P— c> — w- 




qucs-ti dol - ci ki - mi, dol-ci lu - mi che tan-to 






2=[r-.t:=±ii:«L 



E_1^E=EE-^ 



dol-cc-mcn-te, che tan -to dol-ce-mente mi 



iii^^pi^E^Ea^^ fe^liiEE:!^^:^^!^ 



--Vfi 



Fir 



Dol-ce mi-o ben ij 



son questi dol-ci 



t 



?r&^.K^^=:r^ 



-> — o 

:t:=zt— p— pzis: 



li-±iiT;1=^:ifei=3^ 



Jl- 



con-su-mi, che tan -to dol-ccmen-te mi con - 



:p=:t 



■w- 



i-k— — o— -— 



t: 






E:t?.*E5 



"ffEi'B: 



lu - mi, dol - ci lu - mi, dol - cc mio ben son questi 



- su - mi dol - ce - mcn-te, mi con - su - mi. 



■^^^- 



Z-L. 1 ^ — .4. 






dol-ci lu-mi son questi, dol-ci lu - mi che 



ibj: 



lin*: 



tan - to, dol-cc-men-te che tau - to, dol-ce-men-te 



a 



—jnz 



lEHEl 



— ^ 



-0— c— --1— -1 — ^ — -J 



■w 



=w-: 



Dol-ce mi-o ben ij 



son ques-ti 



:^-: 



111=1 






iiiii^^=:i 



i~T^ 



mi con-su-mi, che tan-to dol-ce-men-to fan - no, l3:^z:!^=z:^pzi:tz. 



dol-ci lu-mi, dol-ce mi-o ben ij 
P— o — «■— ^~H — -" ^"^" 



=11 



k — I — — — -— — ~— 

3iitz=±--p-pz=ip-*-^ — 



-4zzil-tez3^ 



:t-2.-H=:U- 



son ques-ti dol-ci lu-mi che tan-to dol-ce 



II ' che dol.ce-men-te mi con-su-mi, mi con- su- mi. -^-^k— R — A — H — tm'^L'll'^ 

Z±PL_2 SZZlp—p — p — ^ 



LS; 



-0 — 



men-te 



fan - no, che 



Sa^^i=SEa^t7 









--t— p=p=p: 



j^ 



Dol-ce mio bcu ij 



son questi dol - ci 



mi con-su-mi, che dol-ce-men-te mi con - 



:13 



SF 



2_<s__Y. — — r — 0— 0-li— ^ — — 



m 



"W 



t$^^ 



t 



i 



lu-mi, dol-ce mi - o ben ij 



son ques-ti, 




q1: 



d2zr)r_o__, 



dol-ci lu-mi, dol-ci lu-mi, che tan-to, che tan- to, 



?&=5 



:fl^;p^-p3=p 



P0- 



:fc 






-0 



i:- 



i <5— W- 

:Ez:zP=-z 



dol - ce-mente fan-no, che dol-cemen-te, die dol - 



:fe 



Ifl 



L-zzp: 



svrzpr^-^izrp: 



-0 — 



-<>-w- 



:t-t; 



P^=^=Hitl: 



i-dzzqiup— 



- ce-mente mi con-su-mi, mi con-su-mi, fan-no che 



m^l^^^^l^i 



dol-ce-men-te mi con-su-mi, mi con - su - mi. 






=q-~q: 



i^r-rl 



M 



-0— -0-)^ 0- 



ri: 



:±ii-izzp=p=p=t=: 



iq-zmi 



Dol-ce mi-o ben son questi dol-ci lu 



» - mi, dol-ce mio ben son ques-ti dol-ci lu-mi, son 



- su - mi, mi con - su - mi. Hay - me. 

Kircher seems to think that Vicentino has suc- 
ceeded in this his attempt to restore the ancient 
genera ; and if he has, either the discovery was of 
no worth, or the moderns have a great deal to 
answer for in their not adopting it. The following 
are the sentiments of Kircher touching Vicentino 
and his endeavours to reduce the ancient music to 
modern practice : — ' The first that I know of who 
' invented the method of composing music in the 
' three genera, according to the manner of the ancients, 
' was Nicolaus Vicentinus ; * who when he perceived 
' that the division of the tetrachords according to the 
' three genera by Boetius could not suit a poly- 
* phonous melothesia and our ratio of composition, 
' devised another method, which he treats of at large 
'in an entire book. There were, however, not 
' wanting some, who being strenuous admirers and 

* Kirclicr is mistaken in liis assertion that Vicentinowas the first who 
attempted the revival of the ancient genera; for it seems tliat Giovanni 
Spataro, of Bologna, in the year 1512,' made an attempt of that kind, but 
■without success. Storia della Musica di Giambatista Martini, torn. I. 
pag. 12G, in not. 

But notwithstanding the discouragem.ents the two writers above- 
mentioned met with, Domenico Mazzochi, of Rome, about the year 1600, 
attempted a composition in all the three genera, entitled Planctus Matria 
Euryalis, wliich is printed in the Musurgia, torn. I. pag 660. 



Chap. IX. 



AND PRACTICE OF MUSIC. 



45 



' defenders of ancient music, cavilled at him wrong- 

* fully and undeservedly for having changed the 
' genera that had been wisely instituted by the 
' ancients, and put in their stead I know not what 
' spurious genera ; but those who shall examine 
' more closely into the affair will be obliged to con- 
' fess that Vicentinus had very good reason for what 

* he did, and that no other chromatic enarmonic 

* polyphonous melothesia could be made than as he 
' taught.' * 

This declaration of Kircher is not easily to be 
reconciled with those positive assertions of his in the 
Musurgia, that the ancients were strangers to poly- 
phonous music ; and the examples above given are 
all of that kind. 

But waving this consideration, whoever will be at 
the pains of examining these several compositions, 
will find it a matter of great diificulty to reconcile 
them with the accounts that are given of the manner 
of dividing the tetrachord in the several genera ; he 
will not be able easily to discover the chromatic in- 
terval of three incomposite semitones ; much less 
will he be able to make out the enarmonic diesis ; 
and much greater will be his difficulty to persuade 
himself, or any one else, that either of the above 
compositions can stand the test of an ear capable of 
distinguishing between harmony and discord. 

But all wonder at this attempt of Vicentino must 
cease, when it is known that he contended with some 
of the greatest musicians, his contemporaries, that the 
modern or Guidonian system was not simply of the 
diatonic kind, but compounded of all the three genera. 
He has himself, in the forty-third chapter of his 
fourth book, given a most curious relation of a dis- 
pute between him and a reverend father on this 
subject, which produced a wager, the decision 
Avhereof was referred to two very skilful professors, 
Avho gave judgment against him. An account of this 
dispute is contained in a subsequent chapter of the 
present work. 

CHAP. IX, 

It does not anywhere appear that the music which 
gave rise to the controversy between Vicentino and 
his opponents, was any other than what is in use at 
this day ; which that it is the true diatonic of the 
ancients is more than probable ; though, whether it 
be the diatonicum Pythagoricum, or the diatonicum 
intensum of Aristoxenus, of Didymus, or of Ptolemy, 
has been thought a matter of some difficulty to 
ascertain, but is of little consequence in practice. 

But we are not to understand by this that the 
music now in use is so purely and simply diatonic, 
as in no degree to participate of either the enarmonic 
or chromatic genus, for there is in the modern scale 
such a commixture of tones and semitones as may 
serve to warrant a supposition that it partakes in 
some measure of the ancient chromatic ; and that it 
does so, several eminent writers have asserted, and 
seems to be the general opinion. Monsieur Brossard 
says, that after the division of the tone between the 

« Musurg. torn. I. pa^. G37. ' 



Mese and Paramese of the ancients, which answer to 
our A and J], into two semitones, it was thought 
that the other tones might be divided in like manner; 
and that therefore the moderns have introduced the 
chromatic chords of the ancient scale, and thereby 
divided the tones major in each tetrachord into two 
semitones : this, he adds, was effected by raising the 
lowest chord a semitone by means of this character, 
% which was placed immediately before the note 
so to be raised, or on its place immediately after 
the cliff. Again he says, that it having been found 
that the tones minor terminating the tetrachords 
upwards were no less capable of such division than 
the tones major, they added the chromatic chords to 
the system, and in like manner divided the tones 
minor, so that the octave then became composed of 
thirteen sounds and twelve intervals, eight of which 
sounds are diatonic or natural, distinguished in the 
folloAving scheme by white notes thus, o and five 
chromatic by black ones thus, ♦ with the sharp sign, 
which Brossard calls a double diesis prefixed to each 
of the notes so elevated : — 




This, though a plausible, is a mistaken account of 
the matter ; for first it is to be observed, this intro- 
duction of the semitones into the system, was not for 
the purpose of a progression of sounds different from 
that in the diatonic genus : on the contrary, nothing 
more was intended by it than to render it subservient 
to the diatonic progression ; or, in other words, to 
institute a progression in the diatonic series from any 
given chord in the diapason, and we see the design of 
this improvement in its effects. 

For, to assume the language of the moderns, if we 
take the key of E, in which no fewer than four of the 
sharp signatures are necessary, it is evident to demon- 
stration that in the system of the diapason the tones 
and semitones will arise precisely in the same order 
as they do in the key of C, where not one of those 
signatures are necessary, and the same, mutatis 
mutandis, may be said of all the other keys with the 
greater third ; and the like will be found in those 
with the lesser third, comparing them with that of 
A, the prototype of them all. J 

From hence it follows, that the use of the above 
signatures has no effect either in the intension or 
remission of the intervals ; but the same remain, not- 
withstanding the application of them the same as in 
the diatonic genus. 

It is true, that since the invention of polyphonous 
or symphoniacal music, a species of harmony of 
which the ancients seem to have been totally 
ignorant ; among the various combinations that may 
occasionally occur in a variety of parts, some may 
arise that shall nearly answer to the chromatic in- 
tervals, and it shall sometimes happen that a given 
note shall have for its accompaniment those sounds 
that constitute a chromatic tetrachord ; and of this 
opinion are some of the most skilful modern organists, 

P + Dictionaire de Musique, Article Systema. 
f j See this demonstrated in the next book. 



46 



HISTORY OF THE SCIENCE 



Book I. 



who are inclined to think that they sometimes use the 
chromatic intervals, without knowing that they do 
so.* But the question in debate can only be de- 
termined by a comparison of the melody of the 
moderns with that of the ancients ; and in that of 
the moderns we meet with no such progression as 
that which is characterised by three incomposite 
semitones and two semitones, which is the least 
precise division of the tetrachord that any of the 
ancients have given us. 

Our countryman Morley gives his opinion of the 
matter in the following words : — ' The music which 
' we now use is neither just diatonic, nor right 
' chromatic. Diatonicum is that which is now in use, 
' and riseth throughout the scale by a whole note, a 
* whole note, and a lesser or half note. A whole note 
'is that which the Latins call Integer Tonus, and 
' is that distance which is betwixt any two notes, 
'except mi andja; for betwixt mi and Ja is not a 
' full halfe note, but is lesse than halfe a note by a 
' comma, and therefore called the lesser halfe note, in 
' this manner : — 



* Likewise by that which is said it appeareth tliis 
' point, whiclx our organists use — 



f 



:g=?yG5 — ^-^ ^ 



' is not right chromatica, but a bastard point, patched 
' up of halfe chrouiaticke and half diatonick. Lastlie, 
' it appeareth by that which is said, that those vir- 
' ginals which our unlearned musytians cal cromatica 
' (and some also grammatica) l)e not right chromatica, 
' but half enharmonica ; and that al the chi'omatica 
' may be expressed uppon our common virginals ex- 
' cept this : — 



t=±: 



:te 



i 



— <&- 



'Chromaticum is that which riseth by semitonium 
' minus, or the less halfe note, the greater halfe note, 
* and three halfe notes thus : — 



i 



azfes: 



:Bt 



-<»-#»- 



'The greater halfe note betwixt Jh and mi in b 
'Ja J] mi. Enarmonicum is that which riseth by 
'diesis, diesis (diesis is the halfe of the lesse halfe 
' note) and ditonus ; but in our musicke I can give no 
' example of it, because we have no halfe of a lesse 
' semitonum ; but those who would shew it set down 
' this example 



Oi 



-cN O— )^-»- 



-♦— 



of enarmonicum, and mark the diesis thus x as it 
were the halfe of the apotome or greater halfe note, 
which is marked thus ^. This sign of the more 
halfe note we now-a-daics confound with our b 
square, or signe of mi in \j mi, and with good 
reason ; for when mi is sung in b fa }-j mi, it is in 
that habitude to a la mi re, as the double diesis 
maketh F ya ut sharpe to E la mi, for in both 
places the distance is a whole note ; but of this 
enough : and by this which is already set downe, it 
may evidentlie appeare that this kind of musick 
which is usual now-a-daies, is not fully and in 
every respect the ancient diatonicum ; for if you 
begin any four notes, singing ut, re, mi, fa, you 
shall not find either a flat in E la mi, or a sharp in 
F fa ut ; so that it must needes follow that it is 
neither just diatonicum nor right chromaticum. 

" It is also said, that in passages of notes in succession the chromatic 
intervals sometimes occur. The following not uncommon passage is 
eaid to be an example of the hemiolian or sesquialteral chromatic : — 



t 



:5r$5s: 



t- 

' for if you would thinke that the sharpe in g sol re 
' ut would serve tliat turne by experiment, you shall 
' find that it is more than halfe a quarter of a note too 
'low.'t 

From hence we may conclude in general, that the 
system as it stands at present, is not adapted to the 
chromatic genus ; and were there a possibility, which 
no one can admit, of rendering the chromatic tolerable 
to a modern ear, the revival of it would require what 
has often been attempted in vain, a new and a better 
temperament of the system than tlie present. 

From the several hypotheses above stated, and the 
different methods of dividing the tetrachord in each 
genus, it clearly appears that among the most ancient 
of the Greek harmonicians there was a great diversity 
of opinions with respect to the constitution of the 
genera. And it also appears that both the chromatic 
and enarmonic gave way to the diatonic, as being the 
most natural, and best adapted to the general sense of 
harmony ; indeed it is very difficult to account for 
the invention and practice of the former two, or to 
persuade ourselves that they could ever be rendered 
grateful to a judicious ear. And after all that has 
been said of the enarmonic and chromatic, it is highly 
probable that they were subservient to oratory, or in 
short that they were modes of speaking and not of 
singing, the intervals in which they consist not being 
in any of the ratios which are recognized by the ear 
as consonant. 

Another subject in harmonics, no less involved in 
obscurity, is the doctrine of the Modes, Moods, or 
Tones, for so they are indiscriminately termed by 
such as have professed to treat of them. The appel- 
lation of Moods has indeed been given to the various 
kinds of metrical combination, used as well in music 
as poetry, and were the word Tone less equivocal 
than Mode, it might with propriety be substituted in 
the place of the former. Euclid has given no fewer 
than four senses in which the word Tone is accepted;^ 
whereas that of Mode or Mood is capable of but two ; 
and when it is said that these appellations refer to 
subjects so very different from each other as sound 

t Plaine and easie Introduction to Practicall Musicke. Annotations 
on Part I. 

I Introd. Harmon, ex. vers. Meibom. pag. 19. et vide Meib. in loc 
citat. 



Chap. IX. 



AND PRACTICE OF MUSIC. 



47 



and duration, that is to say tone and time, there can 
be little doubt which of the two is to be preferred. 

To consider the term Mode in that which is con- 
ceived to be its most eligible sense, it signifies a 
certain series or progression of sounds. Seven in 
number at least are necessary to determine the nature 
of the progression ; and the distinction of one mode 
from another arises from that chord in the system 
from whence it is made to commence ; in this respect 
the term Mode is strictly synonymous with the word 
Key, which at this day is so well understood as to 
need no explanation. 

As to the number of the modes, there has subsisted 
a great variety of opinions, some reckoning thirteen, 
others fifteen, others twelve, and others but seven ; 
and, to speak with precision, it is as illimitable as 
the number of sounds. The sounds that compose 
any given series, with respect to the degree of 
acumen or gravity assigned to each, are capable of 
an innumerable variety; for as a point or a line may 
be removed to places more or less distant from each 
other ad infinitum ; in like manner a series of sounds 
may be infinitely varied, as well with respect to the 
degree of acumen or gravity, as the position of each 
in the system ;* we are therefore not to wonder at 
the diversity of opinions in this respect, or that 
while some limit the modes to seven, others contend 
for more than double that number. 

At what time the modes were first invented does 
no where clearly appear. Bontempi professes him- 
self at a loss to fix it;f but Aristides Quintilianus 
intimates that they were known so early as the time 
of Pythagoras ; | and considering the improvements 
he made, and that it was he who perfected the great 
or immutable system, it might naturally be supposed 
that he was the inventor of them ; but the contrary 
of this is to be inferred from a passage in Ptolemy, 
who says that the ancients supposed only three modes, 
the Dorian, the Phrygian, and the Lydian,§ denomi- 
nations that do but ill agree with the supposition 
that any of them were invented by Pythagoras, 
who it is well known was a Samian. But farther, 
Aristides Quintilianus, in the passage above referred 
to, has given the characteristical letters of all the 
fifteen modes according to Pythagoras ; so that ad- 
mitting him to have been the inventor of the ad- 
ditional twelve, the institution of the three primitive 
modes is referred backwards to a period anterior 
to that in which the system is said to have been 
perfected. 

Euclid relates that Aristoxenus fixed the number 
of the modes at thirteen, that is say, 1. The Hyper- 
mixolydian or Hyperphrygian. 2. The acuter Mix- 
olydian, called also the Hyperiastian. 3. The graver 
Mixolydian, called also the Hyperdorian. 4. The 
acuter Lydian. 5. The graver Lydian, called also 
the iEolian. 6. The acuter Phrygian. 7. The 
graver Phrygian, called also the lastian. 8. The 
Dorian. 9. The acuter Hypolydian. 10. The graver 
Hypolydian, called also the Hypooeolian. li. The 

* Wallis, Append, de Vet. Harm. pag. 312. 

+ Histor. Mus. pag. 136. 

t Lib. I. pag. 28, ex. vers. Meibom. 

§ Hoimonicor. lib. II. cap. vi. x. ex vers. Wallis. 



acuter Hypophrygian. 12. The graver Hypophry- 
gian, called also the Hypoiastian. 13. The Hypo- 
dorian. || The most grave of these was the Hypo- 
dorian ; the rest followed in a succession towards the 
acute, exceeding each other respectively by a hemi- 
toue ; and between the two extreme modes was the 
interval of a diapason. ^ 

The better opinion however seems to be, that 
there are in nature but seven, and as touching the 
diversity between them, it is thus accounted for. The 
Proslambanomenos of the hypodorian, the gravest of 
all the modes, was, in the judgment of the ancients, 
the most grave sound that the human voice could 
utter, or that the hearing could distinctly form a judg- 
ment of; they made the Proslambanomenos of the 
hypoiastian or graver hypophrygian to be acuter 
by a hemitone than that of the hypodorian; and 
consequently the Hypate of the one more acute by 
a hemitone than the Hypate of the other, and so on 
for the rest ; so that the Proslambanomenos of the 
hypoiastian was in the middle, or a mean between 
the Proslambanomenos of the hypodorian and its 
Hypate hypaton. The Proslambanomenos of the 
acuter hypophrygian w'as still more acute by a hemi- 
tone, and consequently more acute by a whole tone 
than the hypodorian, and therefore it coincided with 
the Hypate hypaton of that mode, as is thus re- 
presented by Ptolemy, lib. II. cap. xi.*''* 



ACUTE 



Tone 



Limma 



Tone 



Tone 



Limma 



Tone 



Tone 



Hypermixolydian 

Mixolydian 

Lydian 

Phrygian 

Dorian 

Hypolydian 

Hypophrygian 

Hypodorian 



GRAVE 



Those who contended for fifteen modes, among 
whom Alypius is to be reckoned, to the thirteen 
above enumerated, added two others in the acute, 
which they termed the Hyperlydian and Hyper- 
£eolian.ff 

But against this practice of increasing the modes 
by hemitones, Ptolemy argues most strongly in the 
eleventh chapter, and also in the four preceding 
chapters of the second book of his Harmonics : and 
indeed were it to prevail, the modes might be 
multiplied without end, and to no purpose. Not- 
withstanding this, Martianus Capella contends for 
fifteen and Glareanus for twelve modes ; but it is to 

II Euclid. Introd. Harm. pag. xx. 

IT Wallis. Append, de Vet. Harm. pag. 312. 

«* Ibid. pag. 313. 

+t Wallis. Append, pag. 312. 



48 



HISTORY OF THE SCIENCE 



Book I. 



be observed, that both those latter writers are, in 
respect of the Greek harmonicians, considered as 
mere moderns ; and besides these there are certain 
other objoetions to their testimony, which will be 
mentioned in their proper place. 

As to the two additional modes mentioned by 
Alypius, they seem to have been added to the former 
thirteen, more with a view to regularity in the names 
and positions of the modes, than to any particnlar 
nse ; and perhaps there is no assignable period of 
time during which it may with truth be said, that 
more than thirteen were admitted into practice. 

Ptolemy however rejects as spurious six of the 
thirteen allowed bj' the Aristoxeneans, and this in 
consequence of the position he had advanced, that 
it was not lawful to encrease the modes, by a hemi- 
tone. It is by no means necessary to give his 
reasons at large for limiting the number to seven, as 
his doctrine contains in it a demonstration that the 
encrease of them beyond that number was rather 
a corruption than an improvement of the harmonic 
science. As to the three primitive modes, the 
Dorian, the Phrygian, and the Lydian, each of them 
was situated at the distance of a sesquioctave tone 
from that next to it,* and therefore the two extremes 
were distant from each other two such tones ; or, in 
other words, the Phrygian mode was more acute 
than the Dorian by one tone, and the Lydian more 
acute than the Phrygian by one tone ; consequently 
the Lydian was more acute than the Dorian by two 
tones. 

To these three modes Ptolemy added four others, 
making together seven, which, as he demonstrates, 
are all that nature can admit of. As to the Hyper- 
mixolydian, mentioned by him in the tenth chapter 
of his second book, it is evidently a repetition of the 
hypodorian. 

MIXOLYDIAN 

LYDIAN 

PHRYGIAN 

DORIAN 

HYPOLYDIAN 

HYPO PHRYGIAN 

HYPODORIANf 

The above is the order in which they are given 
by Euclid, Gaudentius, Bacchius, and Ptolemy him- 
self, though the latter, in the eleventh chapter of his 
second book, has varied it by placing the Dorian 
first, and in consequence thereof transposing all the 
rest ; but this was for a reason which a closer view 
of the subject will make it unnecessary to explain. 

Having proceeded thus far in the endeavour to 
distinguish between the legitimate and the spurious 
modes, it may now be proper to enter upon a more 
particular investigation of their natures, and see 
if it be not possible, notwithstanding that great 
diversity of opinion that has prevailed in the world, 
to draw from those valuable sources of intelligence 
the ancient harmonic writers, such a doctrine as may 

* Wallis. Append, pag. 312. 

t Called also the Locrensian. Euclid Introd. Harm. pag. 16. 



afford some degree of satisftiation to a modern en- 
quirer. It must bo confessed that this has been 
attempted by several writers of distinguished abil- 
ities, and that the success of their labours has 
not answered the expectations of the world. The 
Italians, jiarticularly Franchinus, or as he is also 
called, Gaffurius, Zaccone, Zarlino, Galilei, and others, 
have been at infinite pains to explain the modes of 
the ancients, but to little purpose. Kircher has also 
undertaken to exhibit them ; but notwithstanding 
his great erudition and a seeming certainty in all he 
advances, his testimony is greatly to be suspected ; 
and, if we may believe Meibomius, whenever ho 
professes to explain the doctrines of the ancients, 
he is scarcely intitled to any degree of credit. The 
reason why these have failed in their attempts is 
obvious, for it was not till after most of them wrote, 
that any accurate edition of the Greek harmonicians 
was given to the world : so lately as the time when 
Morley published his Introduction, that is to say in 
the reign of queen Elizabeth, it was doubted whether 
the writings of some of the most valuable of them 
were extant even in manuscript ; and it seemed to 
be the opinion that they had perished in that general 
wreck of literature which has left us just enough 
to guess at the greatness of our loss. 

To the several writers above-mentioned we may 
add Glareanus of Basil, a contemporary and intimate 
friend of Erasmus ; but he confesses tl;at he had 
never seen the Harmonics of Ptolemy, nor indeed 
the writings of any of the Greek Harmonicians, and 
that for what he knew of them he was indebted to 
Boetius and Franchinus. From the perusal of these 
authors he entertained an opinion that the number 
of the modes was neither more nor less than twelve ; 
and, confounding the ancient with the modern, or, as 
they are denominated, the ecclesiastical modes, which, 
as originally instituted by St. Ambrose, were only 
four in number, but were afterwards by St. Gregory, 
about the year 600, encreased to eight, he adopted 
the distinction of authentic and plagal modes, and 
left the subject more perplexed than he found it. 

To say the truth, very few of the modern writers 
in the account they give of the modes are to be 
depended on ; and among the ancients, so great is 
the diversity of opinions, as well with respect to the 
nature as the number of them, that it requires a great 
deal of attention to understand the designation of 
each, and to discriminate between the genuine and 
those that are spurious. In general it is to be 
observed that the modes answer to the species of 
diapason, which in nature are seven and no more, 
each terminating or having its final chord in a regular 
succession above that of the mode next preceding : 
for instance, the Dorian, which had its situation in 
the middle of the lyre or system, had for its final 
note hypate meson or E ; the Hypolydian, the next 
in situation towards the grave, had for its final chord 
parhypate meson or F ; and the Hypophrygian, the 
next in situation towards the grave to the Hypo- 
lydian, had for its final chord lychanos hypaton or G; 
so that the differences between the modes in suc- 
cession, with respect to their degrees of gravity, 



Chap. X. 



AND PRACTICE OF MUSIC. 



49 



corresponded with the order of the tones and semi- 
tones in the diatonic series. But it seems that those 
of the ancient harmonicians, who contended for 
a greater number of modes than seven, effected an 
encrease of them by making the final chord of each 
in succession, a semitone more acute than that of the 
next preceding mode : and against this practice of 
augmenting the modes by semitones Ptolemy has 
expressly written in the eleventh chapter of the 
second book of his Harmonics, and that with such 
force of reason and argument, as cannot fail to con- 
vince every one that reads and understands him, to 
which end nothing can so much conduce as the 
attentive perusal of that learned Appendix to his 
Harmonics of Dr. Wallis, so often cited in the course 
of this work. 

Besides this Appendix, the world is happy in the 
possession of a discourse entitled, An Explanation of 
the Modes or Tones in the ancient Graecian Music, 
by Sir Francis Haskins Eyles Stiles, Bart., F. R. S., 
and published in the Philosophical Transactions for 
the year 1760; and by the assistance of these two 
valuable tracts it is hoped that this abstruse part of 
musical science may be rendered to a great degree 



which we sing in ascending from the grave to the 
acute by the syllables fa, sol, la ; by the second, 
the series from Parhypate hypaton to Parhypate 
meson, sol, la, fa ; and by the third, that from 
Lychanos hypaton to Lychanos meson, fa, sol. la.§ 
As to the other series here under exhibited from 
Hypate meson to Mese, it is inserted to sliew that 
the diatessaron is capable of but three mutations ; 
for this latter will be found to be precisely the same 
as, or in truth but a bare repetition of, the first, || as 
is evident in the following scales, in which the 
extreme or grave sound from which we ascend, is 
distinguished by a difference of character ; the syl- 
lables being ever intended to express the intervals 
or ratios, and not the chords themselves. 

SPECIES of the DIATESSARON III. 



intelligible. 



Mese 


a la 






Gsol 






F fa 




Hypate meson 


E la 


la 




D sol 


sol 




C fa 


fa 


Hypate hypaton 


B MI 


Mr 
1 







la 




sol 


sol 


fa 


fa 


fa 


la 


la 


la 


sol 


SOL 


1 


FA 


3 


2 







CHAP. X. 



To conceive aright of the nature of the modes, it 
must be understood, that as there are in nature three 
different kinds of diatessaron, and also four diflPerent 
kinds of diapente ; and as the diapason is composed 
of these two systems, it follows that there are in 
nature seven species of diapason.* The difference 
among these several systems arises altogether from 
the different position of the semitone in each species. 
To explain this difference in the language of the 
ancient writers would be very difficult, as the terms 
used by them are not so well calculated to express 
the place of the semitone as those syllables invented 
by the moderns for that sole purpose, the practice 
whereof is termed solmization. We must therefore 
so far transgress against chronological order, as, in 
conformity to the practice of Dr. Wallis, to assume 
these syllables for the purpose of distinguishing the 
several species of diatessaron, diapente, and diapason, 
reserving a particular account of their invention and 
use to its proper place. 

To begin with the diatessaron ; it contains four 
chords and three intervals : its species are also three : 
the first is said to be that which has la, the character- 
istical ratio or sound of the diatessaron, as mi is of 
the diapente and diapason, in the first or more acute 
place ; the second which hath it in the second, and 
the third which hath it in the third.f 

Euclid defines these several species by the appel- 
latives that denote their situation on the lyre, viz., 
BapvwvKi'oi Barypyknoi, MecroTrvKvoi Mesopyknoi, 
and 0£,vTrvKvoL Oxypyknoi,| meaning by the first 
the series from Hypaton hypaton to Hypate meson, 

* Vide Ptolem. Harm. lib. II. cap. ix. ex vers. Wallis. Wallis. 
Append, de Vet. Harm. pap. 310. Euclid. Introd. Harm. pag. 15. 
ex vers. Meibom. Kirch. Musurg. tom. I. cap. xv. Xvi. 

t Wall. Append, de Vet. Harm. pag. 310. 

t Introd. Harm. pag. 15, ex vers. Meib. 



The above is the tetrachord hypaton of the great 
system ; but as a diapente contains five chords and 
four intervals, to explain the nature of the several 
species included in that system a greater series is 
required ; it is therefore necessary for this purpose 
to make use of those two tetrachords between which 
the diezeuctic tone may be properly interposed ; and 
these can be no other than the tetrachord Meson, and 
the tetrachord Diezeugmenon. It has been just said 
that the characteristic syllable of the diapente is mi, 
and this will be found to occur in the first, second, 
third, and fourth places of the following example of 
the possible variations in that system, the consequence 
whereof is, that the first species is to be sung fa, sol, 
LA, mi, the second sol, la, mi, fa, the third la, mi, 
fa, sol, and the fourth mi, fa, sol, la, as in the 
following scales : — 

SPECIES of the DIAPENTE IV. 



Nete diezeugmenon 


e la 








la 




d sol 




sol 


sol 




c fa 




fa 


fa 


fa 


Paramese 


b mi 


mi 


mi 


mi 


mi 


Mese 


a la 


la 


la 


la 


LA 




Gsol 


sol 


sol 


SOL 


4: 




F fa 


fa 


FA 


3 


Hypate meson 


Ela 


LA 


2 






1 









These are all the mutations of which the diapente 
is capable ; that an additional series, namely, that 
from J] to f, was not inserted as a proof of it, agree- 
able to what was done in respect to the next pre- 
ceding diagram, was because between J] and f the 
diazeuctic tone marked by the syllable mi does no 
where occur : or, in other words, that series is 
a semidiapente or false fifth, containing only three 
tones, which is less by a semitone, or, to speak with 

S Wallis. Append, de Vet. Harm. pag. 310. 

y Ibid. p. 



60 



HISTORY OF THE SCIENCE 



Book 1. 



precision, a limma, than a true diapente. As for 
example : 

J] Semitone c Tone d Tone e Semitone f 
and were another series to be added, it must begin 
from MI or J] ; now the d^azeuetic tone is the interval 
between a and Jj, and consequently is out of the 
pentachord.* 

To distinguish the seven species of diapason, two 
conjunct diapasons are required ; for example, from 
Proslambanomenos to Nete hyperboleon, to be sung 
by the syllables la, mi, fa, sol, la, mi, fa, sol, la, 
PA, SOL, LA,j- in which series will be found all the 
seven species of the diapason ; and that there are no 
more will appear by a repetition of the experiment 
made in the case of the diatessaron ; for were we to 
proceed farther, and after the seventh begin from 
a or LA, the succession of syllables would be in pre- 
cisely the same order as in the first series, which is 
a demonstration that those two species are the same.l 

SPECIES of the DIAPASON VII. 

Nete hyperboleon aa la la 

g sol sol sol 

f fa fa fa fa 

e la la la la la 

d sol sol sol sol sol sol 

c fa fa fa fa fa fa fa 

b mi mi mi mi mi mi mi mi 

Mese a la la la la la la la la la 

G sol sol sol sol sol sol sol SOL 

F fa fa fa fa fa fa fa 
E la la la la la la 

D sol sol sol sol SOL 

C fa fa fa fa 
B mi mi MI 
Proslambanomenos A la la ^ 



From hence it appears, that to exhibit all the 
various species of diapason, a less system than the 
disdiapason would have been insufficient ; for though 
the same sounds, as to power, return after the single 
diapason, yet all the species are not to be found 
therein. Ptolemy defines a system to be a con- 
sonance of consonances ; adding, that a system is 
called perfect, as it contains all the consonances with 
their and every of their species ; || for that whole 
can only be said to be perfect, which contains all the 
parts. According therefore to the first definition, 
the diapason is a system, as is also the diapason and 
diatessaron, the diapason and diapente, and the dis- 
diapason ; for every of these is composed of two or 
more consonances ; but, according to the second defi- 
nition, the only perfect system is the disdiapason ; 
for that, whicb no less system can do, it contains six 
consonances, namely, the diatessaron 1, diapente 2, 
diapason 3, diapason and diatessaron 4, diapason and 
diapente 5, and disdiapason 6 ;^ and nature admits 
of no other. 

The above scales declare the specific difference 
between the several kinds of diatessaron, diapente, 
and diapason, by shewing the place of the semitone 
in each. 

Salinas,** by a discrimination of the greater and 
lesser tone, has increased the number of combinationa 
of the diatessaron to six in this manner : — 



• Wallis. Append, de Vet. Harm. pag. 311. 
t Ibid, 
t Ibid. 
§ Ibid. 

11 Lib. II. cap. iv. 

II Vide Euclid. Introd. Harm, ex vers. Meib. 
«* Lib. IV. cap. iii. 



II. 



III. 



Three species of Diatessaron 



Six species of Diatessaron. 




144 I 135 ) 120 } 108 



A 



C 



DD 



E 



G 



Tone minor. Tone major. Semit. Tone min. Tone min. Semit. Tone mai. Tone min 

I. I. II. 3 



Tone maj. Tone maj. 
2. III. 



Chap. X. 



AND PRACTICE OF MUSIC. 



61 



According to which, each of the diatessarons is 
made to consist of a hemitone, tone, and tone ; yet 
out of the above six combinations, we see that these 
intervals do not occur twice in the same order. 



Besides these, Salinas has shewn the following six 
other species of diatessaron ; in his opinion not less 
true than those above exhibited : — 



I. 



IV. 



V. 



II. 



III. 



VT 




C 108. D sup. 160. E 144. F 135. G 120. a 108. }j 96. c 90. d 81. e 72. 

Tone major. Tone minor. Semit. Tone major. Tone min. Tone maj. Semit. Tone min. Tone major. 



it seems however that he has considered that as 
ia diatessaron, which in truth is only nominally so, 
namely, the Tritonus between F and J] ; * the situ- 
ation whereof, in respect to the others in the above 
diagram, seems to have suggested to him a motive 
for inserting from Bede an account of a very curious 
method of divination, formerly practised, which is 
here, with some small variation, translated from 
Salinas : — 

' It is very credible that this disposition gave 

* rise to that well-known game, the design whereof 
' is to divine when three men placed in order have 
' distributed among themselves three lots of different 
' magnitudes, which of those lots each person has 
' received ; which must be done after six manners, 
' and those the same by which the diatessaron is 
' divided, and its intervals placed in order as we 
' have shewn, that is to say, each lot may be twice 

* placed in each of the three situations ; for the three 
' men answer to the three places, the first to the 
' grave, the second to the mean, and the third to the 

* acute ; and the three lots of different magnitudes to 
' the three intervals also of different quantity ; the 
' greater to the greater tone, the middle to the lesser 
' tone, and the least to the semitone. This method 

* of divination is performed by the help of twenty- 
' four little stones, of which the diviner himself 
' gives one to the first, two to the second, and three 
' to the third, with this injunction, that he who has 
'received the greatest lot, do take up out of the 
' remaining eighteen stones as many as were at first 
' distributed to him; he who has the lot in the middle 
' degree of magnitude, twice as many as he has ; and 
' he that has the least lot, four times as many as he 

* also has. By this means the diviner will be able to 
' know from the number of stones remaining, which 
' of the things each person has ; for if the distri- 
' bution be made after the first manner, there will 

* Salinas l)e Musica, lib. IV. cap. iii. 



' be one left ; if after the second two, if after the 
' third three, if after the fourth five, if after the fifth 

* six ; and, lastly, if after the sixth seven ; for there 
•' can never four remain, for which a twofold reason 
' may be assigned ; the one from the disposal of the 

* instituent, who from the truth of the thing, though 
' perhaps the reason thereof was not known by him, 
' was impelled to constitute the game in this manner. 

" Hand equidem sine mente reor, sine numine divum." 
* The other taken from the constant and settled 
' order of the harmonical ratio ; but four cannot 

* possibly remain, because the first and third persons 
' having received an uneven number of stones, either 
' of them must, if he have the greatest lot, take up 
' an uneven niimber also ; as by the injunction of the 
' instituent, he was to take up as many stones as 
' were at first distributed to him ; and an uneven 
' number being taken out of an even one, the re- 
' mainder must necessarily be uneven ; but as each 
' of them may have the greatest lot twice, there 
' must be four uneven remainders of stones out ot 
' the six changes : as to the second, he can have it 
' only twice ; because as he has an even number, and 
' takes up a number equal thereto, there must an 
' even number remain ; for the others must also take 

* up even numbers, as they are enjoined to take up 

* twice, and four times as many as they had received ; 
' and the greatest lot may fall to the second person 
' in two cases, for either the first may have the 
' middling, and the third the smallest, and then the 
' remainder will be two ; or contrary wise, and then 
' there will remain six ; and as the greatest lot can- 
' not come three times to the second, it is plain that 
' the third even number, which is four, cannot by any 
' means be left. But the other reason taken from 
' the harmonical ratio, is much truer and stronger ; 
' for as it is shewn in the seven sounds of a diapason 

* from C to c, that a diatessaron may be produced 
' towards the acute from six of them, that is to say, 



62 



HISTORY OF THE SCIENCE 



Book L 



' the first, second, third, fifth, sixth, and seventh, the 
'fourth being passed over because the diatessaron 
' cannot be produced therefrom ; so also in this play 
' the number four is passed over as having no con- 
' cern therein ; but it does not happen so in the 
'composition of instrumental harmony, for though, 
'as is shewn in the last example above, the fourth 
' sound from C makes a tritone, with its nominal 

* fourth above it, it is not to be excluded from the 
'series. Neither is the diapason from this fourth 
^ iAjtmd from C, viz., P, to be totally rejected ; for 

though by reason of the tritone it cannot be arith- 
'metically divided as the other six may, yet may 
' it be divided harmonically. I should by no means 
'have made mention of this game, being appre- 
' hensive that I may be thought to trifle on so serious 
'an affair, but that I look upon it as an example 
'very much suited to explain the subject we are 
'treating of; and I did n the more willingly, be- 

• cause I found it particularly treated of by Bede, 
'surnamed the Venerable, a most grave man, and 
'deeply learned both in theology and secular arts, 
' from whence we may conjecture that it has been 
' invented above one thousand years." * 

But, to retu-rn from this digression, notwithstand- 
ing the species of diapason are manifestly seven, the 
modes seem originally to have been but three in 

^ The passage on which this assertion is grounded, has eluded a cur- 
sory search among the writings of Bede ; nevertheless it may possibly be 
found in some one or other of those numerous little tracts on arithmetic, 
music, and other of the sciences, contained in his voluminous works, 
many whereof as yet exist only in manuscript. The description given by 
Salinas of this method of divination is in nearly these words : — 

Ab hac etiam dispositione credendum est, ortum habuisse lusum ilium 
notissimum, cujus propositum est, tribus hominibus ordine dispositis, tres 
res diverscE magnitudinis inter se distrlbuentibus, quam quis eorum 
acceperit, divinare. Quod sex modis fieri, necesse est : atque eisdem, 
quibus diatessaron dividitur, et eodem ordine dispositis, quo tria ipsius 
intervalla, tribus in locis bis singula in singulis ostendimus collocari. 
Tribus enim locis respondent tres homines : primus gravissimo, seeundus 
medio, tertius acutissimo. Et tres res diversEe magnitudinis, tribus 
intervallis etiam varise quantitatis, maxima tono majori, media minori, 
minima semitonio. Conficetur autem hie lusus 24 lapillis, ex quibus 
primo unum, secundo duos, tertio tres divinaturus ipse tradit; ea lege, 
ut ex 18 reliquis, qui rem maximam accipiet, tot, quot habet : qui 
mediam, bis totidem : qui mininiam, tntidem quater assumat : quo ex 
eorum, qui supererunt numero, quae cuique obvenerit, possit cognoscere. 
Nam si primo modo fiet distributio, relinquetur unus : si fiet secundo, 
duo: si tertio, tres: si quatuor, quinque : si quinto, sex: et si denique 
sexto, septem. Neque quatuor unquam poterunt superesse, cujus duplex 
ratio potest assignari. Altera, ex arbitrio instituentis ab ipsa rei veritate 
forsitan illi non cognita ad lusum sic instituendum impulsi, 

' Haud equidem sine mente reor, sine numine divflm.' 
Altera ex Ktema rationis harmonice dispositione desumpta. Quod autem 
ad instituendum attinet, quatuor id circo remanere non possunt, quoniani 
primus, et tertius lapillos impares susceperunt : et cum ex lege tot, quot 
habent, accipere teneantur, si maximam habebunt, assument impares : 
quibus ex paribus sublatis, impares relinqui necesse est, quod alterutri 
bis evenire continget, unde quater impares restabunt. Et cum seeundus 
etiam bis maximam possit accipere, quoniam habet pares, totidem 
assumptis relinquentur pares : nam reliquos necesse est pares assumere, 
cum duplicare, et quadiuplicarelapillos, quos habent, teneantur. Quod 
bis evenire continget ; aut enim primus mediam habebit, et tertius mini- 
mam, et restabunt duo ; aut contra, et restabunt sex. Et cum maxima 
secundo ter evenire nequeat, constat, tertiam parem, qui quatuor est, 
nullo modo posse relinqui. Sed multo verior, et fortior est, quae ex 
ratione harmonica desumitur. Nam quemadmodum in septem sonis 
diapason ostensum est, k sex illorum diatessaron in acutem protrahi 
posse, qui sunt primus, seeundus, tertius, quintus. sextus, Septimus : et 
quartum praeteriri neque in eo reperiri posse : sic etiam in lusu ipso 
prsteritur quarta dictio, quae occisa est ; quod non ita evenit in harmoniae 
instrumentalis corapositione. Quandoquidem (ut dictum est) significat 
tritonum, quod a quarto sono inter septem sonos diapason invenitur, cum 
^ sex aliis omnibus, diatessaron inveniatur. Unde etiam in septem diapa- 
son speciebus, quae a septem son is oriuntur, sex arithmetic^ dividi possunt; 
una vero nequaquam, quae a C cum i)rima sit, prngrediendo in acutum, 
erit quarta. Hujus autem lusus neuti(iuam ego mentionem fecissem, ne 
in re tam seria liuiere velle viderer, nisi ad rem, qua de agimus, facilius 
explicandam, aptissimum esset exeniplum Quod e6 libentius feci, 
quoniam eum comperi ex professo traditum d Beda, cognomento Venera- 
bili, viro gravissimo et in divinis Uteris, ac secularibus disciplinis erudi- 
tissimo. Unde coujectari licet, ante mille annos excogitatum fuisse. 
Salinas de Musica, lib. IV. cap. v. 



number, namely, the Dorian, the Phrygian, and the 
Lydian : f the first proceeding from E to e, the 
second from D to d, and the third from C to c, J how 
these are generated shall be made appear. 

And first it is to be remarked that the place of the 
diazeuctic tone is the characteristic of every mode. 
In the Dorian the diazeuctic tone was situated in the 
middle of the heptachord, that is to say, it was the 
interval between mese or a, and paramese |], the 
chords mese and paramese being thus stationed in 
the middle of the system, three in the acute, namely, 
Trite diezeugmenon, Paranete diezeugmenon, and 
Nete diezeugmenon ; and three in the grave, namely, 
Lychanos meson, Parhypate meson, and Hypate 
meson, determined the species of diapason proper to 
the Dorian mode. The series of intervals that con- 
stituted the Dorian mode, had its station in the 
middle of the lyre, which consisted, as has been 
already mentioned, of fifteen chords, comprehending 
the system of a disdiapason ; and to characterise the 
other modes, authors make use of a diapason with 
precisely the same boundaries ; and that because the 
extreme chords, both in remission and intention, are 
less grateful to the ear than the intermediate ones. 
Ptolemy takes notice of this, saying, that the ear is 
delighted to exercise itself in the middle melodies : § 
and he therefore advises, for the investigation of the 
modes, the taking the diapason as nearly as may be 
from the middle of the lyre. || 

The Dorian mese being thus settled at a, and the 
position of the diazeuctic tone thereby determined, 
a method is suggested for discovering the constitution 
of the other six modes, namely, the Mixolydian, 
Lydian, Phrygian, Hypolydian, Hypophrygian, and 
Hypodorian, making together with the Dorian, seven, 
and answering to the species of the diapason ; all 
above which number, according to the express de- 
claration of Ptolemy, are to be rejected as spurious.^ 

But in order to render this constitution intelligible, 
it is necessary to take notice of a distinction made 
by Ptolemy, lib. II. cap. xi. between the natural, or, 
which is the same, the Dorian Mese and the modal 
Mese ; as also between every chord in the lyre or 
great system, and its corresponding sound in each of 
the modes, which he has noted by the use of the two dif- 
ferent terms Positions and Powers. In the Dorian mode 
these coincided, as for example, the Mese of the lyre, 
that is to say the Mese in position, was also the Mese 
in power, the Proslambanomenos in position was also 
the Proslambanomenos in power, and so of the rest.** 

But in the other modes the case was far otherwise ; 
to instance, in the Phrygian, there the Mese in 
position was the Lychanos meson in Power, and the 
Proslambanomenos in position the Paranete hyper- 
boleon in power. In the Lydian the Mese in position 

t Ptolem. Harm. lib. TI. cap. vi. Wallis Append, de Vet. Harm. p. 312. 

t Vide Kirch. M\isurg. torn. I. cap. xvi. 

§ Harmonicor. lib. II. cap. xi. 

II Ibid. lib. II. cap. xi. 

if Lib. II. cap. viii. ix. xi. ex. vers. Wallis. 
*» Vide Sir Francis Stiles on the Modes, pag. 702. 

By the Mese in power is to he understood not the actual Mese or the 
middle chord of the septenary, but that which marks the position of the 
diazeuctic tone which varies in each mode. In the Dorian, for instance, 
it holds the middle or fourth, in the Phrygian the third, and in the 
Lydian the second place, reckoning from the acute towards the grave. See 
the diagram of the species of diapason in the seven Ptolemaic modes 
hereafter inserted. 



Chap. X.— Book II, Chap. XL 



AND PRACTICE OF MUSIC. 



5.S 



was the Parhypate meson in power, and the Pros- 
lambanomenos in position was the Trite hyperboleon 
in power ; and to the rule for transposition of the 
Mese the other intervals were in like manner subject. 
From this distinction between the real, and the 
nominal or potential Mese, followed, as above is 
noted, a change in the name of every other chord on 
the lyre, which change was regulated by that relation 
which the several chords in each mode bore to their 
respective Mesas, and the term Mese not implying 
any thing like what we call the Pitch of the sound, 
but only the place of the diazeuctic tone in the lyre, 
this change of the name became not only proper, but 
absolutely necessary : nor is it any thing more than 
is practised at this day, when by the introduction of 
a new cliff, we give a new name, not only to One, 
but a series of sounds, without disturbing the order 
of succession, or assigning to them other powers than 
nature has established. 

The following scale taken from the notes of Dr. 
Wallis on the eleventh chapter of the second book 
of the Harmonics of Ptolemy, exhibits the position 
on the lyre, of each of the modal Meses : — 
aa Nete hyperboleon 
g Paranete hyperboleon 
f Trite hyperboleon 
e Nete diezeugmenon 
d Paranete diezeugmenon 
c Trite diezeugmenon 
J] Paramese 
a Mese 
4 G Lychanos meson 
F Parhypate meson 
E Hypate meson 
D Lychanos hypaton 
C Parypate hypaton 
J] Hypate hypaton 
A Proslambanomenos* 

Now that diversity of stations for the Mese above 
represented, necessarily implies the dislocation of the 
diazeuctic tone for every mode ; and from the rules 
in the tenth chapter of the second book of Ptolemy, 
for taking the modes, it follows by necessary con- 
sequence that in the Mixolydian mode the diazeuctic 
tone must be the first interval, reckoning from acute 
to grave ; in the Lydian the second, in th6 Phrygian 
the third, in the Dorian the fourth, in the Hypolydian 
the fifth, in the Hypophrygian the sixth, and in the 
Hypodorian the last.f 

The situation of the Mese, and consequently of the 
diazeuctic tone being thus adjusted, the component 

* Ptolem. Harmonic, ex vers. Wallis, pa^. 137, in not. 
+ Sir Francis Stiles on the Modes, pag. 709. And see the diagram of 
the seven Ptolemaic modes hereinafter inserted. 



intervals of the diapason above and below it, follow 
of course as they arise in the order of nature ; and 
we are enabled to say not only that the species of 
diapason answering to the several modes in their 
order are as follow :— 



Mixolydian 

Lydian 

Phrygian 

Dorian 

Hypolydian 

Hypophrygian 

Hypodorian 



VMESE 



Mixolydian 

Lydian 

Phrygian 

Dorian 

Hypolydian 

Hypophrygian 

Hypodorian 



^ B to b 
C to c 
Dtod 
- from -^ E to e 
Ftof 
G to g 
^ A to a, or a to aaj 



But that the follov^dng is the order in which the 
tones and semitones occur in each series, proceeding 
from grave to acute : — 

Mixolydian — Semitone, tone, tone, semitone, tone, 

tone, tone. 
Lydian — Tone, tone, semitone, tone, tone, tone, 

semitone. 
Phrygian — Tone, semitone, tone, tone, tone, semi- 
tone, tone. 
Dorian — Semitone, tone, tone, tone, semitone, tone, 

tone. 
Hypolydian — Tone, tone, tone, semitone, tone, tone, 

semitone. 
Hypophrygian — Tone, tone, semitone, tone, tone, 

semitone, tone. 
Hypodorian — Tone, semitone, tone, tone, semitone, 

tone, tone.§ 

And this, according to Ptolemy, is the constitution 
of the seven modes of the ancients. 

t Sir F. S. on the Modes, 708. Kirch. Musurg. tom. I. cap. xvi. 

§ Upon the constitution of the first of the above modes a great difficulty 
arises, namely, how to reconcile it to the rules of harmonical progression, 
for it is expressly said by Kircher and also by Sir Francis Stiles, in his 
Discourse on the Modes, pag. 407, and may be inferred from what Ptolemy 
says concerning them in his Harmonics, lib. II. cap. x. that the Mixo- 
lydian answers to the species of diapason from Hypate hypaton to 
Paramese, that is to say, from \j to J], and that the semitones in it are 
the first and fourth intervals in that series ; now if this be the case, as 
most clearly it is, the interval between the chord }] and the chord 
Parypate meson or F, must be a semidiapente, which is a false relation, 
arising from two inconcinnous chords, and consequently is unfit for 
musical practice. 

Again, in the Hypolydian, from Parhypate meson to Trite hyper- 
boleon, or F to f , a tritone occurs between F and J], which is a false 
relation, and renders this species equally with the former unfit for musical 
practice. 

Dr. Wallis seems to have been aware of this difficulty, and has at- 
tempted to solve it in a diagram of his, containing a comparative view of 
the ancient modes with the several keys of the modern.s, by prefixing the 
flat sign b, to Hypate hypaton ; agreeable to what he says in another 
place, that in the Mixolydian mi is placed in E la mi, and to get rid of 
the tritone in the latter case he prefixes a second flat in E ta mi, ex- 
cluding thereby mi from thence, and placing it in A la mi re. 

Sir Francis Styles has done the same, and farther both these writers 
have made use of the acute sign ti for similar purposes. In all which 
instances it is supposed they are justified by the practice of the ancients , 
for it is to be noted that they had a particular tuning for every key, 
which could be for no other purpose than that of dislocating the inter- 
vals from their respective stations in the several species of diapason, and 
might probably reduce them to that arrangement observable in the keys 
of the modems, which, after all that can be said about them, are finally 
resolvable into two. 



BOOK II. 



CHAP. XI. 



In the foregoing enquiry touching the modes, remains, namely, whether the progression in each of 

endeavours have been used to demonstrate the coin- the modes was in the order prescribed by nature or 

cidence between the seven genuine modes and the not. In what order of succession the tones and 

seven species of diapason. But supposing the rela- semitones arise in each species of the diapason has 

tion between them to be made out, a question yet already been declared ; and it seems from the repre- 



54 



HISTORY OF THE SCIENCE 



Book U. 



sentation above given of the species, that as the keys 
of the moderns are ultimately reducible to two, do 
MI, and KE FA, so the seven modes of the ancients by 
the dislocation of the Mese for each, and that con- 
sequent new tuning of the diapason for each, which 
is mentioned by Ptolemy in the eleventh chapter of 
his second book, are by such dislocation of the Mese 
and a new tuning reduced to two. To this purpose 
Dr. Wallis seems uniformly to express himself, and 
particularly in this his description of the modes taken 
from Ptolemy : — 

' Ptolemy, in the eleventh chapter of his second 
book, and elsewhere, makes the Dorian the first of 
the modes, which, as having for its Mese and 
Paramese the Mese and Paramese both in position 
and power, or, to speak with the moderns, having 
its 7ni in \j, may be said to be situated in the midst 
of them all ; he therefore constitutes the Dorian 
mode so as that between the real and assumed names 
of all the chords, there is throughout a perfect coin- 
cidence : and to this mode answers that key of the 
moderns in which no signature is placed at the head 
of the stave to denote either flat or sharp. 

' Secondly he takes a mode more acute than the 
former by a diatessaron, which therefore has for its 
Mese a chord also more acute by a diatessaron, 
namely the Paranete diezeugmenon of the Dorian, 
and consequently its Paramese, which is our 7)ii, 
must answer to the Nete diezeugmenon, that is as 
we speak, mi is placed in E la mi, and this he calls 
the Mixolydian. The moderns for a similar pur- 
pose place a flat on B fa, and thereby exclude mi. 

' And from hence he elsewhere, lib. II. cap. vi. 
concludes, that there is no necessity for that which 
the ancients called the conjimct system, namely, the 
system from Proslambanomenos to Nete synem- 
menon, since that is sufficiently supplied by the 
change made in Mese from the Dorian to the Mixo- 
lydian mode ; for here follows after the two conjunct 
tetrachords in the Dorian, from Hypate hypaton to 
the Mese, that is from B mi to A la mi re, a third in 
the Mixolydian from its Hypate Meson, which is the 
Mese in the Dorian to its Mese, that is from A la 
mi re to D la sol re ; so that there are three con- 
junct tetrachords from B mi, the Hypate hypaton 
of the Dorian, to D la sol re, the Mese of the 
Mixolydian. 

' Thirdly, as another diatessaron above that in the 
acute, could not be taken without exceeding that 
diapason in the midst whereof the Mese of the 
Dorian was placed, Ptolemy assumes in the room 
thereof a diapente towards the grave, which may 
answer to a diatessaron taken towards the acute, in 
as much as the sounds so taken, differing from each 
other by a diapason, may in a manner be accounted 
the same. The Mese therefore of this new mode 
must be graver by a diapente than that of the 
Mixolydian ; that is to say, it is the Lychanos 
hypaton of the Mixolydian, or, which is the same, 
the Lychanos meson of the Dorian, and consequently 
its Paramese will be the Mese of the Dorian ; that 
is as we should say, mi in A la mi re. This is 
what Ptolemy calls the Hypolydian mode, to denote 



which we put besides the flat placed before in B Jd 
b mi, a second flat in E la mi, to exclude mi from 
thence, and thereby mi is removed into A la vii re. 

' Fourtlily, as he could not from hence towardg, 
the grave, take either a diapente or diatessaron, 
without going beyond the above diapason, Ptolemy 
takes a mode more acute than the Hypolydian by 
a diatessaron, which he calls the Lydian, the Mese 
whereof is the Paranete diezeugmenon, and its 
Paramese the Nete diezeugmenon of the Hypo- 
lydian ; which latter is also the Paranete diezeugr 
menon of the Dorian, that is as we speak, mi in D 
la sol re. We, to denote this mode, besides the 
two flats already set in b and e, put a third in A la 
mi re, whereby we exclude mi from thence, and 
transfer it to D la sol re. 

' Fifthly, as the Mixolydian was taken from the 
Dorian, and made a diatessaron more acute, so is the 
Hypodorian to be taken from the same Dorian 
towards the grave, and made more grave than that 
by a diatessaron : the Mese therefore of the Hyr 
podorian is the Hypate meson of the Dorian ; and 
its Paramese, wliich is our mi, is the Parhypate 
meson of the Dorian, that is as we speak, mi in F 
fa ut. We, to denote this mode, leaving out all; 
the flats, place an acute signature or sharp in F ^a 
ut, which would otherwise be elevated by a hemi- 
tone only, and called Ja, but it is now called 7m, and 
elevated by a whole tone above the next note under 
it ; by reason whereof the next note in the acute 
will be distant only a hemitone fi;om that next 
under it, and be called Ja, and 7ni will return in 
a perfect diapason in the FJa lit next above it. 

' Sixthly, as another diatessaron towards the grave 
cannot be assumed from the Hypodorian thus 
situated, without exceeding the limits of the above 
diapason, he takes the Phrygian mode a diapente 
more acute, which is the same thing in effect, since 
between any series in the fifth above and in the 
fourth below, the distance is precisel}' a diapason ; 
the Mese therefore of this mode is the Nete die- 
zeugmenon of the Hypodorian, that is the Paramese 
of the Dorian, and consequently its Paramese is the 
Trite diezeugmenon of the Dorian, that is as we> 
speak, 7ni in c fa ut ; to denote which, besides the. 
sharp placed before in F fa ut, we put another 
sharp in G fa ut, which would otherwise be. 
elevated by only an hemitone above the next note 
under it, but is now elevated by a whole tone ; and 
as before it would have been cnWed fa, it must now 
be called wi ; and from hence to g sol ve ^^ is now 
only a hemitone, which is therefore to be called fa, 
7ni returning either in cc sol fa above, or in cfa ut 
below. 

' Seventhly and lastly, the Hypophrygiao is taken 
from the Phrygian, as above defined, and is distant 
therefrom by a diatessaron towards the grave. Its 
Mese therefore is the Hypate meson of the Phrygian, 
that is to say the Parhypate meson of the Dorian, 
consequently its Paramese, which is our 7ni, is the 
Lychanos meson of the Dorian. That is as we 
speak, mi in G sol re ut, to express which, the rest 
standing as above, we place a third 8hai:p in G sol 



Chap. XI. 



AND PRACTICE OF MUSIC. 



55 



^e ut, which otherwise, by reason that FJa ut was 
made sharp before, would be elevated by only a 
hemitone, and called fa, is now elevated by a whole 
tone and called 7ni, and therefore A la mi re, distant 
from G sol re ut by a hemitone, is called fa, and 
mi returns in g sol re ut above, or in V tit below. 

' The modes being thus determined, we gather 
from thence that the Mixolydian mode is distant 
from the Lydian as in Ptolemy, lib. II. cap. x. by 
a limma, or not to speak so nicely, by a hemitone, 
the Lydian from the Phrygian by a tone, the 
Phrygian from the Dorian by a tone, the Dorian 
from the Hypolydian by a limma, the Hypolydian 
from the Hypophrygian by a tone, and the Hypo- 
Phrygian from the Hj'podorian also by a tone. 

' From these premises Ptolemy concludes, not only 
that the seven modes above enumerated are all that 
are necessary, but even that there is not in nature 
room for any more, by reason that all the chords in 
the diapason are by this disposition occupied : for 
since all the chords, from the Hjrpate meson to the 
Paranete diezeugmenon inclusively, are the Mese of 
some mode, there is no one of them remaining to 
be made the mese of any intermediate mode : for 
example, the Mese in power of the Hypodorian is 
in position the Hypate meson, and the Mese in 
power of the Hypophrygian is the Parhypate meson ; 
and as there is no chord lying between these two 
there is none left, nor can be found to be the Mese 
of any intermediate mode, or which, as Aristoxenus 
supposes, may with propriety be called the graver 
Hypophrygian or Hypoiastian ; and what has been 
said of the Mese may vvath equal reason be said of 
the Paramese, which is our mi' * 
Thus far Dr. Wallis, who has undoubtedly de- 
livered, though in very concise terms, the sense of 
his author ; nevertheless as the whole of the argu- 
ments for restraining the number of modes to seven 
is contained in the eleventh chapter of the second 
book of Ptolemy, and Sir Francis Stiles has bestowed 
his pains in an English version thereof, it may not 
be amiss to give it as translated by him, and his 
words are as follow : — 

' Now these being the modes which we have 
' established, it is plain, that a certain sound of the 
'diapason is appropriated to the Mese in power,, 
* of each, by reason of their being equal in number 
' to the species. For a diapason being selected out 
*of the middle parts of the perfect system, that 
' is the parts from Hypate meson in position to Nete 
'diezeugmenon, because the voice is most pleased 
'to be exercised about the middle melodies, seldom 
'running to the extremes, because of the difficulty 
'and constraint in immoderate intensions, and re- 
' missions, the Mese in power of the Mixolydian will 
'be fitted to the place of Paranete diezeugmenon, 
'that the tone may in this diapason make the first 
' species ; that of the Lydian, to the place of Trite 
' diezeugmenon, according to the second species ; 
' that of the Phrygian, to the place of Paramese, 
'according to the third species; that of the Dorian, 
' to the place of the Mese, making the fourth and 

* Wallis Append, de Vet. Harmon, pag. 314, et seq. 



' middle species of the diapason ; that of the Hy- 
' polydian, to the place of Lychanos meson, accord- 
' ing to the fifth species ; that of the Hypophrygian. 
' to the place of Parhypate meson, according to the 
' sixth species ; and that of the Hypodorian, to the 
' place of Hypate meson, according to the seventh 
' species ; that so it may be possible in the alterations 
' required for the modes, to keep some of the sounds 
' of the system unmoved, for preserving the mag- 
' nitude of the voice, meaning the pitch of the 
' diapason ; it being impossible for the same powers, 
'in different modes to fall upon the places of the 
' same sounds. But should we admit more modes 
' than these, as they do who augment their excesses 
' by hemitones, the Meses of two modes must of 
' necessity be applied to the place of one sound ; sa 
'that in intkrchanging the tunings of those two 
'modee, the whole system in each must be removed, 
'not preserving any one of the preceding tensions 
' in common, by which to regulate the proper pitch 
' of the voice. For the Mese in power of the Hypo- 
' dorian for instance, being fixed to Hypate meson 
' by position, and that of the Hypophrygian to 
' Parhypate meson, the mode taken between these 
' two, and called by them the graver Hypophrygian, 
' to distinguish it from the other acuter one, must 
' have its Mese either in Hypate, as the Hypodorian, 
' or in Parhypate, as the acuter Hypophrygian ; 
' which being the case, when we interchange the 
' tuning of two such modes, which use one common 
' sound, this sound is indeed altered an hemitone in 
' pitch by intension or remission ; but having the 
' same power in each of the modes, viz., that of the 
' Mese, all the rest of the sounds are intended or 
' remitted in like manner, for the sake of preserving 
' the ratios to the Mese, the same with those taken 
' before the mutation, according to the genus common 
' to both modes ; so that this mode is not to be 
' held different in species from the former, but the 
' Hypodorian again, or the same Hypophrygian, only 
' somewhat acuter or graver in pitch, that these 
' seven modes therefore are sufficient, and such as 
' the ratios require, be it thus far declared.' f 

Dr. Wallis continues his argument, and with 
a degree of perspicuity that leaves no room to doubt 
but that he is right in his opinion, shows that the 
modes of the ancients were no other than the seven 
species of diapason : for, as a consequence of what 
he had before laid down, he asserts that the syllable 
mi, to speak, as he says, with the moderns, has 
occupied all the chords by the modes now determined, 
since in the Hypodorian, mi is found in F, and also 
in f, which is a diapason distant therefrom. In the 
Hypophrygian it is found in G, and therefore also 
in F and in g, which are each a diapason distant 
therefrom. In the Hypophrygian it is found in 
a, and therefore in A and aa, each distant a diapason 
therefrom. In the Dorian it is found in \^, and 
therefrom in J] and 1]J]. In the Phrygian rtii is 
found in c, and also in C and cc. In the Lydian it 
is found in d, and therefore in D and dd. And 
lastly, in the Mixolydian it is found in e. and con- 



t Sir F. S. on the Modes, pag. 724. 



o6 



HISTORY OF THE SCIENCE 



Book II. 



sequently in E and ee ; from all which it is evident 
that there can no one chord remain whereon to place 
mi for any other mode, which would not coincide 
with some one of these above specified.* 

Nothing need be added to illustrate this account 
of the modes but an observation, that instead of 
g and c for the respective places of 7ni in the Hypo- 



phrygian and Phrygian modes, their true positions 
will be found to be in g# and ctt and their replicates. 

The following scheme is exhibited by Dr. Wallis 
to show the correspondence between the several keys 
as they arise in the modern system, ajid the modes of 
the ancients : — 



4 


» 




-b-^^ 


_^; 


\^^~ 


—TSV 


-0- 


__fi_. 


[^ - 






— 0-^ 


1^=^ 




1 


r: 


4 


* .$— 






h^-^ 


— *— 


-I- =: 


-)&-ls- 


-_^_ 


•«— 





^1^^= 


-0- 


=2= 


- 




1^ 

1 


a 

^ en 


IV 

<v 

s 

03 
1 


a 
o <u 


ID 

3 


.1 




(D 


•r- 
o a> 


J* 
Ph 


Jo 


as 

a 

2 


1 

t 




Ph 


t 




Q 








a 




ti 






a 




et, 




w 









By which it should seem that the key of A with the 
lesser third answers to the Dorian ; D with the lesser 
third to the Mixolydian ; G with the lesser third to 
the Hypolydian ; C with the lesser third to the 
Lydian ; E with the lesser third to the Hypodorian ; 
B with the lesser third to the Phrygian, and F^ with 
the lesser third to the Hypophrygian. 

These are the sentiments of those who taught that 
the modes were coincident with the species of dia- 
pason. Another opinion however pi'evailed, namely, 
that the word Mode or tone signified not so properly 
any determinate Succession of sounds, as the Place 
of a sound ; and indeed this is one of the definitions 
given by Euclid of the word Tone or Mode ; | or, in 
other words, the difference between one tone and 
another consisted in the Tension, or, as we should 
say, the Pitch of the system. § The occasion of this 
diversity of opinion seems to be this, Aristoxenus. 
the father of that sect which rejected the measure 
by ratios, and computed it by intervals, in his treatise 
on Harmonics, book the second, divides the science 
into seven parts, 1. Of sounds 2. Of intervals 
3, Of genera. 4. Of systems. 5. Of tones. G. of 
mutations. 7, of melopoeia. || Now had he con- 
sidered the species of diapason to have been the 
same as, or even connected with, the modes, it had 
been natural for him to have placed them under the 
fifth division, that is to say, of tones, or at least 
under the sixth, of mutations . instead of which we 
find them ranged under the fourth, namely, that of 
systems ; and even there it is not expressly saia, 
though from their denominations, and other circum- 
stances it might well be inferred, that the species of 
diapason had a relation to the modes.^ The silence 
of Aristoxenus, and indeed of all his followers, in 
this respect, has created a difficulty in admitting a 
connexion between the species of diapason and the 
modes, and has led some to suspect that they were 
distinct ; though after all that can be said, if the 
modes were not the same with the species, it is 
extremely hard to conceive what they could be ; for 
a definition of a mode, according to the Aristoxeneans, 

* Append. <le Vet. Harm. 315. 

t Ptolein. Harmonic, ex vers. Wallis, pas- 137, in not. 

t Introd. Harm. pag. 19, ex vers Meibora. 

§ Sir Francis Stiles on the Modes, pag. 698. 

II Lib. 11. pag. XXXV. et seq. ex vers. Meibom. 

il Vide Sir Francis Stiles on the Modes, pag. 704. 



does by no means answer to the effects ascribed by 
the ancient writers, such as Plutarch and others, to 
the modes ; for instance, can it be said of the Dorian 
that it was grave and solemn, or of the Phrygian 
that it was warlike, or that the Lydian was soft and 
effeminate, when the difference between them con- 
sisted only in a different degree of intension or 
remission ; or, in other words, a difference in respect 
of their acumen or gravity ? On the other hand, the 
keys of the moderns, which, as already has been 
shewn, answer to the modes of the ancients, have 
each their characteristic, arising from the different 
measures of their component intervals ; those with 
the minor third are all calculated to excite the 
mournful affections , and yet amongst these a dif- 
ference is easily noted . the funereal melancholy of 
that of F is very distinguishable from the cloying 
sweetness of that of A ; between those with the 
greater third a diversity is also apparent, for neither 
is the martial ardour of the key D at all allied 
to the hilarity that distinguishes the key E, nor the 
plaintive softness of E b to the masculine energy 
of B b , but sarely no such diversity could exist, 
if the sole difference among them lay in the Pitch, 
without regard to their component intervals. 

This difficulty, whether greater or less, seems 
however to be now removed by the industry and 
ingenuity of the above-named Sir Francis Stiles, 
who in the discourse so often above-cited, namely, 
his Explanation of the Modes or Tones in the 
ancient Grascian Music, has reconciled the two doc- 
trines, and suggested a method for demonstrating 
that to adjust the pitch of any given mode is also 
to atljust the succession of its intervals, the conse 
quence whereof is a discovery that the two doctrines, 
though seemingly repugnant, are in reality one and 
the same. The reasonings of this very able and 
accurate writer are so very close and scientific, that 
it is not easy to deliver his sense in other terms than 
his own ; however it may not be amiss to give 
a short statement of his arguments. 

The two doctrines which he has undertaken thus 
to reconcile, he distinguishes by the epithets of Har- 
monic and Musical ; the former of these, which he 
says had the Aristoxeneans for its friends, taught 
that the difference between one mode and another, 



Chap. XII. 



AND PRACTICE OF MUSIC. 



57 



lay in the tension or pitch of the system ; the latter, 
and which Ptolemy with great force of reasoning 
contends for, teaches that this difference consisted in 
the manner of dividing an octave, or, as the ancients 
express it, in the different species of diapason : the 
task which this writer has undertaken is, to shew 
that between these two definitions of a musical mode 
there is a perfect agreement and coincidence. 

In order to demonstrate this he shews, pag. 701, 
from Bacchius, pag. 12, edit. Meibom. that the Mixo- 
lydian mode was the most acute, the Lydian graver 
l)y a hemitone, the Phrygian graver than the Lydian 
by a tone, the Dorian graver than the Phrygian by 
a tone, the Hypolydian graver than the Dorian 
by a hemitone, the Hypophrygian graver than the 
Hypolydian by a tone, and the Hypodorian graver 
than the Hypophrygian by a tone.* He adds, 
' that as the Guidonian scale answers to the system 
' of the ancients in its natural situation, which was 
' in the Dorian mode, and our A la mi re conse- 
' quently answers to the pitch of the Dorian Mese, 
'■ we have a plain direction for finding the absolute 
' pitch of the Meses for all the seven in our modern 
' notes, and they will be found to stand thus : — 



Mixolydian Mese in 


- d 


Lydian in - 


c^ 


Phrygian in - 


- b 


Dorian in - 


a 



Hypolydian in - - - g^ 

Hypophrygian in - - f ^ 

Hypodorian in - - - 6 f 

But to understand this doctrine as delivered by 
(he ancients, the same author says it will be necessary 
to examine how the Meses of the seven modes were 
stationed upon the lyre ; and in order to that, to 
consider the structure of the instrument ; this he 
explains in the following words : — The lyre, after 

* its last enlargement, consisted of fifteen strings, 
' which took in the compass of a disdiapason or 
' double octave ; these strings were called by the 

* same names as the fifteen sounds of the system, and 

* when tuned for the Dorian mode corresponded 

* exactly with them. Indeed there can be no doubt 
' but that the theory of the system had been origi- 

* nally drawn from the practic of the lyre in this 
' mode, which was the favourite one of the Greeks, 

* as the lyre was also their favourite instrument. In 
' this mode then the Mese of the system was placed 
' in the Mese of the lyre, but in every one of the 

* rest it was applied to a different string, and every 
' sound in the system transposed accordingly. Hence 
' arose the distinction between a sound in Power and 

* a sound in Position ; for when the system was 
' transposed from the Dorian to any other mode, 
' suppose for instance the Phrygian, the Mese of the 
' lyre, though still Mese in position, acquired in this 

* case the power of the Lychanos meson ; and the 

« Sir F. S. on the Modes, 701. 

t Ibid. Dr. Wallis, in his edition of Ptolemy, pag. 137, assigns c, g, 
and f natural, for the positions of the Lydian, Hypolydian, and Hypo- 
phrygian Mese ; but Sir Francis Stiles, for reasons mentioned in his 
discourse, pag. 703, places them in c% g){(, and f «(• 



' Paramese of the lyre, though still Paramese in 
' position, acquired the power of the Mese. In these 

* transpositions, one or more of the strings always 
' required nerv tunings, to preserve the relations of 
' the system ; but notwithstanding this alteration of 

* their pitch they retained their old names when 

* spoken of, in respect to their positions only ; for the 
' name implied not any particular pitch of the string, 
' but only its place upon the lyre in the numerical 
' order, reckoning the Proslambanomenos for the 
'first.':!: 

These are the sentiments of the above-cited author, 
with respect to the Harmonic doctrine : the Musical 
has been already explained ; or if any thing should 
be wanting, the scale hereinafter inserted, shewing 
the position of the Mese, and the succession of chords 
in each of the modes in a comparative position with 
those in the natural system, will render it sufficiently 
intelligible. 

CHAP. XIL 

It now remains to shew the method by which this 
author proposes to reconcile the two doctrines. He 
says that by the Harmonic doctrine we are told the 
pitch of the system for each mode ; and by the 
Musical, in what part of the system to take the 
species of diapason, and that by combining the two 
directions we gain the following plain canon for 
finding any mode required : — § 

CANON. 

' First pitch the system for the mode, as 
' directed by the harmonic doctrine ; then select 
' from it the diapason, directed by the musical ; 
' and we have the characteristic species of the 
' mode in its true pitch.' || 

To make this more plainly appear, he has annexed 
a diagram of the species of diapason, which is here 
also exhibited, and which he says will shew at what 
pitch of the Guidonian scale each sound of the dia- 
pason is brought out by the canon for each of the 
seven modes ; and that as in the construction of this 
diagram the directions of the canon have been strictly 
pursued, so it will appear that the result of it is in all 
respects conformable to the principles of both doc- 
trines. ' Thus,' continues he, ' in the Dorian, for in- 
' stance, it will be seen that the Mese is placed in A 
' la mi re, and that the rest of the sounds exhibited 
' in that diapason, are placed at the proper distances, 
' for preserving the order of the system as required 
' by the harmonic doctrine. It will also be seen that 
' the diapason selected lies between Hypate meson 
' and Nete diezeugmenon ; that the semitones are the 
' first interval in the grave, and third in the acute ; 
' and that the Diazeuctic tone is in the fourth interval, 

* reckoning from the acute. All which circumstances 
' were also required by the musical doctrine for this 
' mode ; and in the rest of the modes all the cir- 
' cumstances required by each doctrine will in like 

* manner be found to obtain : So that no objection 

X Sir Francis Stiles on the Modes, pag. 702. 
§ Ibid, 710. II Ibid. 



68 



HISTORY OF THE SCIENCE 



Book IL 



' can well be raised to the principles on which the ' argument in justification of the manner in which 

' diagram has been framed, by the favourers of either ' I have combined them in the canon.' * 

' doctrine separately : and the very coincidence of Here follows the diagram of the seven species of 

* the two doctrines therein might furnish a probable diapason above-mentioned : — 



« Ibid. 711. 



O 
B 

Q 
H 



H 
P 
O 



> 



O 

Pk 

< 
I— I 

ft 

a 
a 

O 
CO 

I— I 

o 

(in 



HYPOPHRY- 
GIAN. 



PORIAN. 



PHRYGIAN, 



LYDIAN. 



!>* HYPODORIAN. ^ 






9 









HYPOLYDIAN. j 



N 


tu 


_o 


o 


^3 


a 


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H 


PM 



MIXOLYDIAN. i 






Oh 

w 

c 

c6 
Pi 



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til 










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133 


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auoj •ZBici $ 






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By the help of the above diagram it is no very positions from the Dorian, which occupies the middle 

difficult matter to ascertain, beyond the possibility of station : whether after such transposition the inter\-als 

doubt, the situations of the different modes with remained the same or not, is a subject of dispute, 

respect to each other ; or, in other words, to demon- With regard to this question it may be ubserved, 

strate that six of them were but so many ti-ans- that throughout the whole of Ptolemy's treatise. 



Chap. XII. 



AND PRACTICE OF MUSIC. 



59 



nothing is to be met with that leads to a comparison 
between the modes of the ancients and the keys of 
the moderns ; for it seems that with the former the 
characteristic of each mode was the position of the 
diazeuctic tone, and the consequent arrangement of 
the tones and semitones corresponding with the 
several species of diapason, to which they respectively 
answer. But the keys of the moderns are distinguislied 
by the final chord, and therefore unless they could 
be placed in a state of opposition to each other, it is 
very difficult to demonstrate that this or that key 
answers to this or that of the ancient modes, or unless 
a several tuning of the lyre for each mode be sup- 
posed, to ascertain the constituent intervals of the 
latter. Sir Francis Stiles seems to have been aware 
of this difficulty, for though in page 708 of his dis- 
course, he has given a diagram in which the Mixo- 
lydian mode is made to answer to the series from J] 
to j-j, and the others in succession, to the succeeding 
species, he means nothing more by this than to com- 
pare them severally with a species of diapason 
selected from the middle of the lyre, without regard 
to the fundamental chord or key-note. 

Neither does the diagram of the seven species of 
diapason, given by him and above inserted, afford 
^ny intelligence of this kind ; and but for a hint that 
he has dropped at the close of his discourse, that the 
Hypodorian answers exactly to our A 7ni la, with 
a minor third, and the Lydian to our A mi la, with 
a major third,* we should be totally at a loss with 
respect to his sentiments touching the affinity between 
the ancient modes and the modern keys. 

That there was some such affinity between the 
one and the other is beyond a doubt ; f and we see 
Dr. Wallis's opinion of the matter in the diagram 
above inserted from his notes on the eleventh chapter, 
lib. II. of his author, containing a comparative view 
of the keys with the modes. And though it ia to be 

* The anonymous author of a Letter to Mr. Avison, who by the way 
was the late reverend and learned Dr. Jortin, had in that letter blamed 
Sanadon and Cerceau for affirming, in their Observations on Horace, 
that the Dorian mode answered exactly to our A mi la with a minor 
third, and the Phrygian to our A mi la with a major third : from hence 
Sir Francis Stiles takes occasion to give the above as his opinion of the 
matter In which, after all, it seems that he is mistaken, and that the 
author of the letter was in the right: his words are these, and they are 
well worth noting : — 

' Sanadon and Cerceau in their observations on Horace, Carm. v. 9. 
' Sonai^te mixtum tibiis carmen lyra, "■ 
' Hac Dorium, illis barbajum. 

'affirm that the Modus Dorius answered exactly to our A mi to with 
'a minor third, and the Modus Phrygius to our A mi la with a major 
'third: but surely this is a musical error, and a dream from the ivory 
' gate. Two modes, with the same tonic note, the one neither acuter nor 
' graver than the other, make no part of the old system of modes.' 

This is very true ; and the reason of Sir Francis Stiles for asserting the 
contrary was that he had deceived himself into a diffijrent opinion by placing 
the acute signs to f c and g in the Lydian, thereby giving to that series 
the appearance of the key of A)^. But upon his own principlics the 
Lydian answers to our key of C fa ut with the major third, 

Tone, tone, semitone, tone, tone, tone, semitone 

DO RK MI PA SOJ. RE MI 

For though the acute signs require that the final chord be A, the succession 
of intervals is that proper to the diapason C c. 

+ Setbus Calvisiua seems to have been of this opinion in the following 
passage cited by Butler in his Principles of Music, jiag Sfi. in not : — ' In 
'hoc cborali cantu, diligentissime consideret huic Arti deditus, qui sint 
' ubique ; Modulationis progressus, quod Exordium, et quis Finis : ut 
'cognoscat ad quern modum referatur. Inde enim tam primarium illius 
' Modi clausulam, quam Secundariam, eruere, et convenientibus locis 
'annntare, et inserere poterit.' Calvis, c. 17, and Butler himself adds 
that this is the general sentiment of musicians. Notwithstanding that 
CcElius Ilhodoginus out of Cassiodorus distinguishes the modes by their 
several effects. Ibid. 



feared that there is not that precise agreement 
between them which he has stated, there is good 
ground to suppose that, as in the keys, the succession, 
of intervals is in the order which the sense approves, 
so the succession in the modes could not but have 
been in some degree also grateful to the ear. 

This supposition is founded on a passage in the 
eleventh chapter of the second book of Ptolemy, 
importing no less than that each of the modes re- 
quired a peculiar tuning, and these tunings have 
been severally investigated, and are given by Sir 
Francis Stiles ; for what purpose, then, it may be 
asked, but to render the intervals grateful to the 
sense, was a new tuning of the lyre for every mode 
necessary ; and what could that terminate in, but 
two constitutions, in the one whereof the interval 
between the fundamental chord and its third was 
a semiditone, and in the other a ditone ; and when 
the lyre was so tuned, what became of the seven 
species of diapason ? The answer to this latter 
demand is, that as there seem to be in nature but 
the two species above mentioned, proceeding, as will 
presently be shewn, from A and C respectively, the 
remaining five were rejected, and considered as sub-, 
jects of mere speculation. 

But before we proceed to refute the opinion of 
those who without knowing, or even suspecting, that 
the tuning of the lyre was different in each mode, 
contend, that there are in nature seven, not merely 
nominal, but real modes, it is but just tO; state the^ 
reasons on which it is founded. 

And first it is said on the authority of those, 
ancient writers who define a mode to be a given, 
species of di9,pason, that as there are in nature seven 
such species, so are there seven modes, in each whereof 
the succession of tones and semitones must be in that 
order which nature has established, or as they arise 
in the scale, without interposing any of those sig- 
natures to denote remission or intension, which are 
used for that purpose by the moderns. They say 
farther that none of the apecies were at any time 
rejected by the ancients as unfit for practice ; and 
from thence take occasion to lament the depravity of 
the modern system, which admits of no other diversity 
of modes or keys than what arises from the difference 
between the major and the minor third ; for, say they, 
and they say truly, the modern system admits in fact 
of but two, namely A and C ; the first the protoype 
of the flat, as the latter is of the sharp keys, all the 
rest being respectively resolvable into one or the 
other of these.| 

t In the Dissertation sur le Chant Gregorien of Monsieur Nivers, 
Paris 1688, chap. xii. it is said that the eight ecclesiastical tones, which 
all men know have their foundation in the ancient modes, are reducible 
to four, and in strictness to two, as being no otherwise essentially dis- 
tinguished than by the greater and lesser third ; and the same may be 
inferred from a well-known discourse, entitled a Treatise on Harmony, 
containing the chief rules for composing in two, three, and four parts, 
which though at first printed in 1730 by one of his disciples, was indis- 
putably the work of Dr. Pepusch, and was afterwards published by him 
with additions, and examples in notes. In this tract is a chapter on 
transposition, in which the reader is referred to a plate at the end of the 
work, containing a table of the keys, with their characteristics, and 
a stave of musical lines, with certain letters inscribed thereon, which, 
for the purpose of resolving any transposed or factitious key into its 
natural tone by the annihilation of the flat or sharp signatures, he ia 
directed to cut off and apply to the above-mentioned table, by means 
whereof it may be discovered that all the flat keys are transpositions from 
that of A, and all the sharp from that of C This is a process so merely 
mechanical, that no one can be the wiser for having performed it, and 



60 



HISTORY OF THE SCIENCE 



Book XL 



But what, if after all, the ear will not recognise any- 
other succesion of intervals than is found in the con- 
stitution of the keys A and C ? The consequence 

is rather calculated to disguise than explain the true method of reducing 
a transposition to its natural key. But in a small tract, entitled, 
Elements ou Principes de Musique mis dans un novel Ordre, par M. 
Loulie, printed at Amsterdam, in 1698, we meet with a notable rule or 
canon for this purpose, which fully answers the design of its invention. 
This author premises that the dieses, or what we should call the sharps, 
placed at the begining of the musical stave, arise by fifths, beginning 
from F, that is to say, C G D A E, and that the B mols or flats arise by 
fourths, begining from B in this order, E A D G C. The rule or canon 
which he deduces from hence is this : In keys which are determined by 
sharp signatures, call the last sharp si ; or as any but a Frenchman 
would say mi, and place or suppose such a cliff at the head of the stave 
as in a regular course of solmisation, will make it so. To give an in- 
stance of the key of E with the major third : — 




Here the attentive peruser will observe that the interval between the 
third and fourth, and also between the seventh and eighth notes, is 
a semitone ; and that to make the last sharp D, mi, the tenor clilf must 
be placed on the first line of the stave, and when this is done as here it is— 



w 



~m—m- 



irzi 



DO KE MI FA SOL EE MI FA 



the progression of tones and semitones will be exactly in the same order 
as in the key of C, from which this of E is therefore said to be a 
transposition. 

The canon farther directs in the keys mth the flat signatures, to call 
the last of the flats vx, and to place or suppose a cliff accordingly, and to 
shew the effect of the rule in an instance of that kind, the following 
example is given of the key of F with the minor third : — 



m 



^-- 



~C2Z 



zur. 



Here the intervals between the second and third, and also between the 
fifth and sixth notes, are semitones : and to make the last flat, which is 
1), FA, it is necessary to place the bass cliff on the fourth line of the 
stave, which annihilates the flat signatures, and demonstrates that the 
above key of F is a transposition from that of A with the minor third : — 



w. 



BE 



MI FA BE MI FA SOL LA. 



Another rule for the above purpose, and which indeed Dr. Pepusch 
would communicate to his favorite disciples, is, in the case of keys with 
the sharp signatures, to call the last sharp B, and count the lines and 
spaces upwards or downwards till the station of a cliff is found ; and 
the placing that cliff accordingly aimihilates the sharps, and bespeaks the 
natural key. In keys with the flat signatures the rule directs to call the 
.ast flat F, and count as before. 

But amongst the keys with flat signatures, a diversity is to be noted, 
that is to say, between those with a major and those with a minor third ; 
for in the former the process must be repeated, as in this of A b with the 
major third ; — 



W 



itt: 



1231 



In this instance the rule directs to call the last flat, which is the key- 
note, F ; and to count on to the place of a cliff: in doing this the cliff ^&" 

will fall on the first line, and make the key-note F ; by which it should 
seem that the key of A b with the major third is a transposition from F 
also with a major third. 




But as there is in the key of F a flat on b, it is necessary to repeat the 
process, and see what key this of F is a transposition from ; and this by 
the above rule is to be done by calling the flat b F, and proceeding as 
before directed : — 




Gt- 



fe 



-^- 



I 



and this key of F will appear to be a transposition from that of C, and 
by consequence that of A b, from which that of F is transposed, must be 
a transposition from the key of C also. 



then seems to he that there are in nature no other. 
Now if it be true that the sense of hearing is averse 
to those modulations that have no relation to any 
fundamental chord, and that it expects, nay longs for 
some one sound that shall at stated periods determine 
the nature of the progression, there is an end of the 
question. In short, a single experiment of the effect 
of the Mixolydian mode, which answers to the series 
from J] to J], in its natural order, and gives to the 
diapente a semitone less than its true content, will 
offend the ear, and convince any impartial enquirer 
that the existence of seven modes is, in the sense con- 
tended for, nominal and not real.*' 

But notwithstanding the uniformity of keys in the 
modern system, there is a diversity among them worth 
noting, arising from that surd quantity in the dia- 
pason system, which it has been the labour of ages 
to attemper and distribute among the several inter- 
vals that compose it, so as not to be discoverable ; 
the consequences of which temperament is such a 
diversity in the several keys, as gives to each a 
several effect ; so that upon the whole it seems that 
the modern constitution of the modes or keys is 
liable to no objection, save the want of such a division 
of the intervals as seems to be inconsistent with the 
principles of harmonics, and the established order of 
nature. 

The several effects of the modern keys are dis- 
coverable in the tendency which each has to excite 
a peculiar temper or disposition of mind ; for, not to 
mention that soothing kind of melancholy which is 
felt on the hearing music in keys with the minor 
third, and the gaiety and hilarity excited by that in 
keys with the greater third, f each key in the two 
several species is possessed of this power in a different 
degree, and a person endowed with a fine ear will be 

* Vide ante, pag. 59, and Dr. Wallis asserts that there are passages in 
Ptolemy which plainly indicate that the ancients had a several tuning for 
every mode, which could not have been necessary had they followed the 
above order. Farther, to this purpose Malcolm expresses himself in the 
following remarkable passages :— ' If every song kept in one mode, there 
*was need for no more than one diatonic series ; and by occasional 
' changing the tune of certain chords these transpositions of every mode 
•to every chord may be easily performed ; and I have spoken already of 
the way to find what chords are to be altered in their tuning to effect 
' this, by the various signatures of ^ and i? : But if we suppose that in 
' the course of any song a new species is brought in, this can only be 
' effected by having more chords than in the fixed system, so as from any 
' chord of that, any order or species of octave may be found. On Music, 
'pag, 536. 

' If this be the true nature and use of the tones, I shall only observe 
'here, that according to the notions we have at present of the principles 
' and rules of melody, most of these modes are imperfect and incapable 
' of good melody, because they want some of those we reckon the essen 
' tial and natural notes of a tone mode or key, of which we reckon only 
' two species, viz., that from C and A, or the Parhypate hypaton and 
' Proslambanomenos of the ancient fixed system. Ibid. 

' Again, if the essential difference of the modes consists only in the 
' gravity or acuteness of the whole octave, then we must suppose there 
'is one species or concinnous division of the octave, which being applied 
' to all the chords of the system, makes them true fundamentals for 
' a certain series of successive notes. These applications may be made in 
'the manner already mentioned, by changing the tune of certain chords 
' in some cases, but more universally by adding new chords to the system, 
'as the artificial or sharp and flat notes of the modern scale. But in 
'this case, again, where we suppose they admitted only one concinnous 
' species, we must suppose it to be corresponding to the octave a, of what 
'we call the natural scale; because they all state the order of the systema 
'immutatum in the diagram, so as it answers to that octave.' Ibid ^Vi. 

+ Dr. Jortin has discovered a new characteristic for these two species 
of keys ; he calls one the male, the other the female : the thought is 
ingenious, and is thus expressed by him in a letter published at the end 
of the latter editions of Avison's Remarks on Musical Expression : — ' By 
' making use of the major and minor third we have two real and distinct 
' tones, a major and a minor, which may be said to divide music, as nature 
' seems to have intended, into male and female. The first hath strength, 
' the second hath softness ; and sweetness belongs to them both.' 



Chap. XIIL 



AND PRACTICE OF MUSIC. 



61 



variously affected by the keys A and F, each with 
the lesser, as also by those of C and E with the 
greater third. 

Effects like these, but to a degree of extravagance 
that exceeds the bounds of credibility, are ascribed 
to the modes of the ancients : that the Dorian was 
grave and solemn, and the Lydian mild and soothing,* 
may be believed, but who can credit the relation, 
though of Cicero himself, and after him Boetius,f 
that by an air in the Phrygian mode played on 
a solitary pipe (one of the ancient tibiae) a drunken 
young man, of Tauromenium, was excited to burn 
down the house wherein a harlot had been shut up 
by his rival, and that Pythagoras brought him to his 
reason, by directing the tibicenist to play a spondeus 
in a different mode ? Or that not the fumes of wine 
or a disturbed imagination, rather than the flute 
of Timotheus, played on in the Phrygian mode, 
provoked Alexander to set fire to Persepolis. 

CHAP XIII. 

Havikg thus collected into one point of view the 
sentiments of the ablest writers on those two most 
important desiderata in the ancient music, the genera 
and the modes, in order to trace the successive 
improvements of the science, it is necessary to recur 
to those only genuine sources of intelligence, the 
writings of the Greek harmonicians. And here we 



alia est pars 

Theoretica : 

cujus rursus partes duae, 



cannot but applaud the ingenuity and industry of 
those learned men, their remote successors, who from 
ancient manuscripts, dispersed throughout the world, 
have been able to settle the text of their several 
works ; and who with a great degree of accuracy 
have given them to the public, together with Latin 
versions, illustrated with their own learned anno- 
tations. 

Those whom we are most obliged to in this 
respect are, Marcus Meibomius, a German ; and our 
countryman Dr. John Wallis : the former of these 
has given to the world seven of the ancient Greek 
writers, namely, Aristoxenus, Euclid, Nicomachus, 
Alypius, Gaudentius, Bacchius Seniori, and Aris- 
tides Quintilianus ; as also a Discourse on Music, 
which makes the ninth book of Martianus Capella's 
Latin work, entitled De Nuptiis Philologije et Mer- 
curii ; and the latter a complete translation of the 
harmonics of Ptolemy, with notes, and a most 
valuable appendix ; as also translations of Porphyry 
and Manuel Bryennius in like manner. 

Concerning these writers, it is to be observed that 
the Greeks are by far of the greatest authority ; and 
that their division of music into several branches, 
as being more scientific than that of the Latin 
writers, is entitled to the preference. The most 
ample of these is the division of Aristides Quin- 
tilianus, which is thus analyzed by his editor Mei- 
bomius, in his notes on that author, pag. 207 : — 



Musicas 1 



Physica : 

quae dividitur in 



iArithmeticum. 
Ir nysicam, generi cognominem. 



alia 

Practica : 

cujus item partes dus, 



Nevertheless, the most general is that threefold 
division of music into Harmonica, Rhythmica, and 
Metrica ; the two latter of which, as they relate 
chiefly to poetry, are but superficially treated of by 
the harmonic writers. Upon this division of music 
it is observable that the more ancient writers were 
very careful in the titles of their several treatises : 
such of them as confined their discourses to the 
elementary part of the science, as namely, Aris- 

* Milton adopts these characteristics of the Dorian and Lydian modes : 

Anon they move 

In perfect phalanx to the Dorian mood 

Of flutes and soft recorders ; such as rais'd 

To height of noblest temper heroes old 

Arming to battle. Paradise Lost, B. I. line 549. 

And ever against eating cares 

Lap me in soft Lydian airs. L'AtLEORO. 

And Dryden describes the Lydian by its effects, in these words : 
Softly sweet in Lydian measures 
Soon he sooth'd his soul to pleasures. Alexander's Feast. 

From which passage it is to be suspected that the poet thought with 
Cornelius Agrippa and some others, that the epithet Lydian referred to 
the measure, whereas it clearly relates to the harmony, but Dryden knew 
little about music. 



Usualis : 

cujus partes 



t De Musica, lib. I. cap, i. 



iHarmonicam. 
Rythmicam. 
Metricam. 
IMelopoeia. 
Rhythmopoeia. 
Poesis. 
IOrganica. 
Odica. 
TT •!.• 

Hypocritica. 

toxenus, Euclid, Nicomachus, Gaudentius, Ptolemy, 
and Bryennius, call the several treatises written by 
them Harmonica ; whereas Aristides, Bacchius, and 
Martianus Capella entitle theirs Musica ; as does 
Boetius, although he was a strict Phythagorean. 
Porphyry indeed, who professes nothing more than 
to be a commentator on the harmonics of Ptolemy, 
institutes another mode of division, and, without 
distinguishing the speculative part of the science 
from the practical, divides it into six general heads, 
namely. Harmonica, Rythmica, Metrica, Organica, 
Poetica, and Hypocritica; Rythmica he applies to 
dancing, Metrica to the enunciative, and Poetica to 
verses. I The branch of the science, which has been 

t Malcolm has taken notice of this division, but prefers to it that of 
ftuintilian, upon whose analysis he has given the following concise and 
perspicuous commentary : — ' Aristides considers music in the largest 
' sense of the word, and divides it into contemplative and active. The 
' first he says is either natural or artificial ; the natural is arithmetical, 
' because it considers the proportion of numbers ; or physical, which 
' disputes of everything in nature ; the artificial is divided into har- 
' monica, rythmica (comprehending the dumb motions) and metrica : the 
' active, which is the application of the artificial, is either, enunciative 
•{as in oratory) organical, (or instrumental performance) ndical (for 
' voice and singing of poems) hypocritical (in the motions of the 



62 



HISTORY OF THE SCIENCE 



Book it. 



most largely treated by the ancients, is the Har- 
monica, as will appear by the extracts hereinafter 
given from their works. 

From the relation hereinbefore given of the in- 
vention of, and successive improvements made in, 
music, a very accurate judgment may be formed of 
the nature of the ancient system, whicli, together with 
the ratios of the consonances, and the doctrine of the 
genera and the modes, constituted the whole of the 
harmonical science as it stood about the year of the 
World 3500. After which Aristoxenus, Euclid, 
Nicomachus, and other Greek writers, made it a 
subject of Philosophical enquiry, and composed those 
treatises on harmonics which are severally ascribed 
lo them, and of which, as also of their respective 
authors, a full account will hereafter be given. 
What was the state of the science previous to the era 
above-mentioned, can only be learned from those 
particulars relating to music, which are to be met 
with in the several accounts extant of the life and 
doctrines of Pythagoras, who, for any thing that can 
how be collected to the conti'ary, seems indisputably 
intitled to the appellation of the Father of Music. 

Pythagoras, according to the testimony of the 
generality of 'writers, was born about the third year 
of the fifty-third Olympiad, which answers to the 
year of the world 3384, and to about 560 years 
before the birth of our Saviour ; and although he 
was of that class of philosophers called the Italic 
sect, he is supposed to have been a native of Samos, 
and in consequence of this opinion is usually stiled 
the Samian sage or philosopher. His father, named 
Mnesarchus, is reported to have been a merchant, or, 
as some say, an engraver of rings. Of his travels 
into various parts of the world for the acquiring of 
knowledge ; of the wonders related of him, or of 
his doctrines in general, it is needless to give an 
■account in this place. It seems to be agreed that he 
left not any thing behind him of his writing, and all 
that is to be known of his doctrines is grounded on 
the testimony of his disciples, who were very many, 
■and were drawn to hear him from the most distant 
parts of Greece and Italy. Of these Nicomachus 
was one, who because he himself has written on the 
science of harmonics, may well be supposed to under- 
stand the doctrines of his master ; from him there- 
fore, as also from others, as namely, Ptolemy, 
Macrobius, and Porphyry, who, though they lived 
many years after Pythagoras, were of his sect, we 
may with some degree of confidence determine 
as to the tenets of his school. A summary of these 
is given by his learned biographer Stanley, in the 
passages here cited ; and first as to those respecting 
music in general, he gives them in these words : — 

' The Pythagoreans define music an apt com- 
' position of contraries, and an union of many, and 
' consent of differents ; for it not only co-ordinates 

* rythms and modulation, but all manner of systems. 

* Its end is to unite and aptly conjoin. God is the 

* pantomimes). To what purpose some add hydraulical I do not under- 
' stand, foi this is but a species of the organical, in which water is someway 
'used, for producing or modifying the sound. The musical faculties, as 
' they call them, are Melopceia, "which gives rules for the tones of the 
' voice or instrument ; RythmoptEia, for motions ; and Poeais for making 
'of verse.' Treatise of Music, Edinb. 1721, pag. 455. 



reconciler of things discordant, and this is his 
chiefest work, according to music and medicine, 
to reconcile enmities. In music, say they, consists 
the agreement of all things, and aristocracy of the 
universe. For what is harmony in the world, in 
a city is good goverment ; in a family, temperance.' 

* Of many sects, saith Ptolemy, that were con- 
versant about harmony, the most eminent were 
two, the Pythagoric and Aristoxenean ; Pythagoras 
dijudicated it by reason, Aristoxenus by sense. 
The Pythagoreans, not crediting the relation of 
hearing, in all those things wherein it is requisite, 
adapted reasons to the differences of sounds, con- 
trary to those which are perceived by the senses • 
so that by this criterion (reason) they gave occasion 
of calumny to such as were of a different opinion. 

' Hence the Pythagoreans named that which we 
now call harmonic Canonic, not from the canon or 
instrument, as some imagine, but from rectitude ; 
since reason finds out that which is right by using 
harmonical canons or rules even of all sorts of in- 
struments framed by harmonical rules, pipes, flutes^ 
and the like. They call the exercise Canonic, which 
although it be not canonic, yet is so termed, because 
it is made according to the reasons and theorems of 
canonics; the instrument therefore seems to be 
rather denominated from its canonic affection. A 
canonic in general is a harmonic who is conversant 
by ratiocination about that which consists of har- 
mony. Musicians and harmonics differ ; musicians 
are those harmonics who begin from sense, but 
canonics are Pythagoreans, who are also called 
harmonics ; both sorts are termed by a general 
name musicians.' * 

As touching the human voice, the same author 
delivers the following as the Pythagorean tenets : — 

' They \Vho were of the Pythagorean school said 

* that there are (as of one genus) two species. One 

* they properly named Continuous, and the other 

* Diastematic (intermissive) framing the appellations 
' from the accidents pertaining to each. The Dia- 
' stematic they conceived to be that which is sung 
' and rests upon every note, and manifests the muta- 
' tion which is in all its parts, which is inconfused 
' and divided, and disjoined by the magnitudes, 
' which are in the several sounds as coacerved, but 
' not commixt, the parts of the voice being applied 
'mutually to one another, which may easily be 
' separated and distinguished, and are not destroyed 
' together ; such is the musical kind of voice, which 
' to the knowing manifests all sounds of- what magni- 
' tude every one participates : For if a man use it 
' not after this manner, he is not said to sing but to 

* speak.f 

' Human voice having in this manner two parts, 
' they conceived that there are two places, which 
' each in passing possesseth. The place of con- 
' tinuous voice, which is by nature infinite in magni- 
' tude, receiveth its proper term from that wherewith 
' the speaker began until he ends, that is the place 
' from the beginning of his speech to his conclusive 
' silence. So that the variety thereof is in our power, 

• Hist, of Philos. by Thomas Stanley, Esq. folio edit. 1701, pag. 385. 
t Ibid. 



Chap. XIII. 



AND PRACTICE OF MUSIC. 



63 



' but the place of diastematic voice is not in our 
' power, but natural ; and this likewise is bound by 

* different effects. The beginning is that which is 
' first heard, the end that which is last pronounced ; 

* for from hence we begin to perceive the magnitudes 
' of sounds, and their mutual commutations, from 
' whence first our hearing seems to operate ; whereas 

* it is possible there may be some more obscure 
' sounds perfected in nature which we cannot perceive 
' or hear : as for instance, in things weighed there 
' are some bodies which seem to have no weight, as 
' straws, bran, and the like ; but when as by appo^ 
' sition of such bodies some beginning of ponderosity 
' appears, then we say they first come within the 
' compass of static. So when a low sound increaseth 

* by degrees, that which first of all may be perceived 
' by the ear, we make the beginning of the place 

* which musical voice requireth.' * 

These were the sentiments of the Pythagoreans, 
with respect to music in general, and of voice in 
particular. Farther, they maintained an opinion 
which numbers, especially the poets, have adopted, 
and which seems to prevail even at this day, namely, 
that music, and that of a kind far surpassing mortal 
conception, is produced by the motion of the spheres 
in their several orbits. The sum of this doctrine 
is comprised in the following account collected by 
Stanley from Nicomachus, Macrobius, Pliny, and 
Porphyry : — 

' The names of sounds in all probability were 
derived from the seven stars, which move circularly 
in the heavens, and compass the earth. The cir- 
cumagitation of these bodies must of necessity cause 
a sound ; for air being struck, from the intervention 
of the blow, sends forth a noise. Nature herself 
constraining that the violent collision of two bodies 
should end in sound.' 

* Now, say the Pythagoreans, all bodies which are 
carried round with noise, one yielding and gently 
receding to the other, must necessarily cause sounds 
different from each other, in the magnitude and 
swiftness of voice and in place, W'hich (according to 
the reason of their proper sounds, or their swiftness, 
or the orbs of repressions, in which the impetuous 
transportation of each is performed) are either more 
fluctuating, or, on the contrary, more reluctant. 
But these three differences of magnitude, celerity, 
and local distance, are manifestly existent in the 
planets, which are constantly with sound circum- 
agitated through the setherial diffusion ; whence 
■every one is called dc/)p, as void of (rrdaiQ, station, 
and ati €ea>v, always in course, whence God and 
^ther are called Qeog and At'6>/p.'f 

* Moreover the sound which is made by striking 
the air, induceth into the ear something sweet and 
musical, or harsh and discordant : for if a certain 
observation of numbers moderate the blow, it effects 
a harmony consonant to itself ; but if it be teme- 
rarious, not governed by measures, there proceeds 
a troubled unpleasant noise, which offends the ear. 
Now in heaven nothing is produced casually, no- 
thing temerarious ; but all things there proceed 



according to divine rules and settled proportions : 
whence irrefragably is inferred, that the sounds 
which proceed from the conversion of the celestial 
spheres are musical. For sound necessarily proceeds 
from motion, and the proportion which is in all 
divine things causeth the harmony of this sound. 
This Pythagoras, first of all the Greeks, conceived 
in his mind ; and understood that the spheres 
sounded something concordant, because of the 
necessity of proportion, which never forsakes ce- 
lestial beings.' I 

' From the motion of Saturn, which is the highest 
and farthest from us-, the gravest sound in the 
diapason concord is called Hypate, because virarov 
signifieth highest ; but from the lunary, which is 
the lowest, and nearest the earth, Neate ; for vearov 
signifieth lowest. From those which are next these, 
viz., from the motion of Jupiter who is under 
Saturn, Parypate ; and of Venus, who is above the 
moon, Paraneate. Again, from the middle, which 
is the sun's motion, the fourth from each part Mese, 
which is distant by a diatessaron, in the heptachord 
from both extremes, according to the ancient way ; 
as the sun is the fourth from each extreme of the 
seven planets, being in the midst. Again, from 
those which are nearest the sun on each side from 
Mars, who is placed betwixt Jupiter and the sun, 
Hypermese, which is likewise termed Lichanus ; 
and from Mercury, who is placed betwixt Venus 
and the sun, Paramese.'§ 

' Pythagoras, by musical proportion, calleth that 

a tone, by how much the moon is distant from the 

earth : from the moon to Mercury the half of that 

space, and from Mercury to Venus almost as much ; 

from Venus to the sun, sesquiple ; from the sun 

to Mars, a tone, that is as far as the moon is from 

the earth : from Mars to Jupiter, half, and from 

Jupiter to Saturn, half, and thence to the zodiac 

sesquiple. Thus there are made seven tones, which 

they call a diapason harmony, that is an universal 

concent, in which Saturn moves in the Doric mood, 

Jupiter in the Phryfjian, and in the rest the like.'|| 

' Those sounds which the seven planets, and the 

sphere of fixed stars, and that which is above 

us, termed by them Antichton, make, Pythagoras 

affirmed to be the nine Muses ; but the composition 

and symphony, and as it were connexion of them 

all, whereof, as being eternal and unbegotten, each 

is a part and portion, he named Mnemosyne.'^} 

That the above notion of the music of the spheres 

was first entertained by Pythagoras, seems to be 

agreed by most writers. The reception it has met 

with has been different, according as the temper of 

the times, or the different opinions of men have 

contributed to favour or explode it. Cicero mentions 

it in such a way as shews him inclined to adopt it, 

as does also Boetius, lib. I. cap. ii. Macrobius, in 

his Commentary on the Somnium Scipionis, lib. II. 

cap. iii. speaks of it as a divine and heavenly notion. 

Valesius, on the contrary, treats it as an ill-grounded 

conceit. Sacr. Philosoph. cap. xxvi. ifec. pag. 446. 

edit. 1588. 



Notwithstanding which it has ever been 



Ibid. 



f Ibid. 386. 



X Ibid. 



§ Ibid. 



II Ibid. 



•ff Ibid. 



64 



HISTOKY OF THE SCIENCE 



Book IJ. 



favoured by the poets : Milton, who was a great 
admirer of music, while at college composed and 
read in the public school, a small tract De Sphgerarum 
Concentu, which with a translation thereof is pub- 
lished in Peck's Memoirs of him. Mr. Fenton, in 
his notes on Waller, suggests that Pythagoras might 
possibly have grounded his opinion of the music of 
the spheres upon a passage in the book of Job, the 
reasons for this conjecture are very ingenious, and 
will be best given in his own words, which are 
these : — 

' Pythagoras was the first that advanced this doc- 

* trine of the music of the spheres, which he probably 
' grounded on that text in Job, understood literally, 
' " When the morning stars sang together," &c. 
' chap. xxix. ver, 7. For since he studied twelve 
' years in Babylon, under the direction of the learned 

* impostor Zoroastres, who is allowed to have been 
' a servant to one of the prophets, we may reasonably 
' conclude that he was conversant in the Jewish 
' writings, of which the book of Job was ever 
' esteemed of most authentic antiquity. Jamblicus 

* ingenuously confesseth that none but Pythagoras 

* ever perceived this celestial harmony ; and as it 
' seems to be* a native of imagination, the poets have 
' appropriated it to their own province, and our 
' admirable Milton employs it very happily in the 
' fifth book of his Paradise Lost : — 

That day, as other solemn days, they spent 

In song and dance about the sacred hill : 

Mystical dance ! which yonder starry sphere 

Of planets and of fix'd,in all her wheels 

Resembles nearest, mazes intricate, 

Eccentric, intervolv'd, yet regular 

Then most, when most irregular they seem ; 

And in their motions harmony divine 

So smooths her charming tones, that God's own ear 

Listens delighted * 

Censorinus suggests a notable reason why this 
heavenly music is inaudible to mortal ears, viz., its 
loudness, which he says is so great as to cause deaf- 
ness. De Die Natal, cap. xi, which Butler has thus 
ridiculed : — 

Her voice, the music of the spheres. 

So loud it deafens mortal ears. 

As wise philosophers have thought. 

And that's the cause we hear it not. 

HuDiBRAs, Part II. Cant. i. line 617. 

After all, whether the above opinion be philo- 
sophically true or not, the conception is undoubtedly 
very noble and poetical, and as such it appears 
in the passage above-cited from the Paradise Lost, 
and in this other of Milton, equally beautiful and 
sublime : — 

Ring out, ye chrystal spheres, 
Once bless our human ears, 

If ye have power to touch our senses so ; 
And let your silver chime 
Move in melodious time, 

And let the base of heav'n's deep organ blow. 

Hymn on the Nativity. 

Touching the division of the diapason, the follow- 
ing is the doctrine of the Pythagoreans : — 

* One of the earliest editors of Milton has the following note on this 
passage, which Dr. Newton has retained : — 

' There is a text in Job xxxviii. 37. that seems to favour the opinion 
of the Pythagoreans, concerning the musical motion of the spheres, 



' The diatonic genus seems naturally to have thes i 
' degrees and progresses, hemitone, tone and tone, 
' (half note, whole note and whole note) ; this is the 

* system diatessaron, consisting of two tones, and that 
' which is called a hemitone ; and then, another tone 
' being inserted, diapente is made, being a system of 
' three tones and a hemitone. Then in order after 
' this, there being another hemitone, tone and tone, 
' they make another diatessaron, that is to say, 
' another Sesquitertia : so that in the ancienter 

* heptachord, all fourths from the lowest, sound a 
' diatessaron one to another, the hemitone taking 
' the first, second, and third place, according to tlie 
' progression in the tetrachord. But in the Pytha- 
' goric octochord, which is by a conjunction a system 

* of the tetrachord and the pentachord, and that either 
'jointly of two tetrachords, or disjointly of two tetra- 
' chords separated from one another by a tone, the 
' procession will begin from the lowest, so that every 
' fifth sound will make diapente, the hemitone passing 
' into four places, the first, the second, the third, and 
'the fourth.'! 

It appears also that Pythagoras instituted the canon 
of the Monochord, and proceeded to a subdivision of 
the diatessaron and diapente into tones and semitones, 
and thereby laid the foundation for the famous Sectio 
Canonis, which Euclid afterwards adjusted, and is 
given in his Introduction, as also in a foregoing 
chapter of this work. Duris, an author cited by 
Porphyry, mentions a brazen tablet, set up in the 
Temple of Juno by Arimnestus, the son of Pytha- 
goras, near two cubits in diameter, on which was 
engraven a musical canon, which was afterv^'ards 
taken away by Simon, a Thracian, who arrogated 
the canon to himself, and published it as his own. J 

Stanley speaks farther of Pythagoras in those 
words : ' Pythagoras, saith Censorinus, asserted that 
' this whole world is made according to musical pro- 
' portion, and that the seven planets betwixt heaven 
' and the earth, which govern the nativities of mortals, 
' have an harmonious motion, and intervals corres- 

* pondent to musical diastemes ; and render various 

* sounds, according to their several heights, so con- 
' sonant that they make most sweet melody ; but to 
' us inaudible, by reason of the greatness of the noise, 
' which the narrow passage of our ears is not capable 
' to receive. For, as Eratosthenes collected that the 
' largest circumference of the earth is 252000 stadia, 
' so Pythagoras declared how many stadia there are 
' betwixt the earth and every star. In this measure 
' of the world we are to understaiid the Italick sta- 
' dium, which consists of G25 feet, for there are others 
' of a different length, as the Olympic of 600 feet, the 
' Pythic of 500. From the Earth, therefore, to the 
' Moon Pythagoras conceived it to be about 12G000 

* stadia ; and that distance, (according to musical 
' proportion) is a tone. From the Moon to Mercury, 

' though our translation differs therein from «rther versions. " Con- 
' centum Cceli quis dormire faciet ? " Who shall lay asleep, or still the 
'concert of the heaven? But this is to be understood metaphorically 
' of the wonderful proportions observed by the heavenly bodies iu their 
' various motions.' — Hume. 

The above is the Vulgate translation ; that of Beza is less to thi» 
purpose, as is also that of Tremelius. 

t Stanl. Hist, of Philos. pag. 387. 

J Ibid 388, 366. 



Chap. XIV. 



AND PRACTICE OF MUSIC. 



65 



'who ia called a-TiXftcoy, half as much, as it were 
' a hemitone. From thence to Phosphorus, which is 
'the star Venus, almost as much, that is another 
' hemitone : from thence to the Sun twice as much, 
' as it were a tone and an half. Thus the Sun is 
' distant from the Earth three tones and a half, which 
' is called Diapente ; from the moon two and a half, 
' which is Diatessaron. From the Sun to Mars, who 

* IS called Uvpoeie, there is the same interval as from 
' the Earth to the Moon, which makes a tone. From 
'thence to Jupiter, who is called ^ae^wv, half as 

* much, which makes a hemitone. From thence to 

* the supreme heaven, where the signs are, a hemitone 
' also ; so that the diasteme from the supreme heaven 
' to the Sun is Diatessaron, that is two tones and a 
' half : from the supreme heaven to the top of the 
' earth six tones, a diapason concord. Moreover 
' he referred to other stars many things which the 
'masters of music treat of, and shewed that all 
' this world is enarmonic' * Thus Censorinus : ' but 
' Pliny, delivering his opinion of Pythagoras, reckons 
' seven tones from the earth to the supreme heaven ; 
' for whereas Censorinus accounts but a hemitone from 
' Saturn to the zodiac, Pliny makes it Sesquiple.'f 

Stanley represents the intervals of the spheres in 
the following diagram : — 



CHAP. XIV. 




* These positions of the Pythagoreans, that the universe is framed 
according to musical proportion, and that all this world is enarmonic 
refer to the general frame and contexture of the whole. But there are 
arguments in favour of music, deducible from the properties and affec- 
tions of matter, discoverable in its several parts : in short, it may be said 
in other words, that the whole world is in tune, inasmuch as there are 
few bodies but are sonorous. The skin of an animal may be tuned to 
any given note, as is observable in the drum : a cable distended by a 
sufficient power is as much a musical chord as a lute string or one of 
wire. And Strada somewhere mentions six great guns in a fortification 
at Groningen, which from the sounds uttered by them in their explosion 
had the names of ut, re, mi, fa, sot, la. The percussion of all metals' 
of stones, nay of timber, or of the trunks of trees when felled, produces 
a musical sound : hollow vessels, as well of wood, as earth and metal 
when struck do the same. Of this fact the Indian Gong, as it is called' 
is a surprising instance; it is an instrument of brass, er some other 
factitious metal, in form like a sieve, and about two feet in diameter. 
The late duke of Argyle had one in his observatory at Whittoii, near 
Twickenham, in Middlesex, which being susjiended edgeways by a cord, 
and struck with a stick muffled at the end, many times, till the quickest 
vibrations it could make were excited, yielded not only a clear musical 
sound, but the whole harmony of a diapason, namely, the unison third, 
fifth, and octave, so clearly and distinctly, that each was obvious to the 
ear. This instrument is mentioned by Capt. Dampier in one of his 
voyages, and is thus described by him :— 
' In the sultan's mosque [at Mindanao] there is a great drum with but 
one head, called a Gong, which is instead of a clock. This gong is 
I beaten at twelve o'clock, at three, six, and nine, a man being appointed 
for that service. He has a stick as big as a man's arm, with a great 
knob at the end bigger than a man's fist, made with cotton, bound fast 
' with small cords ; with this he strikes the gong as hard as he can about 
twenty strokes, beginning to strike leisurely the first five or six strokes 
' then he strikes faster, and at last strikes as fast as he can ; and then he 
strikes agam slower and slower so many strokes : thus he rises and falls 
three times a-day, and then leaves off till three hours after.' Dampier's 
Voyages, vol. I. pag. 388. ^ 

Glass, and many other bodies, affected by the voice, or the vibrations 
of chords, return the sounds that agitate them. It is credibly reported 
of old Smith, the organ-maker, that he could not tune a certain iiipe in 
St. Pauls organ till he had broken a pane of glass in the sash that 
incloses it. 

t Stanl. Life of Pythag. pag. 393. 



In what manner Pythagoras discovered the con- 
sonances, and adjusted the system, has already been 
mentioned. The particulars of his life are related 
by Jamblichus and other authors ; and a summary 
of his doctrines is contained in the account given 
of him by the learned Stanley, in his history of 
Philosophy. Pythagoras lived to the age of eighty, 
or, according to some writers, ninety years. The 
manner of his death, which all agree was a violent 
one, is as variously reported ; some say, that being 
with others at the house of his friend Milo, one who 
had been refused admittance among them set it on 
fire, and that Pythagoras, running to escape the 
flames, was overtaken and killed, together with 
forty of his disciples, among whom was Aichytas of 
Tarentum.J Others say that he fled to the Temple 
of the Muses at Metapontum, and died for want of 
food, having lived forty days without eating. § He 
had for one of his disciples Philolaus, a Crotonian 
(although he is classed among those of Tarentum, 
his followers) whose system of a septenary is herein- 
before inserted ; and who was also the inventor of 
that division of the sesquioctave tone into commas, 
which Boetius has recognized, and is approved of 
even at this day. This Philolaus is said to have 
been the first that asserted the circular motion of the 
earth, and to have written of the doctrines of the 
Pythagorean school. One of his books was pur- 
chased by Plato of his relations, at forty Alexandrian 
Min», an immense price. || 

Among many tenets of the Pythagoreans, one was 
that there is a general and universal concent oi 
harmony in the parts of the universe, and that 
the principles of music pervade the whole material 
world ; for which reason they say that the whola 
world is enarmonic. And in the comparison they 
assert that those proportions into which the con- 
sonances in music are resolvable, are also to be found 
in those material forms, which from the symmetry 
of their parts excite pleasure in the beholder. The 
effect of this principle is in nothing so discoverable 
as in the works of the architects of ancient times, 
in which the proportions of 2 to 1, answering to the 
diapason; of 3 to 2, or Sesquialtera, 4 to 3, or 
Sesquitertia, are perpetually resulting from a com- 
parison between the longitude and latitude of the 
whole or constituent parts, such as porticos, pedi- 
ments, halls, vestibules, and apertures of all kinds, 
of every regular edifice. 

At a time when philosophy had derived very 
little assistance from experiment, such general con- 
clusions as these, and that the universe was founded 
on harmonic principles, had little to recommend 
them but the bare probability that they might be 
well grounded ; but how great must have been the 
astonishment of a Pythagorean or a Platonist, could 
he have been a witness to those improvements which 
a more cultivated philosophy has produced ! And 
how would he who exulted in the discovery that the 

I Stanley in the Life of Pythagoras, chap. xix. „ 

§ Ibid. ^ 

i Ibid. pag. 436. 



66 



HISTORY OF THE SCIENCE 



Book II. 



consonances had a ratio of 12. 9. 8. 6, have been 
pleased to hear the consonances at the same instant 
in a sonorous body ; or been transported to find, by 
the help of a prism, a similar coincidence of pro- 
portions among colours, and that tlie principles of 
harmony pervaded as well the objects of sight as 
hearing ? For Sir Isaac Newton happily discovered, 
that the breadths of the seven primary colours in the 
sun's image, produced by the refraction of his rays 
through a prism, are proportional to the seven differ- 
ences of the lengths of the eight musical strings, 
D, E, F, G, A, B, C, d, when the intervals of their 
sounds are T, H, t ; T, t, H, T.* 

The earliest of the harmonic writers, whose works 
are now extant, was Aristoxenus; he was the son 
of a musician of Tarentum, in Italy, called also 
Spintharus. Aristoxenus studied music first under 
his father at Mantinea, and made a considerable 
proficiency therein : he had also diverse other tutors, 
namely, Lamprius, Erythrasus, Xenophilus the Pytha- 
gorean, and lastly Aristotle, whom, as some say, he 
greatly reviled after his death, for having left his 
school to Theophrastus, which Aristoxenus expected 
to have had, he being greatly applauded by his 
hearers : though others on the contrary assert, that 
he always mentioned Aristotle with great respect. 
He lived in the time of Alexander the Great, viz., 
about the hundred and eleventh Olympiad, which 
answers nearly to a.m. 3610. There are extant of 
his writing Elements of Harmonics, in three books. 
He is said to have written on music, philosophy, 
history, and other branches of learning, books to the 
number of four hundred and fifty-three, and to have 
expressly treated on the other parts of music, namely, 
the Rythmic, the Metric, and the Organic ; but 
that above-mentioned is the only work of his now 
remaining. 

Touching the elements of Aristoxenus, there is 
great diversity of opinions : Cicero, who, as being 
a philosopher, we may suppose to have studied the 
work with some degree of attention, in his Treatise 
de Finibus, lib. V. 19, pronounces of it that it is 
utterly unintelligible. Meibomius, on the other hand, 
speaks of it as a most valuable relique of antiquity, 
and scruples not to style the author the Prince of 
Musicians. And the principal end of Euclid's Intro- 
duction is to reduce the principles of the Aristox- 
eneans into form. Notwithstanding all this, a very 
learned writer, namely. Sir Francis Stiles, of whom 
mention has already been made, hesitates not to say, 
that the whole three books of harmonics ascribed 
to Aristoxenus are spurious. On what authority 
this assertion is grounded he has forborne to mention ; 
however, as the work is recognized by Ptolemy, and 
is constantly appealed to by him, as the test of the 
Aristoxenean doctrine, its authenticity will at this 
day liardly bear a question. 

In the first book of the Elements of Harmonics 
of Aristoxenus, is contained that explanation of the 
genera, and also of their colours or species, which 
has already been given from him. The rest of that 

* Vide Smith's Harmonics, pag. 31, in a note. And Sir Isaac Newton's 
Optics, book I. part ii. prop. 3. pag. 91 of the quarto edition. 



book consists of some general definitions of terms, 
particularly those of Sound, Interval, and System, 
which, though in some respects arbitrary, all the 
subsequent writers seem to have acquiesced in. 

In his second book we meet with an assertion of 
the author, which at this day must doubtless appear 
unintelligible, namely, that music has a tendency to 
improve or corrupt the morals. This notion, strange 
as it may seem, runs through the writings of all the 
ancient philosophers, as well those who did not, as 
those that did, profess to teach music. Plutarch 
insists very largely on it ; and it is well known what 
effects the Spartans attributed to it, when they made 
it an essential in the institution of their youth. 
Aristophanes, in his comedy of The Clouds, puts 
into the mouth of Justice, whom he represents as 
engaged in a contest with Injustice, a speech so very 
pertinent to this subject, that it is here inserted at 
length, as Mr. Theobald has translated it : — ' I'll tell 
' you then what was the discipline of old, whilst 
' I flourished, had liberty to preach up temperance 
' to mankind, and was supported in it by the laws ; 
' then it was not permitted for the youth to speech it 
' in public, but every morning the young people of 
' each borough went to their music school, marched 
' with a grave composed countenance through the 
' streets, decent and lightly clothed, even when the 
' snow fell thick. Before their master they sat with 
' modesty, in proper ranks, at distance from each 
' other ; there they were taught to sing in lofty 
' strains some hymn to the great and formidable 
' Pallas, or other canto of that kind, in concert with 
' the strong and masculine music of their country, 
' without pretending to alter the tones that had been 
' derived down to them by their forefathers. And 
' if any one were observed to wanton it in his 
' performance, and sing in an effeminate key, like 
' those that now sing your corrupted airs of Phrynis, 
' he was immediately chastised as one that depraved 
' and ruined music. You would not then have seen 
' a single instance of one that should dare commit 
' the least immodesty, or discover ought that honesty 
' enjoined him to hide : they were so scrupulously 
' nice in this respect, that they never forgot to sweep 
' up the sand on which they had sat. None then 
' assumed the lawless minion, or defiled himself with 
' wanton glances ; none were suff'ered to eat what 
' was an incentive to luxury, or injured modesty : 
' radishes were banished from their meals ; the anise 
' and rock-parsley that are proper for old constitu- 
' tions, were forbid them, and they were strangers 
' to high and seasoned dishes : they sat with gravity 
' at table, never encouraged an indecent posture, 
' or the tossing of their legs lazily up and down.'f 

+ Polybius in his fourth hook, chap. iii. has given a description of 
the ancient Arcadian discipline of youth, nearly corresponding with 
that of the Spartans above cited, in a passage, which, as it is often 
alluded to by the writers on music, is here inserted in the words of his 
elegant translator Mr. Hampton :— 

'All men know that Arcadia is almost the only countrv in whicli 
'children, even from their most tender age, are taught to sing in 
' measure the songs and hymns that are composed in honour of tlieir 
'gods and heroes: and that afterwards when tliey have learned the 
' music of Timotheus and Philoxenus, tliey assemble once in every year 
' in the public theatres, at the feast of Hacchus, and tliere dance with 
'emulation to the sound of llutes, and celebrate according to their 
' proper age, the children those that are called the puerile, and the 



Chap. XIV. 



AND PRACTICE OF MUSIC. 



€.7 



It has already been said that this philosopher did 
by no means acquiesce in the opinion of Pythagoras 
and his followers, that the understanding is the 
ultimate judge of intervals ; and that in every system 
there must be found a mathematical coincidence 
before such system can be said to be harmonical : this 
position Aristoxenus and all of his school denied. 
The philosopher himself, in this second book of his 
Elements, expressly asserts, that ' by the hearing v^^e 
' judge of the magnitude of an interval, and by the 
' understanding v^^e consider its several powers.' And 
again he says, ' that the nature of melody is best 
' discovered by the perception of sense, and is re- 

* tained by memory ; and that there is no other way 
' of arriving at the knowledge of music ; ' and though, 
he says, ' others affirm that it is by the study of 
' instruments that we attain this knowledge ; ' this, he 
says, is talking wildly, ' for that as it is not necessary 

* for him who writes an Iambic to attend to the 
' arithmetical proportions of the feet of which it is 

* composed, so it is not necessary for him who writes 

* a Phrygian Cantus to attend to the ratios of the 

* sounds proper thereto.' The meaning of this 
passage is very obvious, and may be farther illus- 
trated by a comparison of music with painting, 
the practice whereof is so little connected wit'h the 
theory of the art, that it requires not the least skill 
in the former to make a painter. The laws of vision, 
or the theory of light and colours, never suggest 
themselves to him who is about to design a picture, 
whether it be history, landscape, or portrait : the 
common places in his mind are ideas of eff"ect and 
harmony, drawn solely from experience and observa- 
tion ; and in like manner the musical composer 
adverts to those harmonies or melodies, those com- 
binations, which from their effect alone he has found 
to be the most grateful, without recurring to the 
ratios that subsist among them. 

Aristoxenus then proceeds to a general division 
of music into seven parts, which he makes to be, 
1. The Genera. 2. Intervals. 3. Sounds. 4. Sys- 
tems. 5. Tones or Modes. 6. Mutations. And 
7. Melopoeia ; and in this method he is followed by 
Aristides, Nicomachus, and most other ancient writers. 

The remainder of the above-mentioned work, the 
Elements of Aristoxenus, is taken up with a dis- 
cussion of the several parts of music according to the 
order which he had prescribed to himself. But it 
must be owned, so great is the obscurity in which his 
doctrines are involved, that very little instruction is 
to be obtained from the most attentive perusal of 
him ; nor will the truth of this assertion be ques- 
tioned, when the reader is told that Cicero himself 
has pronounced his work unintelligible.* The use, 
however, proposed to be made of it is occasionally to 

'young men the manly games. And even in their private feasts and 
' meetings they are never known to employ any hired bands of music 
' for their entertainment, but each man is himself obliged to sing in turn. 
' For though they may without shame or censure disown all knowledge 
'of every other science, they dare not, on the other hand, dissemble or 
' deny that they are skilled in music, since the laws require that every 
' one should be instructed in it ; nor can they, on the other hand, refuse 
' to give some proofs of their skill when asked, because such refusal 
' would be esteemed dishonourable. They are taught also to perform in 
' order all the military steps and motions to the sound of instruments ; 
' and this is likewise practised every year in the theatres, at the public 
' charge, and in sight of all the citizens.' Hampton's Polybius, pag. 359. 
* De Finibus, lib. V. 19. 



refer to such parts of it as are least liable to this 
censure, and this will be done as often as it shall 
appear necessary. 

The next in order of time of the writers on music 
is Euclid, the author of the Elements of Geometry. 
He lived about the year of the world 3617, and 
wrote an Introduction to Harmonics, which he begins 
with some necessary definitions, particularly of the 
words Acumen and Gravitas, terms that frequently 
occur in the writings of the ancient harmonicians : 
the first of these he makes to be the effect of intension 
or raising, and the other of remission or falling the 
voice. He then proceeds to treat of the genera and 
the modes ; what he has said of each is herein-before 
mentioned. His Isagoge or Introduction is a very 
small tract, and little remains to be said of it, except 
that it contains the famous Sectio Canonis, a geo- 
metrical division of a chord for the purpose of 
ascertaining the ratios of the consonances, herein- 
before inserted. In this, and also in his opinion 
touching the diatessaron and diapente, namely, that 
the former is less than two tones and a hemitone, and 
the latter less than three tones and a hemitone, he is 
a Pythagorean, but in other respects he is apparently 
a follower of Aristoxenus.f The fundamental prin- 
ciple of Euclid's preliminary discourse to the Sectio 
Canonis is, that every concord arises either from 
a multiple or superparticular ratio ; the other ne- 
cessary premises are, 1. That a multiple ratio twice 
compounded, that is multiplied by two, makes the 
total a multiple ratio. 2. That if any ratio twice 
compounded makes the total multiple, that ratio is 
itself multiple. 3. A superparticular ratio admits of 
neither one nor more geometrical mean proportionals. 
4. From the second and third propositions it follows, 
that a ratio not multiple, being twice compounded 
the total is a ratio neither multiple nor superpar- 
ticular. Again, from the second it follows that if 
any ratio twice composed make not a multiple ratio, 
itself is not multiple. 5. The multiple ratio, 2 to 1, 
which is that of the diapason, and is the least of the 
kind and the most simple, is composed of the two 
greatest superparticular ratios 3 to 2, and 4 to 3, and 
cannot be composed of any other two that are super- 
particular. | 

The foregoing account of the nature and design of 
Euclid's division is contained in a series of theorems 
prefixed to the Sectio Canonis, and are reduced to 
a kind of Summary by Malcolm, who appears to 
have been extremely well versed in the mathematical 
part of music. 

+ Wallis. Append, de Vet. Harm. pag. 307. 

t Malcolm on Music, pag. 508. 

The above turnis were used by the old arithmetical writers before the 
invention of fractional arithmetic, since which they have in a great 
measure been laid aside. What is tn be understood by those kinds of 
musical proportion to which they are severally applied, will hereafter be 
shewn ; however it may here be necessary to give a short explanation of 
terms, and such a one follows : — 

Multiple proportion is when the antecedent being divided by the con- 
sequent, the quotient is more than unity ; as 25 being divided by 5, it 
gives 5 for the quotient, which is the multiple proportion. 

SupenJarticu'^r proportion is when one number or quantity contains 
another one, and an aliquot part, whose radical or least number is one; 
so that the number which is so contained in the greater, is said to be to 
it in a superparticular proportion 

To these may be added superpartient proportion, which is when one 
number or quantity contains another once, and some number of aliquot 
parts remainmg, as one ^, one ^, kic. 



68 



HISTORY OF THE SCIENCE 



Book II. 



It was not till the time of Meibomius that the 
world was possessed of a genuine and accurate edition 
of the Isagoge of Euclid ; it seems that a MS. copy 
of a Treatise on Harmonics in the Vatican had written 
in it * Incerti Introductio Harmonica ; ' and that 
some person has written therein the name of Cleonidas, 
and some other, with as little reason, Pappus Alex- 
andrinus. Of this MS. Georgius Valla, a physician 
of Placentia, published at Venice, in 1498, a Latin 
translation, with the title of Cleonidse Harmonicum 
Introductorium ; which after all appears to be a brief 
compendium of Euclid, Aristides Quintilianus, and 
Manuel Bryennius, of very little worth : and as to 
Cleonidas, the reader is as much to seek for who he 
was, and where he lived, as he would have been had 
Valla never made the above translation. 

DiDYMUs of Alexandria, an author to be reckoned 
among the scriptores perditi, inasmuch as nothing 
of his writing is now extant, must nevertheless be 
mentioned in this place : he flourished about the year 
of the world 4000, and is said to have first discovered 
and ascertained the difference between the greater 
and lesser tone. Ptolemy takes frequent occasion to 
mention him, and has given his division of the dia- 
tessaron in each of the three genera. 

CHAP. XV. 

Marcus Vitruvius Pollio, the architect, has 
usually been ranked among the writers on music ; 
not so much because he appears to have been skilled 
in the art, but for those chapters in his work De 
Architectura, in ten books, written in Latin, and 
dedicated to the emperor Augustus, in which he 
treats of it. He flourished in the time of Julius 
Csesar, to whom he says he became known by his 
skill in his profession, which it is agreed was super- 
latively great ; though, to consider him as a writer. 
it is remarked that his style is poor and vulgar. 
In some editions of his work, particularly that of 
Florence, 1496, and in another published at Venice 
the year after, by some .unaccountable mistake he is 
called Lucius, whereas his true name was Marcus, 
and so by common consent he is called. In the fifth 
book of the above-mentioned treatise, chap. iii. entitled 
De Theatro, he takes occasion to treat of sound, 
particularly that of the human voice, and of the 
methods practised by the ancients in the construction 
of their theatres, to render it more audible and 
musical : the various contrivances for this purpose 
will doubtless appear strange to modern apprehension, 
and give an idea of a theatre very different from any 
that can be conceived without it. His words are as 
follow : — ' The ancient architects having made very 
' diligent researches into the nature of the voice, 
' regulated the ascending gradations of their theatres 
' accordingly, and sought, by mathematical canons 
' and musical ratios, how to render the voice from the 
' stage more clear and grateful to the ears of the 
' audience.' Chap. iv. harmony, he says, is a musical 
literature, very obscure and difficult to such as under- 
stand not the Greek language ; and, if we are desirous 
to explain it we must necessarily use Greek words. 



some whereof have no Latin appellations ; where- 
fore, says he, ' I shall explain it as clearly as I am 
' able from the writings of Aristoxenus, whose dia- 
' gram I shall give, and shall define the sounds so as 
' that whoever diligently attends may easily conceive 
' them.' He then proceeds, ' For the changes of the 
' voices, some are acute and others grave. The genera 
' of modulations are three ; the first, named in Greek 
' Harmonica, the second Chroma, the third Diatonon ; 
' the harmonic genus is grave and solemn in its 
' effect ; the chromatic has a greater degree of 
' sweetness, arising from the delicate quickness and 

* frequency of its transitions ; the diatonic, as it is 

* the most natural, is the most easy.' He then pro- 
ceeds to describe the genera in a more particular 
manner. Chap. v. intitled De Theatri Vasis, he 
speaks of the methods of assisting the voice in the 
manner following : — ' Let vessels of brass be con- 
' structed agreeably to our mathematical researches, 
' in proportion to the dimensions of the the&tre, and 
' in such manner, that when they shall be touched 
' they may emit such sounds as shall be to each 
' other a diatessaron, diapente, and so on in order, 
' to a disdiapason ; and let these be disposed among 
' the seats, in cells made for that purpose, in a musical 

* ratio, so as not to touch any wall, having round 

* them a vacant place, with a space overhead. They 
' must be placed inversely : and, in the part that 

* fronts the stage, have wedges put under them, at 
' least an half foot high ; and let there be apertures 
' left before these cells, opposite to the lower beds ; 

* these openings must be two feet long, and half a foot 

* high, but in what places in particular they are to 

* be fixed is thus explained. If the theatre be not 
' very large, then let the places designed for the 

* vases be marked quite across, about half way up 
' its height, and let thirteen cells be made therein, 
' having twelve equal intervals between them. In 
' each of these, at the extremes or corners, let there 
' be placed one vase, whose echo shall answer to 
' Nete hyperboleon ; then on each side next the 
' corners place another, answering to the diatessaron 
' of Nete synemmenon. In the third pair of cells, 
' reckoning, as before, from the angles, place the 

* diatessaron of Nete parameson ; in the fourth pair 
' that of Nete synemmenon ; in the fifth the dia- 
' tessaron of Mese ; in the sixth the diatessaron of 
' Hypate meson ; and in the middle the diatessaron 
' of Hypate hypaton. In this ratio, the voice, which 
' is sent out from the stage as from a centre, undu- 
' lating over the whole, will strike the cavities of 

* every vase, and the concords agreeing with each of 
' them, will thereby return clearer and increased ; but 
' if the size of the theatre be larger, then let its height 
' be divided into four parts, and let there be made 
' three rows of cells across the whole, one whereof is 
' designed for Harmonia, another for Chroma, and the 
' other for Diatonos. In the first or lower row, which 
' is for Harmonia, let the vases be placed in the same 
' manner as is above directed for the lesser theatre ; but 
' in the middle row let those be placed in the corners 
' whose sounds answers to the Chromaticon hyperbo- 
leon ; in the pair next to the corners the diatessaron, 



Chap. XV. AND PRACTICE OF MUSIC. 69 

' to the Chromaticon diezeugmenon ; in the third the Flaccus, a freed-man of Claudius ; and that it was 

* diatessaron to the Chromaticon synemmenon ; in the played in some instances, as at the Andria, tibiis 
' fourth the diatessaron to the Chromaticon meson ; in paribus, dextris et sinistris ; and in others, tibiis 

* the fifth the diatessaron to the Chromaticon hypaton; paribus generally ; and at the Phormio tibiis impa- 

* and in the sixth the diatessaron to the Chromaticon ribus, that is to say, by flutes or pipes right-handed 
' Parameson ; for the Chromaticon hyperboleon dia- and left-handed, in pairs, or of unequal lengths. This 
' pente has an agreement of consonancy with the was not at a time when the ancient music was in its 

* Chromaticon meson diatessaron. But in the middle infancy : the system had been adjusted many ages 
' cell nothing need be placed, by reason that in the before ; and we may look on this refinement men- 
' chromatic genus of symphony no other quality of tioned by Vitruvius as the last that the art was 
' sounds can have any concordance. As to the upper thought capable of. It is not here meant to anticipate 
' division or row of cells, let vases be placed in the a comparison, which will come more properly here- 
' extreme corners thereof, which answers to the sounds after ; but let any one take a view of the ancient 
' Diatonon hyperboleon ; in the next pair to them the music at the period above referred to, with even the 
' diatessaron to Diatonon diezeugmenon ; in the third advantage of this improvement drawn from the 

* the diatessaron to Diatonon synemmenon ; in the doctrine of Phonics, and compare it with that of 

* fourth the Diatessaron to Diatonon meson ; in the modern times ; let him reflect on the several im- 
' fifth the diatessaron to Diatonon hypaton ; in the provements which distinguish the modern from the 
' sixth the diatessaron to Proslambenomenos : the ancient music, such as the multiplication of parts, the 

diapason to Diatonon hypaton has an agreement of introduction of instruments, some to extend the com- 

' symphony with the diapente. But if any one would pass of sounds, others to increase the variety of tones, 

' easily arrive at perfection in these things, let him and others more forcibly to impress the time and 

' carefully inspect the diagram at the latter end of the measure, as the drum and other instruments of the 

' book which Aristoxenus composed with great care pulsatile kind are manifestly calculated to do ; the 

' and skill, concerning the divisions of modulations,* use of a greater and lesser chorus ; that enchanting 

' from which, if any one will attend to his reasoning, kind of symphony, known only to the moderns, 

' he will the more readily be able to effect the con- called thorough bass ; and those very artful species 

' structions of theatres according to the nature of the of composition, fugue and canon. Let this com- 

' voice, and to the delight of the hearers.' Thus far parison be made, and the preference assigned to that 

Vitruvius. sera which has the best claim to it. 

We are too little acquainted with the nature of the Although this work of Vitruvius is professedly 

ancient drama to be able to account particularly for written on the subject of architecture, it is of a very 

the effects of this singular invention : to suppose that miscellaneous nature, and treats of matters very little 

in their theatrical representations the actors barely allied to that art, as namely, the construction of the 

pronounced their speeches, accompanying their utter- balista, the catapulta, and other warlike engines ; 

ance with correspondent gesticulations, and a proper clocks and dials, and the nature of colours. In chap, 

emphasis, as is practised in our times, would render xi. lib. X, intitled De Hydraulicis, he undertakes to 

it of no use ; for the vases so particularly described describe an instrument called the hydraulic or water- 

and adjusted by this author, are evidently calculated organ, but so imperfectly has he described it, that to 

to reverberate, not the tones used in ordinary speech, understand his meaning has given infinite trouble 

which have no musical ratio, but sounds absolutely and vexation to many a learned enquirer. | 

musical : and on the other hand, that the actor For the existence of this strange instrument we 

should, instead of the lesser inflexions of the voice have not only the testimony of Vitruvius, but the 

proper to discourse, make use of the consonances following passage in Claudian, which cannot by any 

diatessaron, diapente, and diapason, and consequently kind of construction be referred to any other : — 

sing, as well the familiar speeches proper to comedy, Vel qui magna levi detrudens murmura tactu, 

as those of the more sublime and exalted kind which Innumeras voces segetis modulatur ahenee ; 

distinguish tragedy, is utterly impossible for us to Intonat erranti digito, penitusque trabali 

conceive. Vecte laborantes in carmina concitat undas. 

If it was for the purpose of reverberating the music It is said by some that the hydraulic organ was 
used in the dramatic representations of the ancient invented by Hero, of Alexandria ; others assert that 
Romans, that this disposition of hollow vessels, di- Ctesibus, about the year of the world 3782, invented 
rected by Vitruvius, was practised, we may fairly an instrument that produced music by the compres- 
pronounce that the end was not worthy of the means ; sion of water on the air ; and that this instrument, 
for however excellent the musical theory of the which answers precisely to the hydraulic organ, was 
ancients might be, yet in the number and perfection improved by Archimedes and Vitruvius, the latter of 
of their instruments they were greatly behind the whom has given a very particular description of it. 
moderns ; and were it a question, we need look no Ctesibus the inventor of it w\as a native of Alex- 
farther for a proof of the fact than the comedies of andria, and the son of a barber. He was endowed 

Terence, where we are told that the music performed + Mersennus, speaking of this machine, says it is much more complex 

at the acting of each of them was composed bv than the common pneumatic organ, and that he has laboured to describe 

o vYcio v.uiiijjvjocti u^/ a thmg very obscure, and the meanms of wliicli he could not come at. 

. . though assisted by the commentary of i)aiiiel Barbaro. De Instrumentis 

* This diagram is inserted in Grassineau's Dictionary, article Harmonicis, pag. 138. He farther says tliat Politian in his Panepistcmon 

Genera. jiag i^ ^/^xn attempted to explain it. 



70 



HISTORY OF THE SCIENCE 



Book II. 



with an excellent genius for mechanic inventions, 
which he soon discovered in the contrivance of a 
looking-glass for his father's shop, so hung as that it 
might be easily pulled down or raised higher hy 
paeans of a hidden rope. The manner of this inven- 
tion is thus related by Vitruvius. He put a wooden 
tube under a beam where he had fastened some 
pullies, over which a rope went that made an angle 
in ascending and descending into the tube, which was 
hollow, so that a little leaden ball might run along it, 
which ball, in passing and repassing in this narrow 
cavity, by violent motion expelled the air that was 
inclosed, and forced it against that without ; these 
oppositions and concussions made an audible and 
distinct sound, something like the voice. He there- 
fore on this principle, invented engines which re- 
ceived motion from the force of water inclosed, and 
others that dejjended upon the power of the circle or 
lever ; and many ingenious inventions, particularly 
clocks that move by water. To set these engines at 
work he bored a plate of gold or a precious stone, 
and chose such kind of materials, as not being subject 
to wear by constant passing of the water, or liable to 
contract filth and obstruct its passage ; this being 
done, the water, which ran throiigh the small hole, 
raised a piece of cork, or little ship inverted, which 
workmen call Tympanum, upon which was a rule 
and some wheels equally divided, whose teeth mov- 
ing one another made these wheels turn very leisurely. 
He also made other rules and wheels, divided after 
the same manner, which by one single motion in 
turning round produced divers effects ; made several 
small images move round about pyramids, threw 
up stones like eggs, made trumpets sound, and 
performed several other things not essential to clock- 
work. Vitruvius de Architectura, lib. IX. cap. viii. 

But to return : The following is the description 
given by Vitruvius of the hydraulic organ : — 

' Autem quas habeant ratiocinationes, quam bre- 
' vissime proxime que attingere potero : et scriptura 
' consequi, non prsetermittam. De materia compacta 
' basi area in ea ex sere fabricata collocatur. Supra 
' basin eriguntur regulse dextra ac sinistra scalari 
' forma compactse : quibus includuntur serei modioli 
' fundulis ambulationibus ex torno subtiliter subactis 
'habentibus infixos in media ferreos an cones ; et 

* verticulis cum vectibus conjunctos pellibusque lana- 

* tis involutos. Item in summa planitie foramina cir- 
' citer digitorum ternum, qiiibus foraminibus proximfe 
' in verticulis collocati ajrei delphini, pendentia habent 
' catenis cymbalia ex ore in fra foramina modiorum 

* celata. Intra aream : quo loci aqua sustinetur in 
' est in id genus uti infundibulum inversum : quern 
'super traxilli alti circiter digitorum ternum sup- 

* positi librant spatium imvim. Ima inter labra phi- 

* gaeos et arae fundum. Supra autem cerviculum ejus 

* coagmenta arcula sustinet caput machinaj quae Grece 
' Canon Musicus appellatur : in cujus longitudine si 
' canalis tetrachordos est fiunt quatuor. Si exachordos 

* sex. Si octochordos octo. Singulis autem canalibus 

* singula epithonia sunt inclusa manubriis ferreis 
' collocata. Quae manubria cum torquentur ex area 
<patefaciunt nares in canales Ex canalibus autem 



' canon habet ordinata in transverso foramina res- 
' pondentia in naribus ; qute sunt in tabula summa : 
'quae tabula Greece Pinas dicitur. Inter tabulara 
' et canona regular sunt interpositaj ad eundem modum 
' foratai ex oleo subactaj : ut laciliter impellantur : 
' et rursus introrsus reducantur : quae obturant ea 
' foramina : plinthidesque appellantur, Quarum itus 
' et reditus alias obturat : alias operit terebrationes. 
' Hae regulae habent ferrea choragia fixa et juncta 
'cum pinnis quarum tactus motiones efficit. Regu- 
' larum continentur supra tabulam foramina quae 
'ex canalibus habent egressum spiritus sunt annuli 
' agglutinati : quibus lingulae omnium includuntur 
' organorum. E modiolis autem fistulae sunt conti- 
' nentes conjunctaj ligneis cervicibus : pertinentesque 
' ad nares : quae sunt in arcida : in quibus axes sunt 
' ex torno subacti : et ibi collocati. Qui cum recipit 
'arcula animam spiritum non patientur obturantes 
' foramina rursus redire. Ita cum vectes extolluntur 
' ancones educunt fundos modiolorum ad imum. Del- 
'phinique qui sunt in verticulis inclusi calcantes 
' in eos cymbala replent spatia modiolorum : atque 
' ancones extollentes fundos intra modiolos vehementi 
' pulsus cerebritate ; et obturantes foramina cymbalis 
' superiora. Aera qui est ibi clausus pressionibus 
'coactum in fistulas cogunt : per quas in ligna 
' concuri'it : et per ejus cervices in arcam. Motione 
' vero vectium vehementiores spiritus frequens com- 
' pressus epithoniorum aperturisinfluit,et replet animae 
' canales itaque cum pinae manibus tactae propellunt 
' et reducunt continenter regulas alterius obturant 
' foramina alterius aperiendo ex musicis artibus multi- 
' plicibus modulorum varietatibus sonantes excitant 
' voces.* Quantum potui niti, ut obscura res, per 
' scripturam diludice pronunciaretur ; contendi. Sed 
' hajc non est facilis ratio : neque omnibus expcdita 
'ad intelligendum praeter eos, qui in his generibus 
'habent exercitationem. Quod si qui parum intel- 
' lexerint e scriptis cum ipsam rem cognoscent : pro- 
' fecto invenient curiose et subtiliter omnia ordinata.' f 
This description, which to every modern reader 
must appear unintelligible, Kircher has not only 
undertaken to explain, but the strength of his imagi- 
nation co-operating with his love of antiquity, and 
his desire to inform the world, he has exhibited in 
the Musurgia an instrument which no one can con- 
template seriously ; and, after all, he leaves it a 
question whether it was an automaton, acted upon 
by that air, which by the pumping of water was 
forced through the several pipes, or whether the 
hand of a skilful musician, sitting at the front of 
it, with the quantity of some tons of water in 
a reservoir under him, was not necessary to produce 
that music which the bigoted admirers of antiquity 
ascribe to this instrument, and affect to be so fond of. 
Isaac Vossius, in his treatise De Poematum Cantu et 
Viribus Rythmi, pag. 100, has given a representa- 
tion of the hydraulic organ, no way resembling that 
of Kircher, but which he yet says is almost exactly 
conformable to the words of Vitruvius ; after which 
follows a description thereof in words not less 

" Vitruvius de Architectura, lib. X. cap. xi. 
+ Ibid. cap. xii. 



Chap. XV. 



AND PRACTICE OF MUSIC. 



71 



o1i?cure than those of Vitruvius and Kircher : neither 
one nor the other of the diagrams will bear the test 
of an impartial examination, or is worthy to be in- 
serted in any work intended to convey information to 
a sober enquirer after truth ; but the confidence with 
which Vossius speaks of his discovery will make 
it necessary to give his delineation of the hydraulic 
organ, together with a description of it in his own 
words. 

Kircher indeed, after all the pains he had taken, 
has the modesty to confess the inferiority of the 
ancient hydraulic to the modern organ ; for he says 
that if the former be compared to the latter it must 
seem a very insignificant work, for, adds he, ' I can- 
' not perceive what harmony a disposition of four, 
' five, six, or eight pipes could produce, and I very 
'much wonder how Nero should be so exceedingly 
' affected by so small and poor an hydraulic, for 
' Vitruvius testifies that when his life and empire were 
' both in danger, and every thing at the last hazard 
' by a sedition of his generals and soldiers, he did not 
' relinquish his great care and affection, or desire 
' thereof. We may from hence easily form a judg- 

* ment what great pleasure he must have taken in our 
' modern organs, not composed of four, five, six, 
' or eight pipes, but such as our greater organs of 
' Germany, consisting of eleven Imndred and fifty-two 
'double pipes, animated by the help of twenty-four 
' different registers ; or had he seen our automata, or 
' engines of this kind which move of their own 
'accord without the help of any hand. Certainly 

* these most enlightened ages have invented several 
' things to which the inventions of the ancients can 
'in no manner be compared.'* 

Of a very different opinion is the before-cited 
Vossius, who declares himself not ashamed to assert, 
not only that the tibise alone of the ancients are by 
very far to be preferred to all the instruments of his 
age, but that, if we except the pipes of the organs, 
commonly used in churches, it will be found that 
scarce any others are worthy to be called by the 
name of tihisQ. And he adds, ' even those very 
' organs which now please so much, can by no means 
' be compared to the ancient hydraulics. And the 
' modern Organarii, to speak after the manner of the 
'ancients, are not in reality Organarii, but Ascaulse 
' or Utricularii, that is to say, Bag-pipers, for by 
' that name were those called who furnish wind to 
' the tibise by the means of bags or wallets, and 
' bellows, as is done in churches.' He farther says 
that 'those are ridiculous who suppose the above 
' appellations to belong to those mendicants who 
' go about the streets with a Cornamusa, and with 
'their arms force out continued and unpleasing 
' so\;nds.' No, says this sagacious writer, ' the 
' Ascaulaa or Utricularii did not in the least differ 
'from our modern organists; and the ancient Or- 
' ganarii were those only who played on the hydraulic 
'organ, and they were so called from Organum, a 
' brazen vessel, constructed like a round altar, out of 
' which the air by the help of the incumbent water is 
' pressed with great force, which yet flows equally 

» Musurg. Univ. torn. II. pap. 333. 



' into the tibise. 'f After remarking on the bad suc- 
cess of many who had attempted to find out the 
meaning of Vitruvius in his description of this 
instrument, and to restore it to practice, he says very 
confidently that he himself has done it, and accord- 
ingly exhibits it in the following form : — 




And describes it in these words : ' fiat basis lignea 
A B C D E F, et in ea constituatur ara rotunda 
G H I K ex sere fabricata et torno fideliter expolita. 
Fiat quoque clibanus seu hemisphserium jereum 
L M N O, quam exactissime huic adaptatum. Sit 
vero in medio perforatus hie clibanus, et insertum 
habeat tubum et ipsum sereum et utrinque apertum 
M P. Habeat quoque clibanus alterum foramen, cui 
insertus sit siphon N I Q, cujus nares pertingunt ad 
modiolum jereum Q R S T. Siphon hie habeat 
assarium seu platysmation ad N. Modiolo vero 
Q R S T aptetur embolus V cui affixa sit regula 
firmiter admodum compacta V X, ita ut a vecte 
X Y Z embolus V commode moveri possit. Mo- 
diolus autem Q R S T habeat in superiori superficie 
aliud foramen 3, 4, cum platysmatio per quod aer 
ingredi possit. Iste vero ingredietur cum vectis 
X Y Z in Z attollitur. Quando vero idem de- 
primitur, platysmation hoc clauditur, et ingressus 
aer per siphonem Q I N, aperto platysmatio ad N, 
exprimitur in clibanum L M N O, unde per tubum 
M P influit in arcam A a C c E e, cujus aflilatu 
tibise animantur. Clibano vero L M N O, quamvis 
magni sit ponderes, veluti aeneo, quo tamen fortius 
subjectum premat aerem et fidelius ne efflnat cus- 
todiat, superinfunditur aqua, puta ad f f, vel altius 
si fortiores velimus efficere sonos. Fiat itaque ex 
continua vectis agitatione, ut attollatur tandem 
clibanus L M N 0, immoto interim perstante tube 
M P, et siphone N I Q, et notandum simulac 
vehementia ingressi spiritus attollitur clibanus, tum 
quoque sequalem fieri compressionem aeris qui in 
area continetur. Licet enim efifluente per tibias 
aere clibanus descendat, idemque rursus agitatione 
vectis attollatur, quamdiu tamen clibanus suspensus 
et a fundo separatus manet, tandiu propter sequali- 
tatem prementis ponderis, sequalis etiam manet, in- 
clusi aeris constipatio, ipsaque clibani et superinfussB 

t Voss. de Poemat. pag. 98. 



72 



HISTORY OF THE SCIENCE 



Book IL 



' aquas inconstans et mobilis altitude efficit ajqualitatem 
' flatus, quo tibije aspirantur.' * 

The same author affects to be very merry with 
those who have asserted that this organ was mounted 
only with six or eight tibise, and cites the foregoing 
verses of Claudian, and the following exclamation of 
TertuUian, to prove the contrary : — ' Specta porten- 
' tosam Archimedis (Ctesibii rectius dixisset) muni- 
' ficentiam : organum hydraulicum dico, tot membra, 

* tot partes, tot compagines, tot itinera vocum, tot 
' compendia sonorum, tot commercia modorum, tot 
' acies tibiarum, et una moles erunt omnia. Spiritus 
' ille qui de tormento aquae anhelat, per partes ad- 
' ministratur, substantia solidus, opera divisus.' f He 
says that the use of the hydraulic organ ceased be- 
fore the time of Cassiodorus; and that the same ap- 
pears from a passage in a discourse of that author on 
the hundred-and-fiftieth Psalm, wherein, without 
making the least mention of the hydraulic, he bestows 
the following very high commendations on the pneu- 
matic organ, then in common use : — ' An organ is as 
' it were a tower composed of several different fistulas 

* or pipes, in which the most copious sound is furnished 
' by the blowing of bellows : and that it may be com- 
' posed of a graceful modulation, it is constructed with 
' certain wooden tongues in the inner part, which 

* being skilfully pressed down by the fingers of the 

* master, produce a great sounding and most sweet 

* cantilena.' | 

He notwithstanding asserts that the hydraulic 
organ continued in use lower down than the time of 
Cassiodorus ; for that in the French annals of a 
certain anonymous writer, he is informed that in the 
year 826, a certain Venetian, called Georgius, or rather 
Gregorius, constructed a hydraulic organ for Lewis 
the Pious, at Aix la Chapelle, and that after the 
manner of the ancients.§ He elsewhere says that tlie 
hydraulic organ of Daniel Barbaro, described in his 
Commentary on Vitruvius, is with great reason ex- 
ploded by all ; II and that those who in his time had 
in their writings concerning music, inserted the con- 
struction of the Vitruvian organ, while they de- 
preciate the inventions of the ancients, may serve as 
an example to shew how customary a thing it is for 
men to despise what they themselves do not under- 
stand. This passage is manifestly intended as a 
censure on Kircher's description of the hydraulic 
organ, and proves nothing but the extreme bigotry 

* l)e Poemat. pa^. 101. 

In the cabinet of Christina, queen of Sweden, was formerly a beautiful 
and large medallion of Valentinian ; having on the reverse one of these 
hydraulic organs, with two men, one on the right, the other on the left 
side thereof, seeming to pump the water which plays it, and to listen to 
the sound of it. It had only eight pipes, and those were placed on 
a round pedestal ; the inscription Placea Spetri. 

t Ibid. pag. 105. In English thus : Behold the wonderful munificence 
of Archimedes ! (he should have said of Ctesibius) I mean the hydraulic 
organ ; so many numbers, so many parts, so many joinings, so many 
roads or passages for the voices, such a compendium of sounds, such an 
intercourse of modes, such troops of tibiae, and all composing one great 
whole ! The spirit or air wliich is breathed out from this engine of 
water, is administered through the parts, solid in substance, but divided 
in operation. 

X Organum itaque est quasi turris diversis fislulis fabricata, quibus 
flatu follium vox eopiosissima destinatur, et tit earn modulatio decora 
componat. Unguis quibusdam ligneis ab interiore parte con.stmitur, quas 
disoiplinabiliter magistrorum digiti reprimentes grandisouem efficiunt 
et iuavissimum caatilenani. Do Poemat. pag. 106. 
§ De Poemat. 106. 
ij Ibid pag. 9y. 



of Vossius.^ As to the hydraulic organs of modern 
Italy of which Grassineau says there are several in 
the grottos of vineyards, particularly one belonging 
to the family d'Este, near the Tiber, described by 
Baptista Porta, he says they are very different, and 
no way resemble the ancient hydraulic organ. These 
perhaps will be found to be nothing more than the 
common organ played on by a barrel, which by 
a very easy contrivance is set in motion by a small 
stream of water : and that these for more than a 
century past have been in use in various parts of 
Italy there is additional evidence. In a book 
supposed to be written by one Dr. Thomas Powell, 
a canon of St. David's, entitled Human Industry, or 
a History of the Manual Arts, it is said that Pope 
Sylvester II. made an organ which was played on by 
warm water ; and that such hydraulics, frequent in 
Italy, are sounded with cold water. Oldy's British 
Librarian, No. I. pag. 51. And in an old English 
comedy of Webster, printed in 1(323, intitled the 
Devil's Law-Case, Romelia, a w^ealthy merchant of 
Naples, speaking of the greatness of his income says, 

My factors' wives 

Weare sliaperoones of velvet; and my scriveners, 
Meerely through my employment, grow so rich 
They build their palaces and belvidears 
With musical water-workes. 

Comedy, which in general exhibits a very just repre- 
sentation of contemporary manners and characters, is, 
in cases of this sort, authority : and the poet, in the 
passage above-cited, would hardly have pointed out 
this instance of Italian profusion, had he not had 
some example in his eye to warrant it. 

CHAP. XV L 

But to return to the ancient hydraulic organ, 
a hundred questions might be asked touching the 
use and application of its several parts, as also what 
system it was adapted to ; and particularly whether 
those who have undertaken to delineate it with such 
exactness, have not formed an idea of it from the 
organ of our own times, and done a violence to 
historical truth by incorporating two instruments, 
which cannot possibly exist in a state of union. 
And after all that can be said in favour of it, the 
censure of Kircher above-cited, must undoubtedly 
appear to be very just, and may serve to show what 

IT The enthusiastic attachmemt to antiquity of this author is strongly 
evinced by the sentiments he entertains of the energy of the ancient 
Tibia, which he scruples not to prefer to every instrument of modem 
invention. His words are these : — ' As to what belongs to the cantus of 
'the Tibia which is blown upon by the mouth, I think it may be truly 
' said that the tibicinists know no more concerning that instrument than 
' the ancient shepherds, and perliaps not so much. This most excellent 
' art is banished among the mendicants ; and the Tibia, which was by 
'far preferred to all stringed instruments, and to all other instruments 
' of music, is now silenced to such a degree, that, if you except the 
'Chinese alone, who excel in this part, you will find none in this age 
' that can even please a moderate ear ; and the very name of the Tibia 
' is justly despised by the European nations. That the Tibia was 
' formerly held in greater esteem, and accounted sweeter than the lyre, 
' is not only evinced by Aristotle, in his problems, but also by the very 
' punishment of Marsyas. How great the care and diligence of the 
'ancients was in improving this instrument, sufficiently appears from 
' what both Theophrastus and Pliny have written conceniing the reeds of 
'the lake Orchomenius. It was not sufficient that they were cut at 
'certain periods of years, when the lake became dry; unless they 
' were also macerated by the sun, rain, and frost, and afterwards softened 
'by long use; and, remaining without any defect, satisfied the wish of 
' the artists. He who reads and considers those things, will the less 
' wonder that sometimes Tibiae have been sold for seven talents, as 
' Lucian testifies.' Vossius De Poemat. 107. 



Chap. XVI. AND PRACTICE OF MUSIC. 73 

little reason there is to lament the loss of many in- The sounds and their names, continues this author, 
ventions of the ancients, particularly those in which are probably taken from the seven planets in the 
the knowledge of mechanics is any way concerned, heavens which surround this earth ; for it is said that 
The hydraulic organ is one of those ancient inventions all bodies which are carried round with any great 
mentioned by Pancirollus as now lost,* a misfortune degree of velocity, must necessarily, and by reason of 
which at this day we lament perhaps with as little their magnitude, and the celerity of their motions, 
reason as we should have for saying that the loss of cause a sound, which sound will vary in proportion 
the ancient Clepsydras f is not amply compensated to the degrees of magnitude in each, the celerity of 
by the invention of clocks and watches. With their motions, or the repression of the orb wherein 
respect to this instrument, it cannot so properly be they act. These differences, he says, are manifest in 
said to be lost, as to have given way to one of a more the planets, which perpetually turn round, and pro- 
artificial construction, and nobler in its effects, as un- duce their proper sounds : for example, the motion of 
questionably the modern organ is. It is remarkable Saturn, the planet most distant from us, produces 
that those who would infer the debility of the later a sound the most grave, in which it resembles the 
ages, from the few remaining monuments of ancient consonance diapason ; as does Hypate, which signi- 
ingenuity, generally confine themselves to poesy, fies the same as principal. To the motion of the 
sculpture, and other arts, which owe their perfection moon, the lowest of the planets, and nearest the earth, 
rather to adventitious circumstances, than to the we apply the most acute term, called Nete, for 
vigorous exertion of the powers of invention : but, Neaton is the same as low. 

with respect to instruments, machines, and engines He then proceeds to declare the supposed analogy 

of various kinds, it is not in the nature of things between the rest of the planets and the intermediate 

possible but that mankind must continue to improve chords, as mentioned in the foregoing account of 

as long as the world shall last. Pythagoras. But here it may be proper to take 

NicoMACHUs Gerasenus, SO Called from his having notice that the ancient writers were not unanimous 

been born in Gerasa, a city of Arabia, lived about in opinion that the graver sounds were produced 

a. c. 60. He was a philosopher, and wi'ote an In- by the bodies of greatest magnitude : Cicero, in 

troduction to Harmony, at the request, as it should particular, is by Glareanus| said to have maintained 

seem by the beginning of it, of some learned female that the lesser bodies produce the graver sounds, and 

contemporary. He w\as a follower of Pythagoras ; the greater the more acute. And from this dictum 

and it is by this work alone that we know how, and of Cicero, Glareanus has been at the pains of forming 

by what means, his master discovered the consonances, a diagram, intended to represent this fanciful coinci- 

He begins his work with an address to his female dence of revolutions and harmonies, which is given 

friend, whom he styles the most virtuous of women ; in a subsequent page of this work, 

and reflects with some concern on the difference in In the Somnium Scipionis, which is what Glareanus 

sentiment of the several writers on the elements of means when he refers to Cicero de Republica, lib. VI. 

harmony. He excuses his inability to reconcile them is a great deal concerning the music of the spheres 

by reason of the long journeys he is obliged to take, in general ; and Macrobius, in his commentary 

and his want of leisure, which he prays the gods to on that fragment, has made the most of it. Never- 

vouchsafe him, and promises to complete a work theless the general sentiment of mankind seems till 

which he has in contemplation, of which what he now very lately§ to have been that the whole doctrine 

gives seems to be but a part. Professing to follow is to be regarded as a poetical fiction ; and as to 

the Pythagoreans, he considers the human voice as the fact, that it has no foiuidation in reason or 

emitting sounds, which are either commensurable by philosophy. 

intervals, as when we are said to sing ; or incom- But to return to our author Nicomachus, and his 

mensurable, as when we converse by speech. In opinion of the harmony of the planets : it is true, 

this latter use of the voice, he says, we are not says he, that it is inaudible to our ears, but to our 

obliged by any rule ; but in the former we are bound reason it is clear. 

to an observance of those intervals and magnitudes Nicomachus proceeds to define the terms made 

in which harmony does consist. use of by him, distinguishing, as others of the 

. „ . . „ . ,, „ „ v,-i- ^ A-. ancients do, between sound and noise. Speaking 

* Guido Pancirollus De Rerum memorabilium sive deperditarum, "">^ >- > n -i • ^ • 

lib. I. cap. ii. of instruments, he says they are oi two kmds, viz., 

t Clepsydra, an hour-glass made with water. The use of Clepsydrae i hlnwn as avp thp flnfp trnmnpt nrcraTi 

■was very ancient, and among the Romans there were several sorts of ^UCU aS aiC DlOWn, aS aiC ine nUtC, irumpet. Organ, 

them ; in general they resembled a sand hour-glass, which is composed and the like ; Or SUCh aS are Stl'Ung, to wit, the lutC, 

of two vessels, so joined at top and bottom, as that which is contained -, JT, fillj.il'1 Til, 

in the upper may run into the under of them. The ClepsydrcB contained lyre, aUQ narp ; 01 tlie latter KinCl are alSO tne 

w-ater, which passing through a small hole, imperceptibly raised a piece mouochord, by many Called the Paudora,!] and by 

of cork with an mdex fixed thereto that pomted to the hours marked on ^ j j mi .; 

the under glass. They were all subject to two inconveniences : the first j Dodecachordon, lib. II. cap. xiu. 

was that which Plutarch takes notice of, to wit, that the water passed 

through with more or less difficulty, according as the air was more or § See a subsequent note, in the present book, containing the senti- 

less thick, cold, or hot, for that hindered the hours from being equal ; ments of Dr. Gregory and Mr. Maclaurin on this subject. 

the other was, that the water ran faster at first, when the vessel from || An appellative from which the English word Bandore seems clearly 

whence the water came was full, than at last. to be derived. Meibomius gives the following note on this passage: — 

These ClepsydrfE were chiefly used in a city called Achanta, beyond the '4>ai'58p8C;. [Phandourous.] Hesychius speaks of it thus: "Pandura 

Nile. In this city there was a huge vessel of this kind, into which " or Panduris is a musical instrument ; Pandurus he who plays on 

three hundred and sixty-five priests daily brought water from the Nile, 'that instrument." Monochords were also by some called Phanduras. 

which running out of the vessel again, declared the hours. The use of ' Nicomachus here says the same, and seems as if he approved of the 

the Clepsydra was to tell the hour in the night, or in cloudy weather ' practice. These instruments are various ; Pollux, lib. IV. cap. ix. 

when it could not he found by the sun-dial. ' says , " The monochord was invented by the Arabians, and the trichord 



74 



HISTORY OF THE SCIENCE 



Book II. 



the Pythagoreans the Canon, and also the Trigon 
or triangular dulcimer. He also mentions crooked 
and other flutes made of the box-tree, of which 
he proposes to speak again. Of the stringed species 
he says those with the greater tensions express the 
more acute sounds ; on the contrary, those with the 
lesser give the more languid and grave ; and in 
instruments that are blown, the more hollow and 
long, the more languid and grave are their sounds. 
He then proceeds to relate how Pythagoras dis- 
covered the consonances, and to give that account 
of his system which Stanley has taken into his life 
of that philosopher, and is inserted in the foregoing 
part of this work, together with some remarks, the 
result of late experiments, which in some degree, 
though not essentially, weaken the credit of the 
relation. 

But vnthout enquiring farther into the weight 
of the hammers, and other circumstances attending 
the discovery of the consonances, we may very 
safely credit Nicomachus, so far as to believe that Py- 
thagoras, by the means of chords of different lengths, 
did discover them ; that the philosopher to the sound 
produced by the first number six, gave the name 
Hypate ; to eight he gave Mese, which is sesqui- 
tertian thereto ; to nine Paramese, which is a tone 
more acute, and therefore sesquioctave of the last ; 
and to the last number, twelve, he gave the name 
Nete ; and afterwards filled up the intermediate 
spaces with sounds in the succession proper to the 
diatonic genus, and thereby completed the system 
of eight chords. The diatonic genus, as this author 
describes it, is a natural progression to the system 
of a diatessaron by a semitone, tone, and tone ; and 
to a diapente by three tones and a semitone. This 
is the manner in which it is said the ancient system 
was adjusted and extended to that of a complete 
octave, an improvement so much the more to be 
valued, as we are told that in the ancient or pri- 
mitive lyre, all the sounds from the lowest were 
fourths to each other ;* whereas in the Pythagorean 
lyre, composed of a tetrachord and pentachord con- 
joined ; or, which is the same, of two tetrachords 
disjoined by an intervening tone, we have a continued 
progression of sounds. 

Nicomachus proceeds to relate that the magnitude 
of the scale in the diatonic genus is two diapasons, 
for that the voice cannot easily extend itself either 
upwards or downwards beyond this limit ; and for 
this reason, to the ancient lyre formed of seven 
strings, by the conjunction of two tetrachords, 
each extending from Hypate to Mese, and thence 
to Nete, were adjoined two tetrachords at the 
outward extremity of the former ; that which began 
at Nete was called Hyperboleon, signifying ex- 
cellent. This tetrachord, he says, consists of three 

" by the Assyrians, who gave it the name of Pandura." He justly says 
' that Pandura was an Assyrian word. But the most learned of the 
' Hebrews do not seem sufficiently to understand the sifjnification of it ; 
' they explain it by a twig or rod, whip, thong of leather, as appears 
' from Buxtorf in the Talraudical Lexicon, from Talmud Hierosol. 
' I imagine the true origin of this appellation to be this, the instrument 
' was mounted or stretched with thongs of bull's hides, in the same 
' manner as the pentachord of the Scythians, concerning which the 
'same Pollux speaks thus: — "The pentachord is an invention of the 
"Scythians, it was stretched or mounted with thongs made of the raw 
" hides of oxen, but their plectra were the jaw bones of she-goats." 
* Nicomach. Harmonic. Manual, pag. 5, ex vers. Mcibom. 



adjoined sounds, whose names are worthy to be 
remembered; as first, Trite hyperboleon, then Para- 
nete hyperboleon, and lastly, Nete hyperboleon. The 
other tetrachord was joined to the chord Hypate, 
and was thence called Hypaton ; and each of the 
three adjoined sounds had the addition of Hypaton 
to distinguish it from the chord of the same denomi- 
nation in the lower of the two primitive tetrachords ; 
thus Hypate hypaton, Parhypate hypaton, Diatonos 
hypaton, or Lychanos hypaton, for it matters not 
which it is called ; and this system from Hypate 
hypaton to Mese is seven chords, making two con- 
joint tetrachords ; and that from Hypate hypaton 
to Nete is thirteen ; so that Mese having the middle 
place, and conjoining two systems of a septenary 
each, reckoning either upwards from Hypate hypaton, 
or downwards from Nete hyperboleon, each system 
contained seven chords. 

From this it is evident that the additional tetra- 
chords were originally adapted to the system of 
Terpander, which did not separate Mese from Trite 
by a whole tone, as that of Pythagoras did. What 
advantages could be derived from this addition it is 
not easy to say ; nor is it conceivable that that 
system could be reducible to practice which gave 
to a nominal diapason four tones and three hemitones, 
instead of five tones and two hemitones. 

But the addition of the new tetrachords to the 
two disjunct tetrachords of Pythagoras was very 
natural, and made way for what this author next 
proceeds to mention, the tetrachord synemmenon, 
which took place in the middle of that interval of 
a tone, by which Pythagoras had divided the two 
primitive tetrachords. The design of introducing 
this tetrachord synemmenon, which placed Trite but 
a hemitone distant from Mese, was manifestly to give 
to Parhypate meson what it wanted before, a perfect 
diatessaron for its nominal fourth ; and this opinion 
of its use is maintained by all who have written on 
the subject of music. 

The author then proceeds to a verbal enumeration 
of the several chords, which by the disjunction made 
by Pythagoras, and the addition of Proslambano- 
menos, it appears were encreased to fifteen, with 
their respective tonical distances : it has already 
been mentioned, that, contrary to the method now 
in use, the ancients gave the most grave sounds the 
uppermost place in their scale ; he therefore begins 
with Proslambanomenos and reckons downwards to 
Nete hyperboleon. 

He gives the same kind of enumeration of the 
several sounds that compose the tetrachord synem- 
menon, having first Trite synemmenon at the distance 
of a hemitone from Mese, then after a tone Paranete 
synemmenon, and after another tone Nete synem- 
menon of the same tenor and sound as Paranete 
diezeugmenon. 

Mese 

Hemitone 
Trite 

Tone 
Paranete 

Tone 
Nete 



Cpap. X\T. 



AND PRACTICE OF MUSIC. 



75 



So that there exist five tetrachords, Hypaton, 
Meson, Synemmenon, Diezeugmenon, and Hyper- 
boleon ; though it is to be remembered that the 
third of these is but auxiliary, and whenever it is 
used it is only in the room of the fourth, for reasons 
before given ; and in these tetrachords there are 
two disjunctions and three conjunctions ; the dis- 
junctions are between Nete synemmenon and Nete 
diezeugmenon, and between Proslambanomenos and 
Hypate hypaton : the conjunctions are between Hy- 
paton and Meson, and, which is the same, Meson 
and Synemmenon, and between Diezeugmenon and 
Hyperboleon. 

We must understand that the foregoing is a repre- 
sentation of the tetrachords as they are divided in 
the diatonic genus, the characteristic whereof is a 
progression by a hemitone, tone, and tone ; for as 
to the other genera, the chromatic and enharmonic, 
this author professes not to deliver his sentiments, 
but promises to give them at large, together with 
a regular progression in all the three in his Commen- 
taries, a work he often speaks of, as having undertaken 
it for the information of his learned correspondent : 
he also engages to give the testimonies of the ancients, 
the most learned and eloquent of men on this subject, 
and an exposition of Pythagoras's section of the canon, 
not as Eratosthenes or Thrasyllus badly understand 
it, but according to Locrus Timseus, the follower of 
Plato, although nothing of his on the subject is re- 
maining at this day ; however he has given an idea 
of the genera in the following words : — ' The first 
' and most simple of consonances is the diatessaron. 
' The diatonic tetrachord proceeds by a hemitone, tone, 
' and tone, or four sounds and three intervals ; and 
' it is called diatonic, as proceeding chiefly by tones. 
' The chromatic progression in the tetrachord is by 
' a hemitone, hemitone, and an incomposite trihemi- 
' tone, and therefore, though not constituted as the 
' other, it contains an equal number of intervals. 
' The enharmonic progression is by a diesis, which 
' is half a hemitone, another diesis, also half a hemi- 
' tone, and the remainder is an incomposite ditone ; 
' and these latter are also eqi;al to a hemitone and 
' two tones. Amongst these it is impossible to adapt 
' sound to sound, for it is plain that the difference of 
' the genera does not consist in an interchange of the 

* four sounds, but only of the two intermelliate ones ; 

* in the chromatic the third sound is changed from 
' the diatonic, but the second is the same, and it 
' has the same sound as the enharmonic ; and in 
' the enharmonic the two intermediate sounds are 
' changed, with respect to the diatonic, so as the 
' enharmonic is opposite to the diatonic, and the 
' chromatic is in the middle between them both ; for 

* it differs only a hemitone from the diatonic, whence 
' it is called chromatic, from Chroma, a word sig- 
' nifying a disposition flexible and easy to be changed : 
' in opposition to this we call the extremes of each 
' tetrachord Stantes, or standing sounds, to denote 
' their immovable position. This then is the system 
' of the diapason, whether from Mese to Proslam- 
' banomenos, or from Mese to Nete hyperboleon ; 

* and as the diatessaron is two tones and a hemitone. 



' and the diapente three tones and a hemitone, the 
' diapason should seem to be six whole tones ; but in 
' truth it is only five tones and two hemitones, which 
' hemitones are not strictly complete ; and therefore 
' the diapason is somewhat less than six complete 
' whole tones : * and with this agree the words of 
' Philolaus when he says that harmony hath five 
' superoctaves and two dieses ; now a diesis is the 
' half of a hemitone, and there is another hemitone 
' required to make up the number six.' 

His second book Nicomachus begins with an ac- 
count of the invention of the lyre of Mercury, 
already related, and which has been adopted by 
almost every succeeding writer on music, adding 
that some among the ancients ascribed it to Cadmus 
the son of Agenor. He proceeds to state the pro- 
portions, which he does in a way not easily recon- 
cileable with the practice of the moderns : he then 
reconsiders the supposed relation between the sounds 
in the harmo^ilcal septenary and the motions of the 
planets ; and endeavours to account for these different 
denominations, which it seems were given them in 
his days. He says that the chord Hypate is applied 
to Saturn, as the chief of the planets, and Nete to 
Luna, as the least. Mese is Sol, Parhypate is attri- 
buted to Jove, Paramese not to Mercury but to 
Venus, by a perverse order, says his editor, unless 
there is an error in the manuscript. Paramese to 
Mars, Trite to Venus, Luna or the Moon is said to 
be acute, as it answers to Nete ; and Saturn grave 
as is Hypate. Those that reckon contrarywise, 
applying Hypate to the Moon, and Nete to Saturn, 
do it, because say they the graver sounds are pro- 
duced from the lower and more profound parts of 
the body, and therefore are properly adapted to the 
lower orbs ; whereas the acute sounds are formed in 
the higher parts, and do therefore more naturally 
resemble the more remote of the heavenly bodies : — 
Saturn - - . - Nete 
Jupiter . - - - Paranete 
Mars ... - Paramese 

Sol ... - Mese 

Venus .... Lichanos 
Mercury .... Parhypate 
Luna .... Hypate 

Nicomachus then proceeds to enumerate the several 
persons who added to the system of the diapason, 
completed as it was by Pythagoras ; but as he ex- 
pressly says the additional chords were not adjusted 
in any precise ratio, and as their names have already 
been given, it seems needless to be more particular 
about them. Speaking of the great system, viz., that 
of the disdiapason, he cites Ptolemy, to show that it 
must necessarily consist of fifteen chords ; but as it 
is certain that Nichomachus lived a. c. GO, and that 
Claudius Ptolemaius flourished about one hundred 
and forty years after the commencement of the 
Christian ^ra, there arises an anachronism, which is 
not to be accounted for but upon a supposition that 
the manuscript is corrupted. From divers passages 
in this author, and others to be met with in the Greek 

* This is (lemnnstrated by Ptolemy, lib I. cap. xi. of his Harmonics, 
and also by Boetius, lib V. cap. xiii. 



76 



HISTORY OF THE SCIENCE. 



Book II, 



writers, it is evident that the ancients were not wholly- 
unacquainted with the doctrine of the vibrations of 
chords : they had observed that the acute sounds 
were produced by quick, and the grave by slow 
motions, and that the consonances arose from a coin- 
cidence of both ; but it no where appears that they 
made any use of the coincidences in adjusting the 
ratios of the consonances ; on the contrary, they 
seem to have referred the whole to the ratio of lengths 
and tensions by weights, and a division of the mono- 
chord ; and in this respect it is unquestionably true 
that the speculative part of music has received con- 
siderable advantages from those improvements in 
natural philosophy which in the latter ages have been 
made. The inquisitive and acurate Galileo was the 
first that investigated the laws of pendulums ; he 
found out that all the vibrations of the same string, 
the longer and the shorter, were made in equal time, 
that between the length of a chord and the number 
of its vibrations, there subsists a duplicate proportion 
of length to velocity ; and that the length quadrupled 
will subduple the velocity of the vibrations, and the 
length subquadrupled will duple the vibrations ; for 
the proportion holds reciprocally : adding to the 
length will diminish, and shortening it will encrease 
the frequency of vibrations. These, and numbers of 
other discoveries, the result of repeated experiments, 
have been found of great use, as they were soon after 
the making of them applied to the measure of time, 
and other most valuable purposes. 

Having given an extract which contains in substance 
almost the whole of what Nicomachus has given us on 
the subject of harmony, it remains to observe that 
his work is manifestly incomplete : it appears from 
his own words to have been written while he was 
upon a journey, and for the particular information of 
the lady to whom he has, in terms of the greatest 
respect, inscribed it ; and is no other than what he 
himself with great modesty entitles it, a Manual ; it 
is however to be esteemed a very valuable fragment, 
as it is by much the most clear and intelligible of the 
works of the Greek writers now remaining. Boetius, 
in his treatise De Musica, cites divers passages from 
Nicomachus that are not to be found in this discourse 
of his, from whence it is highly probable that he had 
seen those commentaries which are ])romised in it, 
or some other tract, of which at this distance of time 
no account can be given. 

CHAP. XVII. 

Plutarch is also to be numbered among the 
ancient writers on music, for in his Symposiacs is 
a discourse on that subject, which is much celebrated 
by Meibomius, Doni, and others. A passage in the 
French translation, by Amyot, of the works of that 
philosopher, has given rise to a controversy con- 
cerning the genuineness of this tract, the merits of 
which will hereafter be considered. This discourse 
contains in it more of the history of the ancient 
music and musicians than is to be met with anywhere 
else, for which reason it is here meant to give a 
copious extract from it. It ia written in dialogue ; 



the speakers are Onesicrates, Soterichus, and Lysias. 
The latter of these, in answer to a request of One- 
sicrates, gives a relation of the origin and progress 
of the science, in substance as follows : — 

' According to the assertion of Heraclides, in a 
Compendium of Music, said to have been written by 
him, Amphion, the son of Jupiter and Antiope, was 
the inventor of the harp and of Lyric poesy ; and 
in the same age Linus the Eubean composed elegies : 
Anthes of Anthedon in Boeotia was the first author 
of hymns, and Pierius of Pieria of verses in honour 
of the Muses ; Philamon the Delphian also wrote 
a poem, celebrating the nativity of Latona, Diana, 
and Apollo ; and was the original institutor of 
dancing about the temple of Delphos. Thamyris, 
of Thracian extraction, had the finest voice, and 
was the best singer of his time, for which reason he 
is by the poets feigned to have contended with the 
Muses ; he wrought into a poem the war of the 
Titans against the gods. Demodocus the Corcyrean 
wrote in verse the history of the destruction of 
Troy, and the nuptials of Vulcan and Venus. To 
him succeeded Phemius of Ithaca, who composed 
a poem on the return of those who came back with 
Agamemnon from the siege of Troy ; and besides 
that these poems were severally written by the 
persons above-named, they were also set to musical 
notes by their respective authors. The same 
Heraclides also writes that Terpander was the 
institutor of those laws by which the metre of verses, 
and consequently the musical measure, were re- 
gulated ; and according to these rules he set musical 
notes both to his own and Homer's words, and sun? 
them at the public games to the music of the lyre. 
Clonas, an epic and elegiac poet, taking Terpander 
for his example, constituted rules which should 
adjust and govern the tuning and melody of flutes 
or pipes, and such-like wind-instruments ; and in 
this he was followed by Polymnestes the Colo- 
phonian. 

* Timotheus is said to have made lyric preludes to 
his epic poems, and to have first introduced the 
dithyrambic, a measure adapted to songs in the 
praise of Bacchus, which songs required a violent 
motion of the body, and a certain irregularity in the 
measure. 

' Farther of Terpander, one of the most ancient of 
musicians, he is recorded to have been four times 
a victor at the Pythian games. 

* Alexander the historian says, that Olympus 
brought into Greece the practice of touching the 
strings of the lyre with a quill ; for before his time 
they were touched by the fingers : and that Hyagnis 
was the first that sang to the pipe, and Marsyas his 
son the next, and that both these were prior to 
Olympus. He farther says that Terpander imitated 
Homer in his verses, and Orpheus in his music ; 
but that Orpheus imitated no one. That Clonas, 
who was some time later than Terpander, was, as 
the Arcadians affirm, a native of Tegea, a city of 
Arcadia ; though others contend that he was born 
in Thebes ; and that after Terpander and Clonas 
flourished Archilochus : yet some writers afifiim 



Chap. XVIL 



AND PRACTICE OF MUSIC. 



77 



' that Ardalus the Troezenian taught wind-music 
' before Clonas. 

' The music appropriated to the lyre under the 
' regulations of Terpander continued without any 
' variation, till Phrynis became famous, who altered 
' both the ancient rules, and the form of the instru- 
' ment to which they were adapted.' 

Having thus discoursed concerning the ancient 
musicians, and stringed and wind-instruments in 
general, Lysias proceeds, and confining himself to 
the instruments of the latter kind, speaks to this 
effect : — 

' Olympus, a Phrygian, and a player on the flute, 
invented a certain measure in honour of Apollo, 
which he called Polycephalus or of many heads. 
This Olympus, as it is said, was descended from the 
first Olympus, the son of Marsyas, who being 
taught by his father to play on the flute, first 
brought into Greece the laws of harmony. Others 
ascribe the invention of the Polycephalus to Crates, 
the disciple of Olympus. The same Olympus was 
the author of the Harmatian mood, as Glaucus 
testifies in his treatise of the ancient poets, and as 
some think of the Orthian mood also.* There was 
also another mood in use among the ancients, termed 
Cradias, which Hipponax the Mimnermian greatly 
delighted in. Sacadas of Argos, being himself a 
good poet, composed the music to several odes and 
elegies, and became thrice a victor at the Pythian 
games. It is said that this Sacadas, in conjunction 
with Polymnestes, invented three of the moods, the 
Dorian, the Phrygian, and the Lydian ; and that 
the former composed a strophe, the music whereof 
was a commixture of all the three. The original 
constitution of the modes was undoubtedly by 
Terpander, at Sparta ; but it was much improved 
by Thales the Gortynian, Xenedamus the Cytherian, 
Xenocritus the Locrian, and Polymnestes the Colo- 
phonian. 

' Aristoxenus ascribes to Olympus the invention of 
the enarmonic genus ; for before his time there 
were no other than the diatonic and chromatic 
genera. 

' As to the measures of time, they were in- 
vented at different periods and by different persons. 
Terpander, amongst other improvements which he 
made in music, introduced those grave -and decent 
measures which are its greatest ornament ; after 
him, besides those of Terpander, which he did not 
reject, Polymnestes brought into use other measures 
of his own ; as did also Thales and Sacadas, who, 
though of fertile inventions, kept within the bounds 
of decorum. Other improvements were also made 
by Stesichorus and Alcmas, who nevertheless re- 

* These moods, the Harmation and Orthian, were unquestionably 
moods of time. The fonner, if we may trust the English translator of 
Plutarch's Dialogue on Music, as it stands in the first volume of his 
Morals, Lond. 1684, was the measure termed by Zarlino, La Curule, in 
which it is supposed was sung the story of Hector's death, and of the 
dragging him in a chariot round the walls of Troy : of the Orthian mood 
the same translator gives the following description : — ' This mood con- 
' sisted of swift and loud notes, and was used to inflame the courage of 
' soldiers going to battle, and is mentioned by Homer in the seventh 
' book of the Iliad, and described by Eustathius. This mood Arion 
'made use of when he flung himself into the sea, as Aulus Gellius 
' writes, lib. XVI. cap. xix. the time of it was two down and four up.' 
Meibomius on Aristides. 



' ceded not from the ancient forms ; but Crexus, 
' Timotheus, and Philoxenus, and others of the same 
' age, affecting novelty, departed from the plainness 
* and majesty of the ancient music' 

Another of the interlocutors in this dialogue of 
Plutarch, Soterichus by name, who is represented 
as one not only skilled in the science but eminently 
learned, speaks of the invention and progress of 
music to this effect : — 

' Music was not the invention of any mortal, 
but we owe it to the god Apollo. The flute was 
invented neither by Marsyas, nor Olympus, nor 
Hyagnis, but Apollo invented both that and the 
lyre, and, in a word, all manner of vocal and 
instrumental music. This is manifest from the 
dances and sacrifices which were solemnized in 
honour of Apollo. His statue, placed in the tem- 
ple of Delos, holds in his right hand a bow, and 
at his left the Graces stand with each a musical 
instrument in her hand, one bearing a lyre, another 
a flute, and another a shepherd's pipe ; and this 
statue is reported to be as ancient as the time of 
Hercules. The youth also that carries the tempic 
laurel into Delphos is attended by one playing 
on the flute ; and the sacred presents of the Hyper- 
boreans were sent of old to Delos, attended by 
flutes, pipes, and lyres ; and some have asserted 
that the God himself played on the flute. Venerable 
therefore is music, as being the invention of Gods ; 
but the artists of these later times, contemning 
its ancient majesty, have introduced an effeminate 
kind of melody, mere sound without energy. The 
Lydian mode, at first instituted, was very doleful, 
and suited only to lamentations ; wherefore Plato 
in his Republic utterly rejects it. Aristoxenus 
in the first book of his Harmonics relates that 
Olympus sung an elegy in that mode on the death 
of Python ; though some attribute the invention of 
the Lydian mode to Menalippides, and others to 
Torebus. Pindar asserts that it was first used at 
the nuptials of Niobe ; Aristoxenus, that it was 
invented by Sappho, and that the tragedians learned 
it of her, and conjoined it with the Dorian ; but 
this is denied by those who say that Pythocleides 
the player on the flute, and also Lysis the Athenian, 
invented this conjunction of the Dorian with the 
Lydian mode. As to the softer Lydian, w^hich was 
of a nature contrary to the Lydian properly so 
called, and more resembling the Ionian, it is said 
to have been invented by Damon the Athenian. 
Plato deservedly rejected these effeminate modes, 
and made choice of the Dorian, as more suitable 
to warlike tempers ; not that we are to suppose him 
ignorant of what Aristoxenus has said in his second 
book, that in a wary and circumspect government 
advantages might be derived from the use of the 
other modes ; for Plato attributed much to music, 
as having been a hearer of Draco the Athenian, 
and Metellus of Agrigentum ; but it was the con- 
sideration of its superior dignity and majesty that 
induced him to prefer the Dorian mode. He knew 
moreover that Alcmas, Pindar, Simonides, and 
Bacchylides, had composed several Parthenioi in 



78 



HISTORY OF THE SCIENCE 



Book IL 



' the Dorian mode ; and that supplications and hymns 
'to the Gods, tragical lamentations, and sometimes 
' love-verses were also composed in it ; but he con- 

* tented himself with such songs as were made in 

* honour of Mars and Minerva, or those other that 
' were usually sung at the solemn offerings called 

* Spondalia. The Lydian and Ionian modes were 

* chiefly used by the tragedians, and with these also 

* Plato was well acquainted. As to the instruments 
' of the ancients, they were in general of a narrow 
' compass ; the lyre used by Olympus and Terpander, 
•and their followers, had but three chords, which 
' is not to be imputed to ignorance in them, for those 
' musicians who made use of more were greatly their 
' inferiors both in skill and practice. 

* The chromatic genus was formerly used by those 
' who played on the lyre, but by the tragedians never. 
' It is certainly of greater antiquity than the enar- 

* monic ; yet the preference given to the diatonic and 
' enarmonic was not owing to ignorance, but was the 
' effect of judgment. Telephanes of Megara was 
*so great an enemy to the syrinx or reed-pipe, that 
' he would never suffer it to be joined to the tibia ; 
' or that other pipe made of wood, generally of the 
' lote-tree, and for that reason he forbore to go to 
'the Pythian games. In short, if a man is to be 
' deemed ignorant of that which he makes no use of, 
' there would be found a great number of ignorant 

* persons in this age ; for we see that the admirers 
' of the Dorian mode make no use of the Anti- 
' genidian method of composition : and other musi- 
' cians refuse to imitate Timotheus, being bewitched 
' with the trifles and idle poems of Polyeides. 

' If we compare antiquity with the present times, 
' we shall find that formerly there was great variety 
' in music, and that the diversities of measure were 

* then more esteemed than now. We are now 
' lovers of learning, they were lovers of time and 
' measure ; plain it is therefore that the ancients did 
' not because of their ignorance, but in consequence 
' of their judgment, refrain from broken measures ; 
' and if Plato preferred the Dorian to the other modes, 
' it was only because he was the better musician ; and 
' that he was eminently skilled in the science appears 
' from what he has said concerning the procreation of 
' the soul in his Timaeus. 

' Aristotle, who was a disciple of Plato, thus 
'labours to convince the world of the majesty and 
' divine nature of music : " Harmony, saith he, 
" descended from heaven, and is of a divine, noble, 
" and angelic nature ; being fourfold as to its efficacy, 
'• it has two mediums, the one arithmetical, the other 
" harmonical. As for its members, its dimensions, 
" and excesses of intervals, they are best discovered 
" by number and equality of measure, the whole 
" system being contained in two tetrachords." 

' The ancient Greeks were very careful to have 
' their children thoroughly instructed in the principles 
' of music, for they deemed it of great use in forming 
their minds, and exciting in them a love of decency, 
' sobriety, and virtue : they also found it a powerful 
' incentive to valour, and accordingly made use of 
' pipes or flutes when they advanced to battle : the 



' Lacedemonians and the Cretans did the same ; and 
' in our times the trumpet succeeding the pipe, as 
' being more sonorous, is used for the same purpose. 

* The Argives indeed at their wrestling matches made 
' use of fifes called Schenia, which sort of exercise 
' was at first instituted in honour of Danaus, but 
' afterwards was consecrated to Jupiter Schenius or 
' the Mighty ; and at this day it is the custom to use 
' fifes at the games called Pentathla, which consist of 
' cuffing, running, dancing, hurling the ball, and 
' wrestling. But among the ancients, music in the 
' theatres was never known ; for either they employed 
' it in the education of their youth, or confined it 
' within the walls of their temples ; but now our 
' musicians study only compositions for the stage. 

' If it should be demanded. Is music ever to remain 
' the same, and is there not room for new inventions ? 

* The answer is that new inventions are allowed, so 
' as they be grave and decent ; the ancients them- 
' selves were continually adding to and improving 
' their music. Even the whole Mixolydian mode was 

* a new invention ; such also were the Orthian and 
' Trochean songs ; and, if we may believe Pindar, 
' Terpander was the inventor of the Scolian song, and 
' Archilocus of the iambic and divers other measures, 
' which the tragedians took from him, and Crexus 
' from them. The Hypolydian mode was the inven- 

* tion of Polymnestes, who also was the first that 
' taught the manner of alternately soft and loud. 
' Olympus, besides that he regulated in a great 
' measure the ancient Greek music, found out and 
' introduced the enarmonic geims, and also the Pro- 
' sodiac, the Chorian, and the Bacchian measures ; all 
' of which it is manifest were of ancient invention. 
' But Lasus Hermionensis* applying these measures 
' to his dithyrambic compositions, and making use of an 
' instrument with many holes, by an addition of tones 
' and hemitones made an absolute innovation in the 
' ancient music. In like manner Menalippides, the 
' lyric poet, Philoxenus, and Timotheus, all forsook 
' the ancient method. The latter, until the time of 
' Terpander, of Antissa, used a lyre with only seven 
' strings, but afterwards he added to that number. 
' The wind-instruments also received a great alter- 
' ation ; and in general the plainness and simplicity 
' of the ancient music was lost in that affected variety 
' which these and other musicians introduced. 

' In ancient times, when Poetry held the precedency 
' of the other arts, the musicians who played on wind- 
' instruments were retained with salaries by the poets, 
' to assist those who taught the actors, till Menalip- 
' pides appeared, after which that practice ceased. 

' Pherecrates, the comic poet, introduces Music in 
' the habit of a woman with her face torn and bruised ; 
' and also Justice, the latter of whom, demanding the 
' reason of her appearing in that condition, is thus 
' answered by Music : — f 

* Lasus Charbini, from Hermione, a city of Achaia, lived about the 
58th Olympiad, in the time of Darius Hystaspes: some reckon liim 
among the seven wise men, in the room of Periander. He was tlie first 
who wrote a hook concerning music, and brought the dithyrambics into 
the games and exercises, where he was a judge or moderator, deciding 
contentious disputations. This Lasus was a musician of great fame, and 
is mentioned by Plutarch as the first who changed any thing in the 
ancient music. Meibom. on Anstoxenus, from Suidas. 

t This Pherecrates, the comic poet, lived in tlie time of Alexander the 



Chap. XVII. AND PRACTICE OF MUSIC. 79 

" It is my part to speak and yours to hear, there- ' been for the tutor first to consider the genius and 

* fore attend to my complaints. I hstve suffered ' inclination of the learner, and then to instruct him 
' much, and have long been oppressed by that beast ' in such parts of the science as he should discover 
' Menalippides, who dragged me from the fountain ' most affection for ; but the more prudent sort, as 
' of Parnassus, and has tormented me with twelve ' the Lacedemonians of old, the Mantingeans, and 
' strings : to complete my miseries, Cinesian, the ' Pellenians, rejected this method.' 

' Athenian, a pretender to poetry, composed such Here the discourse of Soterichus grows very 

' horrid strophes and mangled verses, that I, tortured obscure, and has a reference to terms of which a 

' with the pain of his dithyrambics, was so distorted modern can entertain no idea. Farther on he resumes 

' that you would have sworn that my right side was the consideration of the genera, which he speaks of 

' my left : nor did my misfortunes end here, for to this effect : — 

' Phrynis, in whose brains is a whirlwind, racked me ' Now then, there being three genera of harmony, 

* with small wires, from which he produced twelve ' equal in the quantity of systems or intervals, and 
' tiresome harmonies. But him I blame not so much, ' number of tetrachords, we find not that the ancients 
' because he soon repented of his errors, as I do ' disputed about any of them except the enarmonic, 
' Timotheus, who has thus furrowed my face, and ' and as to that they differed only about the interval 
' ploughed my cheeks ; and Pyrrias, the Milesian. ' called the diapason.' 

* who, as I walked the streets, met me, and with his The speaker, by whom all this while we are to 
' twelve strings bound and left me helpless on the understand Soterichus, then proceeds to shew that a 
'earth." mere musician is an incompetent judge of music in 

' That virtuous manners are in a great measure the general ; and to this purpose he asserts that Pytha- 

effect of a well-grounded musical education, Aris- goras rejected the judgment of music by the senses, 

toxenus has made apparent. He mentions Telesias, and maintained that the whole system was included 

the Theban, a contemporary of his, who being a in the diapason. He adds, that the later musicians 

youth, had been taught the noblest excellencies of had totally exploded the most noble of the modes ; 

music, and had studied the best Lyric poets, and that they made hardly the least account of the enar- 

withal played to perfection on the flute ; but being monic intervals, and were grown so ignorant as to 

past the prime of his age, he became infatuated with believe that the enarmonic diesis did not fall within 

the corrupted music of the theatres, and the inno- the apprehension of sense. 

vations of Philoxenus and Timotheus ; and when he He then enumerates the advantages that accrue 

laboured to compose verses, both in the manner of from the use of music, and cites Homer to prove its 

Pindar and of Philoxenus, he could succeed only in effects on Achilles in the height of his fury against 

the former, and this proceeded from the truth and Agamemnon : he speaks also of a sedition among the 

exactness of his education ; therefore if it be the aim Lacedemonians, which Terpander appeased by the 

of any one to excel in music, let him imitate the power of his music ; and a pestilence among the same 

ancients ; let him also study the other sciences, and people, which Thales, the Cretan, stopped by the 

make philosophy his tutor, which will enable him same means, 

to judge of what is decent and useful in music. Onesicrates, who hitherto appears to have acted 

' The genera of music are three, the diatonic, the the part of a moderator in this colloquy, after be- 

chromatic, and enarmonic ; and it concerns an under- stowing his commendations both on Lysias and 

standing artist to know which of these three kinds Soterichus, addresses them in these terms : — 

is the most pi'oper for any given subject of poetry. ' But for all this, my most honoured friends, you 

' In musical instruction the way has sometimes ' seem to have forgotten the chief of all music. 

Great, and attended him, as we are told, in his expeditions, [Suid. in ' PythagOraS, ArchytaS, Plato, and many OthcrS of 

Pherecrates] and was contemporary with Aristophanes, Plato, Eupolis ' thc auciont philosopcrs maintain that there COuld be 

and Phrynicus, all comic writers [Id. in Plato]. Phrynis, who played on c x- x- xi i -ii i. • • xi ^ 

the lyre, was the son of Gabon [Id. in Phrynis], and scholar of Aristo- ^^ motlOU ot the Spheres Wlthout mUSlC, SmCC that 

cieides who pretended to be of the family of Terpander, and was a 'the Supreme Deity Constituted all thiuffs harmo- 

favounte with Hiero, kmg of Sicily, as some accounts tell us, which , • ^ ^ i. Vt ij-l ii 

would throw him back near one hundred and fifty years in time before niOUSly ; DUt nOW it WOUld DC Unseasonable tO enter 

our poet Pherecrates : but if we may believe Plutarch, he should have < ■^^^^n■n a rliapnnrqp fin tint ciiibippt ' 

been a contemporary with the poet at least, if he personally contended ^POU a QlSCOUrse OU tliat SUDjCCt. 

the music prise with Timotheus, with whose playing we are told Alex- And SO Singing a hymn tO the Gods and the 

ander's spirit was so raised and animated to war. [Suid in Timotheus.] Mnqp"? OTipmVratp<? fli<?Tnis<?pc? thp pninmnv 

But may it not be said that Timotheus did contend the prize against -l^^USeS, UUeSICraiCS CUSmiSSCS tUC Company. 

some piece formerly composed by Phrynis, as the dramatic poets some- Thus Cuds the DialoSTUC of Plutai'ch OU mUsic, 

times contested the priority against a play of some deceased poet ? If so, i- i i.i r i i ? j i p x- •. • • 

Phrynis then might have lived as early as the period mentioned by whlch, though a celebrated WOrk ot antiquity, IS in 

^"r'f ?.■ fr„„ ;„Ho ^ t.1 * u u ,. • .-u- ■ . . the judgment of some persons rendered still more 

It is true mdeed Plutarch, where he gives us this point of hi.story, i , t i .1 p -m , i- . 1 

does not mention Phrynis by name, but distinguishes him only as the Valuable by the passage f I'Oni PherCCratCS, whlch he 

son of Gabon, and by his nickname lu)VOKa^irTr]Q, lonocamptes ; haS introduced iutO it. The least that CaU be Said of 

which sarcastical addition he obtained, because by his effeminate modu- 1 • 1 • .i x -.i . . •. • ^ . • 

lations he had corrupted the old music in the like manner as the Ionic WlllCh IS, tliat WltUOUt a Comment it IS UCXt tO im- 

UbTv! Tap. i'x^1fb\'*"'''''^ *^^ °''* ™^'''"^^ '^^"'"- J"i- Po""''' possible to understand it: the following remarks. 

The same Phrynis is likewise rallied by Aristophanes [in Nubibus, whicll Were COmmunicated tO the late Dr. PepUSCh 

V. 967] and others of the comic poets, for the levity of his compositions! bv a learned but anouvmous Correspondent of his, 

and for overdoing every thing in his performance. He was marked out, x j -i. • j • j. ^^• •^ ^ 

even to infamy, for his innovations in music ; for his ooft and affected ™^.V .^fO ^l^ar tO render it in SOme degree intelligible : 

^»^Jc'''t?VTl''!M'Jpr.',in'?hw^°n!^''"'^"'"*^^"^^ 'The poet, speaking of the successive abuses of 

music; for his internunglnig and confounding the modes; and for , • • f . S^i • 1 c i m- 

debasing the science to parasitism and servile offices. mUSlC, mCUtlOUS first PhryniS, and afterwards i imO- 



80 HISTORY OF THE SCIENCE Book IL 

' theus ; so that Phrynis should seem to have led the ' said to be so offensive to the Lacedaemonians, it was 

' way to the abuses which Timotheus is reprehended ' not the first time of their having been put in practice ; 

' for, or rather gave into, to the prejudice of music ; ' for Phrynis had before done the like, and been 

' and it is probable he did so, from a speech of Agis ' punished, as we shall find, in the same manner. 

' made to Leonidas, which is transmitted to us by ' These accounts therefore go thus far towards an 

' Plutarch in the life of Agis. * explanation of one part of the passage before us ; 

' What we want the explanation of, is that passage ' that as to the five strings, we may be pretty certain 

' of Pherecrates which relates to the five strings and ' that the lyre of Phrynis was not confined to that 

' the twelve harmonies. ' number, nay we have particular testimonies that 

* From the time of Terpander, and upwards, we ' Phrynis himself was noted for playing on the lyre 

* know that the lyre had seven strings, and those ' with more than seven strings ; the system of the 

* adjusted to the number of the seven planets, and as * lyre, from the time of Terpander to that of Phrynis, 

* some suppose to their motions also. For though * had continued altogether simple and plain, but 
' Euphorion in Athenaeus is made to say, that the use * Phrynis beginning to subvert this simplicity by 

* of the instruments with many strings was of very ' adding two strings to his instrument, we are told 
' great antiquity, yet the lyre was reckoned complete, ' by Plutarch, in more than one passage, that Ecprepes 

* and to have attained the full measure of perfect * the magistrate cut off two of his nine strings.' § 

' harmony when it had seven strings ; because, as ' The next thing therefore to be enquired into, is 

* Aristotle obsei-ved, the harmonies consisted in the * what the poet could mean by playing twelve har- 
' number of chords, and because that was the number * monies on five strings '? 

* of old used. ' Perhaps by Harmonies we are to understand 

' And therefore when Timotheus added four ' Modes ; and if so, Phrjoiis may be ridiculed for 

' strings to the former seven, that innovation was so ' such a volubility of hand, and such an affectation of 

' offensive to the Lacjedemonians, that he was formally ' variety, that he extracted a dozen tones from five 

* prosecuted for the presumption ; and it was one of ' strings only, or that he played over the whole 

* the causes for which they were said to have banished ' twelve modes within that compass. For besides 
' him their state. The edict by which they did so, * the seven principal modes, it is said that Aristoxenus 

* still extant, is transmitted to us as a curiosity by ' by converting five species of the diapason, intro- 

* Boetius ; * some however have said that Timotheus ' duced five other secondary modes ; and that the 
' cleared himself from this sentence by producing a ' intermingling of the modes is the sense of ap/xoj'iae 

* very ancient statue of Apollo found at Laceda^mon, ' here, seems plain from another passage in Plutarch,|| 
' holding a lyre with nine strings. f But if he ' where he says, " That it was not allowed to compose 

* avoided this sentence of banishment, he did not " for the lyre formerly, as in his time, nor to inter- 
' wholly escape censure ; for Pausanias, who wrote " mingle the modes apfioviaq and measures of time, 

* as early as Athenaeus, tells us where the Lacedae- " for they observed one and the same cast peculiar to 

* monians hung up his lyre publicly, having pimished " each distinct mode, which had therefore a name to 

* him for superadding four strings, in compositions " distinguish it by ; they were called No^ot or rules 
' for that instrument, to the ancient seven ; and " and limitations, because the composers might not 

* Plutarch likewise tells us that before this, when the " transgress or alter the form of time and measure 

* above-mentioned Phrynis was playing on the lyre " appointed to each one in particular." 

' at some public solemnity, one of the Ephori, Ec- ' For we are certain that both the Athenians and 

* prepes by name, taking up a knife, asked him on ' Lacedaemonians had their laws by which the 
' which side he should cut off the strings that ex- ' particular species of music were designed to be 
' ceeded the number of nine.J ' preserved distinct and unconfused ; and their hymns, 

' But though these innovations of Timotheus were * threni, paeans, and dithyrambs kept each to their 

« Boetius, in his treatise De Musica, Lib. I. cap. i. has given it in the ' several SOrt of odc ;_ and SO the COmpOSCrs for the 

original Greek ; and the author of a book lately published, entitled ' lyre Were not permitted tO blend One mclody With 

Principles and Power of Harmony, has given the following translation ,■ .i i x xi i j. „ j „,„„„ „„,,„. ,„„;! 

of it ._ J ' b o t another, but they who transgressed were censured 

Whereas Timotheus, the Milesian, coming to our city, has deformed < and fined for it.' 

the ancient music ; and laying aside the use of the seven-stringed lyre, _- , ,', . jj.ii.ii 

and introducing a multiplicity of notes, endeavours to corrupt the ears It has already been mentioned that the genuineness 

of our youth by means of these his novel and complicated conceits, f ^j | dialogue has been questioned, some Writers 

which he calls chromatic, by him employed in the room of our established, ^ . . " , . ^ t . j i. 

orderly, and simple music; and whereas, &c. It therefore seemeth good affirming it tO be a SpuriOUS productlOU, and OthcrS 

to us the King and Ephori, after having cut off the superfluous strings pniifpriflino- if tn bp fl crpnuinp WOrk of Plutarch 

of his lyre, and leaving only seven thereon, to banish the said Timotheus COntenQing It tO DC a genuine WOrK OI .TUIUIICU, 

out of our dominions, that every one beholding the wholesome severity WOrtliy of llimsclf, and in merit UOt inferior tO the 

of this city, maybe deterred from bringing in amongst us any unbe- ^ , c ±^ j. x* j. • i • ii, Q . ;„„„ 

coming customs, &c. Infra page u8. best of the treatises Contained m the bymposiacs. 

t Casaub. ad Athenseum, Ub. VIII. cap. xi. It is therefore neccssary to take a view of the con- 

X This fact is alluded to by Agis king of Sparta, in a speech of his to trovcrsv, and to state the arguments of the Contending 

Leonidas, thus recorded by Plutarch : — , • • , /• ii • i • • Tj. 

' And you that use to praise Ecprepes, who being Ephore, cut off two parties in support 01 their several opmions. it SCems 

•of the nine strnigs from the instrument of Phrynis the musician, and that the Orit^inal OTOUud of this dispute WaS a llOte 

'to commend those who did afterwards imitate him in cutting the strings o o r_ r i-i • T 

'of Timotheus's harp, with what face can you blame me for designing to prefixed tO AuiyOt S r rench translation OI thlS dia- 

'cut off superfluity and luxury from the commonwealth? Do you think 1r,(rnP in ihp fnll.iwino- vvnrrici • ' flp trnifp n' anoarticnt 

'those men were so concerned only about a fiddle-string, or intended iOgUC lU tnc lOllOWlUg V\0ras . ^^C iraiie U appaiLlCllb 

' any thing else than by checking the voluptuousness of music, to keep , ,r., ., , .. . ^ x^, ^ >. • r • t *•» .- 

' out a way of living which might destroy the harmony of the city ? § Vide the last preceding note, and Plutarch in Laconic. Institutio. 

'Plutarch in Vita Agidis.' II De Musica. 



Chap. XVIII. 



AND PRACTICE OF MUSIC. 



81 



' point, ou bien peu h la musique de plusieurs voix 
' accordees & entrelacees ensemble, qui est aujourd'hui 

* en usage ; ains a la fa^on ancienne, qui consistoit en 
' la convenance du chant avec le sens & la mesure de 
' la lettre, & la bonne grace du geste ; & le style ne 

* semble point etre de Plutarque.' 

Amyot's translation bears date in 1610 ; not- 
withstanding which, Fabricius. in his catalogue of 
the writings of Plutarch, has mentioned this dis- 
course without suggesting the least doubt of its 
authenticity.* But a dispute having arisen in the 
French Academy of Inscriptions and Belles Lettres, 
on the question, whether the ancients were ac- 
quainted with music in consonance or not, this 
tract of Plutarch, in which there is not the slightest 
mention of any such practice, was urged in proof 
that they were strangers to it. While a doubt re- 
mained of the genuineness of this discourse, its 
authority could not be deemed conclusive ; those 
who maintained the affirmative of the principal 
question, therefore insisted on the objection raised 
by Amyot ; and this produced an enquiry into the 
ground of it, or, in other words, whether Plutarch 
was really the author of that discourse on music 
which is generally ascribed to him, or not : this 
enquiry is contained in three papers written by 
Monsieur Burette, and inserted in the Memoirs of 
the above-mentioned Academy, tome onzieme, Amst. 
1736, with the following titles, Examen du Traite 
de Plutarque sur la Musique — Observations touchant 
I'Histoire litteraire du Dialogue De Plutarque sur la 
Musique — Analyse du Dialogue de Plutarque sur la 
Musique, the publication whereof has put an end to 
a question, which but for Amyot had probably never 
been started. 

Meibomius, in the general preface to his edition 
of the musical writers, and Doni, are lavish in their 
commendations of this treatise : the latter of them, 
in his discourse De Praestantia Musicae Veteris, 
pag. 65, calls it a golden little work ; but whether it 
merits such an encomium must be left to the judg- 
ment of such as can truly say they understand it. 
As to the historical part, it is undoubtedly curious, 
except in some instances, that seem to approach too 
near that species of history which we term fabulous, 
to merit any great share of attention ; but as to that 
other wherein the author professes to explain the 
nature of the ancient music, it is to be feared he is 
much too obscure for modern comprehension. The 
particulars most worthy of observation in this work 
of Plutarch are, the perpetual propensity to inno- 
vation, which the musicians in all ages seem to have 
discovered, and the extreme rigour with which those 
in authority have endeavoured to guard against such 
innovations : the famous decree of the Ephori against 
Timotheus just mentioned, which some how or other 
was recovered by Boetius, and is inserted in a pre- 
ceding note,t is a proof that the state thought itself 
concerned in preser\'ing the integrity of the ancient 
music ; and if it had so great an influence over the 
manners of the Spartan youth, as in the above trea- 

* Biblioth. Graec. lib IV. cap. xi. pap. 364, N. 124. 

♦ A transiation on page 80, tha original infra 118. 



tise is suggested, it was doubtless an object worthy 
of their attention. 

CHAP. XVIII. 

Aristides Quintilianus is supposed to have 
flourished, a. c. 110. This is certain, that he wrote 
after Cicero, for from his books De Republica he 
has abridged all the arguments that Cicero had 
advanced against music, and has opposed them to 
what he urged in behalf of it in his oration for 
Roscius. It is farther clear that Aristides must 
have been prior to Ptolemy, for he speaks of Aris- 
toxenus who admitted of thirteen modes, and of 
those who after him allowed of fifteen, but he takes 
no notice of Ptolemy who restrained the number of 
them to seven. His treatise De Musica consists 
of three books. The first contains an ample dis- 
cussion of the doctrine of the modes : speaking of 
the diagi'am by which the situation and relation of 
them is explained, he says it may be delineated in 
the form of wings, to manifest the difference of 
the tones among themselves ; but he has given no 
representation of it. 

All that has been hitherto said of the modes is to 
be understood of melody, for there is another and 
to us a more intelligible sense of the word, namely 
that, where it is applied to the proportions of time, 
or the succession and different duration of sounds, 
of which whether they are melodious, or such as 
arise from the simple percussion of bodies, the modes 
of time, for by that appellation we. choose to dis- 
tinguish them from the modes of tone, are as so 
many different measures. The effect of the various 
metrical combinations of sounds is undoubtedly what 
the ancients, more particularly this author, meant by 
the word Rythmus. Of time he says there are two 
kinds, the one simple and indivisible, resembling 
a point in geometry ; the other composite, and that 
of different measures, namely, duple, treble, and 
quadruple.:}: The rythmic genera he makes to be 
three in number, namely, the equal, the sesquialteral, 
and the duple ; others he says add the supertertian : 
these are constituted from the magnitude of the 
times ; for one compared to itself begets a ratio of 
equality, two to one is duple, three to two is ses- 
quialteral, and four to three supertertian : He speaks 
of the elation and position of some part of the body, 
the liand or foot perhaps, as necessary to the rythmus, 
probably as a measure ; and this corresponds with 
the practice of the moderns in the measuring of time 
by the tactus or beat. The remainder of the first 
book of this work of Quintilian contains a very 
laborious investigation of measures, with all their 
various inflexions and combinations, in which the 
author discovers a profound knowledge. 

The second book treats of music as a means to 

X This passage in Aristides ftuintilianus has drawn on him a severe 
censure from the late Dr. Pemberton, the Greshara professor of physic, 
who says that he here endeavours to make out four different measures 
of time in verse also. This, says the Dr., is talking nonsense. But, 
adds he, this writer is apt to amuse himself with fanciful resemblances ; 
and having first imagined I know not what analogy between these four 
measures of time, and the four dieses, into which a tone was considered 
as divisable, he must needs try at making out the like in relation to 
words. Observations on Poetry especially the Kpic. Lond. 1738. page 110. 

G 



82 HISTORY OF THE SCIENCE Book IL 

regulate the external behaviour, as that of philosophy sonances ; a method whi-ch this author seems to 

is to improve the mind. Music, he says, by its approve ; and to recommend this practice, he cites 

harmony polishes the manners, and its rythmus the authority of Pythagoras, who he says, when he 

renders the body more agreeable ; for youth being departed this life, exhorted his disciples to strike 

impatient of mere admonition, and capable of in- the monochord, and thereby rather inform their 

struction by words alone, require such a discijiline understandings than trust to their ears in the measure 

as without disturbing the rational part of their of intervals. He speaks also of an instrument for 

natures shall familiarly and by degrees instruct them: the demonstration of the consonances, called a heli- 

he adds that it is easily perceived that all boys are con, which was of a square form, and on which were 

prompt to sing and ready for brisk motions, and that stretched, with an equal tension, four strings.* For 

it is not in the power of their governors to hinder the reason above given, it seems no way necessary 

them from the pleasure which they take in exercises to follow this author through that series of geome- 

of this sort. In human things, continues this author, trical reasoning, which he has applied for the inves- 

there is no action performed without music ; it is tigation of his subject in the succeeding pages of his 

certain that divine worship is rendered more solemn book, wherefore a passage relating to the tetrachords, 

by it, particular feasts and public conventions of remarkable enough in its kind, shall conclude this 

cities rejoice with it, wars and voyages are excited extract from his very learned but abstruse work, 

by it, the most difficult and laborious works are ' The tetrachords are agreed to be five in number, 

rendered easy and delightful by it, and we are 'and each has a relation to one or other of the 

excited to the use of music by divers causes. Nor ' senses ; the tetrachord hypaton resembles the touch, 

are its eff"ects confined to the human species ; irra- ' which is affected in new-born infants, when they 

tional animals are affected by it, as is plain from the 'are impelled by the cold to cry. The tetrachord 

use which is made of pipes by shepherds, and horns ' meson is like the taste, which is necessary to the 

by goatherds. Of the use of music in war, as ' preservation of life, and hath a similitude to the 

practised by the, ancients, he has the following pas- ' touch. The third, called synemmenon, is compared 

sage : — ' Numa has said, that by music he corrected 'to the smell, because this sense is allied to the taste; 

' and refined the manners of the people, which before ' and many, as the sons of art say, have been restored 

' were rough and fierce : to that end he used it ' to life by odours. The fourth tetrachord, termed 

' at feasts and sacrifices. In the wars where it is ' diezeugmenon, is compared to the hearing, because 

'and will be used, is there any need to say how 'the ears are so remote from the other organs of 

' the Pyrrhic music is a help to martial discipline ? ' sense, and are disjoined from each other. The 

* certainly it is plain to every one, and that to issue ' tetrachord hyperboleon is like the sight, as it is the 

' commands by words in time of action would intro- ' most acute of the systems, as the sight is of the 

' duce great confusion, and might be dangerous by ' senses.' Farther, this author tells us that ' the five 

'their being made known to the enemies, if they 'tetrachords do in like manner answer to the five 

' were such as use the same language. To the ' primary elements, that is to say, hypaton to the 

' trumpet, that martial instrument, a particular cantus ' earth, as the most grave ; meson to the water, as 

' or melody is appropriated, which varies according ' nearest the earth ; synemmenon to the air, which 

' to the occasion of sounding it, so as for the attack * passes through the water remaining in the profun- 

' by the van or either wing, or for a retreat, or ' dities of the sea and the caverns of the earth, and 

' whether to form in this or that particular figure, ' is necessary for the respiration of animals, which 

' a different cantus is requisite ; and all this is so ' could not live without it ; diezeugmenon to the fire, 

' skilfully contrived, as to be unintelligible to the ' the motion whereof, as tending upwards, is against 

' enemy, though at the same time by the army it * nature ; lastly, the tetrachord hyperboleon answers 

' is plainly understood.' ' to the aether, as being supreme and above the rest.' 

Thus much of this author is intelligible enough There are, he says, also analogies between the three 

to a reader of this time ; but when he speaks, as he several systems of diapente and the senses ; but we 

does immediately after, of the efficacy of music in hasten to dismiss this fanciful doctrine. Moreover, 

quieting tumults and appeasing an incensed multi- adds he, 'in discoursing of the human soul, systems 'are 

tude, it must be owned his reasoning is not so clear : ' not improperly compared to the virtues. Hypaton 

as little can we conceive any power in music over ' and meson are to be attributed to temperance, the 

the irascent and concupiscent affections of the mind, ' efficacy whereof is double, and consists in an ab- 

which he asserts are absolutely under its dominion. ' stincnce from unlawful pleasures, resembling the 

The remainder of this second book consists of a chain ' most grave of these two systems ; as also in a mo- 

of very abstruse reasoning on the nature of the human ' derate use of lawful enjoyments, not improperly 

soul, no way applicable to any conception that we at ' signified by the tetrachord meson ; but the tetra- 

this time are able to form of music, and much too ' chord synemmenon is to be attributed to justice, 

refined to admit of a place in a work, in which it is ' which being joined with temperance, exerts itself 

proposed not to teach, but to deliver a history of, 'in the discharge of public duties, and in acts of 

the science. ' private beneficence : the diezeugmenon has the 

The third book contains a relation of some experi- * resemblance of fortitude, which virtue delivers the 

ments made with strings, distended by weights in ' soul from the dominion of the body ; lastly, the 

given proportions, for finding out the ratios of con- • See it in a subsequent chapter of this second book. 



Chap. XVIII. AND PRACTICE OF MUSIC. 83 

' hyperboleon emulates the nature of prudence, for Gaudentius, the philosopher, according to Fabri- 

*that tetrachord is the end of the acumen, and cius, || seems to have written before Ptolemy, and 

'this virtue is the extremity of goodness. Again, treading in the steps of Aristoxenus, composed an 

* these virtues may be assimilated to the three systems introduction to harmonics, v^hich Cassiodorus com- 

* of diapente ; * the two first, justice and temperance, mends as an elegant little vi'ork ; though he does not 
' which are always placed together as being a check pretend to say who he was, or where he lived : 
' to the concupiscent part of the mind, resemble the however upon his authority Cassiodorus relates that 
'first of these systems; fortitude may be compared Pythagoras found out the original precepts of the 
' to the second, as that virtue denotes the irascent art by the sound of hammers and the percussion of 
' part and refers to each of our two natures ; and extended chords ; and indeed as to this matter 

* prudence to the third, as declaring the rational Gaudentius is very explicit. For his work in general, 
' essence. Add to this, that the two species of excepting a few definitions and a representation of 
' diapason answer to the twofold division of the mind ; the musical characters in the method of Alypius, it is 
' the first resembling the irrational, and the second little more than an abridgement of Aristoxenus, and 
' the rational part thereof.' that so very short and obscure, that little advantage 

It has been remarked of Quintilian that he is ex- can be derived from the perusal of it. 

tremely fond of analogies, vide pag. 81, in a note; Claudius Ptolemeus was an Egyptian, born at 

and the above passages are a proof that this charge Pelusium ; not one of the Ptolemies, kings of Egypt, 

against him is not ill-grounded. with some one of whom he has been confounded ; 

Alypius, the next in succession of the authors now nor the same with Ptolemy, the mathematician and 

remaining to him above cited, or, as some suppose, a astronomer, who, as Plutarch relates in his life of 

contemporary of his, as flourishing about a.c. 115,f Galba, was the constant companion of that emperor, 

compiled a work, entitled an Introduction to Music, and was also attendant on the emperor Otho, in 

which seems to be little else than a set of tables Spain, and foretold that he should survive Nero, as 

explaining the order of the sounds as they arise in Tacitus tells us, lib. I. cap. xxii. The Ptolemy here 

the several modes of their respective genera in the spoken of flourished in the reign of the emperor 

ancient method of notation. The musical characters Marcus Aurelius Antoninus, as Suidas testifies ; and 

used by the ancients were arbitrary ; they were also himself in his Magnae Syntaxis, where he says 

nothing more than the Greek capitals mutilated, that he drew up his astronomical observations at 

inverted, and variously contorted, and are estimated Alexandria, for which reason he is by Suidas and 

at no fewer than twelve hundred and forty. A others called Alexandrinus, in the second year of 

specimen of them is herein-before inserted in two Antoninus Pius, which answers to the year of Christ 

plates from Kircher. (Appendix, Nos. 35 and 36.) 139.^ He was the author of a treatise on harmonics 

Manuel Bryennius, another of the Greek writers in three books, a work much more copious than any 

on music, is supposed to have flourished under the of those above-mentioned ; and it must be allowed 

elder Palaeologus, viz., about the year of Christ 120. that he of all the ancient writers seems to have entered 

He wrote three books on harmonics, the first whereof the most deeply into the subject of harmonics. In 

is a kind of commentary on Euclid, as the second the first chapter of his first book, he assigns the 

and third are on Ptolemy.;}: He professes to have criteria of harmony, which he makes to be sense and 

studied perspicuity for the sake of young men, but reason : the former of these, he says, finds out what 

has given very little more than is to be found in one is nearly allied to truth, and approves of what is 

or other of the above authors. Meibomius had given accurate, as the latter finds out what is accurate and 

the public expectations of a translation of this work, approves of what is nearly allied to truth. Chap. iii. 

but not living to complete it, Dr. Wallis undertook speaking of the causes of acuteness and gravity, he 

it, and it now makes a part of the third volume of takes occasion to compare the wind-pipe to a flute ; 

his works, published at Oxford in three volumes in and to remark as a subject of wonder, that power or 

folio, 1699. faculty which enables a singer readily and instan- 

Bacchius Senior was a follower of Aristoxenus ; taneously to hit such degrees of dilatation and 

Fabricius supposes him to have been tutor to the contraction as are necessary to produce sounds, grave 

emperor Marcus Antoninus, and consequently to have or acute, in any given proportion, 

lived about a.c. 140. § He wrote in Greek a very In the sixth chapter of the same book he condemns 

short introduction to music in dialogue, which, with the method of the Pythagoreans, and in the ninth 

a Latin translation thereof, Meibomius has published. that of the Aristoxeneans, in the adjusting of the 

It seems it was first published in the original by consonances, but thinks the former the less erroneous 

Mersennus, in his Commentary on the six first of the two : the Pythagoreans, he says, not sufficiently 

chapters of Genesis ; and that afterwards he published attending to the ear, often gave harmonic proportions 

a translation of it in French, which Meibomius, in the to incongruous sounds ; on the contrary, the Aris- 

preface to his edition of the ancient musical authors, toxeneans, ascribing all to the ear, applied numbers, 

censures as being grossly erroneous. the images of reason, not to the differences of sound, 

* The varieties or different systems of diapente are four, and therefore but to their intervals. To COrrect the CrrorS of theSG 

U may be questioned why in this place the autlior has limited them to ^^^ ^^^^ different mCthods, lie COUtrlved au iustru- 

+ Fabr. Biblioth. Grac. lib. III. oap. x. 

j Ibid. II Biblioth. Graec. lib. III. cap. x. 

} Ibid. ^ Ibid. cap. xiv. 



84 



HISTORY OF THE SCIENCE 



Book II. 



ment very simple and inartificial in its constrnction. 
but of singular use in the adjusting of ratios, which, 
though in truth but a monochord, as consisting of one 
string only, he with great propriety called the Har- 
monic Canon, by which appellation it is constantly 
distinguished in the writings of succeeding authors. 
His description of the instrument and its use, as also 
the reasons that led him to the invention, are con- 
tained in the eighth chapter of the same first book, 
and are to the following effect : — ' We omit to explain 
' what is proposed, by the means of pipes or flutes, or 
'by weights affixed to strings, because they cannot 
'make the necessary demonstrations with sufficient 
' accuracy, but would rather occasion controversy ; 
' for in pipes and flutes, as also in the breath which is 
' injected into them, there is great disorder ; and as 
' to strings with weights affixed to them, besides that 
' of a number of such strings, we can hardly be sure 
' that they arc exactly equal in size, it is almost im- 
' possible to accommodate the ratios of the weights 
'to the sounds intended to be produced by them; 
' for with the same degree of tension two strings of 
' different thickness would produce sounds differently 
' grave or acute : and farther, which is more to the 

* present purpose, a string, at first of an equal length 

* to others, by the affixing to it a greater weight than 
' is affixed to the rest, becomes a longer string, from 
'whence arises another difference of sound besides 
' what might be deduced from the ratio of weight 
'alone. The like will happen in sounds produced 
' from hammers or quoits of unequal weights ; and 
' we may observe the same in some vessels that are 
' first empty, and afterwards filled ; and certainly it 
' is difficult in all these cases to provide against the 

* diversity of matter and figure in each ; but in the 
'canon, as I term it, the chord most readily and 
'accurately demonstrates the ratios of the several 
'consonances :' — 



E 



K 



G 




if from the points A D a chord be strained over the 
middle points E and G of the said curved super- 
ficies, the part E G will be parallel to the right line 
A B, D, because of the equal height of the magades, 
and will have its limits at E and G. Transfer then 
the line E G to the line A B C D, and having first 
bisected the whole length at K, and the half of that 
distance at L, place under the chord other magades, 
which must be very thin, and somewhat higher, but 
in every other respect like the former, so that both 
the intermediate magades may be straight with the 
middle of the external ones ; now if the part of the 
chord E K be found equitonal to K G, and the part 
K L to L G, then are we convinced that the chord 
is equable and perfect as to its constitution and make, 
and consequently fit for the experiment ; but if it 
should not prove so, the trial is to be transferred to 
another jjart, or even to a new chord, till we obtain 
this condition of equability under the circumstances 
of similar moveable magades, and a similar length 
and tension of the parts of the chord. This being 
done and the chord divided according to the pro- 
portions of the consonances, we shall by the appli- 
cation of the moveable magades prove by our ears 
the rations of corresponding sounds ; for giving to 
the distance E K four of such parts whereof K G is 
three, the sounds on both sides will produce the 
consonance diatessaron, and have a sesquitertian 
ratio ; and giving to E K three parts whereof K G 
is two, the sounds on both sides will make the con- 
sonance diapente, which is in sesquialteral ratio. 
Again, if the whole length be so divided as that 
E K may be two parts and K G one of them, it shall 
be the unison diapason, which consists in a duple 
ratio. If it be so that E K be eight parts whereof 
K G is three, it will be the consonance diapason and 
diatessaron, in the ratio of eight to three ; farther if 
it be divided so as that E K be three parts and K G 
one of them, it will be diapente and diapason, in 
a triple ratio ; and lastly if it be so divided as that 
E K be four and K G one, it will be the unison dis- 
diapason in a quadruple ratio. 



A B C D The line of the canon. 

A E G D The chord. 

A E, G D The ligament or place where it is 
fastened. 

E B, G C Perpendiculars of the immoveable ma- 
gades or bridges. 

K K, L L The moveable magades. 

B K, L The canon or rule divided. 

Suppose A B C D to be a right line, at each end 
thereof apply magades or little bridges, equal in 
height, and having surfaces as nearly spherical as 
possible ; as suppose the surface B, E to be described 
round the center F, and the surface C, G round the 
center H. Let then the points E, G be taken in the 
middle or bisection of these curved superficies, the 
magades being so placed as that lines E, F, and 
G, H, drawn from the said bisections E and G, may 
be perpendicular to the right line A B, C D. Now 



RATIOS. THE PROOF. CONSONANCES. 
■f- E 4 K 1 G Disdiapason 


f E 


3 




K 1 


G Diapason and 


1 E 


8 




K 3 


diapente 
G Diapason and 


f E 


2 




K 1 


diatessaron 
G Diapason 


f E 


3 




K 2 


G Diapente 


1 E 


4 




K 3 


G Diatessaron 


E 


1 


K 


1 


G 


Z' 


; i 


~\ 



A B K CD 

How the monochord of Pythagoras was con- 
structed, or in what manner he divided it, we are 



Chap. XIX. 



AND PRACTICE OF MUSIC. 



85 



no where told : it seems difficult to conceive that 
for producing the consonances it could be divided in 
any other manner than this of Ptolemy, and yet this 
author censures the followers of Pythagoras for not 
knowing how to reason about the consonances, which 
one would think they could not fail to do from prin- 
ciples so clear as those deducible from experiments 
on the monochord. But as to the Aristoxeneans, 
he censures them for rejecting the reasonings of the 
Pythagoreans, at the same time that they would not 
endeavour to find out better. To understand these 
and other invectives against this sect, it is to be 
observed that they measured the intervals by the 
ear as our practical musicians do now, that is to say, 
the greater by fourths or fifths, and the less by tones 
and semitones ; thus to ascertain the measure of an 
octave, they applied that of a diatessaron or fourth 
above the unison, and another below the octave, and 
between the approximating extremities of these two 
intervals they found the distance of a tone, which 
furnished a common measure for the less intervals 
of a fourth, a fifth, and the rest ; and enabled them 
to say that a tone is the difference between the 
diatessaron and the diapente : this Ptolemy calls 
remitting one question to another, and he adds that 
the ear, when it would judge of a tone needs not the 
help of a comparison of it with the diatessaron or 
any other consonance, and yet adds he, ' if we would 
' ask of the Aristoxeneans what is the ratio of a tone, 
' they will say, perhaps, that it is two of those in- 
* tervals, tliat is to say, hemitones, of which the dia- 
' tessaron contains five, and in like manner that the 
' diatessaron is five, of those of which the diapason is 
' twelve, and so of the rest, till at last they come to 
' say that the ratio of a tone is two, which is not de- 
' finintr those ratios.' 

Ptolemy, lib. I. cap. x. farther denies the assertion 
of the Aristoxeneans, that the diatessaron contains 
two tones and a half, and the diapente three and a 
half ; as also that the diapason consists of six tones, 
as the several contents of those two systems of two 
and a half, and three and a half, supposing this 
estimation of them to be just, woiald make un- 
doubtedly six ; but by his division of the mono- 
chord, he clearly demonstrates that the term by 
which the diatessaron exceeds the diatone, and which 
he calls a limma, is less than a hemitone, in the same 
proportion as 1944 bears to 2048, a difference how- 
ever much too small for the ear to distinguish. His 
demonstration of this proposition is given in a pre- 
ceding chapter of this work. 

To enter into a discussion of that very abstruse 
suV)ject, the division of the diapason, would require 
a much more minute investigation of the doctrine of 
ratios than is requisite in this place ; it must how- 
ever be observed, that supposing the ear alone to 
determine the precise limits of any system, that of 
the diatessaron for example, and that such system 
were transferred to the monochord, a repetition of the 
system so transferred would fail to produce a series 
of systems consonant in the extremities. Thus let 
a given sound be, as we should now call it G, and let 
the monochord be divided by a bridge according to 



the rules above prescribed, so as to give its fourth C ; 
and let a tone, D, be set on by another bridge in like 
manner, and after that another fourth, which would 
terminate at G, and would seem to make what we 
should call a diapason : we should find upon taking 
away the intermediate bridges at C and I), that the 
interval from G to G would be more than a diapason ; 
and that were this method of ascertaining: the terms 
of the consonances repeated through a series of 
octaves, the dissonance would be increased in pro- 
portion to the number of repetitions. Ptolemy has 
taken another method, chap. xi. of this his first 
book, and by an accumulation of sesquioctave tones 
has clearly demonstrated that six such exceed 
the consonance diapason. This deficiency, if it 
may be so called, in the intervals of which the 
diapason is compounded, and the difference between 
timing by the ear and by numbers, has suggested to 
mathematicians what is called a temperament, which 
]n'oposes a certain number of integral parts for the 
limit of the diapason, and the division of the amount 
of the several limmas that occur in the progression to 
it, in such a manner as to make the consonances con- 
tained in it as nearly perfect as possible. 

The remainder of Ptolemy's first book treats of the 
genera. Chap. xii. exhibits the division of Aris- 
toxenus, which he condemns ; and chap. xiii. that of 
Archytas of Tarentum, whom he censures for defining 
the genera by the interjacent intervals rather than by 
the ratios of the sounds among themselves, and 
charges him with rashness and want of thought. 

The use and application of the genera is at this 
day so little understood, that we are greatly at a loss 
to account for any . other division of the tetrachord 
than that which characterizes the diatonic genus : 
Nor does it seem possible, with the utmost strength 
of the imagination, to conceive how a series of sounds 
so extremely ungrateful to the ear as those of which 
the chromatic and enarmonic genera are said to be 
formed, could ever be received as music in the sense 
in which that word is now understood. 

CHAP. XIX. 

In the first Chapter of his second book, Ptolemy 
undertakes to shew by what means the ratios of the 
several genera may be received by the sense, in the 
course of which demonstration he points out the 
different offices of sense, or the ear, and reason, in 
the admeasurement of intervals, by which it should 
seem that the former is previously to adjust the con- 
sonances, and that these being transferred to the 
canon, become a subject of calculation ; and this 
position of his is undoubtedly true ; for the de- 
termination of the senses in all subjects where har- 
mony or symmetry are concerned is arbitrary, and it 
is the business of reason, assisted by numbers, to 
enquire whether this determination has any founda- 
tion in nature or not ; and if it has not, we pronounce 
it fantastical and capricious ; for example, we perceive 
by the ear a consonance between the unison and its 
octave, and we are conscious of the harmony resulting 
from those two sounds ; but little are we aware of 



86 



HISTORY OF THE SCIENCE 



Book II. 



the wonderful relation that subsists between them, or 
that if an experiment be made by suspending weights 
to the chords that produce it. whose lengths are by 
the laws of harmony required to be in the proportion 
of 2 to 1, that the shorter would make two vibrations 
to one of the longer, and that the vibrations would 
exactly coincide in that relation as long as both chords 
should continue in motion. Again with respect to 
the forms of bodies, when we prefer that of a sphere 
to one less regular, we never attend to the properties 
of a sphere, but reason will demonstrate a perfection 
in that figure which is not to be found in an irregular 
polygon. 

In the second chapter of his second book he de- 
scribes an instrument or diagram called the Helicon, 
invented as it should seem by himself, for demon- 
strating the consonances, so simple in its construction 
that its very figure seems to speak for itself, and to 
render a verbal explanation, though he has given a 
very long one of it, unnecessary. It is of this form : — 




X. 



\ l.|N 






K 


M 




""--,, 




F 
o 





C G II D E 

The side of the square A 12 shews the diapason : 
the half of B D, that is to say B F or F D 6 the unison. 
The line G M 8, terminated by the diagonal B 0, the 
diatessaron. The line E K divides the quadrangle 
equally, and H K 9, terminated by the line A F, 
shews the diapente. The lines L G and E H are in 
the ratio of 4 to 3, which is that of the diatessaron ; 
and lastly the lines H K 9 and G M 8 shew the ses- 
quioctave tone. 

To this diagram Ptolemy has added another not 
less easy to be comprehended than the former, in 
which the lines B D, N H, L G, and A C, are supposed 
to be chords of equal lengths but bisected by the line 
A F in the direction A E : this line may be supposed 
to be a bridge, or subductorium, stopping the four 
chords at A K M F, and thereby giving the pro- 
portions 12 9 8 6 ; which proportions will also re- 
sult from a subductorium placed in the direction X E, 
for X C will be duple of D, and the two inter- 
mediate chords sesquialtera and sesquitertia, and with 
respect to each other, sesquioctave ; in all agreeing 
with the ratios in the former diagram. 

In the ninth chapter of book II. Ptolemy takes 
occasion to say that there are only seven tones or 
modes, for that there are but seven species of dia- 
pason ; a position that wall be easily granted him by 
the moderns who suppose the word, tone or mode, 
when applied to sound, to answer to what we term 
the key or fundamental note. What he says farther 
concerning the modes has already been mentioned in 
a preceding chapter of this book. 

Chapter xii. the same author speaks of the mono- 
chord ; and here he proposes, but not for the purpose 



of experiments, a different method of dividing it, not, 
says he, according to one tone or mode only, but ac- 
cording to all the tones together ; by which one 
would imagine he meant somewhat like a tempera- 
ment of its imperfections, and a design to render it 
an instrument not of speculation but practice ; and 
indeed besides exhibiting it in a form more adapted 
to practice, and more resembling a musical instru- 
ment than its primitive one : — * 





He speaks, though not very intelligibly, of the 
manner of performing on it, and recommends, to con- 
ceal its defects, the conjunction with it, either of 
a pipe or the voice. A little after, he speaks of 
Didymus a musician, who endeavoured to correct this 
instrument by a different application of the magades ; 
but for the greater imperfections he says Didymus 
was not able to find out a cure. Towards the close 
of this second book he exhibits a short scheme of the 
three genera, according to five musicians, namely, 
Archytas, Aristoxenus, Eratosthenes, the same Didy- 
mus, and himself; and a little farther on, tables 
of the section of the canon in all the seven modes 
according to the several genera. 

In the third book chap. iv. he speaks in general of 
the faculty of harmony, and of mathematical reasoning 
as applied to it ; the use whereof he says is to con- 
template and adjust the ratios. In the next ensuing 
chapter he proceeds, in the manner of Quintilian, to 
state the analogy of music with the affections of the 
human mind, the system of the universe, and in short 
with every other subject in which number, proportion, 
or coincidence are concerned. In the course of this 
his reasoning, he mentions that Pythagoras advised 
his disciples at their rising in the morning to use 
music, whereby that perturbation which is apt to 
affect the mind at the awakening from sleep, might 
be prevented, and the mind be reduced to its wonted 
state of composure : besides which he says, that it 
seems the Gods themselves are to be invoked with 
hymns and melody, such as that of flutes or Egyptian 
trigons, to shew that we invite them to hear and be 
propitious to our prayers. 

Upon a very careful review of this work of Ptolemy, 
it will appear that the doctrines contained in it, so 
far as they are capable of being rendered intelligible, 
are of singular use in the determination of ratios, and 
his very accurate division of the monochord carries 
demonstration with it. It was doubtless for this 
reason that our countryman Dr. Wallis, a man to 
whom the learned world are under high obligations, 
undertook the publication of it from a manuscript in 
the Bodleian library, in ihe original Greek, with a 
Latin translation of his own, together with copious 
notes, and an appendix by way of commentary, 

* There is very little doubt but that the instrument here delineate^ 
is the pandura of the Arabians, mentioned in a note of Meibomius on 
a passage in Nicomachus, for among the Arabian and Turkish instriv 
ments described bv Mersennus are many in this form. 



3hap. XIX. 



AND PRACTICE OF MUSIC 



87 



which the Doctor was the better qualified to give, as 
it abundantly appears, as well by divers other of his 
writings in the Philosophical Transactions, as the 
work we are now speaking of, that he was very pro- 
foundly skilled in the science of music. How far 
he is to be depended on when he undertakes to 
render the ancient modes in modern characters seems 
very questionable, for were the Doctor's opinion 
right in that matter, all that controversy which has 
subsisted for these many centuries, not only touching 
the specific differences between them, but even as to 
their number, must necessarily have ended ages ago ; 
whereas, even at this day, the ablest writers on the 
subject do not hesitate at saying that the doctrine of 
the modes is absolutely inscrutable ; and perhaps it 
is for this reason only that so many have imagined 
that with them we have lost the most valuable part 
of the art ; but on the contrary it is worth remarking 
that the Doctor, though he was perhaps the ablest 
geometer of his time, and had all the prejudices in 
favour of the ancients that a man conversant with the 
best of their writers could be supposed to entertain, 
never intimates any such matter ; nay, so far is he 
from adjudging a preference to the ancient music 
over that of the moderns, that he scruples not to 
ascribe the relations that are given of the effects of 
the former to the ignorance of mankind in the earlier 
ages, the want of refinement, the charms of novelty, 
and other probable causes. Dr. Wallis gave two 
editions of this work of Ptolemy, the one published 
in quarto at Oxford in 1682 ; another, as also the 
commentary of Porphyry, and a treatise of Manuel 
Bryennius, makes part of the third volume of his 
works, published in three volumes in folio, 1699. 

Censorinus, a most famous grammarian, lived at 
Rome about a.c. 238,* and wrote a book entitled De 
Die Natali. It was published by Erycius Puteanus, 
at Louvain, in 1628, who styles it Doctrinae rarioris 
Thesaurus ; and it is by others also much celebrated 
for the great light it has thrown on learning. It is 
a very small work, consisting of only twenty-four 
chapters ; the tenth is concerning music ; and the 
subsequent chapters, as far as the thirteenth inclusive, 
relate to the same subject. 

He professes to relate things not known even to 
musicians themselves. He defines music to be the 
science of well modulating, and to consist in the voice 
or sound. He says that sound is emitted at one time 
graver, at others acuter; that all simple sounds, in 
what manner soever emitted, are called phthongoi; 
and the difference, whereby one sound is either more 
grave or more acute than another, is called diastema. 

The rest of his discourse on music is here given in 
his own words : — ' Many diastemata may be placed 
* in order between the lowest and the highest sound, 
' some whereof are greater, as the tone, and others 
' less, as the hemitone ; or a diastem may consist of 
' two, three, or more tones. To produce concordant 
' effects, sounds are not joined together capriciously, 
' but according to rule. Symphony is a sweet concent 
' of sounds. The simple or primitive symphonies 
' are three, of which the rest consist ; the first, having 

» Fabricius. Biblioth. Lat. torn. I. pag. 537. 



a diastem of two tones, and a hemitone, is called a 
diatessaron ; the second, containing three tones and 
a hemitone, is called a diapente ; the third is the 
diapason, and consists of the two former, for it is 
constituted either of six tones, as Aristoxenus and 
other musicians assert, or of five tones and two 
hemitones, as Pythagoras and the geometricians say, 
who demonstrate that two hemitones do not com- 
plete the tone ; wherefore this interval, improperly 
called by Plato a hemitone, is truly and properly a 
diesis or limma. 

' But to make it appear that sounds, which are 
neither sensible to the eyes, nor to the touch or 
feeling, have measures, I shall relate the wonderful 
comment of Pythagoras, who, by searching into the 
secrets of nature, found that the sounds of the 
musicians agreed to the ratio of numbers ; for he 
distended chords equally thick and equally long, by 
different weights, these being frequently struck, and 
their sounds not proving concordant, he changed 
the weights ; and having frequently tried them one 
after another, he at length discovered that two 
chords struck together produced a diatessaron ; 
when their weights being compared together, bore 
the same ratio to each other as three does to four, 
which the Greeks call i-KirpiTOQ, epitritos, and the 
Latins supertertium. He at the same time found 
that the symphony, which they call diapente, was 
produced when the weights were in a sesquialtera 
proportion, namely, that of 2 to 3, which they called 
hemiolium. But when one of the chords was 
stretched with a weight duple to that of the other, 
it sounded a diapason. 

' He also tried if these proportions would answer 
in the tibiae, and found that they did ; for he pre- 
pared four tibiae of equal cavity or bore, but unequal 
in length ; for example, the first was six inches 
long, the second eight, the third nine, and the 
fourth twelve ; these being blown into, and each 
compared with the others, he found that the first 
and second produced the symphony of the diates- 
saron, the first and third a diapente, and the first 
and fourth the diapason : but there was the difference 
between the nature of the chords and that of the 
tibiae, that the tibiae became graver in proportion 
to the increase of their lengths, while the chords 
became acuter by an additional augmentation of 
their weights ; the proportion however was the 
same each way. 

' These things being explained, though perhaps 
obscurely, yet as clearly as I was able, I return to 
shew M^hat Pythagoras thought concerning the 
number of the days appertaining to the partus. First, 
he says there are in general two kinds of birth, the 
one lesser, of seven months, which comes forth from 

the womb on the two hundred and tenth day after 
conception ; the other greater, of nine months, which 
is delivered on the two hundred and seventy-fourth 

day.' Censorinus then goes on to relate from Plato 
that in the work of conception there are four periods, 
the first of six days, the second of eight, which two 
numbers are the ratio of the diatessaron ; the third 
of nine, which answers to the diapente, and the 



88 



HISTORY OF THE SCIENCE 



Book II 



fourth, at the end whereof the foetus is formed, of 
twelve, answering to the diapason in duple propor- 
tion. After this he proceeds to declare the relations 
of the above numbers in these words : — 

' These four numbers, six, eight, nine, and twelve, 
' being added together, make up thirty -live ; nor is 
' the number six undeservedly deemed to relate to 

* the birth, for the Greeks call it reXeioc, teleios, and 
' we perfectum, because its three parts, a sixth, 

* a third, and a half, that is one, two, three, make up 
' itself ; but as the first stage in the conception is 
' completed in this number six, so the former number 
' thirty-five being multiplied by this latter six, the 
' product is two hundred and ten, which is the 

* number of days required to maturate the first 
' kind of birth. As to the other or greater kind, 
' it is contained under a greater number, namely, 
' seven, as indeed is also the whole of human life, 

* as Solon writes : the practice of the Jews, and the 
' ritual books of the Etruscans, seem likewise to 
' indicate the predominancy of the number seven 
' over the life of man ; and Hippocrates, and other 
' physicians, in the diseases of the body account the 
•' seventh as a critical day ; therefore as the origin of 
' the other birth is six days, so that of this greater 
' birth is seven ; and as in the former the members 
' of the infant are formed in thirty-five days, so here 

* it is done in almost forty, and for this reason, forty 

* days are a period very remarkable ; for instance, 

* a pregnant woman did not go into the temple till 

* after the fortieth day ; after the birth women are 
' indisposed for forty days ; infants for the most part 
' are in a morbid state for forty days ; these forty 
' days, multiplied by the seven initial ones, make 
' two hundred and eighty, or forty weeks : but 
' because the birth comes forth on the first day of 
' the fortieth week, six days are to be subtracted, 

* which reduces the number of days to two hundred 
' and seventy-four, which number very exactly cor- 
' responds to the quadrangular aspect of the Chal- 
' deans ; for as the sun passes through the zodiac 
' in three hundred and sixty-five days and some 

* hours ; if the fourth part of this number, namely, 
' ninety-one days and some hours, be deducted there- 
' from, the remainder will be somewhat short of two 
' hundred and seventy-five days, by which time the 

* sun will arrive at that place where the quadrature 
' has an aspect to the beginning of conception. But 
' let no man wonder how the human mind is able to 
' discover the secrets of human nature in this respect, 
' for the frequent experience of physicians enables 
' them to do it. 

' It is not to be doubted but that music has an 
' effect on our birth ; for whether it consists in the 
' voice or sound only, as Socrates asserts, or, as 

* Aristoxenus says, in the voice and the motion of 

* the body, or of both these and the emotion of 
' the mind, as Theophrastus thinks, it has certainly 
' somewhat in it of divine, and has a great influence 
'on the mind. If it had not been grateful to the 
' immortal Gods, scenical games would never have 

* been _ instituted to appease them ; neither would 
' the tibiiB accompany our supplications in the holy 



' temples. Triumphs would not have been celebrated 
' with the tibia ; the cithara or lyre would not have 
' been attributed to Apollo, nor the tibia, nor the 
' rest of that kind of instruments to the Muses ; 
' neither would it have been permitted to those who 
' play on the tibia, by whom the deities are appeased, 
' to exhibit public shows or plays, and to eat in the 

* Capitol, or during the lesser Quinquatria,* that 
' is on the ides of June ; to range about the city, 
' drunk, and disguised in what garments they pleased, 
' Human minds, and those that are divine, though 
' Epicurus cries , out against it, acknowledge their 
' nature by songs. Lastly, symphony is made use 
' of by the commanders of ships to encourage the 
' sailors, aud enable them to bear up under the 
' labours and dangers of a voyage ; and while the 
' legions are engaged in battle the fear of death is 

* dispelled by the trumpet ; wherefore Pythagoras, 
' that he might imbue his soul with its own divinity, 
' before he went to sleep and after he awaked was 
' accustomed, as is reported, to sing to the cithara ; 
' and Asclepiades the physician relieved the dis- 
' turbed minds of frenetics by symphony. Etophilus, 
' a physician also, says that the pulses of the veins 
' are moved by musical rhythmi ; so that both the 
' body and the mind are subject to the power of 
' harmony, and doubtless music is not a stranger 

* at our birth, 

' To these things we may add what Pythagoras 
' taught, namely, that this whole world was con- 

* structed according to musical ratio, and that the 
' seven planets which move between the heavens and 
' the earth, and predominate at the birth of mortals, 
' have a rythmical motion and distances adapted to 
' musical intervals, and emit sounds, every one dif- 
' ferent in proportion to its height, which sounds are 
' so concordant as to produce a most sweet melody, 
' though inaudible to us by reason of the greatness 
' of the sounds, which the narrow passages of our 
' ears are not capable of admitting.' Then follows 
the passage declaring the Pythagorean estimate of 
the distances of the planets and their supposed 
harmonical ratio, herein-before cited from him.f 

Censorinus concludes his Discourse on Music with 
saying that Pythagoras compared many other things 
which musicians treat of to the other stars, and de- 
monstrated that the whole world is constituted in 
harmony. Agreealdy to this he says Dorylaus writes 
that this world is the instrument of God : and others, 
that as there are seven wandering planets, which have 
regular motions, they may fitly be resembled to a 
dance. I 

» A feast in honour of Minerva. 
+ See it in page 65, with a diagram. 

t The general opinion of the learned in former ages, touching the 
harmony of tlie spheres, has been mentioned in a preceding page, but 
there appears a disposition in the modern philosophers to revive the 
notion. It seems that Dr. Gregory thought it well founded ; and 
Mr. Maclaurin, in conformity with his opinion, Phil. Discov. of 
Newton, pag. 35, explains it thus: — 'If we should suppose musical 
'chords extended from the sun to each planet; that all these chords 
' might become unison, it would be requisite to encrease or diminish 
' their tensions in the same proportions as would be sufficient to render 
' the gravities of the planets equal ; and from the similitude of these 
' proportions the celebrated doctrine of the harmony of the spheres 
'is supposed to have been derived.' 

The author of a book lately published, entitled Principles and Powei 
of Harmony, has added his suffrage in support of the opinion. ' Certain, 



Chap. XIX. 



AND PRACTICE OF MUSIC. 



89 



PoRPHYRius, a very learned Greek philosopher, of 
the Platonic sect, and who wrote a commentary on the 
Harmonics of Ptolemy, lived about the end of the 
third centm-y. His preceptors in philosophy were 
Plotinus and Amolius ; he was a bitter enemy to the 
Christian religion, which perhaps is the reason why 
St. Jerome will have him to be a Jew ; but Eunapius 
affirms that he was a native of Tyre, and that his true 
name was Malchus, which in the Syrian language 
signifies a king ; and that Longinus the Sophist, who 
taught him rhetoric, gave him the name of Porphyrins, 
in allusion to the purple usually worn by kings. 
Besides the commentary on Ptolemy he wrote the 
lives of divers philosophers, of which only a frag- 
ment, containing the life of Pythagoras, is now 
remaining ; a treatise of abstinence from flesh, an 
explication of the categories of Aristotle, and a trea- 
tise, containing fifteen books, against the Christian 
religion, which he once professed, as St. Augustine, 
Socrates, and others assert : this latter was answered 
by Methodius, bishop of Tyre, and afterwards by 
Eusebius. He died about the end of the reign of 
Dioclesian, and in 388 his books were burned. 

With regard to his commentary, it is evidently 
imperfect; for whereas the treatise of Ptolemy, is 
divided into three books, the second whereof contains 
fifteen chapters. Porphyry's commentary is continued 
no farther than to the end of chapter seven of that 
book, concluding with the series of sounds through 
each of the three genera. He seems to have been 
a virulent opposer of the Aristoxeneans, and like his 
author adheres in general to the tenets of Pythagoras. 
Porphyry has given a description of the harmonic 
canon much more intelligible than that of Ptolemy, 
and has delineated it in the following form : — 




7\ 



A B 



E 



C D 



By which it appears that a chord A D, strained 
over the immoveable magades B and C, which are 
nothing more than two parallelograms, with a semi- 
circular arch at the top of each, together with a 
moveable bridge of the same form E, but somewhat 
higher, will be sufficient for the demonstration of the 
consonances, and this indeed is the "representation 
which Dr. Wallis in his notes on Ptolemy has thought 
proper to give of it. 

Dr, Wallis has contented himself with publishing 
a bare version of this author, without the addition of 

' says he, as this harmonic coincidence is now become, till Sir Isaac 
' Newton demonstrated the laws of gravitation in relation to the planets, 
' it must have passed for the dream of an Utopian philosopher.' Pag. 146 
The same author, pag. 145, agreeably to what Censorinus above asserts, 
says that ' there are traces of the harmonic principle scattered up and 
' down, sufficient to make us look on it as one of the great and reigning 
' principles of the inanimate world.' Some of these have hereinbefore 
been pointed out. Vide pag. 65, in note. To the instances there men- 
tioned, the following may not imjjroperly be added. The web of a spider 
formed of threads is of an hexaiigular figure, and each of the threads 
that divide the whole into six triangles, may be considered as a beam 
intended to give firmness and stability to the fabric ; from one to the 
other of tiiese beams the insect conducts lines in a parallel direction, 
which, supposing them to be ten in number, do, in consequence of their 
different lengths, constitute a perfect decachord. Kircher, who made 
this discovery, says, that were these lines or chords capable of sustaining 
a force sulhcient to make them vibrate, it must necessarily follow from 
the ratios of tht-lr lengths, that between the sound of the outer and the 
innermost, the interval would be a diapason and semidiione ; and that 
the rest of the chords, in proportion to their lengths, would produce the 
other consonances. Musurg. torn. I. pag. 441. 



notes, except a few such short ones as he thought 
necessary to correct a vicious reading, or explain a 
difficult passage. 

The works of the several authors above-named 
declare very fully the ancient Greek theory ; their 
practice may in a great measure be judged of from 
the forms of the ancient instruments, and of these it 
may be thought necessary in this place to give some 
account. 

The general division of musical instruments is into 
three classes, the pulsatile, tensile, and inflatile ; and 
to this purpose Cardinal Bellarmine, in his Exposition 
of the OLth psalm, verse 3, says : ' Tria sunt instru- 
' mentorum genera, vox, flatus, et pulsus ; omnium 

* meminit hoc loco propheta.' 

Of the first are the drum, the sistrum, and bells. 
Of the second, the lute, the harp, the clavicymbalum, 
and viols of all kinds. Of the third are the trumpet, 
flutes, and pipes, whether single or collected together, 
as in the organ. 

And Kircher, in his Musurgia, preface to book VI., 
has this passage : — ' Omnia instrumenta musica ad 

* tria genera, ut plurium revocantur : Prioris generis 
' dicuntur ey^op^a sive evraTa., quae nervis, seu 
' chordis constant quaeque plectris, aut digitis in har- 
' monicos motus incitantur, ut sunt Testudines, 
' Psalteria, Lyrae, Sambucae, Pandorae, Barbita, 
' Nablia, Pectides, Clavicymbala, aliaque hujus 

* generis innumera. Secundi generis sunt efK^vawfieim, 
' wvsvfxariKa, vel ejXTrvEHQa, quae inflata, seu spiritu, 

* incitata sonum edunt ut Fistulae, Tibiae, Cornua, 
' Litui, Tubae, Buccinae, Classica. Tertii generis 
' sunt KpHQa, sive pulsatilia uti sunt Tympana, Sistra, 
' Cymbala, Campanse, &c.' 

This division is adopted by a late writer, Fran- 
ciscus Blanchinus of Verona, in a very learned and 
curious dissertation on the musical instruments of the 
ancients ; * which upon the authority of ancient 
medals, intaglias, bass-reliefs, and other sculptures of 
great antiquity, exhibits the forms of a great variety 
of musical instruments in use among the ancient 
Greeks and Romans, many whereof are mentioned, 
or alluded to, by the Latin poets, in such terms as 
contain little less than a precise designation of their 
respective forms. He has deviated a little from the 
order prescribed by the above division of musical 
instruments into classes, by beginning with the 
inflatile species instead of the tensile ; nevertheless 
his dissertation is very curious and satisfactory, and 
contains in it a detail to the fol- Fig. i. rig. 2. 

lowing effect : — 

One of the most simple musical 
instruments of the ancients is the 
Calamus pastoralis, made of an 
oaten reed ; it is mentioned by 
Virgil and many others of the 
Latin poets, and by Martianus Ca- 
pella. See the form of it fig. 1. 

Other writers mention an instru- 
ment of very great antiquity by the 
name of Ossea tibia, a pipe made 



of the leg-bone of a crane. 



Fig. 2. 




* De tribus Generibus Instrumentorum Musicae veterum Organic^, 
Dissertatio ; Roma;, 1742. 



90 



HISTORY OF THE SCIENCE 



Book II. 



The Syringa or pipe of Pan is 
described by Virgil, and the use of it 
by Lucretius, lib. V. 

Et supra calamos unco percurrere labro. 
The figure of it occurs so frequently 
on medals, that a particular description 
of it is unnecessary. Fig. 3. 

The Tibife pares, mentioned by 
Terence to have been played on, 
the one with the right, and the other 
with the left hand, are diversely 
represented in Mersennus De In- 
Btrumentis harmonicis, pag. 7, and 
in the Dissertation of Blanchinus 
now citing ; in the former they 
are yoked together towards the 
bottom, and at the top, as fig. 4. 
In the latter they are much slen- 
derer, and are not joined. Fig. 5.* 




The ancient Buccina or horn-trumpet, fig. 10, is 
mentioned by Ovid, Vegetius, Macrobius, and others. 



Kg. 10. 




The author last men- 
tioned speaks also of 
other pipes, namely, 
the Tibiae bifores, fig. 
6, the Tibiae gemine, 
fig. 7, instruments used 
in theatrical repre- 
sentations ; the latter 
of these seem to be 
the Tibiae imparos of 
Terence : he also de- 
scribes the Tibife utri- 
culari^, or bag-pipes, 
fig. 8, anciently the entertainment of shepherds and 
other rustics. 

The Horn, fig. 9, was anciently used at funeral 
solemnities ; it is alluded to by Statins. Theb. lib. VI. 

Fig. 8. Fig. 9. 





* The tibiae of the ancients, and especially those mentioned in the 
titles of Terence's comedies, have been the subject of much learned 
enquiry. Caspar Bartholinus the anatomist has written a whole volume 
l)e Tibiis Veterum. jElius lionatus, a Latin f^rammarian, and the 
preceptor of St. Jerome, says that the tone of the tibiae dextra; was 
grave, and adapted to the serious parts of the comedy : and that that of 
the tibiae sinistrse, and also of the tibiae sarranse, or Tyrian pipes, was 
light and cheerful. ' Dextra tibiae sua gravitate seriam comedeE dic- 
' tinnem pronunciabant. Sinistrae et sarranae hoc est Tyriae acuminis 
' suavitate jocum in comedia ostendebant. Ubi aiitem dextra et sinistra 
' acta fabula inscribebatur mistira jocos et gravitatem denunciabnt.' 
Donat. Frasm. de Traged. & Corned. The abbe du Bos says that this 
passage explains that other in Pliny, where it is said that the ancients 
to make left-handed pipes, took the bottom of that very reed, the top 
whereof they had before used for the right-handed. The sense of this 
passage is manifest ; but it does not strictly agree with what Donatus 
gays, unless it can be supposed that, contrary to the order of nature, the 
reeds were small at bottom, and grew tapering upwards. 




The Tuba communis, seu recta, so called in con- 
tradistinction to the Tuba ductilis, is of very ancient 
original ; it was formerly, as now, made of silver or 
brass, of the form fig, 11. Blanchinus hesitates not to 

Fig. u. 




Fig. 12. 



Fig. 13. 



assert that the two trumpets of silver which God 
commanded Moses to make in the wilderness were of 
this form.f It seems that the trumpet has retained 
this figure without the least external diversity, so low 
down as the year 1520 ; for in a very curious picture 
at Windsor, supposed to be of Mabuse, representing 
the interview between Ardres and Guisnes, of Henry 
VIII. and Francis I. are trumpets precisely cor- 
responding in figure with the Tuba recta above 
referred to. 

Of the instruments of the second class, compre- 
hending the tensile species, the Monochord is the 
most simple. This instrument is mentioned by 
Aristides Quintilianus, and other ancient WTiters, but 
we have no authentic designation of it prior to the 
time of Ptolemy, it nevertheless is capable of so 
many forms, that any instrument of one string only 
answers to the name ; for which reason some have 
not scrupled to represent the monochord like the bow 
of Diana. 

Figures 12 and 
13, are the Lyre 
of three and four 
chords, ascribed to 
Mercury, by Ni- 
comachus, Macro- 
bins, Boetius, and 
a number of other 
writers, the forms 
whereof are here 
given from ancient 
sculptures in and 

about Rome, 
referred to 
by Blanchi- 
nus ; as are 
also those 
figures 14 
and 15, repre- 
senting the 
one a Lyre 
with seven 
chords, and 
the other one 
with nine. 

t ' Make thee two trumpets of silver ; of a whole piece shalt thou 
' make them, that thou mayest use them for the calling of the assembly, 
' and for the journeying of the camps. Numbers, chap. x. verse 2. 




Chap. XIX. 



AND PRACTICE OF MUSIC. 



91 



Fig. 16 is the Lyre of Amphion, 
and 17 the plectrum, with which 
not only this, but every species 

Fig. 16. Fig. 17. 



Fig. 18. 



Fig. 21. 



Fig. 22. 






of the lyre was struck, as may be collected from the 

following passage in Ovid : — 

Instructamque fidem gemmis et dentibus Tndis 
Sustinet a laeva : tenuit manus altera plectrum. 
Artificis status ipse fuit, turn stamina docto 
Pollice soUicitat : quorum dulcedine captus 
Pana iubet Tmolus citherse submittere cannus. 

Met. lib. xi. 1. 167.* 

Figures 19 and 20 are other forms of the Lyre in 
a state of improvement. 

Fig. 19. Fig. 20. 





♦ It is very probable that the use of the bow, with which the viol 
Bpeeies of instruments is sounded, was borrowed from a practice of the 
ancients. Of the many kinds of lyre among them, it seems that they 
had one, in which the fingers of one hand were employed in stopping 
the strings, at the instant that they were striokeq with a stick held in 
the other. 

Virgil intimates a practice somewhat like this in the following passage 
of Uie jEneid:— 

Nee non Threicus longa cum veste sacerdos 
Obloquitur numeris septem discrimina vocum : 
Jamque eadem digitis, jam pectine pulsat ebumo. 

Lib. VI. 1. 645. 
The Thracian bard, surrounded by the rest, 
There stands conspicuous in his flowing vest, 
His flying fingers, and harmonious quill. 
Strike sev'n distinguish'd notes, and sev'n at once they fill. 

Dryden's translation, book VI. 1. 877. 
From which it at least appears, that the instrument was placed in 
a horizontal position, and that the strings were struck, not by the fingers, 
but with a plectrum, which might be a quill or a bow, or almost any 
other thing fit for the purpose. 

Plato, in his treatise de Legibus VII. 794. Ed. Serr. advises to train 
up children to use the right and the left hand indifferently. In some 
things, says he, we can do it very well, as when we use the lyre with the 
left hand and the stick with the right. Dr. Jortin says it may be col- 
lected from this, that the fingers <if the left hand were occupied in some 
manner upon the strings, el.se barely to tiold a lyre shewed no very free 
use of the left hand; and it appears from Ptolemy. II. 12, that they 
used both hands at once in playing upon the lyre, and that the fingers of 
the left were employed, not in stopping, but in striking the string. 
But see the figure of an ancient statue, representing Apollo playing on 



Figures 21, 22, 
are two different 
representations of 
the Lyra triplex, 
the one from Blan- 
chinus, the other 
from a writer of 
far less respect- 
able authority ; 
concerning this in- 
strument it is ne- 
cessary to be some - 
what particular. 

Athenaeus lib. 
VIV. cap. XV. de- 
scribes an instrument of a very singular construction, 
being a lyre in the form of a tripod, an invention, as 
it is said, of Pythagoras Zacynthius. This person is 
mentioned by Aristoxenus, in his Elements, page 36 ; 
and Meibomius, in a note on the passage, says, on the 
authority of Diogenes Laertius, that he was the 
author of Arcana Philosophise, and adds, that it was 
from him that the proverbial saying, ipse dixit, had 
its rise ; with respect to the instrument, it is ex- 
hibited, in two forms (see above), the first taken from 
a sarcophagus at Rome, referred to by Blanchinus, 
the other from an engraving in the Histoire de la 
Musique, of Monsieur de Blainville, for which it is to 
be suspected he had no other authority than the bare 
verbal description of Athenseus, who has said, that it 
comprehended three distinct sets of chords, adjusted to 
the three most ancient of the modes, the Dorian, the 
Phrygian, and the Lydian. 

The Trigon, an instrument mentioned by Nicho- 
machus, among those which were adjusted by Pytha- 
goras, after he had di.- covered and 
settled the ratios of the consonances. 
It was used at feasts, and it is said, 
was played on by women, and struck 
either with a quill, or beaten with 
little rods of different lengths and 
weights, to occasion a diversity in the 
sounds. The figure 23 is taken from 
an ancient Roman anaglyph, mentioned 
by Blanchinus. 
Figure 24 is also 
a Trigon, de- 
scribed by the 
same author ; 
figure 25 is the 
reverse of an an- 
cient medal, and 
shews the man- 
ner of playing 
on it. 

The Cymbals 

the lyre, fig. 18, which seems very clearly to evince the practice above 

spoken of. .,,,,- ^v i 

Upon this relic of antiquity, a drawing whereof was found m the col- 
Icclion of the late Mr. N. Haym, it is observable that the lyre is of a form 
verv marly resembling the violin, as having a body, and also a neck, 
which is held in the left hand ; the instrument in the right, undoubtedly 
answers to the modern bow, with this difference, that its use was per- 
cussion and not friction, which latter is a modern and noble improve- 
ment ; the position of the instrument deserves to be remarked, as it 
corresponds exactly with the viol di braccio. 



Fig. 23. 




Fig. 24. 



Fig. 25. 




92 



HISTORY OF THE SCIENCE. 



Book XL 




Fig. 27. 




Fig. 29. 



of Bacchus, figure 26, were two ^'&- se- 

aman brass vessels, somewhat in 
the form of a shield, which being 
struck together by the hands, gave 
a sound. The well-known statue 
of the dancing faun has one of 
these in each hand. 

The Tympanum leve, 
figure 27, an instrument yet 
known by the name of the ' 
Tambouret, and frequently 
used in dancing, was also used 
to sing to ; it is distinguished 
by Catullus, Ovid, Suetonius, 
St. Augustine, and Isidore, 
of Sevil, from the great brazen drum, properly so 
called, this above-mentioned, was covered with the 
skin of some animal, and was struck either with a 
short twig or with Fig. 2s. 
the hand, as fig. 28. 

Crotala, figure 29. 
These were instru- 
ments also of the 
pulsatile kind. The 
Crotalum was made 
of a reed, divided 
into two by a slit 
from the top, ex- 
tending half way 
downwards : the sides 
thus divided being 
struck one against 
the other with dif-' 
ferent motions of the hands, produced M 
a sound like that which the stork ^ 
makes with her bill, wherefore the 
ancients gave that bird the epithet of Crotalistria, i.e., 
Player upon the Crotalum ;* and Aristophanes calls 
a great talker a Crotalum. 

* Pausanias relates, that Hercules did not kill the Stymphalides with 
his arrows, but that he frighted, and drove them away with the noise of 
the crotala, the consequence whereof, supposing the relation to be true, 
is, that the crotalum must be a very ancient instrument. Ovid joins the 
crotalum with the cymbals. 

Cymbala cum crotalis prurientiaque arma Priapo 
Ponit, et adduclt tympana pulsa manu. 

It appears by an ancient poem, entitled Copa, by some ascribed to 
Virgil, that those who played with the crotala danced at the same time. 
It farther appears, that in these dances, which were chietly of women, 




S. 31. 



such a variety of 
wanton gesticu- 
lations and in- 
decent attitudes 
and postures 
were practised, 
that Clemens Al- 
exandrinus says, 
that the use of 
these instru- 
ments ought to 
be banished from 
the festivals of all 
Christians. And 
the same might 
have been said 
of the cymbals. 
See figures 30 
and 31. 

Some authors 

resemble the cmtala to the castanets of the Spaniards, or perhaps of the 
Moors; for castanets are supposed to be of Moorish invention ; but of 
these the crumata of the ancients seem more nearly to approach. These 
were made of bones, or the shells of fish. Scaliger observes, upon the 
above-mentioned poem, that they were very common among the Spaniards, 




Mention is made by some writers on music, of an 
instrument of forty chords, called, from the name of 
its inventor, the Epigonium. Epigonius was a 
native of Ambracia, a city of Epirus, and a citizen of 
Sicyon, a town of Peloponnesus. He is mentioned 
together with Lasus Hermionensis, by Aristoxenus, 
in his Elements, pag. 3. And Porphyry makes him 
the head of one of those many sects of musicians that 
formerly subsisted, giving him the priority even of 
Aristoxenus, in these words : — ' There were many 
' sects, some indeed before Aristoxenus, as the Epi- 
' gonians, Damonians, Eratocleans, Agenorians, and 
' some others ; which he himself makes mention of ; 
' but there were some after him, which others have 
' described, as the Archestratians, Agonians, Philis- 
* cians, and Hermippians.' 

Julius Pollux, in his Onomasticum, lib. IV. cap. ix. 
speaking of the instruments invented by certain 
nations, says, that the Epigonium obtained its name 
from Epigonius, who was the first that struck the 
chords of musical instruments without a plectrum. "{■ 
The same author' adds, that the Epigonium had forty 
chords, as the Simicum had thirty-five. Athenajus, 
lib. IV. speaks to the same purpose. 

As to the Simicum, nothing more is known about 
it, than that it contained thirty-five chords. Vincentio 
Galilei, with good reason, supposes it to be somewhat 
more ancient than the Epigonium. Of both these 
instruments he has ventured to give a representation, 
in his dialogue on ancient and modern music ; but it 
is very much to be doubted, whether he had any 
authority from antiquity for so doing. The form 
which he has assigned them severally, resembles 
nearly that of an upright harpsichord, which seems 
to indicate, that when played on, it was held between 
the legs of the musician, different perhaps from the 
harp, with the grave chords near and the acute re- 
mote from him. - 

The foregoing account comprehends the principal 
instruments in use among the ancient Greeks and 
Romans, so far as the researches of learned and in- 
quisitive men have succeeded in the attempts to re- 
cover them ; their forms seem to be thereby ascer- 
tained beyond the possibility of a doubt, and these it 
may be said, declare the state of the ancient musical 
practice, much more satisfactorily than all the hyper- 
bolical relations extant, of its efficacy and influence 
over the human passions ; and leave it an un- 

especially the inhabitants of the province of Bcetica [Andalusia} about 
Cadiz, to which Martial alludes. 

Nee de Gadibus improbis puella; 

Vibrahunt sine fine prurientes 

Lascivos docili tremore lumbos. Lib. V. epigr. Ixxix. 

The same poet elsewhere speaks of the crumata in these words : — 
Edere lascivos ad Bcetica crusmata gestus, 
Ed Gaditanis ludere docta modis. Lib. VI. epigr. Ixxi. 

From which two passages, it appears clearly, that the above censure 
of Clemens Alexandrinus was well grounded. 

+ Plutarch in his dialogue before cited, relates that Olympus intro- 
duced the plectrum into Greece, which it is supposed was then deemed 
a useful invention. Certainly the lyre was originally touched by the 
fingers, and all that can be meant here, is, that Epigonius recurred to 
the primitive method, and played on his instrument, as the harp is now 
played on with the fingers ; between which, and the touch of a plectrum 
or quill, the difference is very wide, as may be discovered by a com- 
parison of the lute or harp with the harpsichord. 



Chap. XIX.~BooK in, Chap. XX. AND PRACTICE OF MUSIC. 



93 



questionable fact, that the discovei'ies of Pytliagoras, were adapted, as would have disgraced any perform- 

and the improvements made by the Greeks, his ance, even in the least enlightened period, since the 

successors, terminated in a theory, admirable in invention of that species of harmony, which has been 

speculation it is true, but to which such instruments the delight of later ages. 



BOOK III. 

The gradual declension of learning which had 
begun before the time of Porphyry, the last of the 
Greek musical writers, and above all, the ravages of 
war, and the then embroiled state of the whole 
civilized world, put an end to all farther improve- 
ments in the science of harmonics ; nor do we find, 
that after this time it was made a subject of philo- 
sophical enquiry : the succeeding writers were chiefly 
Latins, who, as they were for the most part followers 
of the Greeks, contributed but very little to its ad- 
vancement ; and, for reasons which will hereafter be 
given, the cultivation of music became the care of tlie 
clergy ; an order of men, in whom the little of 
learning then left, in a few ages after the establish- 
ment of Christianity, centered. 

But before we proceed farther to trace the progress 
of the science, it is proper to remark, that the 
writings of the Greeks not only leave us in great 
uncertainty as to the state of music in other countries, 
but that they do not exclude the possibility of its 
having arrived at a great degree of perfection, even 
before that discovery of the consonances, which is by 
all of them allowed to be the very basis of the Greek 
system. For let it be remembered, that Pythagoras 
is supposed to have lived so late as a.m. 3384, 
which is about 560 years before the birth of Christ ; 
and that long before his time, such effects were 
ascribed to music, as well by the sacred as profane 
historians, as are utterly inconsistent with the sup- 
position, that it was then in its infancy. It were 
endless to enumerate the many passages in sacred 
writ, declaring the power of music : the story of 
David and Saul, and the effects attributed to the 
harp ; but more especially the frequent mention of 
instruments with ten strings, would lead us to think, 
that the art had arrived to a state of greater perfection 
than the writers above-mentioned suppose. Here 
then arises a question, the solution whereof is attended 
with great difficulty ; namely, whether the Jews, not 
to mention the various other nations, that had sub- 
sisted for many ages, previous to the times from 
whence we begin our account, in a state of very im- 
proved civilization, had not a musical theory ? or is 
it to be conceived, that mankind, with whose frame 
and structure, with whose organs and faculties, har- 
mony is shewn to be connatural, could remain for so 
many centuries in an almost total ignorance of its 
nature and principles ? 

To this it is answered, that the knowledge of the 
state and condition of past times, is deducible, with 
any degree of certainty, only from history ; that the 
information communicated by the means of writing, 
must depend on an infinite variety of circumstances, 
such as a disposition in men of ability to communicate 
that information which is derived from a long course 



CHAP. XX. 

of study, the permanency of language, a faithful and 
uncorrupt transmission of facts, and an absence of all 
those accidents, that in the course of events hinder 
the propagation of knowledge ; and wherever these 
fail, the progress of human intelligence must neces- 
sarily be intercepted. To obstructions arising from 
one or other of these causes, is to be imputed that 
impenetrable obscurity in which the events of the 
earlier ages lie involved ; an obscurity so intense, 
that no one presumes to trace the origin of any of the 
arts, and a vast chasm is supplied by the mythologists, 
the poets, and that species of history which we dis- 
tinguish from what is truly authentic and worthy of 
credit by the epithet of fabulous ; even antiquity 
itself, which stamps a value on some sort of evidence, 
will in many cases diminish the credit of an historian ; 
and mankind have not yet settled what degree of 
assent is due to the testimony of the most ancient of 
all profane historians, the venerable Herodotus. 

Admitting as a fact, that Egypt in the infancy of 
the world, was as well the seat of learning as of 
empire ; and admitting also the learning of the 
Persian Magi, the Indian Brachmans, and other peo- 
ple of the east, not to mention the Phoenicians and 
the Chinese, to be as great as some pretend, who 
have magnified it to a degree that exceeds the bounds 
of moderate credulity ; nevertheless, the more sober 
researchers into antiquity, have contented themselves 
with a retrospect limited by the time when philoso- 
phy began to flourish in Greece ; and it is only on 
the writers of that country that we can depend. 

An investigation of the Jewish theory would be 
a fruitless attempt, but of their practice we are en- 
abled to form some judgment, by the several passages 
in the Old Testament that declare the names and 
number of the Hebrew instruments, and mention the 
frequent use of them in sacrifices, and other religious 
solemnities ; but it is to be observed, that the cor- 
respondence of the names of their instruments, with 
the names of those in use in modern times, is a cir- 
cumstance from which no argument in their favour 
can be drawn, for a reason herein before given. 

Mersennus, and after him Kircher, whose elaborate 
researches into the more abstruse parts of ancient 
literature, render him in some particulars a re- 
spectable authority, have exhibited the forms of many 
of the ancient Jewish musical instruments : the 
latter of these authors professes to have gone to the 
fountain head for his intelligence ; and the result 
of an attentive perusal of as many of the Rab- 
binical writers and commentators on the Talmud 
as he could lay his hands on, he has given to the 
public in the Musurgia, torn. I. pag. 47. How 
far the authorities adduced by him will warrant 
such a precise designation of their respective forms, 



94 



HISTORY OF THE SCIENCE 



Book III. 



as verges in some instances too near our own times, 
is left to the decision of those who shall have cu- 
riosity enough to peruse them ; but lest it should 
be said that the subject is too important to be passed 
over in silence, the substance of what he has de- 
livered on this head is here given. 

He says that the author of a treatise entitled 
Schilte Haggiborim, i. e. the Shield of the Mighty, 
who he elsewhere makes to be Rabbi Hannase, treats 
very accurately on the musical instruments of the 
Hebrews, and reckons that they were thirty-six in 
number, and of the pulsatile kind, and that David 
was skilled in the use of them all. Kircher however 
does not seem to acquiesce altogether in the first of 
these opinions, for he proceeds to a description 
de instrumentis Hebreorum Polychordis sive Neghi- 
noth ; these it seems, according to his author above- 
named, were of wood, long and round, consisting 
of three strings made of the intestines of beasts ; 
the instruments had holes bored underneath them ; 
and, to make them sound, the strings were rul)bed 
with a bow composed of the hairs of a horse's tail, 
well extended and compacted together. Kircher 
speaks particularly of the Psaltery, or Nabliura, the 
Cythara, or, which is the same thing, the Assur, 
Nevel, Chinnor, the Machul, and the Minnin. He 
says that no one has rightly described the Psaltery 
of David, and that some have thought that the word 
rather denoted certain genera of harmony, or modu- 
lations of the voice, than any kind of instrument : 
that according to Josephus it had twelve sounds, 
and was played on with the fingers ; that Hilarius, 
Didymus, Basilius, and Euthymius call it the straitest 
of all musical instruments — that Augustine says 
it was carried in the hand of the player, and had 
a shell or concave piece of wood on it that caused 
the strings to resound — that Hieronymus describes 
this instrument as having ten strings, and resembling 
in its form a square shield — that Hilarus will have 
it to be the same with the Nablium. Kircher him- 
self is certain that it was a stringed instrument, and 
cites Suidas to prove that the word Psalterium is 
derived from Psallo, to strike the chords with the 
ends of the fingers. He farther says, that many 
writers suppose it to have had a triangular form, and 
to resemble the harp of David, as commonly painted 
in pictures of him ; and that some are express in the 
opinion that the Psalterium and the Nablium, as 
being struck with the fingers of both hands, were 
one and the same instrument ; and to this purpose 
he cites the following passage from Ovid : — 

Disce etiam duplici genialia Naulia palma 
Verrere : conveniunt dulcibus ilia modis. 

Art. Amat. lib. III. 1. 327. 

The Nevel, notwithstanding the resemblance be- 
tween its name and that of the Nablium, and the 
confusion which Kircher has created by using them 
promiscuously, clearly appears to have been a differ- 
ent instrument ; for he says it was in the form 
of a trapezium ; and the Nablium, which he has 
taken great pains to prove to be the same with the 
Psalterium, he shows to have been of a square form. 
Of the Assur, he onlv savs that it had ten chords; 



the Chinnor he supposes to have had thirty -two, the 
Machul six, and the Minnin three or four ; and 
that in their form they resembled, the one the Viol 
and the other the j,. ^^ 
Chelys. To give a 
clearer idea, he has 
exhibited, from an 
old book in the Va- 
tican library, several 
figures representing 
the Psalterium, 
figure 32; the Chin- 
nor, figure 33 ; the 
Machul. figure 34; the Minnin, fig. 35; and the 
Nevel, figure 36.* 

Fig. 35. 




Fig. 34. 



Fig. 36. 




Fig. 37. 



Kircher speaks 
also of another 
instrument men- 
tioned by Rabbi Hannase, who it seems was the 
author of the book before cited, Schilte Haggiborim, 
and also in the Targum, called Haghniugab, consisting 
of six strings, and resembling the greater Chelys or 
Viol di Gamba, differing from it only in the number 
of its chords : he says it is often confounded with the 
Machul. 

He next proceeds to treat of the pulsatile instru- 
ments of the Hebrews, in contradistinction to those 
of the fidicinal or 
stringed kind ; and 
first he speaks of 
the Thoph or Tym- 
panum, figure 37, 
an instrument of 
Egyptian original, 
and used by the 
priests of that country in their piiblic worship. He 
relates on the authority of Rabbi Hannase that it had 
the likeness of a ship ; and that by the Greeks it was 
also called Cymbalum, from cymba, a boat : he adds 
that it was covered with the skin of an animal, and 
was beat on with a pestle or rod of iron or brass. 

He proceeds to say that though the Machul is 
ranked among the fidicinal or stringed instruments, 
this name was given to an instrument of a very 
different form, and of the pulsatile kind ; nay, he 
adds that Rabbi Hannase asserts that it was precisely 
the same with the Sistrum of the Egyptians, or the 
Krousma of the Greeks ; and that it was of a circular 

* The truth of this representation, so far as it relates to the Machul 
and Minnin, is strongly to be suspected ; they both seem to require the 
aid of the hair bow, a kind of plectrum to which the ancients seem to 
have been absolute strangers. Besides their near resemblance to the 
lute and viol, instruments which it is supposed had their origin in 
Provence, is a strong argument against their antiquity. 




Chap. XX. 



AND PRACTICE OF MUSIC. 



95 





form, made of iron, brass, silver, or gold, with little 
bells hung round it. Kircher corrects this descrip- 
tion, and instead of little bells, supposes a number of 
iron rings, strung as it were on a rod or bar in a 
lateral position that went across the circle. Fig. ss. 
He says that a handle was affixed to it, by 
means whereof the instrument was flung 
backwards and forwards, and emitted a kind 
of melancholy murmur, arising from the 
collision of the rings, as well against each 
other as against the sides, the circle, and 
the bar on which they moved, figure 38. 
He adds, that the Thoph, or rather Sistrum 
of the Hebrews was thus 
constructed, and that the 
virgins every where made 
use of it in the dances of the 
Sistri, as we read in the 
books of Exodus and Judges, 
that Mary, the sister of 
Moses, and the daughter of Jephthf 
did : and he farther says, that 
according to accounts which he has 
received from credible witnesses, 
the Syrians in his time preserved 
the use of the Sistrum in Palestine.* 
Gnets Berusim was another of the 
Hebrew pulsatile instruments ; it 
seems by Kircher that there was some controversy about 
the form of it, but that Rabbi Hannase represents it 
as nothing more than a piece of fir in shape like a 
mortar. He says there belonged to it a pestle of the 
same wood, wath a knob at each end, and in the 
middle thereof a place for the hand to grasp it : that 
those that beat on the instrument held it in the left 
hand and struck with the Fig. 4o. 
right on the edge and in the ^'^^^i^%. Fig- -ii. 
middle, using the knobs alter- 
nately. Figures 40, 41. Kir- 
cher compares this instrument ^ 
to the Crotalum already de- 
scribed, but seemingly with little propriety ; and to 
the Gnaccari of the Italians, of which word, con- 
sidered as a technical term, it is hard to find the 
meaning. 

Minagnghinim was the name of another of the 
Hebrew pulsatile instruments, which, according to 
Rabbi Hannase, was a certain square Fig. 42. 
table of wood, having a handle so 
fitted as conveniently to be held by 
it. On the table were balls of wood 
or brass, through which was put either 
an iron chain or an hempen chord, 
and this was stretched from the bottom 
to the top of the table. When the 
instrument was shaken, the striking of 
the balls occasioned a very clear sound, 
which might be heard at a great dis- 
tance. See the representation which 
Kircher gives of it, figure 42. 

* The invention of the Sistrum is not to be ascribed to the Jews : 
it is generally supposed to be of Egyptian original. There are some 
fonn« of it, as that in particular, figure 39, which bears on it a figure 
of one of those many brute animals to which this superstitious and idol- 
atrous people paid divine honours. 




f j^^^.-wJF^-l^ — ^ 



Magraphe Tamid, another of the pulsatile instru- 
ments of the Hebrews, is conjectured by Kircher to 
have been used for convoking the priests and Levites 
together into the. temple : it is said to have emitted 
prodigious sound ; and though Rabbi Hannase says 
no one can describe the form of it, Kircher thinks it 
must have been like one of our largest bells. 

We are now to declare what instruments of the 
pneumatic kind were in use amongst the ancient 
Hebrews ; and. first we meet wath the Masrakitha, 
which consisted of pipes of various sizes, fitted into 
a kind of wooden chest, open at the top, but at the 
bottom stopped with wood covered with a skin ; 
by means of a pipe fixed to the chest, wind was 
conveyed into it from the lips : the pipes were 
of lengths propdi-tioned musically to each other, and 
the melody was varied at pleasure by the stopping 
and unstopping with the fingers the apertures at the 
upper extremity. *■ Kircher Fig. 43. 

thinks it differed but little 
from the instrument which 
Pan is constantly repre- 
sented as playing on ; there 
seems however to be a dif- 
ference in the manner of 
using it. See fig. 43: 

Of the Sampunia, derived, as Kircher conjectures, 
from the Greek Symphonia, as also of the preceding 
instrument, mention is made, as Kircher asserts, in 
the Chaldaic of the book of Daniel, chap. iii. He 
says also that it is described in the Schilte Haggi- 
borim, as consisting of a round belly, made of the 
skin of a ram or wether, into which two pipes 
were inserted, one to fill the belly with wind, the 
other to emit the sound ; the lower pipe had holes 
in it, and was played on by the fingers. In short, 
it seems to have been neither more nor less than the 
Cornamusa, or common bag-pipe ; and Kircher says 
that in Italy, even in his days, it was known by the 
name of the Zampugna. 

The Hebrews had also an instrument, described in 
the Schilte Haggiborim, called Macraphe d'Aruchin, 
consisting of several orders of pipes, which were 
supplied with wind by means of bellows ; it had 
keys, and would at this time without hesitation be 




called an organ. 



See fig. 



44.t 





t This instrument is delineated by Kircher, but the figure of it above 
referred to, is taken from the Musica Historica of Wolfgang Caspar 
Printz, written in the German language, and printed at Dresden in 4to. 
anno. 1690, who cites the Collectaneis Philologicis of Johannes Sehiitterus, 
to justify his deviations from Kircher, in the form of some of the instru- 
ments described in the Musurgia. But it is to be feared, that his author 
has erred in giving to the Machul and Minnin above described, the hair 
bow, of which not the least trace is to be found in the writings of any of 
the ancients. 



96 



HISTORY OF THE SCIENCE 



Book III. 



Of Fistulse it seems the 
Hebrews had sundry kinds ; 
they were chiefly the horns 
or bones of animals, straight or 
contorted, as nature fashioned 
them : the representations of 
sundry kinds of them, in 
figures 45, 46, 47, 48, are 
taken from Kircher. 

Fig. 47. 



Fig. 45. Fig. 46. 




Fig. 48. 





In the account which Blanchinus has given of the 
Jewish musical instruments, he mentions a mallet of 
wood used by them in their worship, and Fig. 49. 
which at certain times is beaten by the people ,r-^ 
on the beams, seats, and other parts of the 
synagogue, in commemoration of the tumult 
preceding the Crucifixion, or, as the modern 
Jews say, at the hanging of Haman, figure 49. 
Instruments of this kind, and which produce 
noise rather than sound, are improperly 
classed among instruments of music. 

Of the Hebrew musicians no very satisfactory 
account can be given. This of Kircher, extracted 
from the Rabbinical writers, is, perhaps, the best 
that can be expected : ' Asaph, according to the 
'opinion of the interpreters, was the composer of 
' certain psalms ; he is said also to have been a singer, 
* and to have sung to the cymbals of brass, and to 
' have praised the Lord, and ministred in the sight 
' of the ark. 

' Eman Ezraita, the singer, the son of Joel, of the 
' children of Caath, was most skilful in the cymbal, 
'and was in a manner equal in knowledge and 
' wisdom to Ethan ; he is the supposed author of the 
' Psalm, beginning Domine Deus salutis meaj, which, 
'because he gave it to be sung by the sons of Coreh, 
'he inscribed both with his own and their name. 

' Ethan of Ezrachus, the son of Assaia, the son 
'of Merari, played on the brass cymbal, and was 
'endued with so much vdsdom, that, according to 
' the Book of Kings, no mortal, except Solomon, was 
' wiser. The three sons of Coreh, Asir, Elcana, and 
' Abiasaph, were famous singers and composers of 
' Psalms.' 

' Idithus was an excellent singer, and player on 
'the cythara; many confound him with Orpheus.' 
Kircher supposes, that he and the other Hebrew 
musicians were inspired with the knowledge of vocal 
and instrumental music, and that their performance 
was equal to their skill. He says, he doubts not but 
that there were many other men, especially in the 
time of king Solomon, who were well skilled in 
divine music, for that the most excellent music was 
fittest for the wisest of mortals, and that of the 



Hebrews must have been more efficacious in exciting 
the affections than that of the Greeks, or of later 
times, but of what kind in particular it was, and by 
what characters expressed, he says, its antiquity 
prevents us from knowing.* 

A much later writer than him above cited, and who 
is now living, Giambatista Martini, of Bologna, has 
entered very deeply into the music of the Hebrews ; 
and it were to be wished, that he had been able to 
give a more satisfactory account of it than is to be 
found in his very learned work, the Storia della 
Musica, now publishing, but of which, as yet [in this 
year, 1771] the public are in possession of only one 
volume. Having few other sources of intelligence 
than the Talmud, and the writing of the Rabbins, we 
are not to expect much information in this particular. 

CHAP. XXL 

From accounts so vague, and so abounding with 
conjectures, as are given of the ancient Hebrew music 
and musicians, and more especially of their instru- 
ments, even by writers of the best authority, it is 
very difficult to collect any thing whereon an in- 
quisitive mind may rest. With regard to the Hebrew 
instruments, it is evident from the accounts of Kircher, 
and others, that some of them approach so nearly to 
the form of those of more modern times, as to give 
reason to suspect the authenticity of the representa- 
tion : others appear to have been so very inartificially 
constructed, that we scarce credit the relation given 
of their effects. It is clear, that Kircher and 
Sch utter us had from the Rabbinical writers little 
more than the bare names of many of the instruments 
described by them ; yet, have they both, in some in- 
stances, ventured to represent them by forms of 
a comparatively late invention. Who does not see, 
that the Minnin, as represented by the former, and 
the lute, are one and the same instrument ? and what 
difference can be discerned between the Machul and 
the Spanish Guitar ? or can we believe, that the 
Macraphe d' Aruchin, and such rude essays towards 
melody as the Gnets Berusim, the Sistrum, or the 
Minagnghinim, could subsist among the same people, 
in any given period of civilization ? 

As to Martini's account, it speaks for itself : it is 
extracted from the sacred writings, which, at this 
distance of time, even with the assistance of the most 

* The confusion of Idithus with Orpheus, suggests a remark on the 
endeavours of some, to establish tlie identity of eminent persons of 
different names and countries, and perhaps of different ages, upon hardly 
any other ground, than some one particular in their history common to 
them both : how far it is possible to extend a hypothesis of this kind, 
the present bishop of Gloucester has shewn in his Divine Legation of 
Moses. In the course of that work, the author has thought it necessary 
to controvert an assertion of Sir Isaac Newton ; namely, that Osiris and 
Sesostris, both kings of Egypt, were one and the same person ; in order 
to do this, he has undertaken to prove that the British king Arthur and 
William the Conqueror were not two distinct beings, but identically one 
person ; and, as far as the method of reasoning usual in such kind of 
arguments will serve him, he has established his proposition. 

The conclusion from this correspondence of such a variety of circum- 
stances, is mucli stronger in favour of the identity of Arthur and William, 
than could liave been imagined, and yet, it has no other effect on the 
mind, than to discredit this method of reasoning, which is fraught with 
fallacy, and must terminate in scepticism. 

What tlicn can we say to the opinion of those, who confound the 
Hebrew musician Idithus with the ancient Orpheus; what rather can 
we tliink of him, who has attempted to show that this latter, and the 
royal prciphet David, were one and the same person. See the Life of 
David, by Dr. Delany. 



Chap. XXI. 



AND PKACTICE OF MUSIC 



97 



learned comments, fall short of affording tliat satis- 
faction, which is to be wished for in an enquiry of 
this kind. 

Under these disadvantages, which even an enquiry 
into the instruments of the Hebrews lies under, an 
attempt to explain their musical theory must seem 
hopeless. Nor is it possible to conceive any thing 
like a system, to which such instruments as the 
Thoph, or the Gnets Berusim could be adapted : if 
the strokes of the pestle against a mortar, like those 
of the latter, be reducible to measure ; yet, surely the 
rattling of a chain, like the music of the Minagng- 
hinim, is not ; or what if they were, would the sounds 
produced in either case make music ? To speak 
freely on this matter, whatever advantages this peo- 
ple might derive from the instructions of an inspired 
law-giver, and the occasional interpositions of the 
Almighty, it no where appears that their attainments 
in literature were very great : or that they excelled 
in any of those arts that attend the refinement of 
human manners ; the figure they made among the 
neighbouring nations appears to have been very in- 
considerable ; and with respect to their music, there 
is but too much reason to suppose it was very bar- 
barous. The only historical relation that seems to 
stand in the way of this opinion, is, that of the effects 
wrought by the music of David on the mind of Saul, 
a man of a haughty irascible temper, not easily sus- 
ceptible of the emotions of pity or complacency, and, 
at the time when David exercised his art on him, 
under the power of a demon, or, at best, in a frenzy. 

Kircher has taken upon him to relate the whole 
process of the dispossession of Saul, by David, and 
has done it as circumstantially as if he had been 
present at the time ; his reasoning is very curious, 
and it is here given in his own woi-ds : — 

' That we may be the better able to resolve this 
' question, how David freed Saul from the evil spirit, 
' I shall first quote the words of the Holy Scripture, 
' as found in the first book of Samuel, chap. xvi. ver. 
' 23.' " And it came to pass when the evil spirit from 
" God was upon Saul, that David took an harp, 
" and played with his hand : so Saul was refreshed, 
" and was well, and the evil spirit departed from him." 
' The passage in the holy text informs us very clearly, 
' that the evil spirit, whatsoever it was, was driven 
' away by music ; but how that came to pass is 

* differently explained. The Eabbins on this place 

* say, that when David cured Saul, he played on 
' a cythara of ten strings ; they say also, that David 

* knew that star, by which it was necessary the music 
' should be regulated, in order to effect the cure : 

* thus Rabbi Abenezra. But Picus of Mirandola says, 
' that music sets the spirits in motion, and thereby 
' produces the like effects on the mind, as a medicine 
' does on the body ; from whence it may seem, that 
' the comment of Abenezra is vain and trifling, and 
' that David regarded not the aspects of the stars ; 
' but trusting to the power of his instrument, struck 
' it with his hand as his fancy suggested. 

' And we, rejecting such astrological fictions, assert, 
' that David freed Saul, not with herbs, potions, or 
'other medicaments, as some maintain, but by the 



sole force and efficacy of music. In order to de- 
monstrate which, let it be observed, that those appli- 
cations which unlock the pores, remove obstructions, 
dispel vapours and cheer the heart, are best calculated 
to cure madness, and allay the fury of the mind ; 
now music produces these eftects, for as it consists 
in sounds, generated by the motion of the air, it 
follows that it will attenuate the spirits, which by 
that motion are rendered warmer, and more quick 
in their action, and so dissipate at length the 
melancholy humour. On the contrary, where it is 
necessary to relax the spirits, and prevent the 
wounding or affecting the membranes of the brain ; 
in that case, it is proper to use slow progressions of 
sound, that those spirits and biting vapours, which 
ascend thither from the stomach, spleen, and hypo- 
condria, may be quietly dismissed. Therefore, the 
music of David might appease Saul, in either of 
these two ways of attenuation or dismission : by the 
one, he might have expelled the melancholy from 
the cells of the brain, or he might by the other have 
dissolved it, and sent it off in thin vapours, by in- 
sensible perspiration. In either case, when the 
melancholy had left him, he could not be mad 
until the return of it, he being terrestial, and as it 
were, destitute of action, nnless moved thereto by 
the vital spirits, which had led him here and there ; 
but they had left him, when for the sake of the har- 
mony they had flown to the ears, abandoning, as 
I may say, their rule over him. And though, upon 
the cessation of the harmony they might return, yet, 
the patient having been elevated, and rendered 
cheerful, the melancholy might have acquired a 
more favourable habit. From all which, it is mani- 
fest, that this effect proceeded not from any casual 
sound of the cythara, but from the great art and ex- 
cellent skill of David in playing on it ; for, as he 
had a consummate and penetrating judgment, and 
was always in the presence of Saul, as being his 
armour-bearer, he must have been perfectly ac- 
quainted with the inclination and bent of his mind, 
and to what passions it was most subject : hence, 
without doubt, he being enabled, not so much by 
his own skill, as impelled by a divine instinct, knew 
so dexterously, and with sounds suited to the humour 
and distemper of the king, to touch the cythara, or 
indeed any other instrument ; for, as has been 
mentioned, he was skilled in the use of no fewer 
than thirty-six, of different kinds. It might be, 
that at the instant we are speaking of, he recited 
some certain rhythmi, proper for his purpose, and 
which Saul might delight to hear ; or, that by the 
power of metrical dancing, joined to the melody of 
the instrument, he wrought this effect : for Saul was 
apt to be affected in this manner, by the music and 
dancing of his armour-bearer ; as he was a youth of 
a very beaiitiful aspect, these roused up the spirits, 
and the words, which were rhythmically joined to 
the harmony, tickling the hearing, lifted up the 
mind, as from a dark prison, into the high region 
of light, whereby the gloomy spirits which oppressed 
the heart were dissipated, and room was left for 
it to dilate itself, which dilation was naturally 



II 



98 



HISTORY OF HE SCIENCE 



Book III. 



' followed by tranquillity and gladness.' Musurgia, 
'torn. II. pag. 214, et seq. 

Whoever will be at the pains of turning to the 
original from \\lience this very circumstantial relation 
is taken, will think it hardly possible for any one 
to compress more nonsense into an equal number of 
words than this passage contains, for which no better 
apology can be made than that Kircher, thougli 
a man of great learning, boundless curiosity, and 
indefatigable industry, was less happy in forming 
conclusions than in relating facts ; his talents were 
calculated for the attainment of knowledge, but they 
did not qualify him for disquisition ; in short he was 
no reasoner. With regard to the dispossession of 
Saul, supposing music to have been in any great 
degree of perfection among the Hebrews in his time, 
there is nothing incredible in it ; and besides it has 
the evidence of sacred history to support it : it 
would therefore have argued more wisdom in the 
Jesuit to have admitted the fact, without pretending 
to account for it, than by so ridiculous a theory 
as he has endeavoured to establish, to render the 
narration itself doubtful. 

After this censure above passed on the music 
of the Hebrews, it would argue an unreasonable 
prejudice against them, were it not admitted that 
their poetry carries with it the signatures of a most 
exalted sublimity : to select instances from the pro- 
phets might be deemed unfair, as there are good 
reasons to believe that something more than mere 
human genius dictated those very energetic com- 
positions ; but if we look into those of their writings 
which the canon of our church has not adopted, 
we shall find great reason to admire their poetical 
abilities. It is true that the boldness of their tigures, 
and those abrupt transitions, which distinguish the 
oriental compositions from those of most other coun- 
tries, are not so well relished by a people with 
whom the false refinements on life and manners 
have taken place of the original simplicity of nature ; 
but in the more regular and less enthusiastic spirit 
of expression, we feel and admire their excellence. 
Not to mention the numberless instances of this sort 
that occur in the Psalms, there is one poem among 
them, which for its truly elegiac simplicity, pathetic 
expression of the woes of captivity, and the lamen- 
tations for the sufferings of an afflicted people, has 
perhaps not its fellow in any of the dead or 
living languages. The poem here meant is the 
CXXXVilth Psalm.* 

From the manner in which it appears the ancients 
treated music, we may observe that they reasoned 
very abstractedly about it ; the measure of intervals, 
either by their ratios, or by their ear, was in their 
judgment a very important branch of the science, 
and we are not to wonder at that close connection, 
which in the writings of the Pythagoreans at least, 

" It has nlrendi/ been mentioned, page 93, that nmnnij the Jews the chief 
use of music was in, sacrifices and other religious ceremonies. To this mail 
be added that it also accompanied the celebration of the funereal rites. 
When Je.ius approached the Ruler's house, in order to revive his daughter, 
we arc told by the Evangelist, Matthew, chap ix., v. 23., that he saw " the 
Minstrels and People making a noise." Dr. Hammnnd. in a very learned 
■note on this passage, informs us that the custom of having tnusic at funerals 
came to the latter Jews from the Gentiles. 



is discoverable between the three sciences, music, 
arithmetic, and geometry. In this view it mav 
perhaj^s be said that the study of music had an 
influence on the minds and tempers of men, as we 
say that the study of the mathematics has a tendency 
to induce a habit of thinking, to invigorate the 
jiowers of the understanding, and to detect the fallacy 
of specious and delusive reasoning, but in what other 
way it could ai¥ect the manners, or indeed the mind, 
unless in that very obvious one of an address to the 
passions, which we at this day are all sensible of, 
is utterly impossible to determine. 

And indeed the investigation of proportions and 
the properties of numbers may be said to be very 
different from the art of combining sounds, so as to 
excite that pleasure which we ascribe to music ; and 
perhaps it may not be too much to say that the 
understanding has little to do with it, nay, some 
have carried this matter so far as to question whether 
the delight we receive from music does not partake 
more of the sensual than the intellectual kind ; f 
however this at least may be said, that it is some 
faculty, very different from the understanding, that 
enables us to perceive the eifects of harmony, and 
to distinguish between consonant and dissonant sounds, 
and in this respect, the affinity between music, and 
that other art, which for more reasons than all are 
aware of, has ever been deemed its sister, is very 
remarkable. That painting has its foundation in 
mathematical principles, is certain, nay, that there 
is a harmony between colours, analogous to that 
of sounds, is demonstral)le ; now the laws of optics, 
the doctrine of light and colours, and the principles 
of perspective, connected as they are with geometry, 
all of which painting has more or less to do with, 
are things so different from the representation of cor- 
poreal objects, from the selection and artful arrange- 
ment of beautiful forms, from the expressions of 
character and passion as they appear in the human 
countenance, and, lastly, from that creative faculty 
in which we suppose the perfection of painting to 
consist, that we scruple not to say that a man may 
be an excellent painter with a slender knowledge 
of the mathematics ; and the examples of the most 
eminent professors of the art, are a proof of the 
assertion. 

But the reason why the ancient writers treated 
the subject in this manner is, that they used the 
word Harmony to express relation and coincidence 
in general ; nay, so extensively was this appellation 
used, that many authors of treatises on this subject 
have thought it previously necessary to a discussion 
of mu.sic in its three most obvious divisions of 
rythmic, metric, and harmonic, to treat of mundane, 
humane, and political music ; the three last of which 
species, if at all intitlcd to the name of music,| must 

t This metapliysical question is discussed and determined in the 
negative, i. e. that music is an intellectual pleasure, by the ingenious 
Jlr. John Norris, of Bemerton. See his Miscellanies, paj?. 309, 12mo. 

t Aristoxenus's division is rhythmic, metric, organic, lib. 11. That of 
Boetius. mundane, humane, and instrumental. By the first is to be un- 
derstood the harmony of the spheres, before spoken of; by the second, the 
harmony suhsistinf; between the body and the rational soul as united 
together, each being actuated by the other ; and also that other kind of 
harmony, consent, relation, or whatever else it may be called, between 
the parts of the body, with respect to each; and again between those 



Chap. XXL 



AND PRACTICE OF ^lUSIC. 



99 



owe it to a metaplior, and that a very bold one : 
Aristides Quintiliauus uses another method of divi- 
sion, which it must be confessed is the more natural 
of the two, and says that music is of two kinds, the 
contemplative and the active ; the first of these he 
subdivides into natural and artificial ; which latter 
he again divides into the harmonic, the rhythmic, 
and the metric ; the active he divides into the usual 
and the enunciative ; the usual, containing melopoeia, 
rhythmopoeia, and poesia ; and the enunciative the 
organic, the odiac, the hypocritic* 

Thus we see that the ancients, when they treated 
of music, used the word Harmony in a sense very 
different from that in which it is understood at 
this day ; for there is doubtless a harmony between 
sounds emitted in succession, which is discernible 
as long as the impression of those already struck 
remains uneffaced ; yet we choose to distinguish this 
kind of relation by the word Melody, and that of 
Harmon}^ is appropriated to the coincidence of dif- 
ferent sounds produced at the same instant : if it be 
asked why the ancients used the word Harmony in 
a sense so very restrained, as is above represented, 
the answer is easy, if that position be true which 
many writers have advanced, namely, that their 
music was solitary, and that they were utter strangers 
to symphoniac harmony. This the admirers of an- 
tiquity will by no means allow; and, to say the 
truth, there are very few questions which have more 
divided the learned world than this. In order that 
the reader may be able to form a judgment on 
a matter of so great curiosity, the authorities on 
both sides shall now be produced, and submitted to 
his consideration. 

To avoid confusion, it will be necessary first to 
reduce the proposition to the form of a question, 
which, to take it in -the sense in which it has 
generally been discussed, seems to be, \Yhether the 
ancients had the knowledge of music in symphony 
or consonance, or not ? 

The advocates for the affirmative are Franchinus, 
or, as he is frequently named, Gaffurius, Zarlino, 
Gio. Battista Doni, Isaac Vossius, and Zaccaria 

affections of the human mind, which, opposed to, or counterbalancing 
>each other, and aided by reason, produce a kind of moral harmony, the 
effects whereof are visible in an orderly and well-regulated conduct. 

To these Kircher and otliers have added musica politica, which, say 
they, consists in that harmonical proportion, which in every well-regu- 
lated government subsists between the three several orders of the people, 
the high, the low, and the middle state. 

Kircher, whose inventive faculty never fails him, has given scales 
demonstrating each oi these supposed kinds of harmony ; but whoever 
would be farther informed as to the nature of mundane music, as it is 
above called, or is desirous of knowing to what extravagant lengths the 
human imagination may be led, may consult the writings of our country- 
man Dr. Robert Fiudd, or de I'luctibus, a physician, and a Rosicrusian 
philosopher; and who, though highly esteemed for ii:s learning by 
Selden, was perhaps one of the greatest mystics that ever lived. In 
a work of his entitled, Utriusque Cosml majoris scilicet et minoris 
metaphysica, physica, atque technica Historia, printed at Oppenheim 
1617, folio, is one btiok intitled De Musica mundana, wherein the author 
exhibits the form of what he calls Monochordum mundanum, an instru- 
ment lepresenting a monochord, with the string screwed up by a hand 
that issues from the clouds. Fludd supposes the sound of the chord, 
when open, to answer to terra or tlie earth, and to correspond with the 
note gamut in the scale of music : from thence he ascends bv tones and 
semitones, in regular order, to water, and the other elements, through 
the planets, and so to the empyrsean, answering to g g in the ratio of the 
disdiapason. 

Mersennus has thought this diagram worthy of a place in his Latin 
■wcrk ; and, to say the truth, most of the plates in this and other of 
Fludd's works, and by the way they abound with them, are to the last 
degree curious and diverting. There will be farther occasion to speak of 
this extraordinary man, Fludd, in the course of this work. 

* See the Analysis of Quint ilian, in cliap. x viii. of the next preceding book. 



Td^o, all, excepting Vossius, musicians, and he con- 
fessedl}^ a man of learning, but a great bigot, and of 
little judgment : the sum of their arguments is, that 
it appears by the writings of the ancients that their 
skill in harmony was very profound, and that they 
reasoned upon it with all the accuracy and precision 
which became philosophers ; that the very first dis- 
coveries of the nature of musical consonance, namely, 
those made by Pythagoras, tended much more natu- 
rally to establish a theory of harmou)^ than of mere 
melody or harmony in succession, that supposing 
Pythagoras never to have lived, it could not have 
happened, but that the innumerable coincidences of 
sounds produced by the voice or by the percussion 
of different bodies at the same instant, which must 
necessarily occur in the course of a very few years, 
could not fail to suggest a trial of the effects of 
concordant sounds uttered together, or at one and 
the same point of time : that those passages of sacred 
writ that mention commemoration of remarkable 
events, or the celebration of public festivals, as that 
of the dedication of Solomon's temple, with a great 
number of voices and instruments, hardly allow of 
the supposition that the music upon these occasions 
was unisonous. 

All this it may be said is mere conjecture, let us 
therefore see what farther evidence there is to coun- 
tenance the belief that the ancients were acquainted 
with the use of different parts in music ; Aristotle 
in his treatise concerning the world, lib. V. has 
tliis question, ' If the world is made of contrary 
' principles, how comes it that it was not long ago 

* dissolved ? ' In answer to this he shows that its 
beauty, perfection, and duration are owing to the 
admirable mixture and temperament of its parts, 
and the general order and harmony of nature. In 
his illustration of this argument he introduces music, 
concerning which he has this passage : Mmnic)] ce 
b^tiQ iijia Kj €apeic, fia^pvc re ic. ^po^alc (pBuyyuq 
fxi^aaa, kv Ciacpopaig dxovaic, fJiiciy aTrtrt'XecrfV upnoriav. 

* Music, by a mixture of acute and grave, and of 
' long and short sounds of different voices, yields an 
' absolute or perfect concentus or concert.' — Again, 
lib. VI. explaining the harmony of the celestial 
motions, he says, that ' though each orb has a motion 
' proper to itself, yet is it such a motion as tends to 
' one general end, proceeding from a principle com- 
' mon to all the orbs, which produce, by the concord 
' arising from tlieir motions, a choir in the heavens :' 
and he pursues the comparison in these words : 
KaQctTTEp he kv xopw tcopvcpaia KaTapL,avreg, avveirrf'^^el 
vaQ o xopoQ a.vCpo)v 'iQ\ ore Kj yvvaiKwv ev cia^vpaic 
(piovaic 6t,VTEpaiQ icj €apvTipaiQ f-iiav apuoviav tfifXEXij 
Kepuvi'vi'Tuii'. 

Seneca, in his Epistles, has this passage. ' Do you 
' not see of how many voices the chorus consists, 
' yet they make but one sound ? In it some are acute, 
' others grave, and others in a mean between both ; 
' women are joined with men, and pipes are also 
' interposed among them, yet is each single voice 
' concealed, and it is the whole that is manifest.' | 

t ' Non vides quam multorum vocibus chorus constet? unus tamen ex 
'omnibus sonus redditur. Aliqua illic acuta est, aliqiia gravis, aliqua 
' media. Accedunt viris femina', interponuntur tibia;, singulorum 
' latent voces, omnium apparent.' Seneca Epist. 84. 



100 



HISTORY .OF THE SCIENCE 



Book III. 



Cassiodorus lias the following passage, wliich may 
seem somewhat sti-onger : ' Symphony is the adjust- 
* ment of a grave sound to an acute, or an acute to 
' a grave sound, making a melody.' 

From the several passages above-cited it appears, 
that the ancients were acquainted with symphonetic 
music of a certain kind, and that they employed 
therein voices differing in degrees of acuteness and 
gravity ; and thus far the affirmative of the qnestiou 
in debate may seem to be proved. 

But in support of the negative we have the au- 
thorities of Glareanus, Salinas, Bottrigari, Artusi, 
Cerone, Kircher, Meibomius, Kepler, Bontempi, our 
countrymen Morley, ^Yallis, and others, a numerous 
band, who infer an absolute ignorance among the 
ancients of harmony produced by different and con- 
cordant sounds, affecting the sense at the same instant, 
from the general silence of their writers about it, for 
the exceeding skill and accuracy with which they 
discussed the other parts of music, leave no room to 
imagine but that they would have treated this in the 
same manner had they been acquainted with it : what 
discoveries accident might produce in that long series 
of years prior to the tirde of Pythagoras no one can 
say ; history mentions none, nor does it pretend that 
even he made any use of his discovery, other than to 
calculate the ratios of sounds, regulate the' system, 
and improve the melody of his time. 

That voices and instruments, to a very great 
number, were employed at public solemnities is not 
denied, but it is by no means a consequence that 
therefore the music produced by them consisted of 
different parts ; at this day among the reformed 
churches singing by a thousand different voices of 
men, women, and children, in divine worship is no 
very unusual thing ; and yet the result of all this 
variety of sound is hardly ever any thing more than 
mere melody, and that of the simplest and most art- 
less kind. Thus much in answer to the arguments 
founded on the improbability that the ancients could 
be ignorant of symphonetic harmony, in the sense 
wherein at this day the term is understood. 

^\ ith respect to the several passages above-cited, 
they seem each to admit of an answer ; to the first, 
produced from Aristotle, it is said that the word 
Symphony, by which Ave should understand the har- 
mony of different sounds uttered at one given instant, 
is used by him to express two different kind of con- 
sonance, symphony and antiphony ; the first, ac- 
cording to him, is the consonance of the unison^ the 
other of the octave. In his Problems, § xix. prob. 
16. he asks why symphony is not as agreeable as 
antiphony ? the answer is, because in symphony the 
one voice being altogether like the other, they eclipse 
each other ; tlie symphony can therefore in this place 
signify nothing but unisonous or integral harmony : 
and he elsewhere explains it to be so, by calling that 
species of consonance, Omophony ; as to Antiphony, 
it is clear that he means by it the harmony of an 
octave, for he constantly uses the word in that sense ; 
and lest there should any doubt remain about it, he 
says that it is the consonance between sounds pro- 
duced by the different voices of a boy and a man, that 
are as Nete and Hypate ; and that those sounds form 



a precise octave is evident from all the representations 
of the ancient system that have ever been given. 
The sum of Aristotle's testimony is, that in his time 
there was a commixture of sounds, which produced 
a concinnous harmony : no doubt there was, but what 
is meant by that concinnous harmony his own words 
sufficiently explain. 

As to Seneca, it must be confessed that the vox 
media must imply two extremes ; but wdiat if in the 
chorus W'hich he speaks of, the shrill tibiai were a 
disdiapason above the voices of the men, and that the 
women sung, as they ever do, an octave above them, 
would not these different sounds produce harmony ? 
Certainly they would ; but of w'hat kind V Why the 
very kind described by him, such as seems to make 
but one sound, which can be said of no harmony but 
that of the unison or octave. 

Lastly, as to Cassiodorus, his words are 'Sym- 
' phonia est temperamentum sonitus gravis ad acutum 
' vel acuti ad gravem, modulamen efficiens, sive in 
* voce, sive in percussione, sive in flatu : ' * as to the 
word Temperamentum, it can mean only an adjust- 
ment ; and Modulamen was never yet applied to 
sounds but as they followed each other in succession : 
to modulate is to pass, to proceed from one key or 
series to another ; the very idea of modulation is 
motion : the amount then of this definition is, that 
the attemperament or adjustment of a grave to an 
acute sound, or of an acute to a grave one, constitutes 
such a kind of symphony as nothing wdll answer to 
but melody ; which is above shewii to be not in- 
stantaneous, but successive symphony or consonance. 

There is yet another argument to the purpose. 
The ancients did not reckon the' third and sixth 
among the consonances ; this is taken notice of by 
a very celebrated Italian writer, Giov. Maria Artusi,. 
of Bologna, wlio, though he has written expressly on 
the imperfections of modern music, scruples not 
therefore, and because the third and sixth are the 
beauty of symphoniac music, to pronounce that the 
ancients must have been unacquainted with the 
harmony of music in parts, in the sense in which the 
term is now understood :f ar.d an author w-hom we 
shall presently have occasion to cite more at large, 
says expressly that they aclaiowledge no other con- 
sonances than the diapason, diapente, and diatessaron,. 
and such as were composed of them ; | nor does it 
any where appear that they were in the least ac- 
quainted with the use of discords, or with the pleasing- 
effects produced by the preparation and resolution of 
the dissonances ; and if none of these were admitted 
into the ancient system, let any one judge of its 
fitness for composition in different parts. 

In Morley's Introduction is a passage from whence 
his opinion on this question may be collected ; and, 
as he was one of the most learned musicians that this 
nation ever produced, some deference is due to it ; 
speaking of Descant, § he uses these words : • \^'Tien 
' descant did begin, by whom, and where it was in- 

* M. Aur. Cassiodor. Opera. De Musica. 

+ Artusi delle Imperfettioni della Moderna Musica. Ragioiiam. primo, 
Cart. 14. 

t Musurg. torn. I. pag. 540. 

5 DebCant, as used by this author, has two significations ; the one 
answers precisely to music in consonance, the other ■will be explained 
hereafter. 



Chap. XXII. 



AND PRACTICE OF jMUSIC. 



101 



' vented, is iincertaine ; for it is a great controversie 

* amongst the learned if it were knowne to the 
' antiquitie, or no ; and divers do bring arguments to 
' prove, and others to disprove the antiquitie of it ; and 
' for disproving of it, they say that in all the workes 

* of them who have written of musicke before Fran- 

* chinus, there is no mention of any more j^arts then 
' one ; and that if any did sing to the harpe (which 
' was their most usual instrument) they sung the same 
^ which they plaied. But those who would affirme 
•■ that the ancients knew it, sale. That if they did not 
' know it, to what ende served all those long and 
' tedious discourses and disputations of the conso- 
' nantes, wherein the moste part of their workes are 
' consumed ; but whether they knew it or not, this 
' I will say, that they had it not in halfe that variety 
' wherein we now have it, though we read of much 
' more strange effects of their musicke then of ours.' 
Annotations on Morley's Introduction, part II. 

CHAP. XXII. 

The suffrage of Kircher, in a question of this 
nature, will be thought to carry some weight : this 
author, whose learning and skill in the science are 
universally acknowledged, possessed every advantage 
that could lead to satisfaction in a question of this 
nature, as namely, a profound skill in languages, an 
extensive correspondence, and an inquisitive dis- 
position ; and for the purpose had been indulged 
with the liberty of access to the most celebrated 
repositories of literature, and the use of the most 
valuable manuscripts there to be met with ; and who, 
to sum up all, was at once a philosopher, an antiquary, 
an historian, a "Scholar, and a musician, has given his 
opinion very much at large in nearly the following 
words : — 

' It has for some time been a question among 
' musicians whether the ancients made use of several 
^ parts in their harmony or not : in order to determine 
' which, we are to consider their polyodia as three- 
■' fold, natural, artificial, and unisonous ; I call that 
'' natural which is not regulated by any certain rules 
' or precepts, but is performed by an extemporary and 
■* arbitrary symphony of many voices, intermixing 
' acute and grave sounds together ; such as we observe 
' even at this time, happens amongst a company of 
' sailors or reapers, and such people, who no sooner 
' hear any certain melody begun by any one of them, 
' than some other immediately invent a bass or tenor, 
' and thus is produced an harmony extemporary, and 
' not confined by any certain laws, and which is very 
' rude and imperfect, as it is almost always unison, 
' containing nothing of harmony, except in the closes, 
'' and therefore of no worth ; that the Greeks had 

* such a kind of music none can doubt. But the 

* question is not concerning this kind of polyodia, 
' but whether they had compositions for several 
' voices, framed according to the rules of art. I have 

* taken great pains to be satisfied in this matter ; and 
' as in none of the Greek and Latin writers I have 
' met with, any mention is made of this kind of music, 

* it seems to me that either they were ignorant of it, 



or that tliey did not make use of it, as imagining 
perhaps that it interrupted the melody, and took 
away from tlie energy of the words ; as to the term 
Harmonici concentns, it is only to be understood of 
the agreement between the voice and the sound of 
the instrument. 

' Those who attempt to prove from Euclid that the 
ancients did compose music in really different parts, 
do not seem to understand his meaning ; for when 
he mentions the four parts of a song, ayuj-yi), roi'i), 
TiETTda, irXoKYj, he does not thereby mean the four 
polyodical parts of cantus, altus, tenor, and bass, 
but so many different affections of the voice, certain 
harmonical figures or tropes, whefeby the song- 
acquired a particular beauty and grace ; for what 
else can the word ' Ay wy;7 mean than a certain transi- 
tion of the voice from some given sound to another 
that is related to it. Toj'j) signifies a certain stay or 
dwelling on a sound ; XlXofo), or implication, is a 
particular species or colour of the 'Aywyz/.as litTrda, 
frisking or playing on, is of Tor;) : what the'Aywyj/ 
is to Tovj), such is the UXoo) to the Jlerreia. 

' Some imagine that the ancients had a polyodical 
instrumental music from the diversity of their pipes ; 
and are of opinion that at least an organical or 
instrumental harmony or symphony, regulated by 
art, was in use among the ancients, because their 
authors make mention of certain pipes, some of 
which were termed YlapBevioi, or fit for girls ; some 
XlaioiKoi, or fit for boys ; some TeKioi, as being in a 
mean between the acute and grave sounds ; and 
others 'TTreprtXtot, as agreeing with the grave. The 
better to clear up this doubt, we must consider the 
organical polyodia as twofold, natural and artificial ; 
and both these I make no doubt were in i;se as well 
as the vocal polyodia ; for it is very probable that 
such as played on those pipes, becoming skilful by 
such practice, invented certain symphonies adapted 
to their purpose, and which they played on their 
public festivals, distributing themselves into certain 
chorusses. Symphonies of this sort are at this time 
to be heard among the country people, who, though 
ignorant of the musical art, exhibit a symphony, 
such a one as it is, on their flutes and pipes of 
different sizes, and this merely through the judgment 
of their ear ; and it is also probable that the ancient 
Hebrews by this means alone became enabled to 
celebrate the praises of God on so many Cornua, 
Fistulae, Litui, Tubae, Buccinse, as they are said to 
have been used at once in their temple ; and I 
remember to have heard the ^Mahometan slaves in 
the island of Malta exhibit symphonies of this kind. 
An affection therefore of the polyodia is implanted 
in the nature of man ; and I doubt not but that the 
ancients knew and practised it in the manner above 
related : but though I have taken great pains in my 
researches, I could never find the least sign of their 
having any artificial organical Melothesia of many 
parts ; which, had they been acquainted with it, 
they would doubtless have mentioned, it being so 
remarkable a thhig. What Boetius, Ptolemy, and 
others speak concerning harmony, is to be under- 
stood only as to a single voice, to which an instru- 



102 



HISTORY OF THE SCIENCE 



Book III. 



* ment was joined ; add to this that the ancients 
acknowledged no other concords than the diapason, 

' the diapente, and the diatessaron, and such as wei'e 
' composed of them ; for they did not reckon as now, 

* the ditone, semiditone, and hexachord among the 
' consonances. It tlierefore follows that the ancient 
' Greeks acknowledged nothing more than the Mo- 
' nodia, adapted, it must be confessed, with much care 
' and the greatest art to the sound of the lyre or the 
' tibia ; so that nothing was deficient either in the 

* variety of the modulation, the sweetness of the 

* singing, the justness of the pronunciation, or the 
' gracefulness of the body in all its gestures and 
' motions : and I imagine that the lyre of many 
' strings was sounded in a harmonical concentus to 

* the voice, in no other manner than is used in our 
' days.' * 

Dr. Wallis has given his opinion on this important 
question in terms that seem decisive ; for speaking 
of the music of the ancients he makes use of these 
words : — 

' "We are to consider that their music, even after it 
' came to some good degree of perfection, was much 
' more plain and simple than ours now-a-days. They 
' had not concerts of two, three, four, or more parts 
' or voices, but one single voice, or single instrument 
' a-part, which to a rude ear is much more taking 
' than more compounded music ; for that is at a pitch 

* not above their capacity, whereas this other con- 
' founds it with a great noise, but nothing distingtiish- 

* able to their capacity.' f And again in the same 
paper he says : ' I do not find among the ancients 
' any footsteps of what we call several parts or voices 
' (as bass, treble, mean, &c. sung in concert), answering 
' to each other to complete the music' And in the 
Appendix to his edition of Ptolemy, pag. 317, he 
expresses himself on the same subject to this pur- 
pose : — ' But that agreement which we find in the 
' modern music, of parts (as they term it) or of two, 
' tliree, four, or more voices (singing together sounds 
' which are heard altogether), was entirely unknown 

* to the ancients, as far as I can see.' 

From the several passages above-cited, it appears 
that the question, whether the ancients were ac- 
quainted with music in consonance or not, has l)een 
fre(|uently and not unsuccessfully agitated, and that the 
arguments for the negative seem to preponderate. 
Nevertheless the author of a book lately published, 
entitled ' Principles and Power of Harmony,' after 
taking notice that Dr. AYallis, and some others, main- 
tained that the ancients were strangers to symphoniac 
music, has, upon the strength of a single passage in 
Plato, been hardy enough to assert the contrary : his 
words are these : — 

' The strongest passage which I have met with in 
' relation to this long-disputed point, is in Plato ; a 
' passage which I have never seen quoted,' and which 
' I shall translate : " Young men should be taught to 
" sing to the lyre, on account of the clearness and 
" precision of the sounds, so that they may learn to 
" render tone for tone. But to make use of different 

♦ Musurn;. torn. 1. pa^. 537, et seq. 

+ Abridgment of Philosoph. Transactions by Lowthorp and Jones, 
vol. I. pag. 618. 



" simultaneous notes, and all the variety belonging to 
" the lyre, this sounding one kind of melody, and the 
" poet another — to mix a few notes with many, swift 
" with slow, grave with acute, consonant with dis- 
" sonant, &c. must not be thought of, as the time 
" allotted for this part of education is too short for 
" such a work." Plat. 895. I am sensible that 
' objections may be made to some parts of this trans - 
' lation, as of the words TrvKrorrj^, jxavorrjc, and 
' avrt(piovoic, but I have not designedly disguised 
' what I took to be the true sense of them, after duo 
' consideration. It appears then upon the whole, that 
' the ancients were acquainted with music in parts, 
' but did not generally make use of it.' | 

"V\Tioever will be at the pains of comparing the 
discourse of Dr. Wallis, above-cited, and his appendix 
to Ptolemy, with the several paragraphs in the 
Principles and Power of Harmony, relating to the 
question in debate, and calculated, as the author pro- 
fesses, to vindicate the Greek music, will discover in 
the one the modesty of a philosopher, and in the 
other the arrogance of a dogmatist. 

Opinions delivered in terms so jiositive, and indeed 
so contemptuous, as this latter writer has chosen to 
make use of,§ are an affront to the understandings of 
mankind, who are not to be supposed ready to 
acquiesce in the notions of others merely because 
they are propagated with an unbecoming confidence : 
and as to the judgment of this author on the question 
in debate, the least that can be said of it is, that it is 
founded in mistake and ignorance of his subject ; for, 
first, it is very strange, seeing how much the powers 
of harmony exceed those of mere melody, that the 
ancients, when once they had found themselves in 
possession of so valuable an improvement as sym- 
phoniac music, should ever forego it. The moderns 
in this respect were wiser than their teachers, for no 
sooner did they discover the excellence of music in 
parts than they studied to improve it, and have culti- 
vated it with great care ever since. Secondly, this 
writer, in support of his opinion, has been driven to 
the necessity of translating those words of his author 
which he thinks make most for his purpose, in a 
manner which he confesses is liable to objections, and 
into such English phrase as, in the opinion of many, 

t Principles and Power of Harmony, p. 133. The speech in the 
original, containing the passage of which it is pretended that above is 
a translation, is here given at lenfjth, as it stands in the edition of Plato, 
by Marsilins Ficinus ; which is what this author appears to have made 
use of: — Thtiov To'tvvv ?n xn|Oij' toIq <p96yyoig r»)c Xvpag 
•TrpocTxprjaQaL, cra^jyj'Ei'af 'iviKa rwi' xopSojv, rov Tt KiOapi'^iiv 
K] Tuv TraiSsvofiivov, cnroSidovrac irpoaxopSa ru (pOey/iara 
Totg (pOiy^afff rijv S' tnpo^ioi'iai' K/ TroiKiXiav tTiq Xvpag, 
ciWa ptv j^dXr] tmv xopSiov tiKjuiv, ciXXa H th tiiv fitXipSiav 
'^vi'OivTog TTonjTH' icj S)) (Jj TTVKVoTrira {.lat'oTTiTi, K) ra^oc 
PpaSyTTiri, kj o^vtijth fiapvTi)Ti, avp<j>u)Vov Ki civt'kjiwvov 
vapixofth'sg, Kf Tuiv pvd^iojv, waavTiog ■KavToScnra ttoikiX- 
fiara TrpoaapfiOTTovrag rdiai <pQ6yyoic tTjq Xrpag' TTavTa BV 
Ta ToiavTa p>) 'rrpo(r(peptn' roTg /(eXasctiv h' rpialv 'inai to 
Ti'ig fxaaiicTjQ xP'I'^'l^ov tKXijiperjQai Old ra%8C' ''« yup ii'avTia, 
aXXr)\a rnpciTTOvra ?vff^a6iav Trapsxii' ^il ^t oTi finXiffa 
ii'ifiaOtlg ilvai rag 7'ksg. 

§ As where he insinuates a resemblance between those who doubt the 
truth of his assertions and the most ignorant of mankind, in these 
words: ' If all these circumstances are not sufficient to gain our belief, 
' merely because we moderns have not the same musical power, then 
' have the Kamschatcans a right to decide that it is impossible to foretel 
' an eclipse, or to represent all the elements of speech by about twenty- 
' four marks.' 



Chap. XXIL 



AND PRACTICE OF MUSIC. 



103 



is not intelligible. Thirdly and lastly, this very 
passage of Phito, npon which he lays so much stress, 
was discovered about fifty years ago, and adduced 
for the very purpose for which he has cited it, by 
Mons. I'Abbe Fraguier, a member of the Academy 
of Inscriptions and Belles Lettres, and occasioned 
a controversy, the result whereof will presently be 
related. 

INIonsieur Fraguier had entertained a high opinion 
of the Greek music, and a belief that the ancients 
were acquainted with music in consonance ; in 
support of which latter opinion he produced to the 
academy the passage above-cited, which is to be 
found in Plato de Legibus, lib. VII.* He also pro- 
duced for the same purpose a passage in Cicero de 
Republica, and another from Macrobius, both which 
are given in the note subjoined.f 

The arguments deduced by Mons. Fraguier from 
these several passages, were learnedly refuted by 
Mons. Burette, a member also of the academy : and 
as to the interpretations which Mons. Fraguier had 
put upon them, the same Mons. Burette demonstrated 
that they were forced and imwarranted, either by the 
context or the practice of the ancients. 

The substance of these argiiments is contained in 
a paper or memoir entitled Examen d'un Passage de 
Platon sur la Musique, which may be seen in the 
History of the Academy of Inscriptions, tom. III. 
pag. 118. This question was farther prosecuted by 
the same parties, as appears by sundry papers in the 
subsequent volumes of the History and Memoirs of 
the above Academy ; and in the course of the con- 
troversy the passages above-cited from Aristotle, 
Seneca, Cassiodorus, and others, were severally insisted 
on. As to those from Cicero and Macrobius, and 
this from Horace, 

Sonante mistum tibiis carmen lyra, 
Hac Dorium, illis Barbarum. 

Ad Mecaenat. Epod. ix. 

which had formerly been adduced for the same pur- 
pose, they went but a very little way towards proving 
the affirmative of the question in debate. Mons. 
Burette took all these into consideration ; he admits, 
that the ancients made use of the octave and the 
fifteenth, the former in a manner resembling the 
drone of a bag-pipe ; and he allows th^at they might 
accidentally, and without any rule, use the fourth and 
fifth ; but this is the farthest advance he will allow 
the ancients to have made towards the practice of 
symphoniac music ; for as to the imperfect con- 
sonances and the dissonances, he says they were 
ignorant of the use and application of all of them in 
harmony : and finally he demonstrates, by a variety 

* In Stephens's edition it is pag. 812, and in that of Marsilius Ficinus 
895. 

+ ' Ut in fidibus, ac tibiis atque cantu ipso, ac vocibus concentus est 
' quidam tenendus ex distinctis sonis, quem immutatum ac discrepantem 
' aures eruditae ferre non possunt ; isque concentus ex dissimilimarum 
' vocum moderatione concors tamen efficitur et congruens : sic ex sum- 
' mis, et infiinis, et niediis interjectis ordinibus, ut sonis, moderata 
' ratione civitas, consensu dissimilimorum concinit ; et qu:e liarmonia a 
' niusicis dicitur in cantu, ea est in civitate concordia.' Cicer. lib. ii. de 
Kepub. Fragm. pag. 527, tom. III. 

' Vides quam multorum vocibus chorus constet una tamen ex omnibus 
' redditur. Aliqua est illic acuta, aliqua gravis, aliqua media : accedunt 
' viri.i feminffl : interponuntur fistula. Ita singulorum illic latent voces, 
'omnium apparent, et fit concentus ex dissonis.'— Macrob. Saturnalior 
Proero. 



of arguments, that the ancients were absolute strangers 
to music in parts. :j: 

IMartini, in his Storia della INIusica, vol. I. pag. 172, 
haa given an abridgement of this controversy, as it lies 
dispersed in the several volumes of the Memoirs of 
the Academy of Inscriptions, and acquiesces in the 
opinion of Mons. Burette, who, upon the whole, 
appears to have so much the advantage of his op- 
ponents, that it is highly probable this dispute will 
never be revived. 

To speak of the ancient Greek music in general, 
those who reflect on it will be inclined to acquiese 
in the opinion of Dr. Wallis, who says, he takes it 
for granted, ' that much of the reports concerning the 
' great effects of music in former times, beyond what 
' is to be found in latter ages, is highly hyperbolical, 
* and next door to fabulous ; and therefore, he adds, 
' great abatements must be allowed to the elogies of 
' their music' Certainly many of the relations of 
the effects of music are either fabulous or to be in- 
terpreted allegorically, as this in Horace : — 

Silvestres homines sacer interpresque Deorum, 
Cfedibus & victu fcedo deterruit Orpheus ; 
Dictus ob hoc lenire tigres rabidosque leones. 
Dictus & Amphion, TliebaniB conditor Arcis, 
Saxa movere sono testudinis, & prece blanda. 
Ducere quo vellet. 

Arte Poetica, lib. II. 1. 391. 

The wood-born race of men, when Orpheus tam'd, 
From acorns and from mutual blood reclaim'd, 
This priest divine was fabled to assuage 
The tiger's fierceness, and the lion's rage. 
Thus rose the Theban wall ; Amphion 's lyre 
And soothing voice the list'ning stones inspire. 

Francis. 

Hyperbolical expressions of the power and efficacy 
of music signify but little ; for these convey nothing 
more than the ideas of the relator : and every man 
speaks in the highest terms he can invent of that, 
whatever it be, that has administered to him the 
greatest delight. How has the poet, in the Prolusions 
of Strada, laboured in describing the contest between 
the nightingale and the lutenist 1 and what does that 
celebrated poem contain, but a profusion of words 
without a meaning ? 

To conclude, every one that understands music is 
enabled to judge of the utmost effects of a single 
pipe, by hearing the flute, or any other single stop, 
finely touched on the organ : and as to the lyre, 
whether of three, four, seven, or ten strings, it is 
impossible but that it must have been greatly in- 
ferior to the harp, the lute, and many other instru- 
ments in use among the moderns. 

Havins: taken a view of the state of music in the 

I The learned Dr. Jortin, who, Avith the character of a very worthy 
man and a profound scholar, possessed that of a learned musician, has 
deliverrd his sentiments on this question in the following terms : — ' One 
' would think that an ancient musician, who was well acquainted with 
' concords and discords, who had an instrument of many strings or many 
' keys to play upon, and two hands and ten fingers to make use of, would 
' try experiments, and would fall into something like counterpoint and 
' composition in parts. In speculation nothing seems more probable, 
' and it seemed more than probable to our skilful musician Dr. Pepusch, 
' when I once conversed with him upon the subject; but in fact it doth 
' not appear that the ancients had this kind of composition, or rather it 
' appears that they had not ; and it is certain, that a man shall overlook 
• discoveries which stand at his elbow, and in a manner intrude them- 
' selves upon him.' Letter to Mr. Avison, published in the second edi- 
tion of his Essay on Musical Expression, pag. ^G. 



104 



HISTORY OF THE SCIENCE 



Book III. 



earlier ages of the world, and traced the ancient 
system from its rudiments to its perfection, and 
thereby brought it down to nearly the close of the 
third century, we shall proceed to relate the several 
subsequent improvements that have from time to 
time been made of it, in the order in which they 
occurred ; and shew to whom we owe that system, 
which for its excellence is now universally adopted 
by the civilized world. 

We have seen that hitherto the science of music, 
as being a subject of very abstracted speculation, 
and as having a near affinity with arithmetic and 
geometry, had been studied and taught by such only 
as were eminent for their skill in those sciences : 
of these the lar greater number were Greeks, who, 
in the general estimation of mankind, held the rank 
of philosophers. The accounts hereafter given of the 
Latin writers, such as Martianus Capella, Macrobius, 
Cassiodorus, and others, will shew how little the 
Romans contributed to the improvement of music ; 
and in general tlieir writings are very little more 
than abridgements of, or short commentaries on the 
works of Nicomachus, Euclid, Aristides Quintilianus, 
Aristoxenus, and others of the ancient Greeks. As to 
Boetius, of whom we shall speak hereafter, it is clear 
that his intention was only to restore to those barba- 
rous times in which he lived, the knowledge of the 
true principles of harmony, and to demonstrate, by 
the force of mathematical reasoning, the proportions 
and various relations to each other, of sounds ; in the 
doing whereof he evidentlj'^ shews himself to have 
been a Pythagorean. As this was the design of his 
treatise De Musica, we are not to wonder that tlie 
author has said so little of the changes that music 
underwent among the Latins, or that he does but 
just hint at the disuse of the enarmonic and chro- 
matic genera, and the introduction of the Roman 
characters in the room of the Greek. 

It must however be admitted, that for one im- 
provement of the system we are indebted to the 
Latins, namely, the application of the Roman capital 
letters to the several sounds that compose the scale, 
whereby they got rid of that perplexed method of 
notation invented by the Greeks : we have seen, by 
the treatise of Alypius, written professedly to explain 
the Greek musical characters, to what an amazing 
number they amounted, 12iO at the lowest computa- 
tion ; and after all, they were no better than so many 
arbitrary marks or signs placed on a line over the 
words of the &ong, and, having no real inherent or 
analogical signification, must have been an intole- 
rable burthen on the memory. These the Latins re- 
jected, and in their stead introduced the letters of 
their own alphabet. A, B, C, D, E, F, G, H, I, K, L, 
M, N, 0, P, fifteen in number, and sufficient to ex- 
press every sound contained in the disdiapason. If 
it be asked, how could this small number serve the 
purpose of more than 1200? the answer is, that this 
amazing multiplicity of characters arose from the ne- 
cessity of distinguishing each sound with respect to the 
genus, and also the mode in which it was used ; and 
before this innovation of the Romans, we are assured, 
that both the enarmonic and chromatic genera were 



grown out of use, and tliat the diatonic genus, on 
'account of its sweetness and conformity to nature, 
was retained amongst them : and as to the modes, 
there is great reason to susj^ect, that even at the time 
when Ptolemy wrote, the doctrine of them was but 
ill understood ; fifteen characters, we know, are at 
this time sufficient to denote all the sounds in a dia- 
tonic disdiapason, and consequently must have been 
so then. 

It has already been observed, that the science ot 
harmony was anciently a subject of philosophical 
enquiry ; and it is manifest, from the account herein 
before given of them and their writings, that the 
Greeks treated it as a subject of very abstract specu- 
lation, and that they neither attended to the physical 
properties of sound, nor concerned themselves with 
the practice of nmsic, whether vocal or instrumental. 
Ptolemy was one of the last of the Greek harmo- 
niciaus ; and from his time it may be observed, that 
the cultivation of music became the care of a set of 
men, who, then, at least, made no pretensions to the 
character of philosophers. This may be accounted 
for either by the decline of philosophy about this 
jieriod, or by the not improbable supposition, that 
the subject itself was exhausted, and that nothing re- 
mained but an improvement in practice on that foun- 
dation which the ancient writers, by their theory, had 
so well laid. But whatever may have been the cause, 
it is certain, that after the establishment of Chris- 
tianity the cultivation of music became the concern 
of the church : to this the Christians were probably 
excited by the example of the Jews, among whom 
music made a considerable part of divine worship, 
and the countenance given to it in the writings of 
St. Paul. Nor is it to be wondered at by those who 
consider the effects of music, its influence on the pas- 
sions, and its power to inspire sentiments of the most 
devout and affecting kind, if it easily found admit- 
tance into the worship of the primitive Christians : 
as to the state of it in the three first centuries, we are 
very much at a loss; yet it should seem from the 
information of St. Augustine, that in his time it had 
arrived at some degree of perfection ; possibly it had 
been cultivating, both in the Eastern and Western 
empire, from the first propagation of Christianity. 
The great number of men who were drawn off from 
secular pursuits by tlieir religious profession, amidst 
the barbarism of the times, thought themselves laud- 
ably employed in the study of a science which was 
found to be subservient to religion : while some were 
engaged in the oppugning heretical opinions, others 
were taken up in composing forms of devotions, 
framing liturgies ; and others in adapting suitable 
melodies to such psalms and hymns as had been re- 
ceived into the service of the church, and which made 
a very considerable part of the divine offices : all 
which is the more probable, as the progress of human 
learning was then in a great measure at a stand. 

But as the introduction of music into the service 
of the church seems to be a new ^ra, it is necessary 
to be a little more particular, and relate the opinions 
of the most authentic writers, as well as to the recep- 
tion it at first met with, as its subsequent progress 



Chap. XXII. 



AND PRACTICE OF MUSIC. 



lOo 



among tlie converts to Christianity. If among the 
accounts to be given of these matters, some should 
carry the appearance of improbability, or should even 
verge towards the regions of fable, let it be remem- 
bered, that very little credit would be due to history, 
were the writer to suppress every relation against 
the credibility whereof there lay an objection. His- 
tory does not propose to transmit barely matters of 
real fact, or opinions absolutely irrefragable ; false- 
hood and error may very innocently be propagated, 
nay, the general belief of falsehood, or the existence 
of any erroneous opinion, may be considered as facts ; 
and then it becomes the duty of a historian to relate 
them. WTioever is conversant with the ecclesiastical 
historians must allow that the superstition of some, 
and the enthusiasm of others of them, have some- 
what abated the reverence due to their testimony. 
But notwithstanding this, the characters of Eusebius, 
Socrates, Sozomen, Theodoret, and Evagrius, for 
veracity and good intelligence, stand so high in the 
opinion of all sober and impartial men, that it is im- 
possible to withhold our assent from the far greater 
part of what they have written on this subject. 

The advocates for the high antiquity of church- 
music urge the authority of St. Paul in its favour, 
who, in his Epistle to the Ephesians, chai'ges them 
to speak to themselves in psalms, and hymns, and 
spiritual songs, singing and making melody in their 
hearts to the Lord;* and who exhorts the Colos- 
sians to teach and admonish one another in psalms, 
hymns, and spiritual songs.f Cardinal Bona is one 
of these ; and he scruples not to assert, on the autho- 
rity of these two passages, that songs and hymns 
were, from the very establishment of the church, sung 
in the assemblies of the faithful. Johannes Damas- 
cenus goes farther back ; and relates, that at the 
funeral of the Blessed Virgin, which was celebrated 
at Gethsemane, tlie apostles, assisted by angels, con- 
tinued singing her requiem for three whole days 
incessantly. The same author, speaking of the an- 
cient hymn called the Trisagion, dates its original 
from a miracle that was performed in the time of 
Proclus, the archbishop : his account is, that the 
people of Constantinople being terrified with some 
portentous signs that had appeared, made solemn 
processions and applications to the Almighty, be- 
seeching him to avert the calamities that seemed to 
threaten their city, in the midst whereof a boy was 
caught from among them, and taken up to heaven ; 
who, upon his return, related, that he had been taught 
by angels to sing the hymn, in Greek, 

Ayiog fc)£Oc,aytoc iffx^poe^aytoe adayaroc, eXerjaov rj/jiac. 

Holy God, holy and strong, holy and immortal, have mercy 

upon us. 

The truth of this relation is questioned by some, 
who yet credit a vision of St. Ignatius; of which 
Socrates, the ecclesiastical historian, gives the fol- 
lowing account : ' St. Ignatius, the third bishop of 
' Antioch, in Syria, after the apostle Peter, who also 
' conversed familiarly with the apostles, saw the 
' blessed spirits above singing hymns to the Sacred 



Chap. V. verse 19. 



t Chap. iii. verse IG. 



' Trinity alternately, which method of singing, says 

* the same historian, Ignatius taught to his church ; 
' and this, together with an account of the miracle 

* which gave rise to it, was communicated to all the 
' churches of the East.' J Nicephorus, St. Chrysos- 
tom, Amalarius, and sundry others, acquiesce in this 
account of the origin of antiphonal singing ; as do 
our countrymen, Hooker, Hammond, Beveridge, and 
Dr. Comber. 

By the Apostolical Constitutions, said to have been, 
if not compiled by the apostles themselves, at least 
collected by Clement, a disciple of theirs, the order of 
divine worship is prescribed ; wherein it is expressly 
required, that after the reading of the two lessons, 
one of the presbyters should sing a psalm or hymn 
of David ; and that the people should join in singing 
at the end of each verse. It would be too little to 
say of this collection, that the authority of it is 
doubted, since it is agreed, that it did not appear in 
the world till the fourth century ; and the opinions 
of authors are, that either it is so interpolated as to 
deserve no credit, or that the whole of it is an abso- 
lute forgery. 

Hitherto, then, the high antiquity of church-music 
stands on no better a foundation than tradition, 
backed with written evidence of such a kind as to 
have scarce a pretence to authenticity : there are, 
however, accounts to be met with among the writers 
of ecclesiastical history, that go near to fix it at about 
the middle of the fourth century. 

In short, the aera from whence we may reasonably 
date the introduction of music into the service of 
the church, is that period during which Leontius 
governed the church of Antioch ; that is to say, be- 
tween the years of Christ 347 and 35G, when Flavi- 
anus and Diodorus, afterwards bishops, the one of 
Antioch and the other of Tarsus, divided the choris- 
ters into two parts, and made them sing the Psalms 
of David alternately, Theodoret. Hist. Eccl. lib. II. 
cap. xxiv. ; a practice, says the same author, which 
began first at Antioch, and afterwards spread itself 
to the end of the world. Valesius acquiesces in this 
account, and professes to wonder whence Socrates 
had the story of Ignatius's vision, Vales, in Socrat. 
lib. VI. cap. viii. The occasion of antiphonal singing 
seems to have been this : Flavianus and Diodorus, 
although then laymen, but engaged in a monastic 
life, were in great repute for their sanctity ; and 
Leontius, their bishop, was an avowed Arian, whom 
they zealously opposed : in order to draw off the 
people from an attendance on the bishop, who, in the 
opinion of Flavianus and Diodorus, was a preacher 
of heresy, they set up a separate assembly for reli- 
gious worship, in which they introduced antiphonal 
singing, which so captivated the people, that the 
bishop, to call them back again, made use of it also 
in his church. Flavianus, it seems, had a high 
opinion of the efficacy of this kind of music ; for it 
is reported, that the cit}'' of Antioch having, by a 
popular sedition, incurred the displeasure of the Em- 
peror Theodosius, sent Flavianus to appease him, and 
implore forgiveness ; who, upon his first audience, 

I Hist. Eccles. lib. VI. cap viii. 



lOG 



HISTORY OF THE SCIENCE 



Book III. 



though in the imperial palace, directed the usual 
church-service to be sung before hiin : the emperor 
melted into pity, wept, and the city was restored to 
his favour. Other instances are to be met witli in 
history, that show the fondness of the people of An- 
tioch for this kind of music ; and which favour tlie 
supposition, that amongst them it took its rise. 

Antioch was the metropolis of Syria ; the example 
of its inhabitants was soon followed by the other 
churches of the East ; and in a very few ages after its 
introduction into the divine service, the practice of 
singing in churches not only received the sanction of 
public authority, but those were forbidden to join in it 
who were ignorant of music. For at the council of 
Laodicea, held between the years of Christ, 3G0 and 
370, a canon was made, by which it was ordained, 
That none but the canons, or singing men of the 
church, which ascend the Ambo,* or singing-desk, 
and sing out of the parchment, [so the words are] 
should presume to sing in the church. Balsamon 
seems to think that the fathers intended nothing 
more than to forbid the setting or giving out the 
hymn or psalm by the laity : but the reason assigned 
by Baronius for the making of this canon, shews that 
it was meant to exclude them totally from singing in 
the church-service ; for he says that when the people 
and the clergy sang promiscuously, the former, for 
want of skill, destroyed the harmony, and occasioned 
such a discord as was very inconsistent with the 
order and decency requisite in divine worship. Zo- 
nanus confirms this account, and adds, that these 
canonical singers were reckoned a part of the clergy .f 
Balsamon, in his scholia on this canon, says, that 
before the Laodicean council, the laity were wont, in 
contempt of the clergy, to sing, in a very rude and 
inartificial manner, hymns and songs of their own 
invention ; to obviate which practice, it was ordained 
by this canon that none should sing but those whose 
office it was. Our learned countryman, Bingham, 
declares himself of the same opinion in his Anti- 
quities of the Christian Church, book III. chap. vii. 
and adds, that from the time of the council of Lao- 
dicea the psalmistae, or singers, were called icaroriKOL 
xpoKrai, or canonical singers, though he is inclined to 
think the provision in the canon only temporary. 

CHAP. XXIIL 

Great stress is also laid on the patronage given 
to church-music by St. Basil, St. Ambrose, and St. 
Chrysostom ; as to the first, he had part of his edu- 
cation at Antioch, where he was a continual spectator 
of that pompous worship which prevailed there. He 

* The Ambo was what we now call the reading-desk, a place made on 
purpose for the readers and singers, and such of the clergy as ministered 
in the first service called Missa Catechumenorum. It had the name of 
Ambo, not as Walafridus Strabo imagines, ' ab anibiendo,' because it 
surrounded them that were in it, but from avaiaivtiv, because it was 
a place of eminency. to which they went up by degrees or steps. Bing- 
ham's Antiquities of the Christian Church, book VIII. chap. v. § 4. 

+ It seems they were one of the many orders in the primitive church, 
and that they received ordination at the hands, not of the bisliop or 
choriepiscopus, but of a presbyter, using this form of words, prescribed 
by the canon of the fourth council of Carthage : ' See that thou believe 
'in thy heart wliat thou singest with thy mouth ; and approve in thy 
'works wliat tliou believest in thy heart." Bingh. Antiq. book 111. 
chap. vii. § 1. 



w^as first made a deacon l)y Meletius, and afterwards, 
that is to say about the year 371, was promoted to 
the bishopric of Csesarea in Cappadocia, his own 
country ; and in this exalted station he contracted 
such a love for church-music, as drove him to the 
necessity of apologizing for it.J In his epistle to the 
Neocaesarian clergy, still extant, he justifies the prac- 
tice, saying, that the new method of singing, at which 
they were so offended, was now become common in 
the Christian church, the people rising before day 
and going to church, wliere, having made their con- 
fessions and prayers, they proceeded to the singing 
of psalms : and he adds, that in his holy exercise, 
the choir being divided into two parts, mutually 
answered each other, the i^recentor beginning, and 
the rest following him. He farther tells them, that 
if to do thus be a fault, they must blame many 
pious and good men in Egypt, Lybia, Palestine, 
Arabia, Phoenicia, and Syria, and sundry other places. 
To this they urged that the practice was otherwise 
in the time of their bishop Gregory Thaumaturgus ; 
in answer to which Basil tells them, that neither was 
the Litany u.sed in his time ; and that in objecting 
to music, while they admitted the Litany, they 
strained at a gnat and swallowed a camel. 

St. Chrysostom, whose primitive name was John, 
was a native of Antioch, and received his education 
there, ho was ordained a deacon by Meletius, and 
presbyter by Flavianus ; and having been accustomed 
to the pompous service introduced by the latter into 
the Church of Antioch, he conceived a fondness for 
it. When he became bishop of Constantinople, which 
was about a. c. 380, he found occasion to introduce 
music among his people : the manner of his doing 
it is thus related : The Arians in that city were 
grown very insolent : they held conventicles at a 
small distance without the walls ; but on Saturdays 
and Sundays, which were set apart for the public 
assemblies, they were wont to come within the city, 
where, dividing themselves into several companies, 
they walked about the porticos, singing such words 
as these : ' Where are they who affirm three to 
be one power ? ' and hymns composed in defence 
of their tenets, adding petulant reflexions on the 
orthodox ; § this they continued for the greatest part 

J Vales, in Socrat. lib. IV. cap. xxvi. 

§ It seems that the orthodox could in their turns not only be petulant, 
but industrious in provoking their enemies to wrath, as may be collected 
from the following relation of Thcodoret : — 

' Publia, the deaconess, a woman admired and celebrated for her 
' piety, was the mother of the famous John, who for many years was first 
' presbyterofthe church ofthe Antioch, and though often and unanimously 
' elected to the apostolic tlirone, refused that dignity. She, aiid a chorus 
' of consecrated virgins with her, spent great part of their time in singing 
'anthems and divine songs; and once when the emperor [Julian] had 
' occasion to pass by them, they sung psalms chosen purpoSf-ly to expose 
' and ridicule the extravagancies of heathenism and idolatry, singing 
' them with an exalted voice ; and among tlie rest they applied, very 
'properly to the occasion, the hundred and fifteenth, from the fourth to 
' the eighth verse, "Their idols are silver and gold, even the work of 
" men's hands, &c." " Let those that make them be like unto them, and 
" also all such as put their trust in them." This so disturbed the empe- 
' ror, that he commanded silence should be kept whenever he came by 
' that place, but to so little purpose, that upon his returning, at the 
' motion of Publia tliey gave him another welcome in these words : — 
"Let God arise, and let his enemies ne scattered." And now his anger 
'was raised so high, that he ordered the cliantress to be brout;ht before 
' him, and had her beat on the face till her cheeks were stained with, 
'blood; which efl^orts of the tyrant's unmanly passion the aged good 
'woman received with pleasure, went home, and, as often as an oppor- 
' tunity offered, entertained liim still with the very same sort of dis- 
' agreeable compositions.' Hist. Eccles. 



Chap. XXIII. 



AND PEACTICE OF MUSIC. 



107 



of the night ; in the morning they marched through 
the heart of the city, singing in the same manner, 
and so proceeded to the place of their assembly. 
In opposition to these people, St. Chrysostom caused 
hymns to be sung in the night ; and to give his 
performance a pomp and solemnity, which the other 
wanted, he procured crosses of silver to be made at 
the charge of the empress Eudoxia, which, with 
lighted torches thereon, were borne in a procession, 
at which Briso, the empress's eunuch, officiated as 
precentor ; this was the occasion of a great tumult, 
in which Briso received a wound in the forehead 
with a stone, and some on both sides were slain.* 
This was followed by a sedition, which ended in the 
expulsion of the Arians. This manner of singing, 
thus introduced by them, was, as Sozomen relates,t 
used in Constantinople from that time forwards ; 
however, in a short time it was performed in such 
an unseemly way as gave great offence ; for the 
singers, affecting strange gestures and boisterous 
clamours, converted the church into a mere theatre ; 
for which Chrysostom reproved them, by telling 
his people that their rude voices and disorderly 
behaviour were very improper for a place of worship, 
in which all things were to be done with reverence 
to that Being who observes the behaviour of every 
one there. 

St. Ambrose, who had entertained a singular vene- 
ration for St. Basil, like him was a great lover of the 
church-service : it is true he was not originally an 
ecclesiastic, but having been imexpectedly elected 
bishop of Milan, he applied himself to the duties of 
the episcopal function. Justina, whom the emperor 
Valentinian had married, proving an Ai'ian, com- 
menced a prosecution against Ambrose and the ortho- 
dox ; during which the people watched all night in 
the church, and Ambrose appointed that psalms and 
hvmns should be suns: there after the manner of the 
oriental churches, lest the people shoiild pine away 
with the tediousness of sorrow ; and from this event, 
which happened about 374, we may date the intro- 
duction of singing into western churches. 

But the zeal of St. Ambrose to promote this 
practice, is in nothing more conspicuous than in his 
endeavours to reduce it into form and method ; as 
a proof whereof, it is said that he, jointly with St. 
Augustine, upon occasion of the conversion and 
baptism of the latter, composed the hymn Te Deum 
laudamus, Avhich even now makes a part of the 
liturgy of our church, and caused it to be sung in 
liis church at Milan ; but this has been discovered 
to be a mistake: I this however is certain, that he 
instituted that method of singing, known by the 
name of the Cantus Ambrosianus, or Ambrosian 

* Socrat. Hist. Eccles. lib. VI. cap. viii. 

+ Hist. Eccles. lib. VIII. cap. viii. 

I The very learned Dr Usher, upon the authority of two ancient 
manuscripts, asserts the Te Deum to have been made by a bishop of 
Triers, named Nicetlus or Nicettus, and that not till about the year 500, 
which was almost a century after the death both of St. Ambrose and 
St. AuRustine. L'Estrange's Alliance of Divine Offices, 79. The Bene- 
dictines, wlio published the works of St. Ambrose, judge him not to 
have been the author of it ; and Dr. Cave, though at one time he was 
of a different judgment, and bishop Stillinglleet, concur in the opinion 
that the Te Deum was not tlie composition of St. Ambrose, or of him 
and St. Augustine jointlv. Bingham's Antiquities of the Christian 
Church, book XIV. chap'ii. § •). 



Chant, a name, for ought that now appears, not 
applicable to any determined series of notes, but 
invented to exj^ress in general a method of singing 
agreeable to some rule given or taught by hira> 
This method, whatever it was, is said to have had 
a reference to the modes of the ancients, or rather 
to those of Ptolemy, which we have shewn to have 
been precisely coincident with the seven species of 
the diapason ; but St. Ambrose conceiving all above 
four to be superfluous, reduced them to that number,, 
retaining only the Dorian, the Phrygian, the Lydian, 
and the Mixolydian,§ which names he rejected, 
choosing rather to distinguish them by epithets of 
number, as protos, deuteros, tritos, tetrartos. His 
design in this was to introduce a kind of melody 
founded on the rules of art, and yet so plain and 
simple in its nature, that not only those whose 
immediate duty it was to perform the divine service, 
but even the whole congregation might sing it ; 
accordingly in the Romish countries the people now 
join with the choir in chanting the divine offices ; 
and if we may credit the relations of travellers in 
this respect, this distinguished simplicity of the 
Ambrosian Chant is even at this day to be remarked 
in the service of the church of Milan, where it was 
first instituted. 

A particular account of the ecclesiastical modes, 
as originally constituted by St. Ambrose, with the 
subsequent improvement of them by Gregory the 
Great, is reserved for another place : in the interim 
it is to be noted that the ecclesiastical modes are also 
called tropes, but more frequently tones ; which latter 
appellation was first given to them by Martianus 
Capella, as we are informed by Sir Henry Spelman, 
in his Glossary, voce FRiGDORiE. The following' 
scheme represents the progression in each : — 
d e f 



c 

h 

a 

G 
F 
E 
D 



d 
c 

h 

a 

G 
P 
E 



6 

d 
c 

h 

a 
G 
F 



o 

i 

e 
d 
c 

h 

a 
G 



And this was the original institution of what 
are called, in contradistinction to the modes or 
moods of the ancients, the ecclesiastical modes or 
tones. These of St. Ambrose, however well cal- 
culated for use and practice, were yet found to be 
too much restrained, and not to admit of all that 
variety of modulation which the several offices in 
the church-service seemed to require ; and accord- 
ingly St. Gregoiy, surnamed the Great, the first 
pope of that name, with the assistance of the most 
learned and skilful in the music of that day, set 
about an amendment of the Cantus Ambrosianus, 
and instituted what became known to later times by 
the name of the Cantus Gregorianus, or, the Gre- 
gorian Chant : but as this was not till near two 
hundred and thirty years after the time of St. 
Ambrose, the account of this, and the other improve- 

§ Sir Henry Spelman in his Glossary, voce Frigsors, in the place ot 

the Mixolydian puts the jEolian. 



108 



HISTORY OF THE SCIENCE 



Book III. 



ments made in music by St. Gregory, must be re- 
ferred to another place. 

With respect to the music of the primitive church, 
though it consisted in the singing of psalms and 
hymns, vet was it performed in sundry different man- 
ners, that is to say, sometimes the psalms were sung 
by one person alone, the rest hearing with attention ; 
sometimes they were sung by the whole assembly ; 
sometimes alternately, the congregation being for 
that purpose divided into separate choirs; and, lastly, 
by one person, who repeated the first part of the 
verse, the rest joining in the close thereof.* 

Of the four different methods of singing above 
•enumerated, the second and third were very properly 
distinguished by the names of symphony and anti- 
phony, and the latter was sometimes called respon- 
.saria;f and in this, it seems, women were allowed 
to join, notwithstanding the apostle's injunction on 
them to keep silence. 

The method of singing in the last place above 
mentioned, clearly suggests the origin of the office 
of precentor of a choir, whose duty, even at this day, 
it is to govern the choir, and see that the choral 
service be reverently and justly performed. 

It farther appears, that almost from the time 
when music was first introduced into the service 
of the church, it was of two kinds, and consisted in 
a gentle inflection of the voice, which they termed 
plain-song, and a more artificial and elaborate kind 
of music, adapted to the hymns and solemn offices 
■contained in its ritual ; and this distinction has been 
maintained through all the succeeding ages, even to 
this time. 

Besides the reverend fathers of the church above- 
mentioned, we are told, and indeed it appears from 
many passages in his writings, that Saint Augustine 
was a passionate lover of music ; this which follows, 
taken from his Confessions, lib. IX. cap. vi. is the 
most commonly produced as an evidence of his ap- 
probation of music in the church-service, though, it 
must be owned, he lived to recant it: 'How abundantly 

* did I weep before God, to hear those hymns of 

* thine ; being touched to the very quick, by the 
' voices of thy sweet church song. The voices flowed 
' into my ears, and thy truth pleasingly distilled into 
' my heart ; which caused the affections of my dc- 
' votion to overflow, and my tears to run over ; and 
' happy did I find myself therein.' From hence 
there is little reason to doubt, that he enjoined the 
use of it to the clergy of his diocese. He wrote 
a treatise De Musica, in six books, chiefly, indeed, on 
the subject of metre and the laws of versification, but 
interspersed with such observations on the nature 
of the consonances, as shew him to have been very 
well skilled in the science of music. 

It is not necessar}' to enter into a particular 
character, either of St. Augustine or of this his work : 

' Bingham's Antiq. book XIV. chap. i. 

t In this distinction between symphoniac and antiphonal psalmody, 
v,e may discern the origin of the two different methods of singiiiR 
practised in tlie Romish and Lutheran churches, and of those that 
follow the rule of Calvin, and others of the reformers ; in the former 
the singinp is antiphonal, in the latter it is a plain metrical psalmody, 
in which all join ; so that for each practice the authority of the primitive 
■ church may be appealed to. 



those who are acquainted with ecclesiastical history 
need not be told, that he was a man of great learning, 
for the time he lived in, of lively parts, and of exem- 
plary piety. To such, however, whose curiosity is 
greater than their reading, the following short ac- 
count of this eminent father of the church may not be 
unpleasing : — 

He was born at Thagaste, a city of Numidia, on 
the 13th of November, 354. His father, a burgess of 
that city, was called Patricius ; and his mother, 
Monica, who he'mg a woman of great virtue, instructed 
him in the principles of the Christian religion. In 
his early youth he was in the rank of the catechumens, 
and falling dangerously ill, earnestly desired to be 
baptized ; but the violence of the distemper ceasing, 
his baptism was delayed. His father, who was not 
yet baptized, made him study at Thagaste, Madaura, 
and afterwards at Carthage. St. Augustine, having 
read Cicero's books of philosophy, began to entertain 
a love for wisdom, and applied himself to the study 
of the Holy Scriptures ; nevertheless, he suffered 
himself to be seduced by the Manicheans. At the 
age of nineteen, he returned to Thagaste, and taught 
grammar, and also frequented the bar : he afterwards 
taught rhetoric at Carthage, with applause. The 
insolence of the scholars at Carthage made him take 
a resolution to go to Rome, though against his 
mother's will. Here also he had many scholars ; but 
disliking them, he quitted Rome, and settled at 
Milan, and was chosen public professor of rhetoric in 
that city. Here he had opportunities of hearing the 
sermons of St. Ambrose, which, together with the 
study of St. Paul's Epistles, and the conversion of 
two of his friends, determined him to retract his 
errors, and quit the sect of the Manicheans : this was 
in the thirty-second year of his age. In the vacation 
of the year 38G, he retired to the house of a friend of 
his, named Verecundus, where he seriously applied 
himself to the study of the Christian religion, in order 
to prepare himself for baptism, which he received at 
Easter, in the year 387. Soon after this, his mother 
came to see him at Milan, and invite him back to 
Carthage ; but at Ostia, Avhither he went to embark, 
in order to his return, she died. He arrived in 
Africa about the end of the year 388, and having 
obtained a garden-plot without the walls of the city 
of Hippo, he associated himself with eleven other 
persons of eminent sanctity, who distinguished them- 
selves by wearing leathern girdles, and lived there in 
a monastic way for the space of three years, exercising 
themselves in fasting, prayer, study, and meditation, 
day and night : from hence sprang up the Augustine 
friars, or eremites of St. Augustine, being the first 
order of mendicants ; those of St. Jerome, the Car- 
melites, and others, being but branches of this of St. 
Augustine. About this time, or as some say before, 
Valerius, bishop of Hippo, against his will ordained 
him priest : nevertheless, he continued to reside in 
his little monastery, with his brethren, who, re- 
nouncing all property, possessed their goods in 
common. Valerius, wlio had appointed St. Augustine 
to preach in his place, allowed him to do it in his 
presence, contrary to the custom of the churches in 



Chap. XXIIl. 



AND PRACTICE OF MUSIC. 



10^ 



Africa. He explained the creed, in a general council 
of Africa, held in 393. Two years after, Valerius, 
fearing he might be preferred to be bishop of another 
church, appointed him his coadjutor or colleague, and 
caused him to be ordained bishop of Hippo, by 
Megalius, bishop of Calame, then primate of Numidia. 
St. Augustine died the 28th day of August, 430, 
aged seventy-six years, having had the misfortune to 
see his country invaded by the Vandals, and the city 
where he was bishop besieged for seven months. 

The works of St. Augustine make ten tomes ; the 
best edition of them is that of jMaurin, printed at 
Antwerp, in 1700; they are but little read at this 
time, except by the clergy of the Greek church and 
in the Spanish universities ; our booksellers in 
London receive frequent commisions for them, and 
indeed for most of the fathers, from Russia, and also 
from Spain. 

About this time flourished Ambrosius Aueelius 
Theodosius IMacrobius, an author whose name ap- 
pears in almost every catalogue of musical writers 
extant ; but whose works scarcely entitle him to a 
place among them. He lived in the time of Theo- 
dosius the younger, who was proclaimed emperor of 
the East, anno 402. He was a man of singular 
dignity, and held the office of chamberlain to the 
emperor. Fabricius makes it a question whether 
he was Christian or a Pagan. His works are a com- 
mentary on the Somnium Scipionis of Cicero, in two 
books, and Saturnalia Convivia, in seven books ; in 
both which he takes occasion to treat of music, and 
more especially the harmony of the spheres. The 
chief of what he says concerning music in general is 
contained in his Commentary on the Somnium 
Scipionis, and is taken from Nicomachus, and others 
of the followers of Pythagoras. ]\Iartini mentions 
also a discourse ou mundane music of his, which was 
translated into Italian by Ercole Bottrigari, with 
notes ; but he speaks of it as a manuscript, and by 
the list of the works of Macrobius, it does not appear 
to have ever been printed. 

Of such writers as Macrobius, and a few other of 
the Latins who will shortly be mentioned, that have 
written not professedly on music, but have briefly or 
transiently taken notice of it in the course of a work 
written with some other view than to explain it, 
little is to be said. There is nevertheless a Greek 
writer of this class, who lived some considei-able time 
before Macrobius, and indeed was prior to Porphyry, 
the last of the Greek musical writers that deserves to 
be taken notice of, not so much because he has con- 
tributed to the improvement of the science, as because 
in a voluminous work of his there are interspersed 
a great variety of curious particulars relating to it, 
not to be found elsewhere. The author here meant 
is Athenajus the grammarian, called, by way of 
eminence, the Grecian Varro ; he was born at 
Naucratis in Egypt, and flourished in the third 
century ; of many works that he wrote, one only 
remains, intitled The Deipnosophists, that is to say, 
the Sophists at Table, where he introduces a number 
of learned luen of all professions, who converse iipou 
various subjects at the table of a Roman citizen 



named Larensius. In this work there are many 
very pleasant stories, and an infinite variety of facts, 
citations, and allusions, which make the reading of it 
extremely delightful. The little that he has said of 
music lies scattered up and down in this work, which,, 
with the Latin translation of it, makes a large folio 
volume. 

In his fourth book, pag. 174, he gives the names 
of the supposed inventors of the ancient musical in- 
struments, and, among others, of Ctesibus, and of 
tlie hydraulic organ constructed by him ; and it is 
supposed that this is the most ancient and authentic 
account of that instrument now extant. He says, 
pag. 175, that the Barbiton or lyre, or, as Mersennus 
will have it, the viol, was the invention of Anacreon ; 
and the 3Ionaulon, or single pipe, of the Egyptian 
Osiris. 

Elsewhere, viz., in his fourteenth book, he speaks 
of the power of music, and of the fondness which the 
Arcadians, above all other people, entertained for it : 
and in the same book, pag. 637, he describes that 
strange instrument, invented by Pythagoras Zacyn- 
thius, called the tripod lyre, corresponding in every 
particular with the description of it hereinbefore 
given from Blanchinus ; to which may be added, that 
Athenasus expressly says that the three several sets 
of chords between the legs, were in their tuning^ 
adjusted to the three primitive modes, the Dorian, 
the Lydian, and the Phrygian. 

Of this learned, curious, and most entertaining 
work, the best edition is that of Dalechamp, with the 
Greek original and Latin translation in opposite 
columns. To this are added the animadversions of 
Isaac Casaubon, which are very curious, and make 
another volume. In these it is said that the Music- 
orum ciayco-fjLfxara, or Tablatura, i. e., the art of 
writing or noting down of music, was invented by 
Stratonicus of Rhodes. Is. Casaub. Animadvers. in 
Athenaeum, lib. VIII. cap. xii. 

Martianus Mineus Felix Capella was born, as 
Cassiodorus testifies, at Madaura, a town in Africa,, 
situated between the countries of Getulia and 
Numidia, lived at Rome under Leo the Thracian, 
viz., aboi;t the year of Christ 457 ; he was the author 
of a woi'k intitled, De Nuptiis Philologise et Mercurii, 
the style whereof, in the opinion of some, is harsh, 
and rather barbarous, though others, and Fabricius 
in particular, who terms it a delightful fable,* think 
it in nowise deserves such a character : this work, 
which consists of prose and verse intermixed, is in 
fact a treatise on the seven liberal sciences, and con- 
sequently includes a discourse on music, which makes 
the ninth book thereof, and is introduced in the 
following manner : the author supposes the marriage 
of Philologia, a virgin, to Mercury, and that Venus 
and the other deities, as also Orpheus, Amphion, and 
Arion, are assembled to honour the solemnity; the 
Sciences, who, to render the work as poetical as may 
be, are represented as persons, also attend, among 
whom is Harmonia, described as having her head 
decked with variety of ornaments, and bearing 
symbols of the faculty over which she is feigned to 

* Biblioth. Lat. Art. Capella. 



110 



HISTORY OF THE SCIENCE. 



Book III. 



preside. She is made to exhibit the power of sounds 
by such melody as Jupiter himself commends, which 
is succeeded by a request of Apollo and Minerva to 
unfold the mysteries of harmony. She first craves 
leave to relate that she formerly was an inhabitant 
of the earth, and that through the inspirations of 
Pythagoras, Aristoxenus, and others, she had taught 
men the use of the lyre and the pipe ; and by the 
singing of birds, the wliistling of tlie winds, and the 
murmuring of water-falls, had instructed even the 
artless shepherds in the rudiments of melody. That 
by the power of her art she had cured diseases, 
quieted seditions, and composed and attempered the 
irregular affections of mankind ; notwithstanding all 
which, she had been contemned and reviled by those 
sons of earth, and had therefore sought the heavens, 
where she found the motions of the orbs regulated by 
her own principles. She then proceeds to explain 
the precepts of harmony in a short discourse, which, 
if we consider the substance and method rather than 
the style of it, must be allowed to be a very elegant 
composition, and by much the most intelligible of 
an}^ ancient treatise on the science of music now 
extant. 

Capella concludes this ninth book of his treatise 
De Nuptiis thus : ' When Harmonia had run over 

* these things concerning songs, and the sweetness of 

* verse, in a manner both august and persuasive, to 
' the gods and heroes, who were very intent, she de- 
cently withdrew ; then Jupiter rose up, and Cymesis 
modulating in divine symphonies, came to the 

''chamber of the virgin,. to the great delight of all.' 
The above discoiu'se of Martianus Capella is mani- 
festly taken from Aristides Quintilianus, of which, 
to say the truth, it is very little more than an abridg- 
ment, but it is such a one as renders it in some 
respects preferable to the original ; for neither is it 
so prolix as Quintilian's treatise, nor does it partake 
of that obscurity which discourages so many from 
the study of his work ; and when it is said, as it has 
been by some, that the style of Capella is barbarous, 
this must be taken as the opinion of grammarians, 
who, without regarding the intrinsic merit of any 
work, estimate it by certain rules of classical elegance, 
which they themselves have established as the test 
of perfection. It is by these men, and for this 
reason, and perhaps because he had not the good 
fortune to be born at Rome, that Capella is termed 
a semi-barbarian, and his writings reprobated as 
unworthy the perusal of men of science.*-' But, 
notwithstanding these opinions, one of the best gram- 
marians of the present age, the learned and ingenious 

* The learned bishop of Avranches is somewhat less severe in his 
censure. He gives the foUowinfr character of Capella and his work: — 
' Martianus Capella has piven the name of satire to his work because it 

* is written in verse and prose, and the profitable and entertaining parts 
'are agreeably interwoven. His design is to treat of the arts, which 
'have the appellation of liberal; and these he represents by certain 
' allegorical personages, with attributes proper to each. The principal 

* action in this fable is the marriage of Mercury and Philology, a feigned 
' being, intended to signify the love of literature. The artifice of this 
'allegory is not very subtle, and as to the style it is barbarism itself ; 
'and for the figures, they are unpardonably' bold and extravagant; 
'besides all which it is so obscure as hardly to be intelligible; otherwise 
'it is learned, and full of notions not common. Some write that the 
' author was an African ; if he was not, his harsh and forced style would 

* induce one to believe he was of that country. The time he lived in is 
' unknown ; it only appears that he was more ancient than Justinian.' 
Huetius de I'Origine des Remains. 



author of Hermes, or a Philosophical Inquiry con- 
cerning Universal Grammar, has forborne to pass 
a censure of barbarity on the style of this author : 
his sentiment of him is, that he was rather a philo- 
logist than a philosopher ; a testimony that leaves 
him a better character than some of those deserve 
who have been so liberal in their censures of him. 
It has been said above, that Fabricius has given to 
the treatise De Nuj^tiis the character of a delightful 
fable ; and Gregorj^ of Tours delivers his opinion 
of it at large in the following words: 'In gram- 
' maticis docent legere, in dialecticis altercationum 
' propositiones advertere, in rhetoricis persuadere, in 
' geometricis terrarum linearumque mensuras col- 
' ligere, in astrologicis cursus siderum contemplari, 
' in arithmeticis numerorum partes colligere, in har- 
' moniis sonorum modulationes suavium accentuum 
' carminibus concrepare.' Hence it may seem that 
Mr. IMalcolm was rather too hasty in condemning 
this work ; and that in pronouncing of its author as 
he has done in his Treatise on Music, pag. 498, that 
he was but a sorry copier from Aristides, he has 
done him injustice. Of Capella's work, De Nuptiis 
Philologife et Mercurii, there have been many edi- 
tions ; that of Meibomius is the most useful to 
a nmsician ; but there is a very good one, with 
corrections and notes, by Grotius, in octavo, published 
in 1559, when he was but fourteen years of age. 

CHAP. XXIV. 

The several works hereinbefore enumerated con- 
tain the whole of what, in the strict sense of the 
term, we are to understand by the ancient system 
of music ; and as many of them appear to be of 
very great antiquity, we are to esteem it a singular 
instance of good fortune that they are yet remaining; 
that they are so, is owing to the care and industry 
of very many learned men, who, from public li- 
braries, and other repositories, have sought out the 
most correct manuscripts of the respective authors, 
and given them to the world in print ; As to Aris- 
toxenus, the first in the list of the harmonical writers, 
it is doubtful whether his Elements ever appeared 
in print, till near the middle of the seventeenth 
century, inasmuch as Morley, who lived in the reign 
of our queen Elizabeth, and was a very learned and 
inquisitive man in all matters relating to musical 
science, professes never to have seen the Elements 
of Aristoxenus ; Euclid indeed had been published 
in the year 1498, in a Latin translation of Georgius 
Valla, of Placentia, but under the name of Cleonidas, 
It was also, in 1557, published at Paris in Greek, 
with a new Latin translation by Johannes Pena, 
mathematician to the French king, but in a very 
incorrect manner ; other editions were also published 
of it, in which the errors of the former were multi- 
plied. At length, ynih the assistance of our countiy- 
nien Selden, and Gerard Langbaine, Marcus Mei- 
bomius, a man well acquainted with the science, and 
well skilled in Greek literature, published it, to- 
gether with Aristoxenus Nicomachus, Alypias, Gau- 
dentius, Eacchius Senior, Aristides Quintilianus, 



Chap. XXIV. AND PRACnCE OF MUSIC. Ill 

and the ninth book of the fable de Nuptiis Philo- a design of giving it to the workl, he generously sent 

logise et Mercurii of Martianus Capella, with a Latin him his papers, and remitted the care of publishing 

translation of the first seven of the above-named them to him. 

writers, a general preface replete vv^ith excellent Bacchius Senior was first published in the original 

learning, and copious notes on them all. Greek, and with a French translation by Mersennus, 

Besides the general preface, Meibomius has given in a commentary on certain chapters in the book of 

a particular one to each author as they stand in his Genesis, written by him to explain the music of the 

edition, which prefaces, as they contain a variety of ancient Hebrews and Greeks, intitled ' Questiones et 

particulars relating to the respective authors and ' Explicatio in sex priora capita Geneseos, quibus 

their works, and are otherwise curious, are well ' etiam Graecorum et Hebrajorum Musica instauratur.' 

worthy of attention. The Manual of Nicomachus Of this translation Meibomius, in his general preface, 

was first published and translated into Latin by speaks in very severe terms ; he says he did not know 

Meibomius, who gives the author a very great cha- that any such was extant, till he was informed thereof 

racter, and with great ingenuity fixes the time when by his friend Ismael Bullialdus ; he says that he then 

he lived ; for he observes that Nicomachus in the had it brought to him from Paris by the courier, and 

course of his work mentions Thrasyllus, who he that if he had seen it before he had published his 

says he thinks to be the same with one of that name notes on that author, they would have been made 

mentioned frequently by Suetonius in Augustus and much fuller by observations on his errors. However 

Tiberius, and by the old commentator on Juvenal, the only error that Meibomius here charges Mer- 

Sat. VI. as a famous mathematician ; and from hence sennus with, is that of having confounded the Stantes 

he infers that he lived after the time of Augustus. with the Mobiles in his representation of the Systema 

To the Isagoge of Alypius the preface is but very maximum, 
short, but in that to Gaudentius, which follows it next Aristides Quintilianus is taken from a manuscript 
in order Meibomius cites a passage from Cassiodorus, which Meibomius frequently mentions as belonging 
a Latin writer on music, who flourished in the fifth to Joseph Scaliger, in which was contained Alypius, 
century, and will presently be spoken of, from whence Nicomachus, Aristoxenus, Aristides, and Bacchius. 
he thinks the age when Alypius lived may in some This manuscript was deposited in the library of Ley- 
measure be learned. He observes also that it appears den, and communicated to him by Daniel Heinsius, 
from the same passage of Cassiodorus that Gaudentius together with two manuscripts of Martianus Capella. 
had been translated into Latin by a Roman, a friend With the assistance of the several manuscripts 
of his, named Mutianus ; * the whole passage, to above-mentioned, and a correspondence with the 
give it together as it stands in Cassiodorus, is in most learned men of his time, namely, Selden, Lang- 
these words : ' Gratissima ergo nimis utilisque cog- baine, Salmasius, Leo Allatius, and many others, 
' nitio, quae et sensum nostrum ad superna erigit, et Meibomius completed his edition of the ancient mu- 
' aures modulatione permulcet : quam apud Graecos sical authors, and published it at Amsterdam in the 
' Alypius, Euclydes, Ptolemaeus, et caeteri probabili year 1G52, with a dedication to Christina, queen of 

* institutione, docuerunt. Apud Latinos autem vir Sweden. 

' magnificus Albinus librum de hac re, compendio, With respect to the other Greek writers, namely, 

* sub brevitate conscripsit, quem in bibliotheca Romse Ptolemy, Manuel Bryennius, and Porphyry, the 

* non habuisse atque studiose legisse retinemus. Qui former of these was published, together with Por- 
' si forte gentili incursione sublatus est, habetis hie phyry's Commentary, by Antonius Gogavinus, at 
' Gaudentium Mutiani Latinum : quem si solicita Venice, with a Latin version in 1562, but, as it 
' intensione legitis, hujus scienti* vobis atria patefacit. should seem from Dr. Wallis's censure of it, in a very 
' Fertur etiam latio sermone et Apuleium Madauren- inaccurate manner : Meibomius somewhere says that 

* sam instituta hujus operis eflicisse, scripsit etiam et he had intended to publish both Porphyry and 
' pater Augustinus de Musica sex libros, in quibus Manuel Bryennius, but he not having done it. Dr. 
' humanam vocem, rhythmicos sonos, et harmoniam Wallis imdertook it, and has given it to the world in 
' modulabilem in longis syllabis atque brevibus the third volume of his works. Most of the manu- 
' naturaliter habere monstravit. Censorinus quoque scripts that were made use of for the above pub- 
' de accentibus voci nostrse ad necessarise subtiliter lications, had been carried to Constantinople upon 
' disputavit, pertinere dicens ad musicam disciplinam : the erection of the eastern empire, to preserve them 
' quem vobis inter cseteros transcriptum reliqui.' from the ravages of the northern invaders : and as 
Cassiod. de Musica. that city continued to be the seat of learning for 

Gaudentius is published from a manuscript, which some centuries, they, together with an immense col- 

the editor procured of his friends Selden and Lang- lection of Greek and Latin manuscripts, containing 

baine, who collated it for him, with two others which the works of the most valuable of the Greek and 

had been presented to the Bodleian library, the one Roman writers, were preserved there with _ great 

by Sir Henry Savil, and the other by William, Earl care. But the taking and sacking of Constantinople 

of Pembroke, formerly chancellor of the university by the Turks, in the year 1453, was followed by an 

of Oxford. It seems that our countryman Chilmead emigration of learning and learned men, who, 

had undertaken to publish an edition of Gaudentius, escaping from the destruction that threatened them, 

but being informed that Meibomius had entertained settled chiefly in Italy, and became the revivers of 

* Mutianus also translated the Homilies of St. Chrysostom. Fabr. literature in the western parts of Europe. 
Eiblioth. Uraec. lib. III. cap. x. 



112 



HISTORY OF THE SCIENCE 



Book III. 



These men upon their removal from Constantinople 
brought with them into Italy an immense treasure of 
learning, consisting of ancient manuscripts in all the 
several branches thereof, which they disseminated by 
lectures in the public schools : many of these manu- 
scripts have at different periods been printed and 
dispersed throughout Europe, and others of them 
remain unpublished, either in public libraries, or in 
the collections of princes and other great persons.* 

These men are also said to have introduced into 
Italy the knowledge of ancient music, which they 
could no otherwise do than by public lectures, and by 
giving to the world copies of the several treatises of 
the Greek harmonicians, hereinbefore particularly 
mentioned ; and the effects of these their labours to 
cultivate that kind of Ivuowledge were made apparent 
by Gaffurius, or Franchinus, as he is otherwise 
called, who, before the end of the fifteenth century, 
published those several works of his, which have 
justly entitled him to the appellation of the Father of 
Music among the moderns. 

Before the migration of learning from the East, all 
that was known of the ancient music in the western 
parts of Europe was contained in the writings of 
Censorinus, Macrobius, Martianus Capella, Boetius, 
Cassiodorus, and a few other Latin writers, who, as 
Meibomius says of Capella, might very justly be 
termed Pedarians, inasmuch as they were strict fol- 
lowers of the ancient harmonicians ; or else in the 
works of a very learned and excellent man, to whom 
this censure cannot be extended, namely, Boetius, of 
whom, and of whose inestimable work De Musica a 
very particular account will shortly be given ; in the 
interim it will be necessary to mention some inno- 
vations that had been made in music subsequent to 
Ptolemy, and before Boetius, of whom we are about 
to speak ; and first it is to be noted that in this in- 
terval, if not before the commencement of it, the 
genera, at least in practice, were reduced to one, 
namely, the diatonic : and next it is to be remarked, 
that the method of notation used by the ancients, the 
explanation whereof is almost the sole purpose of 
Alypius's book, was totally changed by the Romans, 
who to the great system, which consisted, as has been 
shewn, of a bisdiapason, containing fifteen sounds, 
applied as many letters of their own alphabet ; so 
that assigning to Proslambanomenos the letter A, the 
system terminated at P. It does not appear that at 
this time, nor indeed till a long time after, any marks 
or characters had been invented to denote the length 
or duration of musical sounds ; nor, notwithstanding 

* The manuscripts relatins to music -which Kircher procured access to 
for the purpose of compiling his Musurgia, are by him said to be extant in 
the library of the Roman College ; and he speaks of one huge tome in 
particular, in which he says are the several works of Aristides Quin- 
tilianus, Bryennius, Plutarch, Aristotle, Callimachus, Aristoxenus, 
Alvpius, Ptolemy, Euclid, Nicomachus, Boetius, Martianus Capella, 
Valla, and some others. In the account of the late discoveries in the 
ruins of Herculaneum, given by the Abbe Winckelman, mention is 
made of an ancient Greek treatise on music found there, written by 
one Philodemus, an author who has escaped the researches of the 
industrious Fabricius. Nevertheless, a philosopher of that name occurs 
among the Locrians, in Stanley's list of tlie Pythagorean School. Hist, 
of Philosophy, Pythagoras, chap. xxiv. This manuscript the anti- 
quaries employed by the King of Naples, though it is burned to a crust, 
have begun to unroll ; but the condition of it, and the -nature of the 
process made use of for developing it, render it almost impossible that 
the world can ever be the better for its contents. See the Letter of the 
Abbe AVinckelman to Count Bruhl on this subject. 



all tliat has been said about the rhythmiis of the an- 
cients, does it in the least appear that they had any 
rule for determining the length of the sounds, other 
than that Avhich constituted the measure of the versesf 
to which those sounds were severally applied ; which 
consideration leaves it in some sort a question whe- 
ther among the ancients there was any such thing as 
merely instrumental music. 

In this method of notation by the first fifteen let- 
ters of the Latin alphabet, a modern will discover a 
great defect ; for, being in a lineal position, they by 
their situation inferred no diversity between grave 
and acute, whereas in the stave of the moderns the 
characters by a judicious analogy are made to ex- 
press, according to their different situations in the 
stave, all the diifcrences of the acute and grave from 
one extremity of the system to the other. 

Anitius Manlius Torquatus Severinus Boetius,"}" 
Avas the most considerable of all the Latin writers on 
music ; indeed his treatise on the subject supplied for 
some centuries the want of those Greek manuscripts 
which were supposed to have been lost ; for this 
reason, as also on account of his superior eminence in 
literature, he merits to be very particularly spoken 
of. He was by birth a Ptoman, descended of an an- 
cient family, many of whom had been senators, and 
some advanced to the dignity of the consulate : the 
time of his birth is related to have been about that 
period in the Roman history when Augustulus, whose 
fears had induced him to a resignation of the empire, 
was banished, and Odoacer, king of the Herulians, 
began to reign in Italy, viz., in the year of Christ 47G, 
or somewhat after. The father of Boetius dying 
while he was yet an infant, his relations undertook 
the care of his education and the direction of his 
studies ; his excellent parts were soon discovered, 
and, as well to enrich his mind with the study of 
philosophy, as to perfect himself in the Greek lan- 
guage, he was sent to Athens. Returning young to 
Rome, he was soon distinguished for his learning and 
virtue, and promoted to the principal dignities in 
the state, and at length to the consulate. Living in 
great affluence and splendour, he addicted himself to 
the study of theology, mathematics, ethics, and logic ; 
and how great a master he became in each of these 
branches of learning appears from those works of his 
now extant. The great offices which he bore in the 
state, and his consummate wisdom and inflexible 
integrity, procured him such a share in the public 
councils, as proved in the end his destruction ; for as 

t In the Chronology of Sir Isaac Newton, pag. 14, is the following 
passage: — 'In the year 1035 [before Christ] the Idtei Dactyli [a people 
' supposed to have come from Numidia, vide Heyl. Cosm. pag. 555. edit. 
' 1703J find out iron in mount Ida in Crete, and work it into armour and 
' iron tools, and thereby give a beginning to the trades of smiths and 
' armourers in Europe ; and by singing and dancing in their armour, 
' and keeping time by striking upon one another's armours with their 
' swords, they bring in music and poetry, and at the same time they 
' nurse up the Cretan Jupiter in a cave of the same mountain, dancing 
' about him in their armour.' 

The origin of metrical numbers, and of the rhythmus, as it is called, 
is by some referred to this event ; but admitting this as a fact, it docs 
not a.«certain the time when the characters declaring the length or dura- 
tion of sounds were first invented ; and the truth is that these are, com- 
paratively speaking, a modern improvement in music. 

* The name of this eminent person is sometimes icritten Boethius. Hoff- 
man, in his lexicon, determines in favour of Boeti/is, and it is to be noted, 
that in the edition of the works nf Boetius, printed at Venice in 1499, the 
same reading is uniformly adhered to. 



Chap. XXIV. 



AND PRACTICE OF MUSIC. 



113 



he ever employed his interest in the king for the 
protection and encouragement of deserving men, so 
he exerted his utmost efforts in the detection of 
fraud, the repressing of violence, and the defence of 
the state against invaders. At this time Theodoric 
the Goth had attempted to ravage the Campania; 
and it was owing to the vigilance and resolution of 
Boetius that that country was preserved from de- 
struction. At length, having murdered Odoacer, 
Theodoric became king of Italy, where he governed 
thirty -three years with prudence and moderation, 
during which time Boetius possessed a large share of 
his esteem and confidence. It happened about this 
time that Justin, the emperor of the East, upon his 
succeeding to Anastasius, made an edict condemning 
all the Arians, except the Goths, to perpetual banish- 
ment from the eastern empire : in this edict Hor- 
misda, bishop of Rome, and also the senate concurred; 
but Theodoric, who, as being a Goth, was an Arian, 
was extremely troubled at it, and conceived an aver- 
sion against the senate for the share they had borne 
in this proscription. Of this disposition in the king, 
three men of profligate lives and desperate fortunes, 
Gaudentius, Opilio, and Basilius, took advantage ; 
for having entertained a secret desire of revenge 
against Boetius, for having been instrumental in the 
dismission of the latter from a lucrative employment 
under the king, they accused him of several crimes, 
such as the stifling a charge, the end whereof was to 
involve the whole senate in the guilt of treason ; and 
an attempt, by dethroning the king, to restore the 
liberty of Italy ; and, lastly, they suggested that, to 
acquire the honoiirs he was in possession of, Boetius 
had had recourse to magical arts. 

Boetius was at this time at a great distance from 
Rome ; however Theodoric transmitted the com- 
plaint to the senate, enforcing it with a suggestion 
that the safety, as well of the people as the prince, 
was rendered very precarious by this supposed design 
to exterminate the Goths : the senate perhaps fearing 
the resentment of the king, and having nothing to 
hope from the success of an enterprize, which, sup- 
posing it ever to have been meditated, was now ren- 
dered abortive, without summoning him to his defence, 
condemned Boetius to death. The king however, 
apprehending some bad consequence frpm the exe- 
cution of a sentence so flagrantly unjust, mitigated 
it to banishment. The place of his exile was Ti- 
cinum, now the city of Pavia, in Italy : being in 
that place separated from his relations, who had not 
been permitted to follow him into his retirement, he 
endeavoured to derive from philosophy those com- 
forts which that alone was capable of affording to 
one in his forlorn situation, sequestered from his 
friends, in the power of his enemies, and at the 
mercy of a capricious tyrant ; and accordingly he 
there composed that valuable discourse, entitled De 
Consolatione Philosophias. To give a more par- 
ticular account of this book would be needless, it 
being well known in the learned world : one re- 
markable circumstance relating to it is, that, by those 
under affliction it has in various times been applied 
to. as the means of fortifying their minds and re- 



conciling them to the dispensations of Providence, 
almost as constantly as the scriptures themselves. 
Our Saxon king Alfred, whose reign, though happy 
upon the whole, was attended with great vicissitudes 
of fortune, had recourse to this book of Boetius, at 
a time when his distresses compelled him to seek 
retirement ; and, that he might the better impress 
upon his mind the noble sentiments inculcated in it, 
he made a complete translation of it into the Saxon 
language, which, within these few years, has been 
given to the world in its proper character : Chaucer 
made a translation of it into English, which is 
printed among his works, and is alluded to in these 
verses of his : — 

Adam Scrivener, yf ever it the befalle 

Boece or Troiles for to write nevv', 

Under thy longe lockes thou muft have the fcalle : 

But after my makynge thou write more true j 

So ofte a daye I mote thy werke renewe, 

It to corrcfte, and eke to rubbe and fcrape, 

And al is thorow thy negligence and rape. 

And Camden relates, that queen Elizabeth, during 
the time of her confinement by her sister Mary, to 
mitigate her grief, read and afterwards translated it 
into very elegant English. 

It is more than probable that Boetius would have 
ended his exile by a natural death, had it not been 
for an event that happened about two years after the 
pronouncing his sentence ; for, in the year 524, 
Justin, the emperor, thought fit to promulgate an 
edict against the Arians, whereby he commanded, 
without excepting the Goths, as he had done lately, 
on another occasion, that all bishops who maintained 
that heresy should be deposed, and their churches 
consecrated after the true Christian form. To avert 
this decree, Theodoric sent an embassy to the emperor, 
which, to render it the more splendid and respectable, 
consisted of the bishop or pope himself, who at that 
time was John the Second, the immediate successor 
of Hormisda, and four others, of the consular and 
patrician orders, who were instructed to solicit with 
the emperor the repeal of this decree, with threats, 
in case of a refusal, that the king would destroy 
Italy with fire and sword. Upon the arrival of the 
ambassadors at Constantinople, the emperor very 
artfully contrived to receive them in such a manner 
as naturally tended to detach them from their master, 
and make them slight the business they were sent to 
negociate, and he succeeded accordingly ; for as soon 
as they approached the city, the emperor, the clergy, 
and a great number of the people, went in procession 
to meet them. In their way to the church, the upper 
hand of the emperor was given to the bishop ; and 
upon their arrival there, the holy father, to shew his 
gratitude for the honour done him of sitting on the 
right of the imperial throne, celebrated the day of 
the Resurrection after the Roman use, and crowned 
Justin emperor. Of the insufferable pride and arro- 
gance of this John so many instances are related, 
that no one who reads them can lament the fate 
which afterwards befel him, viz., that he died in 
a dungeon. It is recorded, that upon his arrival 
at Corinth, in his way to Constantinople, great 
enquiry was made for a gentle horse for him to 



114 



HISTORY OF THE SCIENCE 



Book III. 



ride on ; upon which, a nobleman of that city sent 
him one that, for the goodness of its temper, had 
been reserved for the use of liis lady ; the bishop 
accepted the favour, and, after travelling as far as 
he thought fit, returned the beast to the owner : but 
behold what followed, the sagacious animal, conscious 
of the merit of having once borne the successor of 
St. Peter, refused ever after to let the lady mount 
him ; upon which the husband sent him again to the 
Pope, with a request that he would accept of that 
which was no longer of any use to the owner. This 
event, it is to be noted, is recorded as a miracle ; but 
if we allow it the credit due to one, it will reflect 
but little honour on the worker of it, since the 
utmost it proves is, that the Pope had the power of 
communicating to a horse a quality which had ren- 
dered the primitive possessor of it to the last degree 
odious. 

It is not easy to see how, with any degree of pro- 
priety, or consistent with justice, the misbehaviour 
of the ambassadors could be imputed to Boetius, who, 
all this while, was confined to the place of his exile, 
and seemed to be employing his time in a way much 
more suited to his circumstances and character than 
in the abetting the misguided and malevolent zeal of 
either of two enthusiastic princes ; nevertheless, we 
are told, that Theodoric no sooner heard of the be- 
haviour of John and his colleagues, than he began to 
meditate the death of Boetius : he however suppressed 
his resentment, till he had received a formal complaint 
from his people of the infidelity of those trusted by 
him. Immediately on his arrival, he committed the 
bishop to close confinement, wherein he shortly after 
ended his days. Had his revenge stopped here, his 
conduct might have escaped censure, but he completed 
the ruin of his character by sentencing Boetius to 
death, who, together with Symmachus, the father of 
his wife, was beheaded in prison on the tenth of the 
kalends of November, 525. In order to palliate the 
cruelty of the king, it has been insinuated, that the 
treachery of his ambassadors was a kind of evidence 
that the conspiracy had a foundation in truth ; and 
that fact once established, the intimacy which had 
subsisted for several years between Boetius and the 
bishop, before the banishment of the former, furnished 
a ground for suspicion that he was at least not 
ignorant of it. It is farther said, that, as if he 
believed the conspiracy to be real, the king sent to 
Boetius, in prison, offers of pardon, if he would dis- 
close the whole treason ; but the protestations which 
he made upon that occasion of his innocence, afford 
the strongest evidence that could be given that he 
was not privy to it. 

But the causes of this severe resolution of Theo- 
doric are elsewhere to be sought for : he was arrived 
at the age of seventy-two, and for some years had 
been infected with the vices usually imputed to old 
age : he had reigned more than thirty-three years ; 
and though the mildness and prudence of his govern- 
ment, and that paternal tenderness with which he had 
ruled his people, were greater than could be expected 
from a prince who had made his way to dominion 
by the murder of the rightful sovereign, the dis- 



appointments he had met with, the insults that had 
been offered him, one particularly in the person of 
his sister, who had received some indignities from 
the African Vandals, the contempt that had been 
shewn him in this late embassy, and, above all, his 
utter inability to resent these injuries in the way he 
most desired, these misfortunes concurring, deprived 
him of that equanimity of temper which had been 
the characteristic of his reign : in short, he grew jea- 
lous, timid, vindictive, and cruel ; and after this, 
nothing he did was to be wondered at.* But to 
return to Boetius. 

The extensive learning and eloquence of this great 
man are conspicuous in his works ; and his singular 
merits have been celebrated by the ablest writers that 
have lived since the restoration of learning. His first 
wife, for he was twice married, was named Helpes, a 
Sicilian lady of great beauty and fortune, but more 
eminently distinguished by the endowments of her 
mind, and her inviolable affection for so excellent a 
man. She had a genius for poetry, and wrote with 
a degree of judgment and correctness not common to 
her sex. He desired much to have issue by her ; 
but she dying young, he embalmed her memory in 
the following elegant verses : — 

Helpes dicta fui, Siculte regionis alumna, 
Quam procul a patria, conjugis egit amor. 
Quo sine, mcesta dies, nox anxia, flebilis hora 

Nee solum caro, sed spiritus unus erat. 
Lux mea non clausa est, tali remanente marito, 
Majorique anima;, parte superstes ero. 
Porticibus sacris tarn nunc peregrina quiesco, 

Judicis eterni testificata thronum. 
Ne qua manus bustum violet, nisi forte jugalis, 
Haec iterum cupiat jungere membra suis. 
Ut Thalami cumuHq ; comes, nee morte revellar. 
Et socios vitse nectat uterque cinis. 

His other wife, Rusticiana, was the daughter of 
Quintus Aurelius Menius Symmachus, a chief of the 
senate, and consul in the year 485 : with her he 
received a considerable accession to his fortune. He 
had several children by her ; two of whom arrived 
to the dignity of the consulate. His conjugal tender- 
ness was very exemplary ; and it may be truly said, 
that, for his public and private virtues, he was one of 
the great ornaments of that degenerate age in which 
it was his misfortune to be born. 

The tomb of Boetius is to be seen in the church of 
St. Augustine, at Pavia, near the steps of the chancel, 
with the following epitaph : — 

Moeonia et Latia lingua clarissimus, et qui 
Consul eram, hie perii, missus in exilium ; 
Et quia mors rapuit? Probitas me vexit ad auras, 
Et nunc fama viget maxima vivit opus. 

Many ages after his death the emperor Otho the 
Third enclosed his bones, then lying neglected 

• Procopius relates that he was frighted to death ; the following is his 
account of that strange accident : — 

' Symmachus and his son-in-law, Boetius, just men and great relievers 
' of the poor, senators and consuls, had many enemies, by whose false 
' accusations Theodoric, being persuaded that they plotted against him, 
'put tliem to death, and confiscated their estates. Not long after, his 
' waiters set before him at supper the head of a great fish, which seemed 
' to him to be the head of Symmachus, lately murthered ; and with his 
'teeth sticking out, and fierce glaring eyes, to threaten him. Being 
' frighted, he grew chill, went to bed lamenting what he had done to 
' Symmachus and Boetius, and soon after died.' De Bello Gothico, lib. I. 



Chap. XXIV. 



AND PRACTICE OF MUSIC. 



115 



amongst the rubbish, in a marble chest ; upon which 
occasion Gerbert, an eminent scholar of that time, 
and who was afterwards advanced to the papal chair 
by the name of Sylvester the Second, did honour to 
his memory in the followinf? lines : — 

Roma potens, dum jura suo declarat in orbe, 
Pu pater, et patriae lumen, Severine Boeti, 
Consulis officio, rerum disponis habenas, 
Infundis kimen studiis, et cedere nescis 
Graecorum ingeniis, sed mens divina coercet 
Imperium mundi. Gladio bacchante Gothorum 
Libertas Romana perit : tu consul et exul, 
Insignes titulos prfeclara morte relinquis. 
Tunc decus Imperii, summas qui pr^gravat artes, 
Tertius Otho sua dignum te judicat aula ; 
jEternumque tui statuit monumenta laboris, 
Et bene promeritum, meritis exornat honestis. 

The writings of Boetius, the titles whereof are 
given below,* seem to have been collected with great 
care : an edition of them was printed at Venice, in 
one volume in folio, 1499. In 1570, Glareanus, of 
Basil, collated that with several manuscripts, and 
published it, with a few various readings in the 
margin. To render his author more intelligible, the 
editor has inserted sundry diagrams of his own ; but 
has been careful not to confound them with the 
original ones of Boetius. 

But before these, or indeed the doctrines of Boetius, 
can be rendered intelligible, it is necessary first 
to state the general drift and tendency of the author. 
in his treatise De Musica ; and next to explain the 
several terms made use of by him in the demonstra- 
tion of the proportions of the consonances and 
other intervals, as also the proportions themselves, 
distinguishing between the several species of arith- 
metical, geometrical, and harmonical proportion. 

The design of Boetius in the above-mentioned 
treatise was, by the aid of arithmetic, to demonstrate 
those ratios which those of the Pythagorean school 
had asserted subsisted between the consonances. 
These ratios are either of equality, as 1 : 1, 2 : 2, 
8 : 8, or of inequality, as 4 : 2, because the first con- 
tains the latter once, with a remainder : and of these 
ratios, or proportions of inequality, there are five 
kinds, as, namely, multiplex, superparticular, super- 
partient, multiplex superparticular, and miiltiplex 
superpartient ; all which will hereafter be explained. 

* In Porphyrium 4 Victorino translatuni, lib. II. In Porphyrium 4 
se Latinum factum, lib. V. In Prsdicamenta Aristotelis, lib. IV. In 
librum de Interpretatione Commentaria minora, lib. II. In eundem de 
Interpretatione Commentaria majora, lib. VI. Analyticomm pri- 
orum Aristotelis, Anitio Manlio Severino Boethio interprete, lib. II. 
Analyticomm posteriorum Aristotelis, Anitio Manlio Severino Boethio 
interprete, lib. II. Introductio ad categoricos Syllogismos, lib. I. De 
Syllogismo categorico, lib. II. De Syllogismo hypothetico, lib. II. De 
Divisione, lib. I. De Diffinitione, lib. I. Topicorum Aristotelis, Anitio 
Manlio Severino, interprete, lib. VIII. Elenchorum Sophisticorum 
Aristotelis, Anitio Manlio Severino Boethio interprete, lib. II. In 
Topica Cironis, lib. VI. De Differentiis Topicis, lib. IV. De Consola- 
tione PhilosophiEe, luculentissimis Johannis Murmelli (partim etiam 
Rodolphi Agricolce) Commentariis illustrati, lib. V. De Sancta Trini- 
tate, cum Gilbert! episopi Pictaviensis, cognemento porretae doctissimi 
olim viri commentariis, jam primum ex vetustissimo scripto codice in 
lucem editis, lib. IV. Quorum primus continet excellentem & piam 
doctrinam, de Trinitate & Unitate Dei : quomodo Trinita sit Unus 
Deus, & non Tres Dii, lib. I. Secundus tractat Questionem An Pater, 
& Filius, & Spiritus Sanctus substantialiter praedicentur, lib. I. Tertius 
cnmplectitur Hebdomaden : An omne quod sit, bonum sit, lib. I. 
Quartus evidenter & pie doeet, in Christo duas esse Naturas, & unam 
Personam, adversus Eutychen & Nestorium, lib. I. De Unitate & Uno, 
lib. I. De Disciplina Scholarium, lib. I. De Arithtica, lib. II. De 
Musica, lib. V. De Geometria, lib. II. 



These terms are made use of by Euclid, and others 
of the Greek writers, and were adopted by Boetius, 
and through him have been continued down to the 
Italian writers, in whose works they are perpetually 
occurring ; and though the modern arithmeticians 
have rejected them, and substituted in their places, 
as a much shorter and more intelligible method of 
designation, the immbers that constitute the several 
proportions, it is necessary to the understanding of 
the ancient writers, that the terms used by them 
should also be understood. 

Another thing necessary to be known, in order 
to the understanding not only of Boetius and his 
followers, but all who have written on those abstruse 
parts of music the ancient modes, the ecclesiastical 
tones, and their divisions into authentic and plagal, 
is the nature of the three different kinds of pro- 
portion, namely, arithmetical, geometrical, and har- 
monical ; a'l explanation whereof, as also of the 
several kinds of proportion of inequality can hardly 
be given in terms more accurate, precise, and in- 
telligible, than those of Dr. Holder, in his treatise 
on the Natural Grounds and Principles of Harmony, 
chap. V. wherein, after premising that all harmonic 
bodies and sounds fall under numerical calculations, 
he speaks thus of proportion in general : — 

' We may compare {i. e. amongst themselves) 
'either (1) magnitudes (so they be of the same 
' kind) ; or (2) the gravitations, velocities, durations, 
' sounds, &c. from thence arising ; or, farther, the 
' numbers themselves, by which the things compared 
' are explicated ; and if these shall be unequal, we 
' may then consider either, first, how much one of 

* them exceeds the other ; or, secondly, after what 
' manner one of them stands related to the other 
' as to the quotient of the antecedent (or former 

* term) divided by the consequent (or latter term) 
' which quotient doth expound, denominate, or shew, 
' how many times, or how much of a time or times, 
' one of them doth contain the other : and this by 
' the Greeks is called \oyoQ, ratio, as they are wont 

* to call the similitude or equality of ratios avcCkoyia 
' analogic, proportion, or proportionality; but custom 

' and the sense assisting, will render any over-curious 
' application of these terms minecessary. 

From these two considerations last mentioned, the 
same author says, there are wont to be deduced three 
sorts of proportion, arithmetical, geometrical, and 
a mixed proportion, resulting from these two, called 
harmonical. These are thus explained by him : — 

' 1. Arithmetical, when three or more numbers 
' in progression have the same difference ; as 2, 4, 
' 6, 8, &c. or discontinued, as 2, 4, 6 ; 14, 16, 18.' 

' 2. Geometrical, when three or more numbers 
' have the same ration, as 2, 4, 8, 16, 32 ; or dis- 
' continued, as 2, 4 ; 64, 128.' 

' Lastly, Harmonical, (partaking of both the other) 
' when three numbers are so ordered, that there be 
' the same ration of the greatest to the least, as there 
' is of the difference of the two greater to the dif- 
' ference of the two less numbers, as in these three 
' terms, 3, 4. 6, the ration of 6 to 3, (being the 

* greatest and least terms) is duple ; so is 2, the 



116 



HISTORY OF THE SCIENCE 



Book III. 



' difference of 6 and 4 (the two greater numbers) to 
' 1, the difference of 4 and 3 (tlie two less numbers) 

* duple also. This is proportion harmonical, which 
' diapason, 6 to 3, bears to diapente, 6 to 4, and 
' diatessaron, 4 to 3, as its mean proportionals.' 

' Now for the kinds of rations most properly 
' so called ; i. e. geometrical : first observe, that in 
' all rations, the former term or number, (whether 
' greater or less) is always called the antecedent ; 
' and the other following number, is called the con- 

* sequent. If therefore, the antecedent be the greater 
' term, then the ration is either multiplex, super- 
' particular, superpartient, or (what is compounded of 
' these) multiplex superparticular, or multiplex super- 
' partient.' 

* 1. Multiplex ; as duple, 4 to 2 ; triple, 6 to 2 ; 

* quadruple, 8 to 2.' 

' 2. Superparticular ; as 3 to 2, 4 to 3, 5 to 4 ; 
' exceeding but by one aliquot part, and in their 
' radical, or least numbers, always but by one ; and 
' these rations are termed sesquialtera, sesquitertia, 
' (or supertertia) sesquiquarta, or (superquarta) &c. 
' Note, that numbers exceeding more than by one, 
' and but by one aliquot part, may yet be super- 
' particular, if they be not expressed in their radical, 
' i. e. least numbers, as 12 to 8, hath the same ration 
' as 3 to 2 ; i. e. superparticular ; though it seem not 
' so till it be reduced by the greatest common divisor 
' to its radical numbers, 3 to 2. And the common 

* divisor, (i. e. the number by which both the terms 
' may severally be divided) is often the difference 
' between the two numbers ; as in 12 to 8, the dif- 
' ference is 4, which is the common divisor. Divide 
' 12 by 4, the quotient is 3 ; divide 8 by 4, the 
' quotient is 2 ; so the radical is 3 to 2. Thus also, 
' 15 to 10, divided by the difference, 5, gives 3 to 2 ; 
' yet in 16 to 10, 2 is the common divisor, and gives 

* 8 to 5, being superpartient. But in all super- 
' particular rations, whose terms are thus made larger 
' by being multiplied, the difference between the 
' terms is always the greatest common divisor ; as in 

* the foregoing examples.' 

' The third kind of ration is superpartient, exceed - 
' ing by more than one, as 5 to 3 ; which is called 
' superbipartiens tertias, (or tria) containing 3 and 
' § 8 to 5, supertripartiens quintas, 5 and |^.' 

' The fourth is multiplex superparticular, as 9 to 
' 4, which is duple, and sesquiquarta ; 13 to 4, which 
' is triple and sesquiquarta.' 

' The fifth and last is multiplex superpartient, as 
' 11 to 4; duple, and supertripartiens quartas.'* 

' When the antecedent is less than the consequent, 
' viz., when a less is compared to a greater ; then the 
' same terms serve to express the rations, only pre- 
' fixing sub to them ; as, submultiplex, subsuper- 
' particular, (or subparticular) subsuperpartient, (or 

* subpartient) &c. 4 to 2 is duple ; 2 to 4 is subduple, 
' 4 to 3 is sesquitertia ; 3 to 4 is subsesquitertia, 5 to 

* The above terms were used by the ancient geometers and arithme- 
ticians ; and therefore, for the understanding of such, and of Boetius in 
particular, it is very necessary that their meaning should be ascertained : 
but the manner now is to express the proportions by the numbers them- 
selves, rather than by the terms ; and briefly to say, as 31 is to 7, or as 
7 is to 31, rather than to say, quadrupla superbipartiens septimas, or 
subquadmpla supertri partiens septimas. Vide Harris's Lex. Tech. 

vol. I. l-'ROPOKTION. 



* 3 is superbipartiens tertias ; 3 to 5 is subsuper- 

* bipartiens tertias, &c.' 

The same author proceeds to find how the habi- 
tudes of rations are found in these words : — 

' All the habitudes of rations to each other, are 
found by multiplication or division of their terms, 
by which any ration is added to or subtracted from 
another ; and there may be use of progression of 
rations or proportions, and of finding a medium, 
or mediety, between the terms of any ration : but 
the main work is done by addition and subtraction 
of rations, which, though they are not performed 
like addition and subtraction of simple numbers in 
arithmetic, but upon algebraic grounds, yet the 
praxis is most easy.' 

' One ration is added to another ration, by mul- 
tiplying the two antecedent terms together, i. e. the 
antecedent of one of the rations, by the antecedent 
of the other. (For the more ease, they should be 
reduced into their least numbers or terms) ; and 
then the two consequent terms, in like manner. 
The ration of the product of the antecedents to 
that of the product of the consequents, is equal to 
the other two, added or joined together. Thus, 
for example, add the ration of 8 to 6 ; i. e. (ia 
radical numbers) 4 to 3, to the ratio of 12 to 10 
i. e. 6 to 5 ; the product will be 24 and 4 — — 3 
15, i.e.Q to 5; you may set them thus, 
and multiply 4 by 6, they make 24; 6 — 

which set at the bottom ; then multiply 

3 by 5, they make 15 ; which likewise 24 15 
set under, and you have 24 to 15 : which is a ration 
compounded of the other two, and equal to tlienL 
both. Reduce these products, 24 and 15, to their 
least radical numbers, which is by dividing as far 
as you can find a common divisor to them both 
(which is here done by 3), and that brings them to 
the ration of 8 to 5. By this you see that a third 
minor, 6 to 5, added to a fourth, 4 to 3, makes 
a sixth minor, 8 to 5. If more rations are to be 
added, set them all under each other, and multiply 
the first antecedent by the second, and that product 
by the third ; and again that product by the fourth, 
and so on ; and in like manner the consequents.' 

' This operation depends upon the fifth proposition 
of the eighth book of Euclid ; where he shows 
that the ration of plain numbers is compounded of 
their sides. 



See these diagrams : — ' 



L_ 1. 



12 



6 



' Now compound these sides. Take for the ante- 
' cedents, 4, the greater side of the greater plane, 
' and 3, the greater side of the less plane, and they 
' multiplied give 12. Then take the remaining two 
' numbers, 3 and 2, being the less sides of the planes 
' (for consequents), and they give 6. So the sides ot 
' 4 and 3, and of 3 and 2, compounded (by multiplying 



Chap. XXV. 



AND PRACTICE OF MUSIC. 



117 



the antecedent terms by themselves and the con- 
sequents by themselves) make 12 to 6 ; i. e. 2 to 1, 
which being applied, amounts to this ; ratio sesqui- 
altera 3 to 2, added to ration sesquitertia, 4 to 3, 
makes duple ration, 2 to 1. Therefore, diapente 
added to diatessaron, makes diapason.' 

' Subtraction of one ration from another greater, 
is performed in like manner, by multiplying the 
terms ; but this is done not laterally, as in addition, 
but crosswise ; by multiplying the antecedent of 
the former (i. e. of the greater) by the consequent 
of the latter, which produceth a new antecedent ; 
and the consequent of the former by the antecedent 
of the latter, which gives a new consequent ; and 
therefore, it is usually done by an oblique de- 
cussation of the lines. For example, if 
4 3 you would take 6 to 5 out of 4 to 3, you 
•^ may set them down thus : Then 4, mul- 
■^ tiplied by 5, makes 20 ; and 3, by 6, gives 
6 5 18 ; so 20 to 18, i. e. 10 to 9, is the re- 
20 18 mainder. That is, subtract a third minor 
10 9 out of a fourth, and there will remain a 

tone minor. 
' Multiplication of ratios is the same with their 
addition ; only it is not wont to be of divers rations, 
but of the same, being taken twice, thrice, or oftener, 
as you please. And as before, in addition, yoii added 
divers rations, by multiplying them ; so here, in mul- 
tiplication, you add the same ration to itself, after 
the same manner, viz., by multiplying the terms of 
the same ratio by themselves ; %. e. the antecedent 
by itself, and the consequent by itself, (which in 
other words, is to multiply the same by 2) and will 
in the operation be to square the ration first pro- 
pounded (or give the second ordinal power ; the 
ration first given being the first power or side) and 
to this product, if the simple ration shall again be 
added, (after the same manner as before) the aggre- 
gate will be the triple of the ration first given ; or 
the product of that ration, multiplied by 3, viz., the 
cube, or third ordinal power. Its biquadrate, or 
fourth power, proceeds from multiplying it by 4 ; 
and so successively in order, as far as you please 
you may advance the powers. For instance, the 
duple ration, 2 to 1, being added to itself, dupled 
or multiplied by 2, produceth 4 to 1, (the ration 
quadruple) ; and if to this, the first again be added, 
(which is eqiiivalent to multiplying that said first 
by 3), there will arise the ration octuple, or 8 to 1. 
Whence the ration, 2 to 1, being taken for a root, 
its duple 4 to 1, will be the square ; its triple, 8 to 1, 
the cube thereof, &c. as hath been said above. And 
to use another instance ; to duple the ration of 3 to 2, 
it must be thus squared :— 3 by 3 gives 9 ; 2 by 2 
gives 4, so the duple or square of 3 to 2 is 9 to 4. 
Again, 9 by 3 is 27, and 4 by 2 is 8 ; so the cubic 
ration of 3 to 2 is 27 to 8. Again, to find the 
fourth power or biquadrate, {i. e. squared square,) 
27 by 3 is 81, 8 by 2 is sixteen ; so 81 to IG is the 
ration of 3 to 2 quadrupled ; as it is dupled by tlie 
square, tripled by the cube, &c. To apply this 
instance to our present purpose, 3 to 2 is the ration 
of diapente, or a fifth in harmony ; 9 to 4 is the 



' ratio of twice diapente, (or a ninth, viz., diapason, 
'with tone major;) 27 to 8 is the ration of thrice 
' diapente, or three fifths, which is diapason, with 
' sixth major, viz., 13 major ; the ration of 81 to 16 
' makes four fifths, i. e. disdiapason, with two tones 

* major, i. e. a seventeenth major, and a comma of 81 
' to 80.' 

' To divide any ration, the contrary way must be 

* taken ; and by extracting of these roots respectively, 

* division by their indices will be performed, E. gr. 

* to divide it by 2, is to take the square root of it ; 

* by 3, the cube root ; by 4 the biquadratic, &c. 
' Thus, to divide 9 to 4 by 2, the square root of 9 

* is 3, the square root of 4 is 2 ; then 3 to 2 is a 
' ration just half so much as 9 to 4.' 

CHAR XXV. 

The nature of proportion being thus explained, 
without a competent knowledge whereof it would be 
in vain to attempt the reading of Boetius, it remains 
to give such an account of his treatise De Musica 
as is consistent with a general history of the science, 
and may be sufficient to invite the studious inquirer 
to an attentive perusal of this most valuable work. 
Here therefore follow, in regular order, the titles of 
the several chapters contained in the five books of 
Boetius's treatise De Musica, with an abridgment of 
such of them as seem most worthy of remark. 

Chap. i. Musicam naturaliter nobis esse conjunc- 
tam, et mores vel honestare vel evertere. 

Boetius in this chapter observes, that the sensitive 
power of perception is natural to all living creatures, 
but that knowledge is attained by contemplation. 
All mortals, he says, are endued vsdth sight, but whe- 
ther the perception be effected by the coming of the 
object to the sight, or by rays sent forth to it, is a 
doubt. When any one, continues he, beholds a tri- 
angle or a square, he readily acknowledges what he 
discovers by his eyes, but he must be a mathema- 
tician to investigate the nature of a triangle or a 
square. Having established this proposition, he 
applies it to the other liberal arts, and to music in 
particular ; which he undertakes to shew is con- 
nected with morality, inasmuch as it disposes the 
mind to good or evil actions ; to this purpose he 
expresses himself in these terms : ' The power or 
' faculty of hearing enables us not only to form a 
'judgment of sounds, and to discover their differ- 
' ences, but to receive delight, if they are sweet and 
' adapted to each other ; whence it comes to pass that, 
' as there are four mathematical sciences,* the rest 

* The four mathematical arts are arithmetic, geometry, music, and 
astronomy ; these were anciently termed the quadrivium, or fourfold 
way to knowledge ; the other three, grammar, rhetoric, and logic, com- 
pleting the number of the seven liberal sciences, were termed the 
trivium or threefold way to eloquence. Vide Du Cange, voce Qua- 
drivium. 

This scholastic division is recognized in an ancient monumental 
inscription in Westminstef Abbey, in memory of Gilbert Crispin, who 
died abbot of Westminster in 1117. 

Mitis eras Justus prudens fortis moderatus 
Doctus quadrivio nee minus in trivio. 

Widmore's Hist, of Westminster Abbey. 

And these are the arts understood in the academical degrees of bachelor 
and master of arts, for the ancient course of scholastic institution re- 
quired a proficiency in each. The satire, as it is called, of Martianus 
Capella, De Nuptiis Pbilologiae et Mercurii, is a treatise on the seven 



118 



HISTORY OF THE SCIENCE 



Book III. 



labour at the investigation of truth ; but this, besides 

' that it requires speculation, is connected with mo- 

' rality ; for there is nothing that more peculiarly 

distinguishes human nature, than that disposition 

observable in mankind to be one way affected by 

sweet, and another by contrary sounds; and tliis 

'affection is not peculiar to particular tempers or 

* certain ages, but is common to all ; and infants, 

* young, and even old men, are by a natural instinct 
'rendered susceptible of pleasure or disgust from 
' consonant or discordant sounds. From hence we 
'may discern that it was not without reason that 
' Plato said, that the soul of the world was conjoined 

* with musical proportion : and such is the effect^ of 
' music on the human manners, that a lascivious mind 
' is delighted with lascivious modes, and a sober mind 
' is more disposed to sobriety by those of a contrary 
' kind : and hence it is that the musical modes, for 
' instance the Lydian and Phrygian, take their names 
' from the tempers or distinguishing characteristics 
' of those nations that respectively delight in them : 
' for it cannot be that things, in their nature soft, 
' should agree with such as are harsh, or contrary- 
' wise ; for it is similitude that conciliates love ; 
' wherefore Plato held that the greatest caution was 
'to be taken not to suffer any change in a well- 
' moraled music, there being no corruption of man- 
' ners in a republic so great as that which follows a 
' gradual declination from a prudent and modest 
' music ; for, whatever corruptions are made in music, 
' the minds of the hearers will immediately suffer the 
' same, it being certain that there is no way to 
' the affections more open than that of hearing : and 
' these effects of music are discernible among different 
' nations, for the more fierce, as the Getge, are de- 
' lighted with the harder modes, and the more gentle 
' and civilized with such as are moderate ; although 
' in these days few of the latter are to be found.' 

Boetius then proceeds to relate that the Lacedae- 
monians, sensible of the great advantages resulting to 
a state from a sober, modest, and well-regulated 
music, invited, by a great reward, Taletas the Cretan 
to settle among them, and instruct their youth in 
music. And he relates that the Spartans were_ so 
jealous of innovations in their music, that, for adding 
only a single chord to those he found, they banished 
Timothev;s from Sparta by a decree ; which, however 
he could come by so great a curiosity, he gives in the 
original Greek, and is as follows :— EHEI AE TIMO- 
GEOS O MIAESIOS nAPAriMENOS EN TAN 
AMETEPAN HOAIN, TAN HAAAIAN MOARHN 
ATIMASAS. KAI TAN AIA HAN EHTA XOPAAN 
KieAPIZEI, AnOSTPE<&OMENOS nOAYa>aNIAN 
EISAFflN, AYMAINETAI TAS AKOAS TiiN 
NEi2N AIA TE TAS HOAYXOPAAS, KAI TAS 
KAINOTATAS TOYTON MEAE02 ATENNE KAI 
nOIKIAAN ANTIAHAOAN, KAI TETATMENAN 
AM«I)IAYIAN MOAnHN EHI XP^MATOS SY- 
NEISTAMEN TOYTOY MEAEOS, AIASTASIN. 

liberal sciences : Cassiodorus, who lived about half a century after him, 
wrote also De septem Disciplinis ; and others of the learned in like man- 
ner have written professedly on them all. Farther, of Jrannes Basingus 
sive Basingstockius, who flourished in 1252, it is on the authority 
of Matthew Paris, who knew him, related that he was, ' Vir quidem in 
trivis et quadrivis experientissimus.' Tauner's Bibliotheca 431. 



ANTI TAP ENAPMONm HOIAN ANTISTPE<I)ON 
AMOIBAN. HAPAKAAAGEIS AE EN TON ATO- 
NA TAS EAEY2INIAS AAMATPOS AIXOS AIE- 
(MMISATO TAN Ti2 MYOli KIANHSIN: TAN 
TAP SEMEAA OAYNAN OYK ENAEKATOS NEOS 
AIAAXIIN EAIAASE. EITA HEPl TOYTON TON 
BASIAEAN KAI TOY PHTOPOS MEM^ATAI TI- 
MOGEON, ERANATIGETAI AE KAI TAN ENAEKA 
XOPAAN EKTANiiN TA2 HEPIASTAS ERIAEI- 
nOMENOS TAN EHTAXOPAON ASTOS. TO TAP 
nOAIOS BAPOS AHTON TETAP BHTAI ES TAN 
SnAPTAN Eni<&EPEIN : TIGON MH KAAQN NH- 
TilN MHnOTE TAPATTIITAI KAEOS ATOP^N.* 
He then proceeds to declare the power of music in 
these words : — ' It is well known that many wonderful 
' effects have been wrought by the power of music 
' over the mind ; oftentimes a song has repressed 
' anger ; and who is ignorant that a certain drunken 
' young man of Taurominium being incited to violence 
' by the sound of the Phrygian mode, was by the 
' singing of a spondeus appeased ; for when a harlot 
' was shut up in the house of his rival, and the young 
' man, raging with madness, would have set the house 
' on fire, Pythagoras, who, agreeable to his nightly 
' custom, was employed in observing the motions of 
' the celestial bodies, as soon as he was informed that 
' the young man had been incited to this outrage by 
' the Phrygian mode, and found that he would not 
' desist from his wicked attempt, though his friends 
' repeated their admonitions to him for that purpose, 
' ordered them to change the mode, and thereby 
' attemperated the disposition of the raging youth to 
' a most tranquil state of mind. Cicero relates the 
' same story in different words, but in nearly the same 
' manner : — " When (says he) certain drunken men 
" stirred up, as is often the case, by the sound of the 
" tibia, would have broke open the doors of a modest 
" woman, Pythagoras is said to have admonished the 
" tibicinist to play a spondeus, which he had no sooner 
" done than the lustfuhiess of these men was appeased 
" by the slowness of the mode and the gravity of the 
" performer." But to gather some similar examples 
' in few words, Terpander and Arion of Methymne, 
' the next city in Lesbos to Mitylene for grandeur, 
' cured the Lesbians and lonians of most grievous 
' diseases by the means of music ; Hismenias, the 
' Theban, by his music is reported to have freed from 
' their torments divers Beotians, who were sorely 
' afflicted with sciatic pains, f Empedocles also, when 
' a certain person in a fury would have attacked his 
' guest, for having accused and procured the con- 
' demnation of his father, is said to have diverted him 
' by a particular mode in music, and by that means to 
' have appeased the anger of the young man. And 
' so well was the power of music known to the ancient 
' philosophers, that the Pythagoreans, when they had 

* Translation, see pay. 80, note. 

+ There are many relations in history of the efficacy of music in the 
cure of bodily diseases. It is reported that Thales, the Cretan, being by 
the advice of the Oracle called to Sparta, cured a raging pestilence by 
the power of music alone. The assertion of Boetius with respect to the 
Sciatica seems to be founded on a passage in Aulus Gellius, lib. IV. chap, 
xiii. who reports that persons afflicted with that disease were eased of 
their pains by certain gentle modulations of the tibia; and that by the 
same means many had been cured who had been bitten by serpents and 
other venemous creatures. 



Chap. XXV. AND PRACTICE OF MUSIC. 119 

a miiid to refresh tliemselves by sleep after tlie Cap. iii. De vocibus ac de musicae elementis. — 

' laboi;rs and cares of the day, made use of certain Cap. iv. De speciebus inequalitatis. — Cap. v. Quae 

' songs to procure them an easy and quiet rest ; and inequalitatis species consonantiis aptentur. — Cap. vi. 

' when they awaked they also dispelled the dulness Cur multiplicitas, et superparticularitas consonantiis 

' and confusion occasioned by sleep by others, know- deputentur. — Cap. vii. Quae proportiones quibus con- 

' ing full well that the mind and the body were con- sonantiis musicis aptentur. — Cap. viii. Quid sit sonus, 

' joined in a musical fitness, and that whatever affects quid intervallum, quid concinentia. — Cap. ix. Non 

' the body, will also produce a similar effect on the omne judicium dandum esse sensibus, sed amplius 

' mind ; which observation it is reported Democritus, rationi esse credendum, in quo de sensuum fallacia. 

' whom his fellow-citizens had confined, supposing It is the business of this chapter to show, that 

' him mad, made to Hippocrates, the physician, who though the first principles of harmony are taken from 

' had been sent for to cure him. To what purpose the sense of hearing, for this reason, that were it 

' then are all these things ? We cannot doubt but otherwise there could be no dispute about sounds ; 

* that our body and mind are in manner constituted yet, in this case, the sense is not the sole arbiter. 
' in the same proportions by which harmonical modu- Boetius to this purpose expresses himself very ration- 
' lations are joined and compacted, as the following ally in the following terms : — ' Hearing is as it were 

* argument shall shew ; for hence it is that even ' but a monitor, but the last perfection and power of 
' infants are delighted with a sweet, or disgusted with 'judging about it depends upon reason. What need 
' a harsh song : every age and either sex are affected ' is there for many words to point out the error which 
' by music, and though they are different in their ' the senses are liable to, since we know that neither 
' actions, yet do they agree in their love of music. ' is the same power of perception given to every one 
' Nay, such as are under the influence of sorrow, even ' alike, nor is it always equal in the same man ; on the 
' modulate their complaints, which is chiefly the case ' other hand, it is vain to commit the examination of 
' with women, who, by the sweetness of their songs, ' truth to an uncertain judgment. The Pythagoreans 

* find means to alleviate their sorrows ; * and it was ' for this reason took as it were a middle way ; for 
' for this reason that the ancients had a custom for the ' though they did not make the hearing the sole 
' tibia to precede in their funeral processions. Pa- * arbiter, yet did they search after and try some 
' pinius Statins testifies as much in the following ' things by the ears only : they measured the con- 
' verse : — ' sonants themselves by the ears, but the distances by 

' Cornu grave mugit adunco, ' which these consonants differed from each other they 

' Tibia cui tenevos suetum producere manes. « did not trust to the ears, the judgment whereof is 

' And though a man cannot sing sweetly, yet while * inaccurate, but committed them to the examination 

' he sings to himself he draws forth an innate sweet- ' of reason, thereby making the sense subservient to 

* ness from his heart. Is it not manifest that the ' reason, which acted as a judge and a master. For 
' sound of the trumpet fires the minds of the com- ' though the momenta of all arts, and of life itself, 
' batants, and impels them to battle ; why then is it ' depend upon our senses, yet no sure judgment can 
' not probable that a person may be incited to fury ' be formed concerning them, no comprehension of 
' and anger from a peaceful state of mind ? There is ' the truth can exist, if the decision of reason be 
' no doubt but that a mode may restrain anger or * wanting ; for the senses themselves are equally de- 
' other inordinate desires ; for what is the reason that ' ceived in things that are very great or very little : 
' when a person receives into his ears any song with ' and with respect of that of hearing, it with great 
' pleasure, that he should not also be spontaneously ' difficulty perceives those intervals which are very 
' converted to it, or that the body should not form or ' small, and is deafened by those which are very great.' 
' fashion some motion similar to what he hears : from Cap. x. Quemadmodum Pythagoras proportiones 
' all these things it is clear beyond doubt that music consonantiarum investigaverit. — Cap. xi. Quibus 
'is naturally joined to us, and that if, we would we modis varie a Pythagora proportiones consonantiarum 
' cannot deprive ourselves of it ; wherefore the power perpensae sint. 

' of the mind is to be exerted, that what is implanted The account delivered in the two preceding chap- 

' in us by nature shoidd also be comprehended by ters, and which is mentioned in almost every treatise 

'science. For as in sight it is not sufficient for on the subject of music extant, is evidently taken from 

' learned men barely to behold colours and forms, Nicomachus, whose relation of this supposed dis- 

' unless they also investigate their properties ; so also covery of Pythagoras is hereinbefore given at length. 

' is it not sufficient to be delighted with musical songs. Cap. xii. Dedivisione vocum, earumque explana- 

' unless we also learn by what proportion of voices or tione. — Cap. xiii. Quod infinitatem vocuni humana 

' sounds they are joined together.' natura finierit. — Cap. xiv. Quis sit modus audiendi. — 

Cap. ii. Tres esse musicas, in quibus de vi musicae Cap. xv, De ordine theorematum, id est speculati- 

narratur. onum. — Cap. xvi. De consonantiis proportionum, et 

The three kinds of music here meant are, mundane, tono et semitonio. — Cap. xvii. In quibis primia 

humane, and instrumental ; and of each of these numeris semitonium constet. — Cap. xviii. Diatessaron 



mention has been made in a preceding page. a diapente tono distare. — Cap. xix. Diapason quinque 

* Modem history furnishes a curious fact to prove the truth of this 



tonis, et duobus semitoniis jungi. — Cap. xx. De ad 
dition 
Th. 
of Rodez. , given 



observation ; for it is related of the princess of Navarre, mother of Henry dltlOUC Chordarum, CarumqUC nommiDUS. 

IV. of France, that at the instant when she was delivered of him she sung mi KiihstauPP of this cbflntpr bfls nlrpnfl-ir liPPn 

a song in the Bearnois language. Life of Henry le Grand by the Bishop J-HC SUUSldUCe 01 lUlS Cliapicr uas aireauy Deen 



120 



HISTORY OF THE SCIENCE. 



Book III. 



Cap. xxi. De generibus cantilenarum. — Cap. xxii. 
De ordine chordarum nominibusque in tribus gene- 
ribus. — Cap. xxiii. Quae sint inter voces in singulis 
generibus proportiones. 

These three chapters give a brief and but a very 
superficial account of the genera. 

Cap. xxiv. Quid sit synaphe. — Cap. xxv. Quid 
sit diezeuxis. 

In these two chapters the difference between the 
conjunct and disjunct tetrachords is explained. 

Cap xxvi. Quibus nominibus nervos appellaverit 
Albinus. 

Albinus is said by Cassiodorus to have been a 
great man, and to have written a brief discourse on 
music, which he himself had seen and attentively 
perused in one of the public libraries at Rome ; and 
Cassiodorus seems to prophecy that some time or 
other it would be taken away in an incursion of the 
Barbarians : it has accordingly sustained that fate ; 
for Meibomius, in his preface to Gaudentius, speaks 
of that manuscript as irrecoverably lost. 

Cap. xxvii. Qui nervi quibus syderibus com- 
parentur. 

The substance of this chapter is for the most part 
an extract from Cicero de Repub. lib. VI. and is 
a declaration of the supposed analogy between the 
planets and the sounds in the septenary. 

Cap. xxviii. Quag sit natura consonantiarum. 
— Cap. xxix. Ubi consonantiae reperiuntur. — Cap. 
XXX. Quemadmodum Plato dicat fieri consonantias. 
— Cap. xxxi. Quid contra Platonem Nicomachus 
sentiat. — Cap. xxxii. Quae consonantia quam merito 
prsecedat. — Cap. xxxiii. Quo sint modo accipienda 
quag dicta sunt. — Cap. xxxiv. Quid sit musicus. 

In this, which is a very curious chapter, the author 
observes that the theoretic branch of every science 
is more honourable than the practical, for 'that prac- 
' tice attends like a servant, but reason commands 
' like a mistress ; and unless the head executes what 
' reason dictates, its labour is vain.' He adds, ' the 

* speculations of reason borrow no aid of the exe- 
' cutive part ; but contrarywise, the operations of 
' the hand without the guidance of reason are of no 
' avail ; ' — that the greatness of the merit and glory 

* of reason may be collected from this ; corporeal 
' artists in music receive their appellations, not from 

* the science itself, but rather from the instruments, 
' as the citharist from the cithara ; the tibicen, or 
' player on the pipe, from the tibia ; but he only is 

* the tnie musician, who, weighing every thing in 

* the balance of reason, professes the science of music, 
' not in the slavery of execution, but in the authority 
' of speculation. In like manner he says those who 
' are employed in the erection of public structures, 
' or in the operations of war, receive no praise except 
' what is due to industry and obedience ; but to 

* those by whose skill and conduct buildings are 
' erected, or victory achieved, the honours of inscrip- 
' tions and triumphs are decreed.' He then proceeds 
to declare that three faculties are employed in the 
musical art ; one which is exercised in the playing 
on instruments, another that of the poet, which 
directs the composition of verses, and a third which 



judges of the former two ; and touching these, and 
that which he makes the principal question in this 
chapter, he delivers his opinion thus : ' As to the 
' first, the performance of instruinents, it is evident 
' that the artists obey as servants, and as to poets, 
' they are not led to verse so much by reason as by 
' a certain instinct which we call genius. But that 
' which assumes to itself the power of judging of 
' these two, that can examine into rhythmus, songs, 
' and their verse, as it is the exercise of reason and 
'judgment, is most properly to be accounted music; 
' and he only is a musician who has the faculty of 
'judging according to speculation and the approved 
' ratios of soimds, of the modes, genera, and rhythmi 
' of songs, and their various commixtures, and of the 
' verses of the poets.' 

Lib. II. cap. i. Proemium. — Cap. ii. Quid Pytha- 
goras esse philosophiam constituerit. — Cap. iii. De 
differentiis quantitatis, et q\iai cuique disciplinae sit 
deputata. — Cap. iv. De Relatfe quantitatis diifer- 
entiis. — Cap. v. Cur multiplicitas antecellat. — Cap. 
vi. Qui sint quadrati numeri deque his speculatio. 
— Cap. vii. Omnem inequalitatem ex equalitate pro- 
cedere, ejusque demonstratio. — Cap. viii. Regula 
quotlibet continuas proportiones superparticulares 
inveniendi. — Cap. ix. De proportione numerorum 
qui ab alias metiunter. — Cap. x. Quae ex multi- 
plicibus et superparticularibias multiplicitates slant. 
— Cap. xi. Qui superparticulares quos multiplices 
officiant. 

The nine foregoing chapters contain demonstrations 
of the five several species of proportion of inequality; 
of these an explanation may be seen in that extract 
from Dr. Holder's Treatise on the Natural Grounds 
and Principles of Harmony, hereinbefore inserted, 
with a view to facilitate the study of Boetius, and 
to render this very abstruse part of his work in- 
telligible. 

Cap. xii. De arithmetica, geometrica, harmonica, 
medietate. 

The three several kinds of proportionality, that 
is to say, arithmetical, geometrical, and harmonical, 
are also explained in the extract from Dr. Holder's 
book above referred to. 

Cap. xiii. De continuis medietatibus et disjunctis. 
— Cap. xiv. Cur ita appellatae sint digestae superius 
medietates. — Cap. xv. Quemadmodum ab ajqualitate 
supradictae processerant medietates. — Cap. xvi. Que- 
madmodum inter duos terminos supradictae medie- 
tates vicissim coUocentur. — Cap. xvii. De conso- 
nantiarum modo secimdum Nicomachum. — Cap. xviii. 
De ordine consonantiarum sententia Eubulidis et 
Hippasi. 

Two ancient musicians, of whose writings we have 
nothing now remaining. 

Cap. xix. Sententia Nicomachi quae quibus con- 
sonantiis apponantur. — Cap. xx. Quid oporteat prai- 
mitti, ut diapason in multiplici genere demonstretui 
— Cap. xxi. Demonstratio per impossibile, diapason 
in multiplici genere esse. — Cap. xxii. Demonstratio 
per impossibile, diapente, diatessaron, et tonum in 
superparticulari esse. — Cap. xxiii. Demonstratio 
diapente et diatessaron in maximis superparticularibus 



Chap. XXV. 



AND PRACTICE OF MUSIC. 



121 



collocari.^ — Cap. xxiv. Diapente in sesquialtera, dia- 
tessaron, in sesquitertia esse, tonum in sesquioctava. 
— Cap. XXV. Diapason ac diapente in tripla pro- 
portione esse ; bisdiapason in qiuadrupla. — Cap. xxvi. 
Diatessaron ac diapason non esse consonantiam, se- 
cundum Pythagoricos. 

The two last of the foregoing chapters have an 
immediate connection with each other ; in the first it 
is demonstrated that the diapason and diapente con- 
joined, making together the consonant interval of a 
twelfth, are in triple proportion ; and that the dis- 
diapason is in quadruple proportion, the ratios 
whereof are severally 3 to 1 and 4 to 1 ; but with 
respect to the diapason and diatessaron conjoined, the 
ratio whereof is 8 to 3, the interval arising from such 
conjunction is clearly demonstrated by Boetius to be 
dissonant : from hence arises an evident discrimi- 
nation between the diatessaron and the other perfect 
consonances ; for whereas not only they but their 
replicates are consonant, this of the diatessaron is 
simply a consonance itself, its replicates being disso- 
nant. It is true that the modern musicians do not 
reckon the diatessaron in the number of the con- 
sonances ; and whether it be a concord or a discord 
has been a matter of controversy ; nevertheless it is 
certain that among the ancients it was always looked 
upon as a consonance, and that with so good reason, 
that Lord Verulam* professes to entertain the same 
opinion; and yet after all, the imperfection which 
Boetius has pointed out in this chapter, seems to 
suggest a very good reason for distinguishing be- 
tween the diatessaron and those other intervals, 
which, whether taken singly, or in conjunction with 
the diapason, are consonant. 

Cap. xxvii, De semitonio in quibus minimis nu- 
meris constet. 

The arguments in this chapter are of such a kind, 
that it behoves every musician to be master of them. 
The ratios of the limma and apotome have already 
been demonstrated in those larger numbers which 
Ptolemy had made choice of for the purpose. In 
this chapter Boetius gives the ratio of the limma in 
the smallest numbers in which it can possibly con- 
sist, that is to say, 256 to 243 ; and as this is the 
most usual designation of the Pythagorean limma, or 
the interval, which, being added to two sesquioctave 
tones, completes the interval of a diatessaron, it is a 
matter of some consequence to know how these num- 
bers are brought out ; and this will best be declared 
in the words of Boetius himself, which are as follow : — 
' The semitones seem to be so called not that they 
* are exactly the halves of tones, but because they are 
' not whole tones. The interval which we now call 
' a semitone was by the ancients called a limma, or 
diesis ; and it is thus found : if from the sesqui- 
tertia proportion, which is the diatessaron, two ses- 
quioctave ratios be taken away, there will be left 
' an interval, called a semitone. To prove this, let 
' us find out two consecutive tones ; but because 
these, as has been said, are constituted in sesqui- 
octave proportion, we cannot find two such, until 
that multiple from whence they are derived bo first 



■ found : let therefore unity be first set down, and 

■ then 8, which is its octuple : from this we derive 
' one multiple ; but because we want to find two, 
' multiply 8 by 8, to produce 64, which will be a 

second multiple, from which we may bring out two 
sesquioctave ratios ; for if 8, which is the eighth 
part of 64, be added thereto, the sum will be 72 ; 
and if the eighth part of this, which is 9, be added 
to it, the sum will be 81 ; and these will be the two 
consecutive tones, in their lowest terms. Thus, set 
down 64, 72, 81 :— 



64 



72 



81 



Tone. Tone. 

Sesquioctave. Sesquioctave. 

We are now therefore to seek a sesquitertia to 64 ; 
but it is found not to have a third part : wherefore, 
all these numbers must be multiplied by 3, and all 
remain in the same proportion as they were in 
before this multiplication by 3, Then three times 
64 makes 192, to which if we add its third part, 64, 
the sum will be 256 ; which gives the sesquitertia 
ratio, containing the diatessaron. Then set down 
the two sesquioctaves to 192, in their proper order, 
that is, three times 72, which is 216, and three times 
81, which is that 243 : these two being set between 
the terms of the sesquitertia, the whole will stand 
thus : — 



Tone 


Tone Semit. 




192 


216 1 243 256 

1 1 






Diatessaron. 

v 


-^ 



* Nat. Hist. Cent. II. Numb. 107. 



' In this disposition of the numbers, the first con- 
' stitutes a diatessaron with the last, and the first with 
' the second, and also the second with the third, do 
' each constitute a tone ; therefore the remaining in- 
' tervals 243 and 256, is a semitone in its least terms.' 

Cap. xxviii. Demonstrationes non esse, 243, ad 
256, toni medietatem. 

That the limma in the ratio 256 to 243 is less than 
a true semitone, has been already demonstrated in the 
course of this work. 

Cap. xxix. De majore parte toni in quibus 
minimis numeris constet. 

The apotome has no place in the system, nor can 
it in any way be considered as a musical interval ; 
in short, it is nothing more than that portion of a ses- 
quioctave tone that remains after the limma has been 
taken therefrom. For this reason, its ratio is a matter 
of mere curiosity ; and it seems from this chapter of 
Boetius, that the smallest numbers in which it can be 
found to consist, are those which Ptolemy makes use 
of, that is to say, 2187 to 2048. 

Cap. XXX. Quibus proportionibus diapente, dia- 
pason, constent, et quoniam diapason sex tonis non 
constet. 

The demonstrations contained in this chapter are 
levelled against the Aristoxeneans, and declare so 
fully the sentiments of the Pythagoreans, with respect 



122 



HISTORY OF THE SCIENCE 



Book III, 



to the measure of the consonant intervals, that they 
are worthy of particular attention, and cannot be 
better sciven than in the words of Boetius himself. 

' The diapente consists of three tones and a semi- 
' tone, that is, of a diatessaron and a tone : for let the 



' these intervals are properly disposed in numbers. 
' For let six octuples be thus produced : — 

1, 8, 64, 512, 4096, 32768, 262144. 
' From this last number six tones, constituted in 
' sesquioctave proportion, may be set down, with the 



' above scheme, be set down thus : — 



DIATESSARON. 



' numbers 192, 216, 243, 256, comprehended in the ' octuple terms and their several eighth parts, in the 

' order following : — 

Octuples. 
1, 8, 64, 512, 4096, 32768, 262144. 

^262144 
294912 
331776 
Sesquioctaves. { 373248 
419904 
472392 
.531441 



192 216 243 256 



Tone Tone Semitone. 

' In this disposition, the first number to the second 

and the second to the third, bear the proportions of 

' tones, and the third to the fourth that of a lesser 

' semitone, has been shown above. If then for the 

* purpose of ascertaining the contents of the diapente, 

* 32 be added to 256, the sum will be 288, which is 
' another sesquioctave tone ; for 32 is the eighth part 
' of 256, and 256 to 288, is 8 to 9. The extreme 
' numbers will then be 192 to 288, which is sesqui- 
' altera, the ratio of the diapente : — 



^32768 

36864 

T.. ,,, , 141472 
Eighth parts.^ ^^^.^g 



52488 
59049 



192 



288 



DIAPENTE 

Sesquialtera. 



' Finally, by comparing the first number with the 
' second, the second with the third, and the fourth 
' with the fifth, i. e., 288, it will plainly appear, first. 
' that in the diapente are three tones, and a lesser ' diapason is less than six tones ; and the excess of 



' The nature of the above disposition is this : the 
' first line contains the octuple numbers ; and the 
' sesquioctave proportions in the first column are de- 
' duced from the last of them. The numbers con- 
' tained in the second column are the eighth parts of 
' those to which they are respectively opposite ; and 
' if each of these be added to the number against it, 
' the sum will be the number of the next sesquioctave, 
' in succession. Thias, if to the number 262144 
' 32768 be added, the sum will be 294912 ; and the 
' rest are found in the same manner. And were the 
'last number, 531441, duple to the first, 262144, 
' then would the diapason truly consist of six tones ; 
' but here it is found to be more ; for the duple of 
' 292144 is 524288, and the number of the sixth tone 
' is 531441. Hence it appears, that the consonant 



' semitone. If then the diatessaron consists of two 
' tones and a lesser semitone, and the diapente of three 
' tones and a lesser semitone ; and if the diatessaron 
' and diapente make up together the diapason, it will 
' follow, that in the diapason are five tones and two 
' lesser semitones, which joined together do not make 
' up a full and complete tone, and therefore that the 
* diapason does not consist of six tones, as Aristoxenus 
' imagined, which also will evidently appear when 



' the six tones above the diapason is called a comma, 
which in its lowest terms is 52428 to 531441 : — 



7153 



524288 531441 



COMMA, or the inter- 
val by which six tones 
exceed a diapason. * 



Six Octuples. 



1 1 


8 64 


512 


4096 


32768 


262144 




9 72 


576 1 


4608 


36864 


294912 




/TTT" — -^ 


1 648 


5184 


41472 


331776 






729 1 


5832 


46656 


373248 






6561 


52488 


419904 




"°^s;^$5r-^ 


59049 


472392 






531441 



OJ 



• JT ^ o 

CJ TO 

S c^ 3 



^ ■» 
•^■i^ 



o- 



s »= " ^ 

g § © o 
g ■*-> o 



In the third book Boetius continues his controversy 
with the Aristoxeneans, who, as they assert, that the 
diatessaron contains two tones and an half, and the 
diapente three tones and an half, must be supposed to 
believe that the tone is capable of a division into two 
equal parts, contrary to that maxim of Euclid, that 
' inter superparticulare non cadit medium,' a super- 
particular ration cannot have a mediety. And Boe- 



tius, in the first chapter of his third book, with great 
clearness and precision demonstrates, that no such 
division of the tone can be made, as that which 
Aristoxenus and his followers contend for. 
Lib. III. cap. i. Adversus Aristoxenum demonstratio, 

* This is called the Pythagorean comma, and is taken notice of by 
Mersennus, vide Harmonicor. de Dissonantiis, pag. 88. It is less than 
that of 81 to 80, called the comma majus, or schisma, and which is the 
difference between the greater and lesser tone. 



Chap. XXV. 



AND PRACTICE OF MUSIC. 



123 



superpai'ticularem proportionem dividi in sequa 
non posse, atque ideo nee tonum. — Cap. ii. Ex 
sesquitertia proportione sublatis duobus tonis, toni 
dimidiimi non relinqui. — Cap. iii. Adversum Aris- 
toxenum demonstrationes, diatessaron cousonantiam 
ex duobus tonis et semitonio non constare, nee dia- 
pason sex tonis. — Cap. iv. Diapason eonsonantiam a 
eex tonis commate excedi, et qui sit minimus numerus 
commatis. — Cap. v. Quemadmodum Philolaus, tonum 
dividat. 

Pythagoras found out the tone by the difference 
of a fourth and fifth, subtracting one from the other ; 
Philolaus, who was of his school, proceeded farther, 
and effected a division of the tone into commas. The 
manner of his doing it is thus related by Boetius : — 

' Philolaus the Pythagorean tried to divide the tone, 

* by taking the original of the tone from that number 
' which among the Pythagoreans was esteemed very 
' honoui'able : for as the number 3 is the first uneven 

* number, that multiplied by 3 will give 9, which 
' being multiplied by 3 will necessarily produce 27, 
' which is distant from the number 24 by a tone, and 
' preserves the same difference of 3 ; for 3 is the 
' eighth part of 24, and being added thereto com- 
' plotes the cube of the number 3, viz., 27. Philolaus 
' therefore divided this into two parts ; one whereof 
' was greater than the half, which he called the apo- 
' tome ; and the other less, which he termed the 
' diesis, and those that came after him denominated 
' a lesser semitone ; and their difference he termed 

* a comma. The diesis he supposes to consist of 13 
' unities, because he supposed that to be the difference 
' between 243 and 256, and because the number 13 
' consisted of 9, 3, and unity ; which unity he con- 
' sidered as a punctum. 3 he considered as the first 
' uneven number, and 9 as the first uneven square : 
' for this reason, when he fixed the diesis or semitone 

* at 13, he made the remaining part of the number 27, 
' containing 14 unities to be the apotome. But be- 
' cause unity is the difference between 13 and 14, he 

* imagined unity ought to be assigned to the place of 
' the comma ; but the whole tone he made to be 27 

* unities, that number being the difference between 
' 210 and 243, which are distant from each other by 
' a tone.' 



13 



14 



27 



Diesis 



Apotome 



Cap. vi. Tonum ex duobus semitoniis ac commate 
constare. — Cap. vii. Demonstratio, tonum duobus 
semitoniis commate distare. — Cap. viii. De mi- 
noribus semitonii intervallis. — Cap. ix. De toni 
partibus per cnnsonantias sumendis. — Cap. x. Regula 
sumendi semitonii. — Cap. xi. Demonstratio Archytae, 
superparticularem in equa dividi non posse; ejusque 
reprehensio. 

It seems by this chapter, that this Archytas, who 
it is supposed was he of Tarentum, mentioned in the 
account herein before given of the genera and their 



species, was a Pythagorean. He it seems had under- 
taken to demonstrate that proposition of the Pytha- 
gorean school, that a superparticular ratio cannot be 
divided into two equally ; but Boetius says he 
has done it in a loose manner, and for this he repre- 
hends him. It may he inferred from this chapter, 
that some of the writings of Archytas on music were 
in being in the time of Boetius ; but that there are 
none now remaining is agreed by all. 

Cap. xii. In qua numerorum proportione sit 
comma, et quoniam in ea quae major sit quam 76 
ad 74 minor quam, 74 ad 73. — Cap. xiii. Quod 
semitonium minus majus quidem sit quam 20 ad 19, 
minus quam 19^ ad 18J. — Cap. xiv. Semitonium 
minus, majus quidem esse tribus comatibus ; minus 
vero quatuor. — Cap. xv. Apotome majorem esse 
quam 4 eommata, minorem quam 5. Tonem ma- 
jorem quam 8, minorem quam 9. — Cap. xvi. Superius 
dietorum per numeros demonstratio. 

Lib. IV. cap. i. Voeum differentias in quantitate 
eonsistere. — Cap. ii. Diversae de intervallis specu- 
lationes. 

This, as its title imports, is a chapter of a mis- 
cellaneous kind. Among other things, it contains 
a demonstration somewhat different from that which 
he had given before, that six sesquioctave tones are 
greater than a duple interval. That they are so 
will appear upon a bare inspection of the following 
diagram : — 



Six sesquioctave proportions greater than a duple interval. 

Sesqui- I Sesqui- I Sesqui- | Sesqui- I Sesqui- | Sesqui- I Sesqui- 
octave. octave, octave, octave, octave, octave, octave. 



A 


B 


C 


D 


E 


G 


K 


262144. 


294912. 


331776. 


373248. 


419904. 


472392. 


531441. 


The number A 262144. is half the undervcritten number; and 
therefore the diapason is deficient of the number K by 7153. 



The duple interval reaches to 524288. 

Cap. iii. Musicarum per Grsecus ac Latinas literaa 
notarum nuneupatio. 

In this chapter are contained some of the principal 
characters used b)'^ the Greeks in their musical nota- 
tion. It seems, that at the time when Glareanus 
published his edition of Boetius, they had been cor- 
rupted, which, considering they were arbitrary, or at 
best that they were the letters of the Greek alphabet 
reduced to a state of deformity, is not to be wondered 
at. Meibomius had the good fortune to get in- 
telligence of an ancient manuscript here in England, 
in which this chapter was found, in a state of great 
purity. He had interest enough with Mr. Selden to 
get him to collate his own by it : and the whole is 
very correctly published, and prefixed to the Isagoge 
of Alypius, in his edition of the ancient musical 
authors. 

Cap. iv. Monochordi regularis partitio in genere 
diatonico. — Cap. v. Monochordi netarum hyperboleon 
per tria genera partitio. — Cap. vi. Ratio superius 
digestae descriptionis. — Cap. vii. Monochordi neta- 
rum diezeugmenon per tria genera partitio. — Cap. viii. 
Monochordi netarum synemmenon per tria genera 



124 



HISTORY OF THE SCIENCE 



Book III 



partitio. — Cap. ix. Monochordi meson per tria ge- 
nera partitio. — Cap. x.