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"v . ' < «jtU 'm» - 



"S^t Jbu&stante ot lectURB 





PBomsoB or tooal iruna nr xna'a ooluqi, txa n gran's oollioi, ldhdov. 



AV , ^./s: 


The title of the following work will, it may be hoped, render any expla- 
nation of the object with which it has been written unnecessary. The 
mode of treatment of the subject, and the order in which the different 
branches of it are brought before the student, differing essentially from 
most other works of the same kind, require, however, a few prefatory 

The syllables Do^ Re^ Mi^ &c. are used throughout, instead of the 
letters A, B, C, &c. It might be considered some apology for the 
adoption of the former nomenclature that in Italy and France no other 
is, or for ages has been, in use, and that an Italian or French musical 
work, scientific, historical, or sesthetic, would therefore be absolutely 
unintelligible to a reader conversant only with the latter ; and that in 
Germany the solfa syllables, though not exclusively used, are universally 
understood. This, however, would perhaps, of itself, hardly have justi- 
fied their introduction among our own people, had not the advantages 
attendant on their use been such as must be obvious to reason, and easily 
proved by experiment. For most theoretical, «,nd some practical pur- 
poses, any one set of names for the first seven sounds of the natural scale 
may serve as well as another. In writing, reading, or talking about 
music, everything expressed by Do, Re^ Mi^ Fa^ may be as well ex- 
pressed by A, B, C, D, — ^by 1, 2, 3, 4, — ^by Fee^ Fa, Fo, Fum, — or any 
other syllables equally short and easy of utterance. But in reference to 
the overcoming of one, and that the greatest, difficulty in the study of 
music, the adoption of one set of names-rand one only — ^for the notes, 
is of the greatest importance. The first object of every musical student 
should be to acquire that knowledge, the possession of which, more 
than any other, constitutes a musician — ^the knowledge of the sound of 
what he sees written before him, and, inversely, the power of expressing 
in musical characters what he imagines, or hears. Assuredly the most 
rapid and certain method of attaining this knowledge and this power is 
the practice of singing every fresh passage, so far as it may be singable^ 


that comes before him. In doing, or trying to do this, he will of 
necessity give the notes some names. No one, it may be safely said, 
ever habitually sung to the letters A, B, C, D, &c. ; and the general 
result, with those familiar only with those letters, is the adoption of a 
habit of humming^ or a practice of uttering the sounds on all kinds of 
indistinct, unformed, and unmeaning vocables. The former practice is 
extremely injurious to the voice; and every time the latter is resorted 
to an opportunity is lost of identifying the sound sung with the note 
which represents it, and thereby cultivating that association between 
the one and the other which is, as has been already said, the distin- 
guishing characteristic of a musician. This sympathy between the ear 
and the eye, in its perfection, is referable to, and depends upon, many 
causes. In the earlier ages of music, it might have been enough for 
the musician to know the sound of one note by comparison with^ or in 
its relation to, another; and the old methods of solfaing were all 
devised with the view of enabling him to attain this knowledge. But 
the requirements of modern music are so much greater, the number of 
scales in actual use has so largely increased, modulation has become 
so much more frequent and abstruse, the chromatic genus is so daringly 
and plentifully used, that the modem musician must know, not merely 
the relative, but the absolute pitch of the notes he sees, before he can, 
with readiness and certainty, hear them with his mind's ear. It is not 
to be denied that even the solfa system — with all its advantages over 
the alphabetical — ^is still an imperfect contrivance; inasmuch as Do 
sharp and Do flat are both of them sung to the same syllable as Do 
natural; and it must be admitted that some means of inflecting the 
names of the altered notes is greatly to be desired. It has been pro- 
posed to call Do sharp Di^ Do flat Da^ &c., but the entire septenary 
does not admit of analogous alteration ; and a complete cure of the evil 
could only be made by sweeping the recusant syllables away, and sub- 
stituting others for them, — a change which, it need hardly be said, 
there is no means of forcing on the musical world, and which, even if 
not resisted, would be many years attaining universal acceptance. 

It is common to find the earlier chapters of rudimentary works, 
whether on music or any other subject, occupied, not with attempts 
to convey ideas of the tkiTigs to be first studied, but with explanations 
of the symbols which represent them, — many of these latter, perhaps, 
not being called into requisition till an advanced period in the study, 
when they have to be learned a second time. Thus, under one rigime^ 
the beginner is made to exhaust the subject of the stave before he is in 


the least informed as to the nature of the scale; and, under another, 
may be called upon to consider the peculiarities of five-crotchet time, 
while as yet he has no practical acquaintance with the first principles of 
rhythm. In the following work no attempt is made to introduce the 
student to the alphabet of music till he has learned something about 
musicy or, more properly, the musical system itself ; nor is he instructed 
in the diflferent kinds of measure^ nor even made aware of the existence 
of hars^ until he has acquired some idea of the limits of a musical 
phrase^ and the nature of a musical foot^ — ^things which are alto- 
gether independent of any forms by which they may be represented, 
and which, as they certainly existed ages before the invention of the 
present musical alphabet, will as certainly exist ages after that ingenious 
contrivance has become matter of history, or even of speculation. 

The history of an art or science may often be brought to bear prac- 
tically on the process of teaching it ; and the order in which discoveries 
or improvements have been made will often suggest that in which a 
knowledge of them may best be communicated. So that the considera- 
tion even of exploded theories and obsolete forms may not be without 
its use, as keys to those which have superseded them. The musical 
student, for instance, will never appreciate the special merits of 
modern, unless he have learnt something of ancient, tonality; nor 
would it be easy to devise any shorter or more simple method of 
explaining the nature of a mode^ than through acquaintance with the 
fact that, though but two modes are used by modern musicians, the 
number of modes possible is only limited by that of the sounds of the 
natural scale. This latter fact is briefly alluded to in an early chapter, 
and more fully treated in a later one the object of which has been 
rather to excite than to satisfy curiosity on a very interesting branch of 
musical science. 

The chapters on the Alto and Tenor Staves — ^part of a subject treated 
elsewhere* by the writer more fully — will, it is hoped, be found suffi- 
cient to meet the practical wants of the student. It seemed likely, about 
a quarter of a century ago, that those ingenious contrivances would, 
so far at least as vocal music was concerned, have become obsolete, and 
that the practice of writing alto and tenor parts an octave higher than 
they were to be sung would everywhere supersede the older and more 
simple one of writing them at their proper pitch. More recently, the 
tide has turned; and many cheap editions of popular classical works 

* A Short Treatise on the Stave. J. W. Parker and Son : London. 


have issued from the press, of which the notation is as correct as the 
typography is beautiful. Whether this fashion prove permanent or not, 
the Btudent may rest assured that, unless he make himself familiar with 
at least two of the four different staves headed by the Do clef, a very 
large proportion of the works of the greatest writers must remain 
sealed books to him. 

It can hardly be necessary to say, that the following work, though 
dealing for the most part with first principles, is not adapted to the use 
of beginners^ save in connexion with musical practice of some kind, under 
the direction of a teacher. Music is an art as well as a science ; and no 
art can be learned wholly from books. Nor is it likely that even first 
principles should ever be so simply stated, or so clearly expounded, as 
to be intelligible to those who make no attempt to put them into prac- 
tice. To two classes of persons such a book as this may be of use, 
(1) To those who, having attained some skill in the practice, and 
acquired some knowledge of the theory of music, may desire to have 
a connected view of those parts of the latter which are indispensable to 
the former: — and (2) to those — a very large and increasing class — 
who, familiar with other subjects, and accomplished in other ways, 
with little hope of becoming practical musicians, may still desire to 
make some acquaintance, if not with the syntax, at least with the ortho- 
graphy, etymology, and prosody of the only grammar which can fairly 
be called universal. "Were I to begin life again," said the late 
Sydney Smith, *' I would devote much time to music :" and " not six 
months before the death" of Samuel Johnson, he said to Dr. Bumey, 
" Teach me at least the alphabet of your language." The author is not 
altogether without hope, that in putting together the following pages, 
he may have done something tp enable those who have not had the 
advantage of early training to devote, with pleasure and profit, some 
time to music, without "beginning life again," and to acquire some- 
thing more than the alphabet of the language of musicians. ^ 

December^ 1856. J. H. 





I. Musical Sound •.«•••• 1 

II. Tune. The Scale « 2 

• • • ' » • , 

III. Time. Rhythm • . 4 

lY. Notation. • r • 5 

V. Forms of Notes 8 

VI. Intervals II 

Vn. The Modem Modes 14 

VIII. The Natural Scale 16 

IX. Altered Notes 18 

X. Altered Intervals 20 

XI. Altered Scales 21 

XII. Scales in Actual Use 23 

Xin. The Chain, or Circle, of Scales 26 

XIV. The Minor Mode 29 

XV. The Signatures of Minor Scales 81 

XVI. Bars and Measures •...••.•.; 83 

XVn. Time--i3imple and Compound 86 

XVIII. Time Signatures 88 

XIX. Accidentals . • • • 41 

XX. Chromatic Intervals 43 

• •• 




XXI. Modulation 



XXII. Transposition 48 

XXIII. Bhythmical Licences 51 

XXIV. Graces 


XXY . Signs of Bepetition, Contractions, Ac. 55 

XXTI. Marks of Expression 57 

XXVII. Words relating to Pace, Intensity, and Style .59 

XXVIII. The Tenor and Alto Staves . .62 

XXIX. The Syren and the Metronome .65 

XXX. The Andent Modes . . .... . .'..•.'.. . . . . 68 


■ ' ■ 

i i 


. I 

c » 

» ? I 

I * I 

t « ( » 

m • 

I I 

• « I I « I 

« % 



Musical Sound. 

1. Sound is the result^ or effect on the ear, of motion communicated to the air 
hy some disturbing force. Such motion is called vibration^ or undulation. 

2. When the vibration of air is regular (isochronous^ or equal-timed) the result 
is musical sound ; when it is eVregular the result is f/nmusical sounds or noise, 

3. In the regulated production, by voice or instrument, of musical sounds con- 
sists the art of music ^ in a knowledge of the laws which govern the succession 
and combination of musical sounds consists the science of music. 

4. The art and science of music involve the consideration oifour properties of 
musical sounds^ theix pitch, duratiofiy intefisity, and timbre. 

5. The pitch (acuteness or gravity, height or depth) of a musical sound depends 
on the number of vibrations communicated to the air ifi a given time. As this 
number increases or diminishes so does the sound become more acute (higher), or 
more ^rai;^ (lower). 

6. The duration of a musical sound depends on the time during which the air 
continues to vibrate at the same pace. 

7. The intensity (loudness or softness) of a musical sound depends on the 
extent of the vibrations by which it is caused. 

8. The timbre of (quality by which we are enabled to recognise) a musical sound 
is supposed to depend on ihe forms of the vibrations from which it results. 

limhre (French) literally, stamp. No English word has yet been adopted to express the same 
property of sound. 

9. These properties are, for the most part, relative. Every sound is assuredly 
of a definite and appreciable pitch and duration ; but the musical student is chiefly 
concerned with the pitch or duration of sounds as compared with one another — 
technically, tune and time. 

The ultimate source of the pleasure afforded by musical sounds is time ; since tune entirely depends 
on the order, or regular succession of the vibrations which affect us as sound. As a matter of prac- 
' ticej however, time and tune must be considered separately, — the latter first. 

R. M. G. B 


Tune. The Scale. 


10. Different sounds (sounds of different pitch) produced at the same instant, 
form harmony. Melody results from a succession of different^ or even a repetition 
of the same^ sounds. 

11. Harmony or melody can be produced from the combination or succession 
of such sounds only as are found in the same musical system. 

Fig. 1. 

12. The basis of the modem musical system is the [ 8— Do- 

oonnexion of a given sound with another, standing in |— — 7— iSt- 

the relation to it of 2:1, by means of intermediate sounds . 6— Za- 

also related^ though less simply^ to that (given) sound 

and to each other. A ^^^ 


13. Such sounds, presented in regular succession, r z—^i- 

form a scale^ of which the topmost step is the 8***, or | 2—Ee 

octave, from the 1"*. {Ftp, 1.) 


14. The sounds of that scale which begins on the central sound of the modem 
musical system, are named by letters of the alphabet, or by syllahlesj as follows : — 

























Thd latter nainas will be used exeltuively in this work. 

The student should sing, or play (on a piano-forte or other ifistrumeni) this scale qfDo, until 
he is thoroughly ftiMiliar with the sound of it, 

15. With a little attention, even from an uncultivated ear, it will be perceived 
that the successive steps of this '* natural" scale are not all equal, and that some 
adjacent sounds are less unlike one another than others ; also, that the smaller 
Steps lead to, of immediately precede, places in the scale at which the yoice easily 
pauses, and on which the ear is willing to dwell. These are the 4^ sound. Fa, 
and the 8^, Do, the sounds immediately leadiiig to which. Mi and 8i, are severally 
less unlike Fa or Do than any two other adjacent sounds are to each other. 

16. Moreover, further observation will prove that, notwithstanding the differ- 
ence oi pitchy the musical effect of Do, Re, Mi, Fa, heard in succession^ is strik- 

Chap. II.] 


inglj like that of 8oly La^ 8i^ Do ; in fact^ that the melody or tune of both series 
is the same. 

The student should satisfy himself of the truth of this by singing or pl<tying the two series , or 
any portions of either, in immediate succession, 

17. The cause of this similarity is to be found in the fact that melody, or tune, 
does not depend on the absolute, but on the relative^ pitch of sounds— on their 
distances apart. Fa the 4^ sound of the natural scale, stands in the same rela- 
tion to Do the 1**, as Do the 8**" sound, does to 8oI the S**" ; while Mi the S'*, 
is to Fa the 4*^, as 8i the 7"^, is to Do the 8*^. 

18* The relation of (difference or distance between) two musical sounds is. 
called an interval The intervals found in passing up or down the natural scale 
are tofies and semitones; the (two) semitones falling between the di^ and 4^ sounds 
(Mi and Fa\ and the 7^^ and 8*^ (Si and Do) ; the (five) tones falling between 
every other two adjacent sounds. Each A«^of the scale, therefore, consists oifour 
sounds separated by two tones and one semitone. 

19. A succession of four sounds separated by two tones and a semitone is 
called a tetrachord. The natural scale, therefore, is divisible into two tetrachords, 
the !■* sound of the upper of which (two tetrachords) is separated by a tone from 
the 4*** sound of the lower. 

In fig. 1, the several intervab between the different sounds are expressed by the greater or les8<er 
distances between the lines which represent them. The division into two tetrachords is also shown, 
and the tone whidi separates them specially indicated. 

20. The modern musical system consists in a suc- 
cession of scales of like construction, the highest or 
lowest sound of each of which is identical with the 
lowest or highest of the one immediately above or 
below it. (See fig. 2,) The 8** sound of one scale is 
therefore the 1'* likewise of another, and the 1** of one 
scale the 8^ likewise of another. This similarity in the 
conditions of the 1'^ and 8^ sounds of a scale is the 
cause of their bearing the same names, and, ulti- 
mately, of all sounds bearing the same names as their 
octaves. For as the upper Do of fig. 2 is the octave to 
the lower Do, so the He immediately above the former 
is the octave to the Re immediately above the latter. 
And so of all the other sounds. Thus by a repeated 
application of the seven syllables, Z)o, Re, Mi, Fa, 8ol, 
La, 8iy to the seven corresponding sounds 1, 2, 8, 4, 
5, 6, 7, in each successive scale, names are found for all 
the sounds of the entire musical system, and would 
still be found could that system be extended ad in^ 

Pig. 2, 


Time. Rhythm. 

21. Time and tune^ ultimately so closely connected (Chap. I.), may exist, and 
are often found, independently. Neither, however, can ahne give perfect satisfac- 
tion to the musical sense, which is incapable of appreciating any prolonged succes- 
sion of musical sounds the proportionate durations of which are not regulated by 
some law. The result of this kind of law is rhythm. 

22. Every rhythmical passage or strain of music is divisible into phrases — 
successions of sounds dependent for their meaning on each otheo and presenting 
a certain completeness. 

The first strain of the NatioTial Anthem ooiisists of three phrases, each ending in the word ''queen." 
(See fig. 8.) 

23. Every phrase is further divisible into feet^ and every foot into times or 

Each phrase of the first strain of the National Anthem consists of two feet, ending severally in 
the words " our," " queen," •' the," Ac. (See fig. 8.) 

Fig. 3. 

rf^^-'^'JM J 




Ood saye our 


gra - dons Qaeen, Long liye our 

Foot. i Foot. 

A A. A. f X ^ 

! . Foot. i 

A. 1 >L A A. • 



no - ble Queen, Ood Bsye 

the Quee - - - - n. 

The student, though as yet unacquainted with musical notation, may he supposed to know, by 
ear, " 2%e National Anthem" Otherwise, he must take some means of learning it, 

24. The times, or beats, of a musical foot are accented or «/naccented. A foot 
consists either of two beats, one accented the other unaccented, or of three beats, 
one accented and two unaccented. 

By the old masters the latter form of foot was held in the highest estimation ; a foot of three heats 
heing said by them to be in " perfect" time, and a foot of two beats in " imperfect" time. 
The National Anthem is in "perfect" time. 

25. In the division of musical passages into phrases, of phrases into feet, and 
of feet into beats, musical rhythm resembles poetical rhythm. Here, however, the 
resemblance ceases ; since while the number of syllables into which the poetical 
foot may be divided is very limited, the number of sounds into which the musical 
foot may be divided is very great. And not only may any one foot be divided 
into a vast variety of sounds, but any one somid may be prolonged through an en- 
tire foot, or through any number of feet. 

E.g, The sound sung to the word " queen," in fig. 3, is to be prolonged during an entire foot. 



26. The musical alphabet is chiefly composed of characters called notes ^ the 
relative positions of which on a stave^ or staff, indicate the relative pitch of the 
sounds they represent, and the different forms of which indicate their relative 

Fig. 4 is a stave, on which are placed four notes, of which the ^^' ^' 

second is higher in pitch (and in position) than the first, the third is 
of the same pitch as the second, and the fourth is lower in pitch than 
the third. Moreover, the first is a longer note than any of the others. 



the second a shorter note than any of the others, and the third and fourth are of the same length. 

27. But neither the absolute pitch of sounds, nor even their exact relation to 
each other in that particular, can be indicated hy notes alone, A clef or key (to 
their meaning) is wanted at the beginning of the stave on which they stand. 

28. A clef is the only character by which a musical sound can be absolutely 

29. There are three clefs, and therefore three sounds only which can be abso- 
lutely represented — Do, Sol and Fa. 

30. The Do, or C, clef represents the Do which occupies the middle place in 
the system of musical sounds, — it having about an equal number of sounds above 
and below it. It is the Do nearest the middle of a piano-forte, called therefore 
middle Do^ or C. The Sol, or G, clef represents the 5"^ sound of that scale of 
which middle Do is the !•* ; and the Fa, or F, clef the 4*^ sound of that scale of 
which middle Do is the 8**". 

Fig. 5. 



Do Sol Fa 

C O F 

These three clefs are corruptions of oldfoims of the letters C, G^ F. 

31. Notes may stand in the spaces between the lines of a stave as well as upon 
them. (See fig. 4.) The notes of the natural scale oQQwipy following lines and spaces 
of a stave alternately, without exception. 

32. The lines and spaces of a stave are called indifferently degrees, or posi- 
tions^ and adjacent lines and spaces, following degrees. 


[Chap. IV. 

Fig 5 consLsts of two successive scales of Do. The 1" note of the upper scale is identical with the 
^*^ of the lower. (Com^pa/re pwr, 20.) 

d3. The note on the 2''^ line (from the lowest) of fig. 6 is known as Fa, because 
the Fa clef stands upon it. The note on the 4^ line is known as Doy and that on 
the &^ line as Soly for a similar reason. Moreover, the notes above and below 
those designated by the clefs are recognised by their positions in relation to the 
latter; the note in the space immediately below Fa being Mi^ that in the space 
immediately above it, Sol; and so on. 

84. When higher or lower notes than those in fig. 6 are to be expressed, more 
lines mnst be added to the stave. All the notes (twenty-three) required for 
average vocal music can be placed on a stave of eleven lines, on the middle line of 
which would stand '^ middle" Do — having the same number of notes (eleven) above 
as below it ; and on the 4^^ and 8^ lines Fa and Sol. 

Fig. 7. 

- " ^ ^^ 








A O <^ 










T3 — 

35. No individual voice can utter all the sounds represented in fig. 7. Con- 
sequently, in writing music for individual voices, a smaller number of lines 
suffices. Practically, whether for vocal or instrumental music, a stave oi Jive 
lines is generally adopted ; the particular setSy or staves, most used being the five 
highest and the five lowest of the Great Stave above. (See fig. 8.) 

86. The lower one of these sets or staves of five lines is used for voices and in- 
struments oi\oyr pitch. It is distinguished as the bass stave. The upper stave is 
used for voices and instruments of higher pitch. It is distinguished as the treble 

stave. {(t\ is also called the treble clef, and 0« the bass clef. 


37. The two staves are joined by a brace^ when used together 
for piano'forte or Tiarp music; the upper stave being chiefly 
devoted to the notes to be played by the right hand, the lower to 
those played by the left. (See fig. 8.) 

38. When the middle line of the Great Stave is required, 
it is introduced as a leger line. (Compare fige, 7 and 8.) 

LSger (French) means light. 

Chap. IV.] 


89. Music for the lower voices of women, and the higher voices of men, de- 
mands other staves which are^ equally with the treble and bass staves, extracts 
from, or parts of, the Great Stave. Of these we shall speak fully, later. For the 
present, the trehle and lass staves will be used exclusively, such leger lines being 
added to them as may be required. When more than one leger line has to be 
added to the top of the bass stave, it must be considered as an extract from the 
treble stave : vice versa^ when more than one leger line has to be added to the 
bottom of the treble stave it must be considered as an extract from the bass stave. 

{See Jig, 9.) 

Fig. 9. 



40. The ascending natural scale which 
begins on middle Doy will appear on the 
trehle stave as in fig. 10. The 1'* or lowest 
sound stands on the leger line identical with 
the middle line of the Great Stave. {Par, 38.) 

Fig. 10. 

*■■ II ■ 







41. The descending natural scale which 
begins on middle Bo^ will appear on the 
hass stave as in fig. 11. The 8^ or highest 
sound stands on the leger line identical with 
the middle line of the Great Stave. {Par, 38.) 

Fig, 11. 









42. By joining together (with a brace) 
the staves on which these two scales are 
placed, the relation between them will be 
made plainer. The lowest note of the one 
scale is identical- with the highest of the 
other, and the leger line on which it stands 
is common to both staves. 

Fig. 12. 















It will have been seen already that the variety of intervals in the natural scale {Par. 18) is not 
made manifest by the ordinary musical alphabet, lb the eye, the relation between Mi and Fa is the 
same as that between 861 and La, {See fig. 12.) There is nothing in the arrangement of the lines of 
a stave analogous to that of the lines of the ladder in Chap. I. — ^reminding us always, by the different 
distances between them, that Mi and Fa, and Si and Do are severally a semitone apart, and that 
the other sounds which follow one another scalewise, are separated by tones. On this fact, however, 
depends the modem musical system ; and of all things the stud^t has to learn and to keep in xnindj 
it is incomparably the most important. It will receive further illustration as we proceed. 



Forms of Notes. 

43. The relatiye duration of sounds is known bj the different ^mu of the 
notes which represent them. The namber of these forms, at present in common 
use, is six. 

Fig, 18. 
Semibrere. Minim. CroU^iei. Qnayer. SemiqnmTer. DemisemiqitaTer. 

-^ — ^ — r — f — 

44. These names neither describe the forms, nor even for the most part ex- 
press the relations, of the notes under them. The two first have been retained 
from a period when, with three others, they were the only notes in use. 

Pig. 14. 
Maxim* txmg. Brere. SemibreTO. Mmim- 

1=1 = H 


45. To these the crotchet j originally a hooked minim ^ was afterwards added. 
When the crotchet took its present form the hook was transferred to the quaver. 
The maxim and long are obsolete, and even the breve (short note) is now rarely- 
used ; while the minim {least note) is often with us, practically, the maxim 
(greatest note). 

46. The modem forms are well described by the French names, and their i e • 
lations one to another by the German. 

JPig, 15. 

Bonde. Blanche. Koir. Crocke. Boublecroche. Triplecroche. 

Bonnd. White. Black. Hook. Boublehook. Triplehook. 

-^ — T — r — c 6 f- 

Oancenote. Halbenote. Viertel. AchteL Sechzehntel. Zwei-und-dreiBzigsteL 

Whole note. Half note. Fourth. Eighth. Sixteenth. Thirty-second. 

47. The stems of notes may be turned up or down indifferently. The hooked 
notes are .frequently grouped and contracted, (-fifee fig, 16.) 

Chap, v.] 


48. These notes, as respects their length, stand in ibe most simple relations 
to eaeh other, each note being half the length of the one before it., 

Ft^. le. 

Exceptions to the rule whereby these notes are proportioned to each other are presented in the 
occasional compression of more than its proper complement of notes into a single time, or beat. Of 
these the only instance which need be mentioned here is the triplet, 

49. A triplet is a group of three notes, which (by licence) is performed in 
the time of two notes of the same/ortn, A triplet is generally specially marked 3. 


PiSt. 17 (a). 


Fig. 17 (6). 

50. The hreve, jo[> often found in old 
music, and occasionally in modem, is equal to 
two semibreves,^2/r minims, and so on. 

51. Shorter notes even than the demisemi- 
()(iaver — the ^^mtdemisemiquaver and the demi" 
«^yntdemisemiquaver — have been used in mo- 
dem instrumental music. In choral music even 
the demisemiquaver is of rare occurrence. 

R. M. G. 

Fig, 18. 

|a| *• Ci_ci - OOP 


Fig, 19. 


10 FORMS OF NOTES. [Chap. V. 

52. As musical sounds are represented by notes^ so are the interruptions^ or 
cessations^ of musicp.1 sound represented by restHj the different forms of which indi- 
cate the relative duration of such interruptions, or cessations. 

Fig, 20. 
Setiiibreve Best. Minim Rest. Crotchet Best. Quaver Best. Semiquaver Best. Demisemiquaver Rest.. 

1- =j ^ ; 

53. The stems of rests are invariably turned down. Rests are never grouped. 

Another form of crotchet rest JT is grtidaally superseding that in fig. 20. It has the advan- 
tage of being more readily distinguishable from the quaver rest. 

54. These rests indicate, severally, silence as long as would be the sound of 
the notes whose names they bear. 

bb. The variety afforded by these forms is greatly increased by the use of the 
dot which, being added to a note, or rest, increases its length one-half » 

Fig, 21. Pig, 22. 

O =00 

t* • 


1 • - iq 

The dotted rest is little used ; the last form in fig. 22 is the more common one. 

The dot was called by the old masters " the point of perfection/' because it brought the note to 
which it was added into perfect (i,e., triple) time — making it divisible by three. 

Fig. 28. 

56. The double dot increases the length of a note by 11 

three-fourths ; the second dot standing in the same re- 
lation to the^r«* as the first to the note it follows. I* * " I I L 

Thus, a crotchet followed by a double dot is equal to seven semi- \ ~ I C D 

quavers — the note itself being equal to four, the Jirst dot to two, and ^ 

the second to one. {Fi^,23.) C* * ** C S U 




57. The relation of two sounds in respect to pitch is called an interval. In 
passing up or down the natural scale without missing a step (by degrees)^ we meet 
with no interval greater than a tone; but in skipping from one sound to another 
not next above or below it, we traverse, or measure, a larger interval. Intervals 
are named — 1*^ according to the relative positions of the notes which compose 
them ; 2"^% according to the number of tones and semitones into which they can 
be divided. 

58. For example, Re and Do are said to be a secotid apart, or Re is said to be 
the second above Do because, taking those notes as they appear in the natural 
scale, Re is the 2"* sound from Do. And as Re is the 2** above Do, so is Mi the 3^*, 
Fa the 4*^ Sol the 6*^, La the 6*^, Si the 7"^, Do the 8*^ or octave. Re the 9*^ ; and 
those pairs of notes, severally, are said to form a second^ a thirds &c. {Fig. 24.) 

Second. Third. Fourth. 

Fig, 24. 
Fifth. Sixth. 

Seventh. Octave 










By the same rtile^ Mi is the 2**' to Be, Fa the 3*^, ^. ; and so 
with all the other notes. 

Fig. 25. 
Second. Third. 

<3 ^^ 



59. But intervals admit of, and require, another and more exact kind of mea- 
surement. (Pa/r. 57.) Mi is the 2"* to Re^ and Fa the 2''* to Mi. But it has been 
shown (Pa^. 18.) that Mi is a tone above Re, and Fa only a semitone above Mi. 
Therefore the second between Re and Miy must be a second of different quality 
from that between Mi and Fa. The two qualities of second are distinguished as 
major (greater) and minor (lesser). 

60. The natural scale includes Jive major, and two minor^ seconds j major 
second being but another name for tone, and minor second but another name for 
that kind of semitone which is found in the natural scale. {flompaTt'pw. Id.) 

There is another kind of semitonei which will be explained hereafter* 


Fig. 26. 

O » O 




^■-., -., - -. ^ 



^ riinai-wi j»- 





Minot. H.*ijw# Major. Major. Mvnor. 



[Chap. VI. 

61. As there are major and minor seconds j so there are major and minor thirds. 
The major third is composed of (or divisible into) two tones; the minor third, of 
one tone and a semitone. 

62. From Do to Mi there are two tones ; from Re to Fa^ only ond tone and a 
semitxyxiQ, Consequently, Do-Mi form a major third, Re-Fa a minor third. The 
natural scale presents examples of three major BXiAfoiir minor thirds. 


Fig, 27. 















Minor, Minor, Major. Major. 



63. The intervals produced by the inversion of seconds and thirds are called 
abo major and minor. 

64. By the inversion of an interval is meant the placing the lower note an 
octave higher^ or the higher note an octave lower ; thus producing a different 
interval by notes of the sam£ name. 

65. Two notes a second apart form, on inversion, a seventh ; two notes a third 
apart form, on inversion, a sixth. 

Second. Seventh. 



Fig, 28. 





Fig, 29. 




66. On inversion, two notes form an interval which is not only different in 
hind but in quality. Major seconds become minor sevenths, and vice versa ; major 
thirds become minor sixths, and vice versa. 

Fig, 30 

(Five) Major Seconds. 

(Two) Minor Seconds. 














J'*^. 31. 


(Five) Minor Sevenths. 








(Two) Major Sevenths. 








(Three) Major Thirds. 

(Four) Minor Thirds. 














i^^. 88. 

(Three) Minor Sixths. 





(Four) Mi^or Sixths. 









Chap. VI.] 



67. The fourth and its inversion the fifths together with the octave which is 
the inversion of the unison — not properly an interval — are called, for the most part, 
perfect ; the only exceptions found in the natural scale being ofie plupertect fourth 
and one tmperfect fifth. The octave is, in every case, perfect. 

68. The perfect fourth is composed of two tones and a ^^mttone, the perfect 
fifth of three tones and a semitone. The (one) pluipextect fourth is composed of 
three tones, wherefore it is called also tritone ; the (one) imperfect fifth, of two tones 
and two semitones. (One) 

(Six) Perfect FourthB. Plup. Fourth. 















(Six) Perfect Fifths. 

Fig. 36. 









Imp. Fifth. 




69. On inversion perfect intervals remain perfect, but jp/i^perfect intervals be- 
come i/nperfect, and vice versa* 

70. Intervals greater than an octave are generally to be regarded as mere re- 
duplications of those formed by notes of the same name within the octave. Thus 
fig. 36, practically a tefithj is still considered as a third ; fig. 87, practically an 
eleventh^ as a fourth ; fig. 38, practically a twelfth^ as a fifth, and so on. 


Fig. 87. 

Fig. 88. 


Intervals of this extent are of rare occurrence in melody, 

71. An exception, however, is presented in the case of the ninth, which is not 
always to be regarded as an octave, or compound, second, but often as a distinct in- 
terval. The ninths (like the seconds and sevenths) are called major and mifu>r. 


Fig. 89. 









_ c> — 

Major. Major. Minor. Major. Major. Major. 



72. Intervals greater than an octave do not admit of inversion. The ninth, 
therefore has no inversion. 

The pluperfect fourth and imperfect fifth are less often found in melody than the perfect intervals 
of the same kind; whereas the major and minor intervals are used with equal frequency and freedom; 
presenting no difiBculty in execution nor, in ordinary cases, any striking difference in effect. 



The Modem Modes. 

73. The 1*^ sound of a scale is called its tonicy hey note, or JinaL The tonic of 
the natural scale is Do. 

74. Any note of the natural scale may be used as a tonic ; i.e.j we may pass, 
by steps not greater than tones, or smaller than semitones, from any note to its 
octave. But in the scales up which we shall pass in so doing the tones and semi- 
tones will fall always in different places ; so that we shall find as many different 
kinds of scale, in respect to the succession of tones and semitones, as tonics, viz., 
seven. (Fig, 40.) 

Fig. 40. 

!•• Mode. 






2"* Mode. 

C J > O 

^-'2 8 

< ^> Q ^ 



6 7 

8»* Mode. 

4«» Mode. 

S^ Mode. 

6*^ Mode. 

7** Mode. 






1 2 

5 6 

) ^^ Q 





4 5 

7 8 








8 4 6 7 

2 8 

6 6 

1 2 

4 6 


75. In these seven scales the semitones fall as follows : — 

In the 1**, between the S^ and 4^ and the 7"" and 8*^ sounds. 

— the 2"*, 2"* and 3^* 6**^ and 7*^ 

_ the 3"^, P* and 2"* 5*^ and 6"^ 

_ the 4^ 4*^ and 5*^ 7*^ and 8*^ 

_ the 6^ 3^* and 4*^ 6*^ and 7*^ 

_ the 6*^, 2*^* and 3"* 5*^ and 6*^ 

• — . the 7% l** and 2"^ 4*^ and 6*^ 

76. The order of tones and semitones in a scale is called a mode. Seven 
modes, or forms of scale, are therefore possible ; and at least that number was 
once in use. Among modern musicians only two modes are used, the 1"* and 6**^ 
(of fig. 40), and the latter not without occasional modifications which tend to 
assimilate it to the former. 

77. The former of these (modern) modes is called the major mode, the latter, 
the minor mode ; because the 3"* sound of the one is distant from the l** two 
tones, or a major third ; and because the 3"* sound of the other is distant from 
the 1** only one tone and a semitouej or a minor third. {Compare Part, 61 and 62.) 

Major Third. Minor Third. 

^.«. ^^^ 

Fiff. 42. 

Tone. Tone. '^^^' Semitone. 

From Do to ^« is a tone, and from Re to Mi another ; therefore from Do to Mi is a major third. 
From La to /Si is a tone« and from Si to Do a semitone ; therefore from La to Do is a minor third. 

78. As respects the relation between their !■* and 3"* sounds, all the modes are 
either major or minor; the 1'*, 4% and 5"^ being major^ and the 2"*, 3**, 6*% and 7"* 
being minor. The positions of the tones and semitones are however, in some way, 
different in all the modes ; and without some contrivance by which they could be 
assimilated, only two sounds. Do and La, could be used as tonics at all, and the 
latter only under certain conditions. 

79. For, the modern musical system demands that the 7'^ of a scale be followed 
by the 8'^ at the smallest recognised distance ; in other words, that the 7*^ and 
8*^ sounds of an ascending scale be separated by a ^^i^iitone, the 7*^ in this case 
being called the leading note ; also, that the 4*^ and 6*** sounds form^ re- 
spectively, s. perfect fourth and a, perfect fifth with the tonic. 

80. On the first of these conditions, the 2"*, 3^*, 6*^, 6* and 7*^ modes (of 
fig. 40) are inadmissible ; and on the second, the 4^^ and 7*^. The five former are 
deficient in leaditig notes, and of the two latter, one (the 4*^) has a ^///perfect 
fourth, the other (the 7*^) an «//iperfect fifth. 

The reasons for this rejection of all but the !•* and, " under certain conditions," 6*^ modes, will ap- 
pear as the student becomes better acquainted with the science of music ; the fa>ct of their rejection is 
indisputable. Use is second nature. The modem musician is used to the modem system ; it is the 
idiom in which composers have, for at least a century past, expressed their thoughts ; and every mode 
but that of Do or La, with the modifications alluded to, is, to the modem ear, if not disagreeable 
certainly quaint and unsatisfiu^tory. The modem composer can no more express himself with freedom 
in the obsolete 2"'*, 3"*, 4*^, and 5*^ (the 7*** has never been used) modes, than the modem poet in the lan- 
guage of Chaucer. Indeed, it is a question how far music, prqfeasedly in these modes, was ever pracii" 
cally performed, even in the ages when their existence was recognised, without such modifications as 
must have assimilated them, in most essential particulars, to those with which we are familiar. 


CHAPTER yill. 

The Natural Scale. 

81. ** The !•* sound of a scale," as also the 8^% "is called its toniCj key note, or 
JinaV^ {Par, 73.) The 7*^ sound of the natural scale, and of every scale con- 
structed like it^ is called the leading note, (Par. 79.) 

The fitness of these names needs no demonstration. The 1** and 8'^ sonnds are those on which alone 
a musical passage can be brought to an e?id with perfect satisfaction to the ear ; the 7*^ sound is that 
which MuggesU, or causes expectation, that the 8^^ will follow it. 

82. Every other sound of the natural scale has a like name, i,e,y a name due to 
its position in, and relation to the other sounds of, the scale. 

83. The 5^ sound of a scale is called the dominant^ and the 4^ the «e/(dominant. 

*' Dominant " is one of many old musical terms which have altogether lost their Fig, 43. 

original meaning. The dominant is properly the reciting note, and therefore the 
principal, or governing, note of the ecclesiastical chant. It is applied by modem 
musicians to the 5*^ of a scale, because that sound will bear a combination which, 
as it can only exist in one wsbX^q, governs, or decides, it beyond the possibility of doubt. 

For fwrther explanation of the properties of the dominant, the student is rrferred to the 
Author^ s " Grrammar of Musical Sarmony," Chap, 13. 

84. The 3"^ sound of a scale is called the mediant, and the 6^ the ^t^^mediant. 
The 2"* is called the siipertonic. 

85. ^* Mediant'' and " submediant*' are used in reference to the positions of 
the 3*^ and 6^ of a scale, as the inner, or intermediate, sounds of the triads of the 
tonic and of the subdominant. 

86. The triad to any given note is formed by the addition to it of its 3** and 5*^. 

87. Mi, the 3^* of the scale of Do, is the inner or intermediate sound of the 
triad of Do the tonic (Fig. 44.) La of the triad of Fa the subdominant. {Fig. 45.) 

Fig. 44. Fig. 45 

Chap. VIII.] 



Fig, 46. 
-9— 'Tonic- 

-7 — Leading Note- 

-6 — Submediamt- 

-5 — Domincmt- 

■i — Subdomvnant- 
— 3 — Mediant' 

Fig. 46 shows the name which each soond of the scale derives from 
its position in, and relation to the other sounds of, it. 

" A succession of four sounds separated by two tones and a semitone 
is called a tetrachord" {Par, 19.) 

88. The upper of the two tetrachords, into which a 
scale is divisible (j>ar. 19) begins on the dominant, and the 
lower ends on the subdominant The mediant holds the 
same place in relation to the subdominant, as the leading 
note does to the tonic: and the supertonic holds the same 
place in relation to the tonic as the submediant does to 
the dominant. 

On this account the submediant is sometimes called the awpeV' 

89. As the leading note has a tendency to rise to the tonic {par, 79), so the 
supertonic, the subdominant, and the submediant have each a tendency to rise, or 
fall, to that note of the triad of the tonic which is nearest to them : e, g, that of the 
supertonic is to fall to the tonic ifig- 47), or to rise to the mediant ifig- 48); 
that of the subdominant to fall to the mediant {fig, 49) ; that of the submediant 
to fall to the dominant {fig, 6Q), 

-2 — Supertonic- 
-*1 — Tonic-^ 

Fig, 47. 

Fig. 48. 

Fig, 49. 

F\g, 50. 









90. Thus the triad of the tonic (the 1"*, 3**, and 5*^ of the scale) has an ab* 
sorbing or attractive force, fully justifying the importance attached to it in the 
modern system. 

91. The progressions treated in par. 89 are all parts of one or other of those 
closes or cadences so familiar to the modem musician. They are distinguished as 
the perfect cadence {fig, 51 a and h) and the plagal cadence {fig, 52). The former is 
the more modem and familiar form. Fig. 49 appears in both. 

See also the Author's " Grammar of Musical Marmony" Chap, 30. 

Fig, 51 (a). 

Fig, 51 (6). 

Fig. 52. 


Tz r-^ . 







Z%« student thould take paint to familiarize hit ear to thete progrettiont, playing them on the 
piano-forte, or hearing them placed, and, at the tame time, singing frtt one, then another, qf the 
individual parte. 

B. M. a. 

Altered Notes, 

93. Between every two sonnds separated by a tone another sound ma; be 
placed, whereby the lone is divided into two aemitotm. 

93. On a piano-forte, the natural ^'^- ^^■ 

scale is produeed by striking a buo 
cession oiwhite'keyi exclusively. Most 
of these white keys are separated by 
hUtck keys — the intermediate sounds 
fipoken of above ; the exceptions being 
the keys representing Mi and Fa and 
Si and Do in each octave, which have 
no black key between them, — those 
soands being severally a semitone apart, 
and a semitone being the Bmallest re- 
cognised musical interval (Stefig. ss.) 

94. These intermediate sounds take their names either from the upper or the 
lower sounds adjacent to them ; or, more properly, they are regarded as elevations 
or depressioHB of the latter, and are called such and such notes rharp or j&if, 

In fig. 54, the ruled lines represeiit tlia aouudH of tKe nataral scale (as in Gg. 1), and the dotted 
lines the loiuids which divide each tone into two semitones. Each of the latter, it will be seen, has 
two names, e.g.. Do sharp and Me flat. Strictly speaking, Do sharp and Ke flat are not identical, 
i.e., it is not mathematicBllj true that they are the same sounds — produced by the same number of 
vibrations in a second. (Par. S.) For all practical purposes, however, the; ma; be considered as 
such ; as, indeed, the; ore on the piano-forte. (Sti fig. 65.) 

Pig. 64. 

Fig. 65. 


95. The depression or elevation of one of the sounds of the natural scale a 
semitone, or, in other words, the substitution of a./Zs/ or sharp sound for a natural 

sound of the same name, is indicated by placing jjl, called a sharp, or b, called 
a^tf before the note which represents it. 

The substitation of Fa sharp for Mi natoral, or of 8i flat for 8i natoraly would be expressed as ia 
figs. 56 and 67. 

Fig. 56. ^*r TT — - Fig, 57. 

96. A natural note is specially indicated by placing jjj, called a natural^ 
before the note which represents it. 

The substitation of Fa natural for Fa sharp, or of Si natural for S flat, would be expressed as 
in figs. 58 and 59. 

Fig.S%. /Av ^ ii ^ ^H^-«»- /^N f > PO go ^ ^ 


A natural is only called into requisition when it is necessary to contradict a fijregoing sharp or flat. 

97. Sharps, flats, and naturals are placed before the notes they alter* We Bat/ 
** Fa sharp, Si flat,** &c., but write, « Sharp Fa^ flat Si," &c. 



Altered Intervals. 

98. Bj the alteration of one of the two notes composing it, the quality of an 
interval maj be changed from major to minor^ or from perfect to pluperfect or im- 
perfect; and vice versa. 

99. A major second is made minor hy Jlattefiing its upper or sharpening 
its lower note; and a minor second is made major bj sharpening its upper, 
or flattening its lower, note. (Fin* 00.) 

-F^. CO. 













bo <> 

Major. Major. 

100. A major third is made minor bj flattening its upper, or sharpening 
its lower, note ; and a minor third is made major bj sharpening its upper, or 
flattening its lower, note. (Fig. 61.) 

Fig. 61. 

















101. A i^QiiQot fourth is made j^/uperfect by sharpening its upper, or flattening 
its lower, note ; and vice versa, {Fig. 62.) 

Fig. 62. 














Perfect. Pluperfect. P^perfect. Pluperfect. Perfect. 

102. So also the inversions of these several intervals (the seventh, the sixth, 
and the fifth) admit of alteration ; the two first from major to minor, and the 
last firom perfect to imperfect, and vice versa. 



Altered Scales. 

Fig. 68. 

103. By the alteration of of^ note in 
each, the scales of Fa and of Sol maj be 
arranged in the same (major) mode as that 

of Do, (Ciynvpwrefig, 40.) 

Prom La, the 3"* of the scale of Fa to Si would be a fnajor second (or tone) ; in flattening 
8% (the 4fi) the interval between it and La is reduced to a minor second. (Fig. 63.) 

From Sol (the 8**^ of the scale of Sot) \o Fa ^ wonld be a major second; in sharpening Fa 
(the 7»»') the interval between it and Sol (the S***) ift reduced to a i»Miof second, (i^. 64.) 

i^V^ 65. 

104. Bj a similar alteration, the scales 
of Be and J/t can be arranged in the same 
{niinor) mode as that of La, {Om^part Jlg> 40.) 


'^. o < ^I^Q^ 



i^^. 66. 


From La (the 5*^ of the scale of J^ minor) to Si Q would be a major second; in flattening Si, 
(the 6*^) the interval between it and La (the 5^) is reduced to a minor second. {Pig, 6i.) 

From Sol (the 3*^ of Mi minor) to Fa Q would be a major second ; in sharpening JPa (the 2"') the 
interval between it and Sol (the S'*^) is reduced to a minor second. (Fig, 66.) 

Fig, 67. 

105. The scales of i?^ and of /S'l require, 
each, two alterations to assimilate them, 
severally, to those of Do and of La, 

(Oom^parejlg. 40.) 







8 4 
Fijf. 68. 







V 8 




[Chap. XI. 

106. Moreover, bj still further alteration, the three major scales in fig. 40 
(those of Doy Fa, and Sot) can be made minora and the four minor scales (those of 
JSe, Mi, La, and Si) major. (Fig. 69.) 


Minor Scales. 

Fig. 69. 

Major Scales. 







F F^ 


6 6 






3 4 

7 8 


2 S 




5 6 



^ So^ 


8 i 


7 8 


2 3 

5 6 

8 4 

7 8 

107. In fact, by the alteration of a suflScient number of notes, both a major and 
a minor scale may be constructed, not only on every one of the natural notes, but 
on every one of the altered notes. So that any note, natural, sharp, or flat, may 
be used as a tonic. 



Scales in Actual Use. 

''Any note, natural, sliarp, or flat, may be used as a tonici" {Par, 107.) 

108. There axe seven natural notes, and each of these is alterable boih by a 
sharp and by a flat. It follows, therefore, that no fewer than twenty-one major, and 
twenty -one minor, scales could be expressed in musical characters,— «tfr^» beginning 
on natural notes, seven oujlat notes, and seven on sharp notes. 

109. It has been shown, however (Chap. /X), that every sound raised by a sharp 
\^y practically J identical with the sound a tone above it lowered by a flat ; e,g.^ that 
Do sharp is produced by the same piano-forte key as Re Jlaty Sol sharp by the 
same key as Lajlat^ &c« (Fig, 56.) 

110. The number of major and minor scales, therefore, in actual use is 
much smaller than the number possible : it rarely exceeds twelve, and never, except 
transiently, fifteen. In only one instance, Do^ is the same note, made sharp as 
well as flat, used as a tonic ; the remaining six notes being used as tonics when 
made sharp or flat, — not both. 

111. The sharp tonics are -D^ If ^clj^' 

— natural tonics are Do, Re, Mi, Fa, 8olj La, 8i> 

— flat tonics are Do b, Re bj ^i bj Sol b, La b. Si p. 

In fig. 70, the series of tonics in actual use is given in musical notation. The notes connected by /^ 
are identical. 

Fig. 70. 

l^o fio ^HQ - ^ - ' ^ 

;^Bg3b< >H< >Mo'^^ '^' ' 

112. Each of these scales requires for its completion a different number of 
sharps or flats ; e,g,, the scale of Re requires two sharps, that of Mi b three flats, 
&c. Were the number and order of these sharps or flats irregular, or without 
system, they could only be retained by a very laborious act of memory. Such, 
however, is not the case. The scales grow out of one another, and add to their 
number of sharps and flats^ according to a simple rule which admits of no 



[Chap. XIT. 

113. '' The natural scale is divisible into 
two tetrachords, the 1** sound of the upper 
of which is separated, bj a tone, from the 4^ 
sound of the lower.*' (Par. 19.) 









iBt Tetrachord. 



2iid Tetirachord. 

1 14. What is true of the f natural scale is true oi every scale constructed like it^ 
%.e.y of every major scale. 

115. If the second (or upper) tetrachord of anj one scale be taken as the first 
(or lower) tetrachord of another, the new upper tetirachord added to complete the 
latter scale will demand a new sharps — i,e,^ a sharp not found in the scale to which 
its lower tetrachord is common. {Fig, 72.) 


o o 

X ) 9^ 



The upper tetrachord of Do [fig, 72) consists of Sol, La, Si, Do. Let these four notes he taken 
as the lower tetrachord of a scale of (%,e., heginning and ending on) SoL A new upper tetrachord is 
required to complete this (new) scale of Sol, in which the Fa must be made sharp ; — otherwise, the 
semitone will not fall between the 3'** and 4*** sounds, but between the 2°** and 3"^ ; since Fa natural 
and Sol are separated bj a tone, and Mi and Fa natural bj a semitone. In fact, without the Fa 
sharp, the scale of Sol will be imperfect for want of a leading note. {Compare par, 79.) 

This experiment repeated in any other part of the musical system will be attended with a similar 
result, — the upper tetrachord of the new scale will, in every case, require the introduction of a new 

116. A similar process applied in an opposite direction, will be attended bj a 
similar result, — ^in the production of a series of scales with^/^/«. 

117. If the ^rst (or lower) tetrachord of any one scale be taken as the second 
(or upper) tetrachord of another, the new lower tetrachord added to complete the 
latter scale will demand a new flat, — i,e.y a flat not found in the scale to which its 
lower tetrachord is common. (Fig. 73.) 

Fig. 73. 



Scale of IVi. 





Scale of Jh, 





Fig. 74. 


The lower tetrachord of Do (Jig. 73) consists of Fa, Mi, Re, Do. Let these four notes be taken 
as the upper tetrachord of a (descending) scale of Fa, A new lower 
tetrachord is required to complete this (new) scale of Fa, in which the 
Si must be mstdejlat ; otherwise, the four notes will not include a semi-' 
tone (fig. 74), and will, therefore, not form a tetrachord; for a tetrachord 
is a " succession of four sounds separated by two tones and a semitone.** 
(Par. 19.) 

This experiment, again, repeated in any other part of the musical system will be attended with a 
similar result, — ^the lower tetrachord pf the new scale will, in every case, require the introduction of a 
new fiat. 

<>o < 

Chip. XII.] 


118. The Becond tetracbord of every scale 
begins &Ji/th above the first; vice versa, the 
first tetrachord of every scale begins & Jijih 
below the second. Sharps, therefore, are ge- 
nerated ia an order of ascending, SluAJUiIs in an 
order of desceiulittg, fifths. (Set fig: 76 and 76.) 

From £''. 76 it nill be u 


119. In a aeries, of scales, the tonics of 
Tk'hich are perfect fifths above one another, 
each scale requires a n/iarp more than the one 
before it. This additional sharp is always 
the leading note, and consequently always a 
perfect fifth above the sharp last added to form 
the preceding scale. 

120. The tonics, perfect fifths above each 
other, are, — 

Do, Sol, He, La, Mi, Si, Faj^. Do^ 

Fa natural ia ao imperrect fitlh above Si, 

121. Of these scales the leading notet (also 
perfect fifths above each other) are, — 

Si, Fo|f, Z)(^, So^ Rf^ La^ Mil^ S^ 

From fig. 76 it will be B«en that — 

1-23. In a series of scales the tonics of which 
are perfect fifths below each other, each scale 
requires a Jlat more than the one before it. 
This additional flat is alnays the subdominant 
(4"" sound) of the scale, and cunsequenily 
always a perfect fifth below the flat last added 
to form the preceding scale. 

133. The tonics, perfect fifths helow each 
other, are, — 

Do, Fa, Sh, Mi\}, La^, Se\j, Sol\>, Dob. 

Si natural ia sd imperrect fifUi below Fa. 

134. Of these scales the subdominantB (also 
perfect fifths betow one another) are,— 

Fa, Si\f, Mi\), La]?, Re]}, Solb, Do\f, Fa\>. 

1>J s 



The Chain, or Circle, of Scales. 

126. " Every sound raised by a sharp is practically identical with the sound a 
tone above it lowered by a flat." (Par, 109.) 

126. By availing ourselves of this circumstance once we may form a chain, or 
circle, of scales, connected on the system explained in the last chapter. 

127. The perfect fifth above Do is Sol; above Sol^ Re; above Re, La; above 
Lay Mi; above Mi, 8i; above 5/, Fa ft. i^att is identical with Sol b- {Figs.SiajiddS,) 
The perfect fifth above Solb is Reb; above Re\}y La\^\ above iab, Mi^ ; above 
-J/tb, Sib ; above Sibj Fa; above Fa, Do — the note from which we started, and 
in returning to which we complete the chain, or circle, of scales. {Fig. 77.) 

128. A transition like that from Fa^ to SolQ is called an enharmonic change. 
The enharmonic change in the above series could be made from Si to Do\^, or 
from Do^ to Reb ; indeed, it could be made, though not so conveniently, in any 
part of the series. 

Enharmonic (from the Greek) is a word having reference to a musical system in which intervals 
■mailer than semitones formed part. 

To keep within the limits of the treble stave eveir alternate note in Figs. 77 and 78 is placed a 
fou/rth below instead of a fifth above. The fourth is the inversion of the fifth. {See par, 64.) 





bo , l^< > 

^' 77, /\. _ . . o „ I _ - — - J . . t?0 < ^ 




129. The same process reversed will be attended by the same result. 

130. The perfect fifth below Do is Fa; below Fa, Sib; below Si (7, Mib; 
below J/i'b, jt«b ; below ia b, JB^b; below Reb, Solb. Sol]^ is identical with 
Fa^ The perfect fifth below Fajt is Si; below Si, Mi; below Mi, La; below 
La, Re; below Re, Sol; and below Sol, Do — the note from which we started. 
(Fig. 78.) 

Fig. 78.] 


131. The sharps or flats essential to the scale in which a ( 
musical composition is said " to be," are not placed before 
every individual note which may require aiteratioit, but 
'oy^f/f^r, at the beginning of each scaTo. In this collected 
form they are called the (scale) signature. 

The signature of everf m^or scale is exhibited in fig. 79, which will 
further illuittrate tiie couteatit or the preeeding paragraphs. Za It u placed 
ttjburth beloto Se Tl, instead of a fifth abore, to keep within the limits of 
the treble stave. 

132. In the signatures, the order, whether of the sharps 
or flats, is never changed. If ifaere is one sharp in a signa- 
ture, it is Fa%^\ if there are more sharps than one, fail 
is always the first, DtM. the second, and so on. The same 
rule holds in respect to the flats. 

n fig. 79) 18 the tonic indicated by it 

133. The last added sharp is always the leading note, or 
7*" of the scale — a minor second below the tonic ; and that 
the last added flat is always the subdomi/tatU, or 4*^ of the 
scale — a perfect fifth below the tonic. 'ITierefore — 

184, The tonic of a major scale is always to be found a 
minor second above the last added sharp of a signature, or 
a perfect /aurtft below the last added^at 

Kff. If the last sbarp is iZe jl> the tonic is Mi. If the last flat ia 
Xu [7, the tonic is .^t P- 

135. The signatures over and under each other (in jlg. 79) 
are those of tonics practically identical: viz.. Si and Hob, 
Fa^ and Sol\j, Do^ and Re\}. Without the enharmonic 
change, the next tonic of the ascending series would be So/ft 
— of which the leading note would be Fa double sharp ; 
and the next of the descending series, Fa\} — of which the 
tubdomitiant would be Si double flat. 

136. A double sharp, formerly written JM, is now com- 
monly abbreviated thus X . There is no contraction of the 
double flat, which is expressed thus, \t\f. 

187, A double sharp raises a note, and a double flat 
lowers a note, two semitones. Fa X ia therefore identical 
with So^H, .and SiW mth ia fl, — practically, but not 
theoretically. (Cumpor* Chap. IX.) 

138. It is most important, in respect to the theory of 
scales and intervals, that the distinction in name between 
notes having the same sound be always obserred. 



ICkjlv. XIIL 

139. By substituting Sol fl for Fa X in the scale of Sol^ or La^ for Sol bb in 
iie scale of Fab» we should interrupt the succession essential to a scale, by 
omitting one note, and repeating another. {Oomparefy, 80 with fig. 81, and fig, 82 wUhfig. 83.) 

Fig, 80. 



^) i> . >o i ^<y 

-Piflf. 82. 

Fig, 81. 

ar 4o j ^^^^^fe^ 

^) I, . >boi^< y 


/"(flr. 88. 


140. So again, the interval formed by Do jt and Fa X is the one pluperfect 
fourth of the scale of Solji (fig. Si); that formed by Dott and SoZ U|. the one imperfect 
^/ffc o{ Re {fig. 85) ; while the interval formed by Afib and Si\}9 is the one imper- 
fect fifth of the scale of Fab {fig- 86) ; that formed by Mi bb and La |J|, the one 
pluperfect /owr^fc of Sib. (Pig- 87.) 

Fig. 85. 

Fig. 86. 

2^i>. 87. 






141. No alteration^ by whatever number of sharps or flats, of either of the two 
notes forming an interval, can change its name and kind — which depend on the 
number of positions of the stave, not on the number of tones or semitones, it in- 
cludes. From Do to Fa is SLfourthy whether the Do or the Fa be natural, sharp, 
double sharp, or double flat. 

The intervals in Fig. 88 are all fourths, though of different qualities — some as yet unexplained. 

Fig. 88. 



\\ 7rr 







142. Neither the double sharp nor the double flat ever appear in a signature ; 
they are invariably accidentals, 

143. When the signature is changed, in the course of a piece of music, for 
another of a lesser number of sharps or flats, the places of the latter are sometimes 
taken by naturahj in order that special attention may be directed to the change. 
{Figi. 89 and 90.) The naturals should never appear but once in each part. 

77^.89. gE 


'»■»>■ y B " 

Fig. 89 exhibits a change of signature from 8iioMi\ fig. 90 firom Xa I? to Fa. The naturals in 
both instances indicate the former, as well as the present, scale. 





The Minor Mode. 

144. '* Among modern musicians, only two modes," or forms of scale, " are 
used/' the major and the minor ; " and the latter not without occasional modifi- 
cations which tend to assimilate it to the former." {Par, 76.) As the scale of Do 
is the type, or model, of all major scales, so is the scale of La the type of all 
minor scales. 

145. A minor scale differs from a major scale c/tie/{^ in the circumstance to 
which each owes its name ; — the 3"* sound of the former is a minor third from 
the 1'*, the 3"* sound of the latter, a major third from the 1**. (Compare par, 77.) 

146. This, however, is not the only difference between the two modes. A 
major scale is not liable to change in the quality of its intervals ; a minor scale 
is, — its upper tetrachord assuming no less than three different forms. 

147. The natural minor scale (that of La) is deficient in a leading note^ the 
7^ sound being a tone^ not a semitone, below the 8*^ {Fig, 91.) 

ig, 91. 



o-< > ° ^ ^ " V 

148. Now, a tetrachord in w^hich the semitone is not the interval last heardf 
leaves no impression of completeness on the ear. The upper tetrachord of the 
natural minor scale is, to a certain extent, satisfactory in descending y because the 
semitone is then the interval last heard ; but it is very unsatisfactory in ascending^ 
because this condition is not then observed. {Compare figs, 92 and 93.) 

Fi^. 92. • Fig, 93. 


149. In ascending the minor scale, the last sound but one of the upper tetra- 
chord is usually raised a semitone^ whereby the scale is furnished with a leading 

Fig, 94. 

Thus the upper tetrachord of La minor would appear as in fig. 94. 

150. This elevation of the 7*^ sound of the minor scale induces generally, though 
not alwaysy that of the 6^*" also. For^ in diminishing the interval between the 7^ 
and the b^ sounds^ that between the 0"" and 7*^ is, of necessity, augmented to the 
same extent. 



[Chap. XIV. 

From Fa to Sol jt is an interval greater than a tone, and its introduction renders the npper 
tetrachord of La chromatic, (See Chap. 20.) Chromatic intervals are, in modem music especially, by 
no means forbidden, but their presence essentially alters the character of a passage and, generally, 
renders it more difficult of execution. 

151. In ascending the minor scale, the 6* sound, as well as the 7^\ is usually 
raised a semitone, whereby the interval between the two sounds is reduced to 
a tone. 

Fig. 95. 
See fig. 95, the common form of the npper tetrachord of La minor. 

152. Thus the upper tetrachord of a minor scale admits of three forms — two 
diatonic, one chromatic. (1) The natural diatonic form, rarely used but in descend- 
ing {Jig. 96) ; (-) ^^^ altered diatonic form, used in ascending (fig. 97) ; (3) the chro- 
matic form, used both in ascending and descending {fig, 98). 

Fig. 96. 

Fig. 97. 

r- 4o#<^^ 

Fig, 98. 







O < : 3 

153. The third of these forms (fig, 98) has the advantage that while, equally 
with the second, it presents a leading note — so satisfactory to the modern ear — 
its 6* (to the tonic) remains minor {fig. 99). 

154. The quality of the 6*^ of a scale is hardly less characteristic of its mode 
than that of the 3^. 

^ig.^9. ^^ 


Minor Sixth, 

155. The chromatic form has also the advantap;e over both the others, that it 
is equally practicable (though somewhat difficult) to the voice, and satisfactory 
to the ear, ascending or descending. 

156. Whatever form be adopted for the upper tetrachord of the minor scale, 
the lower tetrachord is invariable ^ so far as the place of the semitone is concerned, 
^— the 3"* is always minor. Hence the term minor mode. 

Fig. 100. 

Minor Third. 



The Signatures of Minor Scales, 

167. Scales which result from different modes of arranging the same sounds 
are said to be relative. The natural scales of Do and La are therefore 
relative ; and as the one is major and the other minor, the scale of La is said to be 
the relative minor of Do, and the scale of Do the relative major of La. 

158. Every major scale has a relative minor, the tonic of which (as in the case 
of the natural scale) is the 6^^ sound of its relative major scale. 

The 6*^ Bound of the scale of Do is La ; La, therefore, is the relative minor to Do. 

159. ^^ The sharps or flats, essential to the scale in which a musical composi- 
tion is said to be,*' placed " together at the beginning of each stave,*' " are called 
the (scale) signature." {Par. 131.) 

160. Every minor scale bears the same signature as its relative major; the 
6^ and 7^ sounds being altered, if necessary, by accidentals. 

In fig. 101 the signature of every major scale, and of its relative minor, is exhibited. It will be 
seen thatr— 

161. The minor, like the major, tonics follow one another in an order of 
ascending and descending fevfectjifths. 

Fig. 101 is a transcript of fig. 79, with the 6*'' to each ms^or tonic added (in small black notes) 
above it. The 6^ of a major scale is the tonic of its relative minor. The black notes, therefore, in 
fig. 101 are the relative minors of the white notes beneath them, and the signatures belong equally to 
both. (Compare par. 160.) 

The table may be read thus : — ^The relative minor of Do is La; signature, neither sharp nor flat. 
The relative minor of Sol is Mi ; signature, -Fajt* And so on. 

162. The signatures of minor scales being identical in every case with those of 
their relative majors, it is of course impossible to decide, /rom the signature alonef 
in w*hat scale a piece of music may be. A slight inspection and a moment's con* 
sideration will, however, generally remove all uncertainty on the matter. With 
rare exceptions, every piece of music ends wiih a combination formed of the tonic, 
its 3"* and 5** — the triad of the tonic — to which the 8^ is as often added ; the 
whole combination forming the common chord of the tonic. (Fi^, 102.) 



[Chap. XV. 

Fig. 102. 











The relative positions of the notes of 
a common chord admit of great variety ; 
e,g,i sometimeB the 8'* ia uppermost, 
sometimes the 3** and sometimes the 5*** 
(see fig. 102, a, ft, c ); hut the notes form 
always the same intervals with the tonic, 
viz,, the 3^ 6*^ and 8*\ 

163. Thus if a piece of modem music has for signature 
two sharps, it will certainly be either in the scale of Re, 
or in that of its relative minor, Si. If it is in Re, the last 
combination will be that of Re with its 3^, 5«^ and (per- 
haps) 8^ viz., Re, Fa|, La, and Re : if it is in the scale 
of Si minor, the last combination will be that of Si, viz. 
Si, Re, Fa^, and Si. Moreover, in the majority of 
modern movements the last chord of the tonic is imme- 
diately preceded by that of the dominant The dominant 
(5**^) of Re is La ; the triad of La is La, Do^, Ml The 
dominant of Si is Fa^ ; the chord of Fa^ is Fa^, La^ 
and Z)ott — ^which iatt, not being in the signature, will be 
specially marked. 

The dominant chord is always major. 

Fig. 103 is the ordinary ending of a piece in Be migor; fig. 104 
that of a piece in Si minor. The signatures of hoth are the same. 

Fig, 103. 

Fig. 104. 




# — ^^ — ^> 



Both figures axe perfect cadences, {Compare par, 91.) 

164. A certain index of the minor mode is the frequent 
recurrence of the sharpened 7*^ and, with it, that of the 
sharpened 6^, The sharpened 7*^ of Si minor is Zaft, 
the sharpened 6^\ Soljt. In a piece of music bearing two 
sharps for its signature, the presence of Lajt, especially 
near the beginning or the end, would indicate the scale 
of Si minor. 

165. The sharpened 6'^ is of itself (as will be shown 
hereafter) by no means so certain an index of the minor 
mode as the sharpened 7^. This, however, is attended 
.with little inconvenience, since the former is generally 
followed immediately by the latter. 













i -\ 







Bars and Measures, 

166. '^ Every rlijthmical passage or strain of music is divisible into phrases." 
(Par, 22.) ** Every phrase is further divisible into feet, and every foot into times, 
or beats" (Par, 23.) 

167. The times or beats of a musical foot are accented or tmaccented. A foot 
consists either of two beats, one accented and one unaccented, or of three beats, 
one accented and two unaccented.** {Par, 2i,) 

168. A musical passage composed of the former kind of feet is said to be in 
duple time ; of the latter kind, in triple time. No kind of time essentially different 
from these two is used or, perhaps, possible. 

169. The places of the accented beats in musical feet are indicated by lines 
drawn at right angles with the stave on which the notes composing them are 
placed. Such lines are called bars. 

170. The group of notes enclosed by two bars is called a measure. The term 
bar is sometimes improperly applied to the measure itself. 

171. The measures in the same musical passage are all of the same value; 
i.e. each measure takes the same time to perform. 

If one measure oonsigts of a minim, each of the other measures will also consist of a minim, or of 
something equal to it; — e.y. two crotchets, four quavers, one crotchet and two quavers, eight semi- 
quavers, &c. <&c. 

Fig. 105 is in duple time ; fig. 106, in triple timd* 

Pig, 105. 



Pig, 166, 


1> J^ 


R. M. G. 




172. The end of a movement, or section of a movement, is nsually marked by 
a dovhU bar. When the last measure of the movement, or section, is complete 
the double bar takes the place of the single bar. When it is incomplete, the 
doable bar serves simply as a sign that the movement or section is ended — ^having 
no effect on the time whatever, (i^- 107.) 

Fig. 107 oonBiBts of the end of one flection and the beginning of another. The measure in which 
the double bar falls is to be performed at the same pace as those measures which precede and follow it. 

Ffg. lOr. 



173. The la«t double bar of a piece of music is generally in- ■%• 108. 
oreased by the addition of two or three bars diminishing towards 
the end» 


174. In practical music time is conveniently marked, or measured, by heats 
made with the hand, or a stick — ^in dwple time, down and 'ujp {fyf. 109), in triple 
time, dowp, right and up. {Fig. iio.) 

Fig. 109. Fig. 110. 

In figs. 109 and 110 the lines indicate the spaceis traversed by 
the hand {ox stick) in beating time, and the arrows^ the Sections in 
which it moves. 





175. It matters not by ^htt form tyt note each beat of a tausical passage is 
represented, provided that the other notes are properly proportioned to it, and to 
one anodier, and tliat the beats are made throughout at the same pace. 

Fig. 105 might, with equal propriety, be written like fig. Ill, each beat being a minim; and 
^. 106 like fig. 112, each beat being a qiiaver : provided only that each minim in fig. Ill, and 
each quaver in fig. 112 was performed at the same pace as each crotchet in figs. 105 and 106. 





Fig. 112. 


176. The monotony arising from a too frequent recurrence of accented notes, 
tog:ether with other practical inconveniences, has given lise to another form, in 
^hich two measures are thrown into one. 

Chap. XVI.] 



Pig. 118. 



177. This form is called common tim^j; and^ m its name would implj^ it is the 
kind of time most frequently used. 

Pig. 114. 

178. In common time the beats are made, — dowiHf left, 
righty up; the note performed when the down beat is made 
receiving a strong accent, and that on the right beat another 
accent, somewhat less strong. sight. 

179. The dovm beat in every form of measure is naturally the accented beat. 
Accentuations at variance with the natural (and ordinary) form are, however, oc- 
casionally made. 

180. Fore:(ample; notes lasting longer than one beat are sometimes begun 
on an i^naccented part of a measure (Fig. 115), or axe prolongedrfrom the end of one 
measure to the beginning of another. (Fig, 116.) In either case the natural and 
ordinary accent is disturbed. 

Pig, 115. Mendblbsohk. 

Pig, 115. Mendblbsohk. Pig, 116. Gbbsv. 


The form in fig. 116 Is generally ezpreseed by modem mnsioiuii in another way. (S^ Par, 277.) 

^m I I <» i n I ^.piytp^— .(..^mii^if^r^w^i^i 

■ » < I II T i 



Time — Simple and Compound. 

181. Music of which the times or beats can be divided, ad infinitvmf hj two, is 
said to be in simple time. 

All the examples in the last chapter are in simple time ; for the value of each beat is in every case 
an entire note — ^a crotchet, a minim, or a quaver — divisible by two, ad vnfinitwn, 

182. Compound time arises from a mixture of the two species, duple and 
triple ; each beat, in a measure of compound time, being a dotted note — divisible 
by three. (Figs. 117 amd 118.) 

Fig. 117. Pig. 118. 

183. A measure is said to be in duple ^ or in triple j time according to the number 
of heats into which it is divisible ; it is said to be in simple or in compound time, 
according to the ^tt&division ^duple or triple) of which each beat is capable. 

Figs. 119 and 120 are both in duj^le time, because each measure consists of two beats; but fig. 

119 is in simple duple time, because each beat is a whole note (divisible ad infinitum by two) ; and fig. 

120 is in compound duple time, because each beat is a dotted note (divisible by three). 

Fig. 119. ' 

Fig. 120. 

Figs. 121 and 122 are both in triple time, because each measure consists of three beats ; but fig. 
121 is in simple triple time, because each beat is a whole note ; and fig. 122 is in compound triple 
time, because each beat is a dotted note. 

Fig. 121. 

Fig, 122 

184. In a measure of simple time there is but one principal accent — that on 
the first heat; in a measure of compound time there is often (and always Toay be) 
a suhordinate accent — on the first note of each heat* 

In fig. 123 the accent falls on but one note and syllable (the first) in each measure — when, lit, 
heigh, &o. 

Fig. 123. Old English Air. 



When that I was a 

lit - tie ti - - ny boy. With a heigh ho ! the 

Chap. XVII.] 



In fig. 124, besides the principal accents (on tongs and rut), there are subordinate accents (on thep 
and round), necessitated by the triple division of the beats to which those notes belong. 

Fig. 124. 

Old English Air. 

8<mg8 of thep - herds and 

rf.pJ'J'J'l " 

rui • ti • cai round - e - lays 

185. When a beat, in a measure of compound time, consists of a nngle note 
the subordinate accent is not felt ; the time being compound to the eye only. 

In the^r^^ measure of fig. 125 the subordinate accent is not expressed, seeing that the second beat 
is entirely filled by the one note over the syllable fooy. In the second measure, the subordinate accent 
is indispensable, because the second beat consists of three notes. The third measure is practically 
in simple time, since both the beats consists o{ single notes. 

Fig. 125. 

Come a • way oome a - way to the wild - woods come. 

186. The beats, as well in compound as in simple time, are sometimes (more 
especially when the pace is very slow) subdivided. 

Thus four beats might be made to each measure of fig. 123, or six to each measure of fig. 124, 
were they to be sung at a slow pace. This, however, is a matter simply of practical convenience, in 
no way interfering with the res! divisions of the measure. Fig. 124 could, by no possibility, be regu- 
lated hjfour equal beats, nor fig. 123 by three. 



Time Signatures. 

187. The number, accent, and kind, of the notes contained in each measure of 
a musical movement are indicated by the time Bignature, placed at the beginning, 
immediately after the scale signature. 

188. Time signatures consist, for the most part, o{ fractions — ^having reference 
to the modern whole iiotCj the semibreve ; the fraction showing how much of, or 
how much more than, a semibreve each measure contains. 

Thus I indicates a time of two crotchets, ue,, tioo fourths of a semibreve, in a measurt ; g * a time 
of six quavers, i.e,, six eighths of a semibreve, in a measure. 

189. Quadniple, or common, time of four crotchets in a measure is specially 
indicated by a character, (^ 

Q^ is not, as might be supposed, the initial of the word '* common," but properly a half circle Q^ 

the symbol of what the old masters held to be imperfect time, — ^in contradistinction to perfect^ or 
triple time, indicated by an entire circle Q. (Compare jpor, 2i.) 

190. Units are occasionally, though not commonly, used as time-signatures. 
1 indicates a time of one semibreve in a measure (common time) \ and 2 the older 
form of two semibreves. 

191. Thus at the opening of a movement we find commonly three characters^ 
or groups of characters— the clef, the essential sharps or flats, and the time signa- 
ture. The first two are usually repeated at the beginning of every stave of each 
part ; the last is never expressed but once in each part — at the beginning. 

Fig. 126. 

Fig. 126 is the commencement of a (piano-forte) movement {compare 
par, 87) in the scale o£ Mi \} {fee fig, 79), and in ''three four" time; 
ue,, triple time of three crotchets in a measure. 

In ^. 127 ail the time signatures in common use are exhibited and explained. 

The number of the notes following each signature shows the number qf beats in each measure ; the 
form of each note shows the value of each beat. 

The forms marked * are only found in ancient music ; those marked f are modem, but rarely used* 

Musical practice is not consistent in regard to the character marked % ; some composers designating 
* time by (ft and others by Q^ , or even Q (^« sign of | time), restricting (n to | time. It is 
greatly to be wished that all three characters were banished from the time table, and that the signa* 
tures were confined to numbers. 

cajl». xvin.] 



192. The numerator in triple time signatures is always an odd number — in 
$imfle triple time, threes in compound triple, nine. The numerator in duple and 
qtuidruple time signatures is always axieven number— in aimpZ^ time, two or four, in 
compound time, six or twelve. 

Fig. 127. 

Table of Time Signatures. 



S 9 



• -2- 

.. ca CL 






• * 

JOk Q O ^ 

-4 1 r I 

c "4 f f f f r 




■iia. '..o 

o ' o » 


t £ 

16 P P 




4 1 111 

193. The fractions in time signatures are not always expressed in iheir 
simplest or lowest forms, i.^., reduced to their lowest denominators. Nor could 
this reduction be made in every instance with safety ; seeing, for example, that \ 
and § are the signatures of two kinds of time differing in every essential particular. 

194. | = §. A measure with the former signature may, and often does, contain 
the same number of the same kind of notes as a measure with the latter signature 
viz.y six quavers. Yet | being the signature of simple triple, and § of compound 
duple J time the accentuation of those six quavers will be altogether different. 



[Chap. XVJLU. 

195. The natural divisions (times or beats) of a measure of § time are 
crotchets, of which it will contain three, or their value. The natural divisions of 
a measure of | time are dotted crotchets, of which it will contain two, or their 
value. These divisions are generally expressed by the grouping. (8ufig%, 128 

a/hd 129.) 

Fig. 128. 

Fig. 129. 

i)\\i;:^^ \ f 


The syBtem of time signatures is certainly far from perfect ; it is, however, universally accepted 
and (among musicians) understood. As any change in the alphabet of a universal language like 
teusic is likely to be made very slowly, and as no change would affect existing music, the student 
must be content, for the present, to remember that though in arithmetic | => § in music, those frac* 
tions represent things essentially different. 

3ee Appendix — " Time Signatures/' 




196. Sharps or dats whichy being over and above those iii the signatv/re of a 
piece V)f music, are placed before individual notes, are called accidentals. Under 
this term are included also those naturals which contradict foregoing sharps or 
flats, whether essential or accidental. 

197. The effect of an accidental lasts throughout the measwre in which it is 
once used ; i.6., it alters every following note in it, of the same name as the one 
which it immediately precedes, — unless it be contradicted by another accidental. 

In fig. 130, the second Fa is sharp as well as the first. In ^» 181, the second 8i is Jlcd as well 
as the first 



198. When ihe first note of one measure is unieonous with the last note of the 
measure immediately preceding it, an accidental placed before the latter note 
affects also the former, and any number of like notes in immediate succession. 
When the two notes ar^ tied {tie Chap. XXVl.), the accidental is usually repeated 
before the second of the ** like notes in immediate succession*^' 

The Fat in the second measare of fig. 182 are sharp ; so alto is the^rf ^ JFa in the second measoro 
of fig. 133. 

Fig. 182. 

- Fig.ld3, 

(§ r cf Wi^ J 

199. When the repetition of a note altered in the foregoing measure is inter* 
niptedy the accidental must be repeated. (Fig, 184.) 

Fig, 184. 

The stndent mnst be prepared to meet with many inconsistendes in masical practice as respects 
accidentals — more especially douhle sharps and flats. 

200. '^ A double sharp raises, and a double flat lowers, a note two semitones,^--^ 

not a tone. {Compare par. 137.) 

Every tone may be divided into two semitones, but every two semitones do not make a tone. 
R. M. G. Q 




[Chap. XIX. 

Pig. \Zh. 

Fig, 136. 

201. When a note essentially sharp or flat is 
required to be raised another semitone, a single sharp 
or flaty in addition to that already in the signature^ 
makes it, assuredly, doubly sharp or flat. (Pig. 185.) 

202. This rule is observed by some composers. 
Others, however, desirous of avoiding ambiguity, inva- 
riably precede double sharp or flat notes by X or bb, 
without reference to the single sharp already marked 
in the signature. (Pig. 136.) 

Theoretically, the Feu in fig. 136 are certainly treble sharp. 

203. Again. When a double sharp or flat note is followed, in the same mea* 
sure, by a single sharp or flat note of the same name, some writers precede the 
latter by a single sharp or flat, and others by a natural, as well as a sharp or 

^♦^.137. d) ' r T^ ' 

^^.188. •j^'i^fl^H ^ ; 

The form of fig. 138 is the more common. The natural is of more recent invention than the sharp 
or fiat; and in music printed as late as the beginning of the last century the sharp is often used, as 
the natural is now, to restore a flat note to its original pitch. 

The following is firom Purcell's Orpheus Brittanieue. Third Edition, 1721. 

ig. 139. 2E 

Teach me in soft me 

lo • diouB gongs to move 

In modem notation the passage would stand thus :— 

Pig. 140 

Teach me in 

soft me 

lo - diouB songs to moye 



Chromatic Intervals. 

204. The epithet diatonic (from the Greek) is applied to the natural scale 
(and to all scales of like construction) because, in singing it, we pass princi- 
pally through tones* A scale purely diatonic would be inconsistent with the modem, 
or perhaps with any, musical system ; it would certainly be intolerable to the 
modern ear. 

205. By a diatonic scale is now understood a series of eight different sounds, 
the extremes of which are octaves to each other, separated by five tones and two 

The scales in fig. 40 are all diatoDic. 

206. The two semitones essential to the (modem) diatonic scale are called 
diatonic semitones. Two notes separated by a diatonic semitone are invariably 
of different names. 

207. A chromatic semitone is the interval between two proximate notes of the 
same name, one of which is altered by a sharp or flat 

208. '^ Between every two sounds separated by a tone, an intermediate sound 
may be placed, whereby the tone is divided into two semitones." (Par, 02.) One 
of these two semitones will, of necessity, be chromatic* 


Pi9.Ul. 1^) cSito <> = ^•"^- m Q^<>H<^ 



Chrom. Chrom« 

Bern. Sem« 

In fig. 141, the first semitone (SoVSom is chromaUc, the second {Soln-La) is diatonic. In 
fig. 142, the first semitone (Sol-Zmf) is diatonic, the second (iaP-ia|J|) is chromatic* 

209. Intervals resulting from any arrangement or juxtaposition of notes 
found in the same diatonic scale are called diatonic intervals. 

210. Diatonic intervals (compare Chap. Vl,) are majof and minor seconds and thirds, 
and their inversions minor and major sevenths and sixths ; perfect fourths, and 
their inversions perfect fifths ; pluperfect fourths, and their inversions imperfect 
fifths (of each of which the same diatonic scale never includes but one)\ and 
the octave, of which the inversion is the wnison— ^not properly an interval.*^ 



[Chap. XX. 

211. When the upper of two notes forming a diatonic interval is raised, or 
the lower depressed, a chromatic semitone, the interval between them is said to 
be augmented. When the upper is lowered, or the lower raised, a chromatic 
semitone^ the interval between them is said to be diminished. 

212. The unison, second, fifth, and sixth admit of augmentation only, and 
their several inversions, the octave, seventh, fourth, and third, of diminution only. 

The unison, though *' not properly an interval/' is, for the sake of system, often classed as such. 
The augmented unison, t. e., chromatic semitone — the agent of all augmentation and diminutien — ^is 
one of the most important of intervals. 

213. The augmented unison, second, fifth, and sixth, and their inversions, the 
diminished octave, seventh, fourth, and third!, are classed under the general name 
of chromatic intervals* 

Fig. 143 oontams an example; of eaok pf the dir<»natic intervals. 

Fig. 143. 














|o 11 jj e^ 









The word chromatic (from the Greek, xP^l"h colour), originally had reference to the ink (of 
different colonr) used to express altered notes; it has been retained possibly on account of the 
pecxdiar effect (figuratively, colour) which such notes gave to passages in which they were introduced. 

214. A scale which contains one or more chromatic intervals is called a ckrO" 
matic scale, 

215. The third form of the minor mode {Pig. 08) is chromatic, because its 
6^ and 7^ sounds are separated by an augmented second. 

216. A scale is more or less chromatic, according to the number of chromatic 
intervals it contains. The third form of the minor scale is only chromatic in so 
far as one interval, the augmented second, is concerned. Fig. 144, the most chro- 
matic form of scale possible, is generally called the chromatic scale. It consists 
exclusively of semitones — in all, twelve; seven diatonic, and five chromatic. 

Fig. 144. 

I^ojjo o < > \ \< ^^ 


As every sound is practically identical with another (•Z>oJl with 2ie(f, &c.), there are many 

different ways of expressing the chromatic scale, the choice among which, will be governed by circum^ 
btances. Fig. 144 is the commonest fi)rm« 

Chap. XX.] 



217. Of the ohromatio intervals {.Pig. 143) the augmented secmid and diminished 
fourth are more frequently used, especially in melody^ than any others, — ^because 
they can be produced by the juxtaposition of notes which form part of the same 
(minor) scale. 

Scale of La minor. 


4^ /^^ • *: : 







Fa and Sorji form an augmented second; Socu. and Do a 
diminished Jburth, The latter intenral indudeB the two most 
charactm«tic notes oi the scale in which it is found — ^the leading 
note and the S^. 

218. The inversion of the first of these intervals, 
the diminished seventh, is more sparingly, and that 
of the latter, the augmented fifth, hardly ever used 
in melody. 

Fig. 146. 



Fig. 147. 



219. The diminished third and the augmented sixth are of still less frequent 
occurrence; the former being, by some theorists, considered altogether inadmis- 
sible in harmony^ the latter in melody* 




220. Accidental sharps, flats, or naturals may arise, as we have seen, from 
either of two causes, — the introduction of the altered 6^ or 7*^ of the minor mode 
(Chap. 14), or a change of genus, from diatonic to chromatic. The sharpened 6^ 
and 7^ of the minor scale, never being marked in the signature, are of necessity 
expressed by accidentals {Par. 160) ; and no chromatic interval can be formed 
without at least one altered note. 

221. To these two causes of accidentals is to be added a third which, though 
partially connected with the first two, must be considered separately — modulation. 

222. Every musical movement is said to be in some particular scale. 
This expression, though true in the main, must be understood with some 
qualification. Since, though in every well constructed movement '^ some par- 
ticular scale^ prevails^ or furnishes the majority of the not«8 of which it is 
made up, few movements, however short or simple, remain throughout in one 
scale ; on the contrary, most movements present points of deviation into other 
scales, and even contain passages the scales of which are equivocal. 

223. This deviation, when made into scales connected with the original scale 
and with one another, is called modulation ; when made, at once, into scales not so 
connected, it is called transition. 

224. Modulation is much more frequently used than transition ; and the most 
common modulations are between scales which contain the greatest number of 
common noteSy and which are therefore most intimately *^ connected." 

225. Thus the scale of Do differs from that of Sol only in one note. Fa, which 
is natural in the former scale, and sharp in the latter, — ^from that of Fa only in 
one note, /St, which is natural in the former scale and flat in the latter. While 
the connexion between the scale of Do and that of La minor is still closer — the 
latter, in its original unaltered form, consisting of the very same notes as the 
former. (Par. 157.) 

226. The commonest modulations, therefore, are from any given scale to that 
of the perfect 5'^ above it — requiring but one additional sharp (Par. 119); to that of 
the perfect 6*>» below it — requiring but one additional flat (Par. 122) ; to that of its 
relative minor ; and to that of the relative minors of the 5^ above, and of the 5^ 

The recognition and conscionsness of the tonic, under whatever variations of tonality (changes of 
scale), is indispensable to the intelligent and certain performance especially of vocal music ; aud its 
frequent modulation constitutes one of the principal difficulties of modem music. This difficulty is 

Chap. XXI.] 



especially felt in performance from single paris,wheTem the modulationB are often but imperfectly ex- 
pressed, lodeed, without examining a score, it is often difficult, and sometimes even impossible, to 
tell by the eye, into what scale a composition has wandered. Two or three rules will however serve 
to meet cases of ordinary difficulty, and enable the vocal performer to ascertain the tonic for the 
time being. 


227. The tonic of the new scale (i.e., the scale into which the last modulation 
has been made) is generally found a minor second above the last added sharp, or 
a (perfect) /ot^rtA below the last added ^f. 

Fig. 148. 

Fig. 149. 





The JFcA in fig. 148 indicates a modulation into Sol: the 8i7, in fig. 159, a modulation 
into Fa, 

228. The new scale is unraistakeably indicated by the presence of a pluper^ 
feet fourth, or an imperfect fifth ; since there is but one of either in every scale. 
These intervals may appear either between two notes following in immediate suc- 
cession or produced simultaneously ; i. e,, either in melody (fy. 150) or in har- 
mony {M 151). 

^4,. 160. (L \} p ^ N^M^ 

_ Fig. 151. 


Fig. 150, an extract from a movement in Fa, ends with a modulation into Do, JSitker 
of the two notes {Fa or 8i^) which mark the modulation might belong to many different scales, but 
both together can only be found in 2>o. So 8ol^ and DM {fig. 151) can only be combined in Be, 

229. The mode (major or minor) of a new scale can only be determined by 
the presence of the S'* from the tonic. (Par. 145.) 

In fig. 152, there is a modulation from Do into Re ; whether it is into Re minor or Re major is 
uncertain, seeing that Fa (the 3^ to Re) is not expressed. The addition of the (major) 3"*, -^^ ^ 
the last chord of fig. 153 decides the mode. 










1280. Inrtfae natural scale of Do are found Jive major and two minor secondiy 
and (their inversions) ^t'« minor and two major sevenths; three major And four 
minor thirds, and (their inversions) three minor and four major sixths : one plu- 

J>erfect and six perfect /(mTtAa, and (their inversions) one imperfect and six perfect 
\fths. (Compare Chap. VI.) 

231. The S'* and 7^ sounds (mediant and leading note) bear minor seconds — 
all the other sounds bear major seconds ; the T^ and 4^ sounds bear major sevenths, 
and all the others, minor sevenths. {See fig. 154.) 

232. The 1**, 4^, and 5^ sounds (tonic, dominant, and subdominant) bear 
major thirds — all the other sounds bear minor thirds ; the 3^*, 6*^, and 7"* sounds 
bear minor sixths, and all the others, major sixths. 

233. The 4*^ Sound (subdominant) bears a ^Zt^perfect fourth — all the other 
sounds bear perfect fourths. The 7**" sound (leading note) bears an imperfect 

fifth — all the others, perfect fifths. 



{Fig. 154.) Intebvals found ik the Natural Scale. 







































c> --- 


















Chap. XXII.] 



The two minor seoonds and the two major sevenths, the three miyor thirds and the three minor 
sixths, and the one pluperfect fourth and the one imperfect fifth, heing severally inversions of each 
other, are foand between notes of the same name. 

The two minor seconds are Mi'Fa and Si- Do, the two major sevenths are Fa-JkR and Do-Si; 
the three mi^jor thirds are Do-Mi, Fa-La, and Sol-Si, the three minor sixths are Mi-Do, La-Fa, 
and Si- Sol; the one pluperfect fourth is Fa-Si, the one imperfect fifth is Si-Fa, {See Jig, 154.) 

234. The natural scale of Do is the type, or model, of aU major scales, in the 
modern system. In all major scales, therefore, the several sounds (I*^, 2^\ &c.) 
bear the same intervals as in the scale of Do ; for the sharps or flats by whose 
agency the order of tones and semitones is adjusted in the scale itself, operate 
equally on every individual interval which may be drawn from it 

235. E.g. " The H^ sound** of the scale of Do */ bears a pluperfect fourth- 
all the other sounds bear perfect fourths." {Par, 233.) So does the 4^ sound of the 
scale of i2e, viz,, Sol^ the 4^ to which is 2>o tt ; the Do in the scale of Re being 
essentially sharp. All the other sounds bear perfect fourths. {Compare fig, 154.) 

Fig. 155. 












C5 — 

236. Again, " the 1**, 4^, and 5** sounds of the scale of Do bear major thirds — 
all the other sounds bear minor thirds." {Par. 232.) So do the l**, 4***, and 5^ 
sounds of the scale of Mi b, viz.y Mi b, La b, and Si b (all flat in the scale of Mi b), 
the 3^^ to which are Sol, Do, and Re, All the other sounds bear minor thirds. 

{Compare fig. 154.) 

Fig. 156. 











Pars. 231-2 and 3 are, therefore true, not only of the scale of Do, hat of ever^ other major scale, 

237. *^ Melody, or tune, does not depend on the absolute, but on the relative, 
pitch of sounds — on their distances apart." {Par. 17.) When the notes of a 
musical passage are separated by the same intervals^ the melody they form will be 
the same. Any musical idea may, therefore, be expressed at any pitch, i.e., in 
any scale. 

238. The expression of a musical idea in a scale other than that in which it 
was first conceived or expressed, is called transposition* 

239. In transposing a passage from one scale to another, we represent each 
note in the one scale by the corresponding note (the note occupying the same 
place) in the other, and adjust the intervals of which it is composed, by substitut- 
ing the signatv/re of the new scale for that of the old one. 

R. M. o. H 




TkiM^ iif. 167 is in ik« Mide of 2)o« wbioh requires nsitlier sharp nor flsL To iaw^oMitinto 
Jls we mnsi.plMe Ikso ikarpt at the hasd of the stavo; to transpose it into lfib» thrmfidi; vk 
J^ffimr tiarpti into Fa, weJUU : into 8olt one iharp, and so on. 

Pig. U7. 



^"^ <f) ^ ^, 






f fJ^^^hTO hn ^f 






The student is recommeDded to try the effect of the above transpositions without sharps or flats. 



Rhythmical Licences. 

240. The rhythmical licences admissible in musical performance consist in the 
compression of more than its proper complement of notes into a single beat, and 
in the slackening, or accelerating, the pace of particular beats. Of the former, the 
most common example, the triplet or triolet, has been already noticed, 

241. ^' A triplet is a group of three notes, which (by licence) is performed in the 
time of two of the same kind.** (Par, 49.) 

242. The triplet is but another mode of indicating a change of time, from simple 
to compouTulf in the particular passages where it is introduced. 

Figs. 168 and 159 are identical. 

Fig. 158. 
Jl- ^- Jt- Ji^. ^ « ^^^ 

Fig. 159. 


243, With the triplet may be classed all groups wfaateTer of irregulaf rhyth* 
mical formation. In modem instrumental music these are found in great numbers 
and variety, — -Jive or more notes being sometimes compressed into the time of/our 
of the same kind,/ot^ or more, into that of three, &c. &c. 

Such groaps are best stndied in connexion with musical practice. 

Departure fix)m the average pace of a movement in the case of " particular heats," is indicated by 
the ItaliviL wovds, JRafleniando, AceeUrcm^, &c.| to be expUined in Chapter XXYII. 





244. Passages not forming an integral part of a moyement — ^which without 
essential loss to it might be, and often are, omitted — ^are called graces^ or embel- 
lishments. The principal graces used in melody Are the appoggiatura, the beat^ the 
shakey the turn, the acciaccatv/raj and the portamento. The principal graces used 
in harmony are the tremolando and the arpeggio, Graces are, for the most part, 
expressed in smaller notes than those used for the integral parts of a movement. 

245. The appoggiatura (from appoggiarCy Ital., to lean) is a small note, which, 
being prefixed to another, robs it of its accent and a portion of its time. 

246. In general, the appogiatura is a note of half the length of the note which 
it displaces ; but its full time should be given to the appoggiatura, whatever be its 
length — the following note being shortened accordingly. 

YigB. 160 and 161 are severally identical with figs. 162 and 163. 

Fig, 160. 


Fig. 161. 






Fig. 162. 

Fig. 168. 


Latterly, the appoggiatura has been falling into desuetude ; modem composers preferring the less 
equivocal forms of ordinary notation. Fig. 164 would certainly have been expressed by an earlier 
master as fig. 165. 

Fig. 164. „ Fig. 165. 

247. The beat is a short appoggiatura, made on the semitone below a principal 
note. Its effect is to give force and especial emphasis to that note. 

Fig. 166 


Chap. XXIV.] 



248. The acciaccatura (from acciaccarey Ital., to pound) is a group of two notes, 
introduced with the utmost rapidity, before another note. The interval formed by 
the two notes should never exceed a minor third. 


249. The appoggiatura, beat, and acciaccatura should severally be uttered on 
the beat due to the note which they precede — not before it. 

250. The shake consists in a rapid alternation of two adjacent notes. It 
is indicated by tr., a contraction of the Italian word triUOf placed over a note 
which is generally preceded by an appoggiatura. 

Fig. 168 is to be performed like fig. 169. 

Fig, 168. 





Fig, 169. 

251. The shake, unless it be a very short one, is always concluded by a twm. 

iJSeeJig. 169.) 

252. The turn is a group composed of a principal note, and two subsidiary 
notes, one above and one below it. It is indicated by /^/, or ^ placed over the 
principal note. ^^^ is the sign of the direct^ and ^ of the inverted, turn. 

Fig. 170, which contains an example of the direct, as well as of the inverted, torn, should 
be performed like fig. 171. 



Fig. 171. 

253. The turn, like the appoggiatura, beat, and acciaccatura, should be begun 
on the beat due to the note over which it is placed. When it is placed between 
two notes, it should follow the first of them. 

Fig. 172 is to be performed like fig. 173. 

Fig. 172. 

i f: J • i^ I 





9M The p&rta7nenta (from portage, Ital. to carry) consiste in the smooth 
tttteranee of two following notes, part of the time due to the first o£ which is gi^ea 
to the anticipation of the second. When (in vooal peiformance) each note has ita 
own syllable, the anticipated portion of the second note is sung to the first 

Fig. 174 is to be performed like i^. 175. 







Fig. 175. 

256^. The tremcAmiio (from tremolarey Ital., to trewibld) is produced either by 
the rapid iteration of the same sound or the alternation of different sounds in 
the same combination. 

Figs. 176 and 177 are performed like figs. 178 and 179. 



Fig. 176 




Fig. 119, 

w w w w w xzr 

256. The arpeggio (from arpeggiare, Ital., to play upon 
^ harp) consists in striking the sounds of a chord in 
rapid suceession, instead of simultaneously. It is indi« 
cated as in fig. 180. 

Fig. 180. 



Signs of Repetition, Contractions, &c. 

257. The alphabet of nnnio inoludet, besides notes, many characters, and 
even words, indtoatitre of the style or manner of performance of the move men ts, 
particular passages, or individual notes, to which they refer. 

258. Repeftition is indicated by dots endosnig the passage io be vepeaitad. 
These dots are generally, though not always, placed at the beginning and end of 
a measure. 

«" '•■• (yi -'\ ifr H^ 


• • 

259. Sometimes one or both of the bars enclosing a passage to be repeated 
are doubled ; but the double bar is most often, though not always, introduced 
when the last measure of the passage to be repeated is incomplete. 

«,. .«. j-fiTl p J- f I J j^ 




260. The beginning of the passage to be repeated is frequently indicated by 
a sign :j^:, referred to at the end of it by the (Italian) words Dal Segno, i. e.,frovi 
the sign. 

Thus, fig. 182 might be eo^tessed'like fig. 1S3. 

i>al Segno. 



261. When the repetition is to be made from the begimting of « moToment fthe 
dots are often omitted, and the words Da Capo (from the 'begiaining)^ x^ Da dxfo 
al Segno {from the beginning^ at the sign)^ if there be a sign, are used. 

Thus fig. 181 might be expressed like fig. 184. 

pa Capo^ 

Fig, 184 




[Chap. XXY. 

262. When, on repetition, any measure or measures are to be omitted, the words 
•* !•* Time" are placed over them] and the words " 2"* Time,^ over those to be sub- 
stituted for them. 


j, Jj>^ I &0. 

263. The repetition of a single measure is sometimes marked by the word bU 
(twice) placed over it in addition to, or instead of, the dots. 



.Pig. 186. 


264. Silence lasting an entire measure (properly represented only by rests 
equal to the contents of that measure) is often expressed by a semihreve rest, 
whatever be the kind of time employed. 

Fig. 187. 

Fig. 188. 

Fig. 189. 

Fig. 190. 




ij_r ^r^n^ 



Figs. 187, 188, 189, and 190, are all occasionally represented by fig. 191— — 

the form properly ^plicable to common time only. ^' — 

265. Silence lasting longer than one measure is, in single parts, generally in- 
dicated by a number, or numbers, placed over a semibreve rest, representing the 
number of measures of silence. 

266. In ancient music the necessity for these figures was obviated by the em- 
ployment of the breve^ and the long {double breve) rest. 

Fig. 192, equally with fig. 193, indicates a rest of eleven measures. The two forms are sometimes 
combined, as in fig. 194. 

'ig. 192. . Fig. 193. Fig. 194. 

11 11 





267. In counting rests of more than one measure the numbers (of the mea- 
sures) should be told off on the first beat of each. Thus fig. 192 should be 
counted, One, two, three, four ; Two, two, three, four ; Three, two, three, four ; 
and so on to Eleven, two, three, four. 

268. A pause placed over or under a note indicates generally that the sound 
due to it may be sustained as long as the performer pleases. (Fig. 195.) A pause is 
sometimes used to mark the end of a movement. 

Fig. 195. 

269. The direct "W* is used to indicate a following note which it is liot con 
venient or necessary to express. It is especially used at the end of a line or 
the bottom of a page, as a preparation for the next. 



Marks of Expression. 

270. A dash placed over or under a note indicates that it is not to be sus- 
tained throughout the beat, or portion of a beat, due to it, but interrupted^ as though 
it were a much shorter note followed by rests. A dot placed over or under a note 
indicates a modified form of the effect due to the dash. 

Fig. 196 Bhoold be performed like fig. 197, and fig. 198 like fig. 199. 

Fig, 196. 

F^f. 197. 


Fig, 198. 

Fig. 199. 

• • • 


271. Dashes are sometimes placed over minims, where they are understood to 
imply the effect represented by the word sforzato (forced). {Su fig, 211.) 

272. Notes with dashes over them are said to be performed staccato, i. «,, cut 
off, separated ; notes with dots over them, mezzo-staccatOy i. e., ^Z/'-staccato. 

273. A slur placed over or under two or more notes indicates that they are to 
be performed legato, t. e^ smoothly (literally, hound together). In vocal music, the 
slur indicates that the notes under or over it are to be vocalized, i. e., sung to one 

^ ^'^ ^v Handel. 

Ptflr. 200. 

Tune your harps to songs to songs of praise. 

274. When two notes only are slurred, a stress should be laid on the first, and 
the second should be made staccato. 

Fig. 201 should be performed like fig. 202. 
Fig, 201. 

Fig. 201 

jnmk^ jj Wl.^.Hj'iji 

275. The last of a group of slurred notes is always short, by virtue of its 

R. M. G. I 



[Chap. XXVI. 

276. When the alar is placed over two or more notes of the same name and 
pitch, it is called a ^ or bindf and has the effect of turning them into one note- 
equal in length to the two added together. (Compart Par, 198.) 

Figs. a03 and 204 are identical. 

Fig. 203. 

Fig. 204. 


277. The tie is generally used to connect two notes, the first of which is un- 
accented, and, more especially, the last note of one measure with the first of 
another. Sounds beginning on accented beats are generally expressed by entire 
notes, or by dotted notes. 

The form fig. 205 (Compare par. 180) is now obsolete, that of fig. 206 having superseded it. Fig. 
207, however, is not incorrect, though more often written as fig. 208. 

Fig. 205. 


Fig. 207. 


^JNJr i rr'ii 


278. Tn prolonging a note begun on an i^naccented beat to an accented beat, 
''the natural and ordinary accent" of the measure in which it appears '^is dis- 
turbed." (Par. 180.) The result of this disturbance is called syncopation. 
Syncopation is rendered more apparent by the employment of the sign ::^=»-, or 
the letters Sz. {See Fig. 211.) 



Words relating to Pace, Intensity, and Style. 

279. The vocabulary of music has been enriched, or corrupted, by the contribu- 
tions of every people among whom musical composers, performers, or even tran- 
scribers, have been found. Lively, Doucement, Feierlich, &c. &c., are used severally 
to indicate the pace, intensity, or style, of music printed in England, in France, 
or m Germany. 

280. These words caiTy with them the disadvantage of being intelligible only 
to the people of those countries, or to those who have studied their language, — 
a disadvantage the more to be deprecated from the fact that musicians possess a 
sort of comrrwn language in Italian, the musical terminology of which is more or 
less accepted by every musical people. 

A complete list of Italian words relating to pace, intensity, and style, would furnish material for a 
Musical Dictionanr. The followiuff lists contam some of the most important, classed under their 
*'®^®™,^«J<^«- , The English wordn immediately following the Italian are such literal translations as 
would be lound m a dictionary. They represent very imperfectly the meanings of the latter as appHed 
to music, which indeed are only to be ascertained from a close study of Italian, or considerable expe- 
rience in musical performance. Thus, Gh-ave, Lento, and Lar^o, may be regarded as equivalents, so 
tar as pace only is concerned; but each indicates a different style of performance,— Graw implymg 
more solemnity than Lento, and Lar^o more dignity or breadth than either. 

281. Words relating to pace, intensitv, and style, admit in every instance of 
contractionyBxid generally of modification, by the augmentation or diminution for 
which the Italian language presents such facility. Sometimes two or more are 
joined together in a way that appears somewhat contradictory, until it is under- 
stood that they refer not only to pace, but to style also. Thus, AUegro Andante 
means lively in manner, but somewhat deliberate in pace. 

Each of the words in fig. 209, excepting the three first, may be considered to express a quicker 
movement than the one before it. 

Fig, 209. 
Words relating to Pace. 

( GRAVE, grave. 
< LENTO, slow. 
( LARGO, broad. 

liABaHETTO, rather broad, not so slow as Labgo* 
Adaoibsimo, very leisurely, slower than ADAaio. 
ADAGIO, leisurely. 

Andani?ino, going gently, slower than AkdaiTte. 
ANDANTE, going at a moderate pace. 

Allegbetto, rather merry, not so fast as ALLBaBO. 
ALLEGRO, merry, lively. 
PRESTO, quick. 

Pbestissimo, very quick. 



[Chap. XXVIL 

Connected with the aboye are the following : — 

Fig. 210. 

AccELEBANDO,* ACCEL"., accelerating (the pace), 

Rallentando,* ball"., slackening ( — ). 

^TBiVG^VDO, f^T^iV*., pressing (mwards, 

Pid M0B8O, more moved, quicker, 

RiTABDANDO, BITAB"., retarding. 

RiTENUTO, BITEN"., holding hack, 

A Tempo, in time, (qfter an Accel", or Rall".). 

Ik Istesbo Tempo, in the same time; i, e., the times, or beats, the 

same, whatever be the forms of the notes, 
Alla Bbeye, by the breve ; i, e,, the breve being regarded as the 

whole note — each beat being a minim. 

Tempo Obdinabio, (in) ordinary time ) ui jf 4 ? 

^ ' ^ ' , ^. > neither fast nor slow, 

' ' ' CoMODO — conventent — > 

* * These words are correlatives. 

Modem composers frequently add to the words above, an exact indication of the pace of their 
music, by a reference to the Metronome. (See Chap, XXIX.) 

Fig. 211. 

Words relating to Intensity. 

PlAKO,* PIA., p, sqft. 

Mezzo Piano, mez. pia., mp, rather soft. 
Pianissimo, pian"".,jc>p, very soft, 

POBTE,* FOB*,^ loud. 

Mezzo Fobtb, mez. fob., iv^ rather loud. 

F0BTI88IMO, FOB""., ff, very loud, 
CBE8CENi>o,f CBES., OT -=r^ increasing (vn loudness), 
DECBESCENDO,t DECBE8., OT ZT"—-*-, decreasing (in loudness). 

To the above may be added : 

FoBTE Piano, ^, loud and (immediately qfler) soft, 
Sfobzato, sz, forced (applicable to single notes only), 
RiNFOBZANDO, RiTSTO^z., forcing (applicable to passages). 
Calendo, descending 

decreasing in speed and 
(generally) in intensity. 

Pebdendosi, losing itself 
Diminuendo, diminishing 
Smobzando, extinguishing 
Dolce, soft. 

* f These and their dependent words are correlatives. 

All these words are liable to modification by the addition of one or more others, expressive partly 
of pace, but more especially of style. The following are some of the most important of them. 

Chip. XXVn.] 



Fig. 212. 

WoTd» relating {chiefly) to Style. 

Agitato, agitated. 

Mabstoso, miyestic. 

AiriiCATO, animated. 

Mabgato, marked. 

A poco A pooo, by degrees. 

MoLTO, much, veiy. 

AssAi, BufficiexitlY. 

Mbno, less i e. g., Meno Allegro. 

Bbk, well ; e.g., Ben Marcato. 

Mbzzo, half. 

Bbillaktb, brilliant. 

MoDBBATO, moderate. 

Con, with. 

Non, not ; e. g., Non troppo Lento. 

(Con) Bbio, mirth. 

Piu, more; e.y.,Piu Animato. 

Ebpbbssionb, expreMion. 

Poco, little. 

Quasi, almost, as though. 

MoTO» motion* 

Sbmpbb, always ; e. g., Sempre pp. 

— TB9BBB2ZA, tendemeM. 

S08TBNUTO, sustained. 

E8PBB88ITO, ezpreaalTe. 

Staccato, cut off. 

GiusTO, exact. 

Tbhuto, held, sustained. 

Gbazioso, graoefnL 

ViTACB, lively. 

Lbgato, bound. 

YoLTi, turn. 

Ma, but ; e. g.. Ma non Ball\ 

Sboub, it follows. 

282. The words in fig. 209 are all used occasionallj as noun-substantiYes. 
We speak of an Adagio, an Andante, an Allegro — as of movements to be per- 
formed in the styles indicated by those words. 



The Tenor and Alto Staves. 

" All the notes (twenty-three) required for average vocal music can be placed on a staye of eUnen 
lines." (Pwr. 34.) But "no individual voice can utter" twenty-three sounds; consequently, in 
writing music for individual voices, a smaller number of lines suffices. ** Practically, whether for 
vocal or instrumental music, a stave oi five lines is generally adopted; ^% particular sets, or staves, 
most used being the five highest and the five lowest of the Great Stave" of eleven. {Par. 35.) 

** The lower one of these sets, or staves, of five lines is used for voices and instruments of low pitch : 
the upper, for voices or instniments of higher pitch." (Par, 86.) " Music for the lower voices of women 
and the higher voices of men demands other staves, which are, equally with the treble and bass staves, 
extracts from, or parts of, the Great Stave of eleven lines." (Par, 39.) 

283. The voices of men (beginning from the lowest) are Bass, Barytone, 
Tenor, and Counter-tenor; those of women are Contralto, Mezzo-soprano, 
Soprano, and Treble. The highest of the former, the Counter-tenor, is almost 
identical in compass with, though very different in timbre from, the lowest of the 
latter, the Contralto. The Treble may be regarded rather as a puerile than a 
female voice. 

The relative places, in the musical system, of these voices is exhibited in fig. 213, and the relations 
of the different staves they occupy to the Great Stave is shown in fig. 214. 


Fig. 213. 









U f > 1 

A «^ ^ 1 


i > 1 


C J 1 


C > 1 

r > 

V-X - 

< > 

• • 

C > 


( > 


€ ^ 


€ > 


Fig. 214. 














3 ■-+ 













284. Of the seyen staves (in fig. 214) two are beaded bj the Fa clef, /our by 
the Do clef, and one only bj the Sol clef. 

285. The 4^ line of the Great Stave (indicated by the Fa clef), is also the 
4"" line of the bass stave ; but it is the 3** line of the barytone stave, the 2*"^ of the 
tenor, and the !•* of the contralto, 

286. The 6*% or middle, line of the Great Stave (indicated by the Do clef), 
which forms no part of the baaa or of the treble stave, is the 6*^ line of the barytone, 
the 4"* of the tenor, the S"" of the contralto, the 2** of the mezzo-soprano, and the 
1'* of the soprano, 

287. The 8**^ line of the Great Stave (indicated by the Sol clef), which forms 
no part of the bass, barytone, ox tenor stave, is the 6*^ line of the contralto stave, 
the 4"* of the mezzo-soprano, the Z^ of the soprano, and the 2"* of the treble. 

288. Two of these staves, the barytone and the mezzo-soprano, have become 
obsolete. Music for the barytone voice is now commonly written on the bass stave ; 
music for the mezzo-soprano voice, on the contralto, the soprano, and even the 
treble stave, which latter, in England, is generally substitated for the soprano. 

The treble stave was once used ezclnsivelj for instrumental music, and has not even yet heen 
universally adopted for vocaL The soprano stave is still much used on the Ck>ntinent. 

289. Thus the staves in actual use are but five, and, in England, only four,— - 
the bass and tenor for the voices of men, the contralto (or alto) and treble for the 
voices of women and children. 

The bass and treble staves, the lowest and the highest of the Great Stave of eleven lines 
(«ee Chap, /7.),can need no further explanation. 

290. On the 4^ line of the tenor stave is found the Do clef. (Seefy, 214.) The 
Do clef, it will be remembered, is the distinguishing mark of the 6% or middle, line 
of the Great Stave of eleven lines. Consequently, the 4^ line of the tenor stave 
is identical with the 6^ of the Great Stave ; and, further, the !•*, 2*% S**, and S^ 
lines of the former are identical with the S'*, 4*^, 6**", and 7"" of the latter. 

291. On the S'* line of the contralto stave (See fig, 214.) is found the Do clef — the 
distinguishing mark of the 6^ or middle line of the Great Stave. Consequently, 
the 3*^ line of the contralto stave is identical with the 6^ of the Great Stave; and 
further, the !•*, 2"*, 4*^, and 5^ lines of the former with the 4*^, 5^, 7^, and 8^ 
lines of the latter. 

Familiarity with the tenor and conti^alto staves is only to be attained by ptactice } but it is certain 
that the difficulty sometimes attendant on this arises entirely from the fact that their relation to the 
Great Stave, and therefore to the more femiliar treble and bass staves, is not at all, or bat imperfectly, 
iinderstood. One stave is of coarse, qf itself, ^ easily mastered as another ; and any difficulty found 
in reading from the tenor and alto staves must arise from a hitherto exclusive use of the treble and 

Let the following facts be borne in mind :^- 



[Chap. XXVIII. 

292. The three lowest lines of the tenor stave are identical with the three hipTiest 
of the bass ; the top line of the tenor stave is identical with the bottom line of the 
treble ; and the 4*** (or clef) line of the tenor stave is that leger line which connects 
the bass with the treble. {Pig. 215.) 

293. The two lowest lines of the contralto stave are identical with the two 
highest lines of the bass ; the two highest lines of the contralto are identical with 
the two lowest of the treble-^ and the 3"^ (or clef) line of the contralto is identical 
with the leger line connecting the bass with the treble. {Fig, 216.) 

Fig. 215. 

Fig, 210. 




The student must he warned that, notwithstanding the recent multiplication of editions of popular 
musical works, in which parts for the alto and tenor voices are printed on the treble stave (the former 
sometimes, and the latter always, an octave higher than their proper pitch), anything like an extensiye 
acquaintance with classical music is quite impossible without familiarity with the alto, tenor, and 
soprano staves. 

This subject has heenfidly treated hy the Author in a " Short Treatise on the Stave" 



The Syren and The Metronome. 

294. ** The pitch of a musical sound depends on the number of vibrations 
communicated to the air in a given time^^ (Par. 6), — its duration, " on the time 
during which the air continued to vibrate at the same paceJ*^ {Par. 6.) 

295. Although " the musical student is chiefly concerned with the pitch and 
duration of sounds as compared with one another,'* yet, " every sound is assuredly 
of a definite and appreciable pitch and duration." \Par. 9.) 

296. Doj the centre of the musical system {Par. 80), is the result of 256 vibrations 
per second ; its octave above, of 512 ; and its octave below, of 128. The highest 
Do on an ordinary Piano- forte is the result of 2048 vibrations per second ; the 
lowest Do, of 32. The octave below the latter, the result of 16 vibrations per 
second, has till lately been thought to be the lowest sound appreciable by the 
human ear. 

297. It is difficult to believe that even the lowest of these numbers is to be 
counted ; yet methods whereby their correctness could be ascertained indirectly 
have been known for a great length of time ; and mechanical science has recently 
made even a direct estimation of it possible. The most perfect of these con- 
trivances is an instrument called the Syren^ invented by a French mathematician, 
Cagniard de la Tour. 

298. The . Syren («ec fig. 218) consists of cylinder A, generally about 2 inches 
long and 3 inches in diameter, the tahle^ or top, of which is pierced with 25 holes 
placed in a circle at equal distances apart. In immediate contact with this table 
is placed a disk B, about 1^ inch in diameter, pierced with the same number of 
holes as, and exactly coinciding with, those in the table of the cylinder. By 
means of a short pipe C, communicating with a bellows, a blast of air, slightly 
compressed, is forced into the cylinder, from which its only means of escape is 
through the holes in the top of it, when those of the disk are brought immediately 
over them. The holes of the disk and of the cylinder being cut obliquely and in 
opposite directions, the air, in its effort to escape from the latter, sets the former 
spinning, and brings each of the holes of the one successively over each of those 
of the other. Every time this happens, the compressed air, in its escape from the 
cylinder, gives a pulsation to the external air, which pulsation, if repeated at 
regular intervals and with sufficient rapidity, produces necessarily a musical sound. 

299. " As the number of vibrations (or pulsations) communicated to the air in a 
given time increases or diminishes, so does the sound become more acute or more 
grave." {Par. 5.) In the case of the Syren, the number of vibrations will depend 
on the pace at which the disk revolves, — ^whicb pace, again, depends on the force 
with which the air is driven into the cylinder. 

B. M. G. K 



[Chap. XXIX. 

300. The number of revolutions, and portions of revolutions, made by t1ie 
disk, are recorded by two hands, somewhat similar to those of a watch, each being 
centred on a separate dial, and acted upon by a mechanical contrivance which 
connects them with the axis of the disk D ; the time in which these revolutions 
are made being ascertained by a stop-watch, or a pendulum beating seconds. 

Thus, suppofiiiig 6 revolations of the disk to be made in a second while a note of Fig. 217. 

a given pitch was maintained, it would prove that that note (e. g., Jig. 217) was the ^ j; 

result of 125 vibrations per second ; seeing that, the disk being pierced with 25 holes, 

each revolution of it wa3 the cause of 25 vibrations. 


Fig. 218. 

The applicatioil of the Syren to practical music is at present too remote to justify a more minute 
account of it here« The exact measurement of the tiffie of sounds is at once more simple, and prac- 
tically more important to the student, than that of their tune. This is effected by means of Ma^lzel s 

301. MaelzeVs Metronome {Jig. 219) consists of a pendulum A B, having an 
index B C, which is furnished with a weight M, easily moveable along its whole 
length. On the position of M depends the pace at which the pendulum A B will 
oscillate to and fro, or, more properly, the number of oscillations it will make m fit 
given time. The figures on tne index B C indicate this number per minute, sup- 
posing the moveable weight M to be ])laced immediately under any one of them. 

Ceit. TTTTT ] 



Tfans, if the top of M be placed against the line marked 160, tlie pendulum A B, 
and the index D C, will malte 160 vibratioos per minute ; if it be placed agunst 
the line 50, it will make 50 vibrationB per minute ; the fonner being the largest 
the latter the smallest, number possible. 

303. A composer or editor, who desires to indicate the exact time at which a 
given tnoTenient is to be performed, has only to mark against the form of note 
which represents each beat the figure under which the weight M is to be placed 
on the index B C, and the pendulum will oscillate at the pace at which each 
beat is to be made. 

Thus J •• 100, meuu that saeh crotchet is to be performed, and each beat (equal to a crotchet) 
made, in the time of one oecillation of the pendnlnin, whea H it placed agaiuit the line marked 100. 

Fig. 21S. 

Although, for the purpou of keeping time in mnglcal performuicei the Uetrottom« never has 
been nor perhaps ever can be used, for the purpose of indicating it, it is most valoable. When at 
band it it, of course, an indisputable evidence of the intention of tbe mnposer g and even when not 
at hand it ii hardlj less usefal, since a moderate degree of practice will enable S conductor, or per- 
former, to remember the pace at which the pendulum vibrates whea the weight is in this or that 
poaition, and thus to aari7 oat the desi^ of the composer. If not perfectly, at Uaat with £ir more 
certain^ than when aided onlj bf sncb words as AndanU, Allegro, Ac &e. 



The Ancient Modes. 

" The order of tones and semitones in a scale is called a mode. Seven modes, or forms, of scale 
are therefore possible; and at least that number was once in use" (Par, 76.) 

303. It has been shown (in Chap. VII.) that of the seven modes " possible" only 
two are available, or have hitherto been made available, in the modern system — 
the 1** and the &^ (of fig. 40) ; that the 2"*, S"^, and 6*^ have been rejected be- 
cause they are wanting in leading notesy and the 4"* because of its pluperfect fourth ; 
and that the 7*^ " has never been used," on account of its imperfect fifth. 

804. The importance of the leading note, though not altogether unappreciated, 
would seem to have been less sensibly felt by the Old Masters than by us ; for 
they certainly recognised and executed music written in the S""*, 8"^, and 5** 
modes (of fig. 40), and, by a different disposition of the notes of each, formed as 
many others — in all twelve. 

Fig. 220. — The Ancient Modes. 



















6th. 8th. 



-&- — 






305. The first six of these modes (those in the upper line of fig. 220) they 
called authentic^ the others (those in the lower line) they called plagal ; giving 
the odd numbers to the former and the even numbers to the latter. 

By the " Old Masters" are generally understood the composers who flourished before the end of 
the sixteenth century ; though the ancient style was maintained in many instances much later. 

The large notes in fig. 220 are the tonics, or raiher Jinals, of each mode. 

306. The final of each authentic mode is identical with that of its plagal ; ^-g-f 
Ue, not Lttf is the final of the 4^^ mode as well as of the 3'*. A passage in an 
authentic mode, therefore, would range between the final and its octave ; ^4iereas 
a passage in a plagal mode would range between the ^^ of the final and its octave^ 
the final being, in an authentic mode^ a boundary ^ and in a plagal mode, & centre. 




807. Of these twelve *^ poesible*' modes only a eertsia number have been in 
common use at any time. Most of the old Theorists limited the nnmber of modes 
to ei^tf four authentio and four plagal, counting the anthentie mode whose final 
is Re as the 1"% and the plagal mode whose final is Sol as the 8*^, and last ; thus 
rejecting Ifte onZy two used in the modem system — those beginning on Do 
and La^ 

The axrangement of fig. 220 is that given by Zarlino in his " Institozioni Armoniche ;*' but the one 
most comnu>nlj adopted was the Ibllowing. {/3te Jig, 221.) 

Fig, 221.— Ths ANomrr Kodsb. 

lit. Srd. (th. 7th. 









4th. 6th. 


_ O 

■^ ^^ 



Fig, 222. 

308. Of the above, the modes most com- 
monly used were the I** and 3**, whose finals 
are Re and Mi. (Figs, 222 and 22i,) They 
are both minor modes, but difiering from the 
modem type 0%^. 228), the former in its major 
6% the latter in its minor 2^\ {Compare figs* 

222 and 22iwUhfig, 223.) 








Fig. 228. 




Fig, 224. 






Two of the most recent examples of the nse of these modes are presented in Handel's Israel in 
■%3^^,— of the 1" in the chorus, " And I will exalt Him," arid of the 3'^ in " Egypt was glad." 

309. The old modes were liable to modifications j akin to those now made in 
the upper tetrachord of the minor scale. (Par. 146.) Thus the 4*^ sound {S'i) of the 
5*^ mode, which is a 2>Jttperfect fourth from the final Fa^ was often made^Zaf, — by 
which means the mode became identical with the modern major scale of Fa. While 
in progressions like the last of the soprano part of fig. 225, the penultimate note 
was sung^ though not written, sharp. 


Until a comparatively recent period, snch modi- 
fications as the above were left to the science or 
taste of the performer, who would, of coui-se, often 
have anticipated many of the effects of modem 

Fig, 226. 


310. The Old Masters were acquainted with transposition; but they never 
carried it (in writing) into scales requiring more than one sharp, or one flat ; and it 
was only recently that even these were placed at the head of the stave. When the 
growing needs of the modem system ctdled more than one sharp or flat into requi- 
sition, scale signatures were introduced — though at first in an imperfect form. So 
lately as the beginning of the eighteenth century, the last sharp, or flat, was 
commonly marked as an accidentaL 

The Bignature of Handel's trio, '* The flocks shall leave the mountains'* (in Acts and Galatea), 
is two flats instead of three. The scale is that of Do minor. 

311. The tonic of a piece of ancient music can only be ascertained by exami- 
nation of the music itself; nor can the signature always be relied on in respect 
to any piece composed before the modem system was thoroughly established. 



The imperfectionB of the time-table, though eyentoally remediable by an act of memory, are the 
cause of perpetual embarraBsment to beginners — especially those who bring any mathematical training 
to bear ovi the study of practical music. 

Those only who have had experience of it can quite estimate the difficulty of making a mathe- 
matical atudent believe, or understand, that a quantity represented by | has properties essentially 
^iifferent from a quantity represented by 2> uid that six quavers represented by the former sign are to 
be treated altogether differently from six quavers represented by the latter. 

The following modes of designating compound times are suggested, not in the expectation of 
altering anything so extensively used and accepted as the existing time-table, but as a means of 
explaining the nature of compound time. 

A measure of compou/nd duple time differs from a measure oi simple triple time in the fact, that 
whereas the latter consists of three entire notes (0. ^., crotchets), the former consists of Uoo dotted 
notes (e. g., dotted crotchets) ; the atnouTit in either being the same, but the accent being essentially 
different. (Compare Par, 195.) A symbol which would represent two qualities, each consisting of ofie 
and a half, as distinguished from three qualities, each consisting of on/e, would seem to be a certain 
means of preventing these two kinds of time from being confounded, which, it is certain, the present 
signatures do not. 

It is proposed, then, to mark all compound times on a uniform sytems, which would at once show 
the number of beats in a measure and the value of each beati— -the former by a fraction (of a semi* 
breve) and the latter by a figure preceded by the common arithmetic symbol qf multiplication. 

Thus the time usually marked § would be expressed by | X 2 ; ». e., three-eighths of a semibreve 
multiplied by two, or, in familiar language, three quavers twice over, in each measure. 



The signatares in the left hand oolomn of the following tahle are identical with those in fig. 127 ; 
those on the right are, one and all, different. (Compwefig, 127.) 



& 9 ^ 

s o 








Proposed new Table of Time Signatwrea. 







£2 cn <-> 




o o o o 
















j^l x3 o . o » <-> ♦ 










" 3 ^ • r r 

o K 4<-^-«- | -nT^. 


^MMWWtWOtXWMMlOrWX'KWWiM'MMWtOK*^^**!'!' " ««'* "" *' "" ' 

The numbers refer to the Paragraphs, which form an uninterrupted series from 

the beginning to the end of the work. 

,.j- i - i -Lr i . i u in - -■ ''--- ■ "• < K « ■« i«<«»«p<»<»«»««r 

Aeeenty 184. 

Acciaceatura, 248. 

Accidentals^ 196; effect of, in the same 

measure, 197, — m the next measure, 

198, 199. 
^ppoggiatura, 245 ; length of, 246. 
Arpeggio^ 256. 

^Bare, 169 ; double, 172, 178. 

Beat, 24.7. 

Beats, accented or unaccented, 24 ; made 
by the hand, 174 ; down beats usually 
accented, 179 ; subdivision of, 186. 

Bis, 263. 

Brace, 37. 

^reve, 60. 

Cadence, perfect and plagal, 91. 
Cflefs, 28, 29, 30. 
I>ash, 270. 
Degrees, 32. 

Demisemiquaver, shorter notes than, 51. 
Direct, 269. 
Dominant, 83. 

Dot, after a note or rest, 55 ; double, 56 ; 
over a note, 270. 

Unharmonic Change, 128. 

Fifth (Imperfect), its place in the natural 

scale, 233. 
R. M. G. 

Fifths, perfect and imperfect, 67, 68; 

augmented, 212, 213. 
Finals, of the ancient modes, 306. 
Flats, 95 ; how generated, 117, 122, 123 ; 

double, 136, 137, — always accidentals, 

142,— how contradicted, 201, 202, 203. 
Feet, divisible into times, or beats, 23. 
Fourth (Pluperfect) its place in the 

natural scale, 233. 
Iburths, perfect and pluperfect, 67, 68 ; 

diminished, 212, 213. 

Graces, the principal, 244; expressed in 
smaller notes than other passages, 244. 

Harmony, 10. 

Idea (Musical), to be expressed at any 
pitch, 237. 

Intensity (Words relating to), 281, fig, 161. 

Intervals, 18 ; in the natural scale, 18 ; 
how named, 57 ; inversion of, 64 ; 
greater than an octave, 70-72 j alte- 
ration of, 98,— Hioea not affect their 
names, 141 ; diatonic, 209, 2l0 ; aug- 
mented and diminished, 211^ 13; 
chromatic, — the most common, 217. 

Inversion, 64 ; quality of an interval altered 

by, 66. 
Italian, the common language of musicians, 





Leading Note, 79, 81, 89; last added 
sharp always the, 119; bow regarded 
by the Old Masters, 306. 

Legato, 273. 

Lines (Leger), 38, 39. 

Long, Jig, 14. 

Maxim, fig, 14. 

Measure, 170, 171. 

Mediant, 84, 85. 

Melody, 10; dependent on the relative 

pitch of sounds, 17. 
Metronome, 301 ; application of, 302. 
Mode, 76 ; not determinable without the 

3"* sound, 229. 
Modes, the modem, 77, the ancient, ^ijr*. 

220, 221,— all, major or minor, 78, — 

authentic and plagal, 305, — ^liable to 

modification, 309. 
Modulation, 222, 223 ; the most common 

form of, 226. 
Musical Sounds, their pitch, 5; duration, 

6 ; intensity J 7; timbre, 8. 

Naturals, 96 ; in signatures, 143. 

Ninths, 71; not invertible, 72. 

Note, position and form of a, 26; un- 
meaning without a clef, 27. 

Notes (Forms of) in common use, 43; 
their names unmeaning, 44 ; stems of, 
47 ; only indicate the relative lengths 
of sounds, 175. 

Face (Words relating to), 281 ; figs. 159, 

Passages, divisible into phrases, 22. 
Fause, 268. 

Phrases, divisible into feet^ 23. 
Portamento, 254. 

Repetition, indicated by dots, 258, — by a 
sign, 260, — ^by words, 261 ; measures 
omitted in, 262. 

Pests, 52-54 ; of a whole measure in any ' 
kind of time, 264 ; of more than one 

measure, 265, — how expressed in an- 
cient music, 266, — mode of counting, 
Mhythm (Musical), how far resembling 
poetical, 25. 

Scale (The Natural), formed of unequal 
steps, 15 ; divisible into two tetra- 
ohords, 19 ; how expressed on a stave, 
31; the type or model of all major 
scales, 234. 

Scales, of Fa and Sol, 103 ; of Re and Mi 
(minor), 104 ; of Be (major) and Si 
(minor), 105; of Do, Fa, and Sol 
(minor), and i?«, Mi, La, and Si 
(major), 106 ; major and minor, why 
so called, 145 ; relative, 157, 158 ; 
diatonic, 204 ; chromatic, 214-216. 

Scales, different kinds of, 74, 75; of Do 
and of La, types, 144 ; not decided 
by signatures alone, 162 ; how de- 
cided, 163, 164 ; the new scale, how 
recognised in modulation, 227, 228. 

Seconds, major and minor, 59, 60; alte- 
ration of, 99 ; augmented, 213. 

Seconds (Minor), their place in the natural 
scale, 231. 

Semitone, the diatonic, 206; chromatic, 

Sevenths, major and minor, 63 ; alteration 
of, 102.; diminished, 213. 

Sevenths (Major), their place in the natural 
scale, 231. 

Shake, 250, 251. 

Sharps, 95 ; how generated, 115, 118, 
119 ; double, 136, 137, — always acci- 
dentals, 142, — ^how contradicted, 201— 

Signatures (lime), l87, 188 ; sometimes 
units, 190 ; imperfection of, 193, 

Signatures (Scale), 131 ; of minor scales, 

Sixths, major and minor, 63, 66 ; alteration 
of, 102 ; augmented, 213. 



Sixthi (Minor), tlieir place in the natural 

scale, 232. 
Slur, 273 ; over two notes, 274 ; over two 

identical notes, 276. 
Sound, cause of, 1 ; musical, 2. 
Spaces, 32. 

Stave, 26; of eleven lines, 8li; of five 
lines, 35 ; the bass and treble, 86 ; 
the barytone and mezzo-soprano ob- 
solete, 288 ; the tenor, 290, 292 ; the 
alto, 291, 293. 
Staves, seven different, Ji^s. 168, 164. 
Staccato, 272 ; mezzo, 272. 
Style CWords relating to), 281, /y. 162. 
Svhdominant, 83; its tendency towards 
the mediant, 89; last added fiat 
always the, 122. 
Submediant, 84, 85 ; its tendency towards 

the dominant, 89. 
Supertonic, 84; its tendency towards the 

tonic, or mediant, 89. 
Syncopation, 278. 
Syren, 298. 
System (The modem musical), basis of, 

12 ; a succession of scales, 20. 
Tetrachord, 19; the upper, variable in 
minor mode, 146, 152. 

i Thirds, major and minor, 61 ; alteration o^ 
100 ; dimbished, 212, 218. 

Hiirds (Major), their place in the natural 
scale, 232. 

Tie, or Bind, 276. 

Time, perfect and imperfect, 24 ; duple 
and triple, 168; quadruple or com- 
mon, 176-178 ; simple and compound, 
181, 182. 

Time Table, fig. 16; suggestions for a new, 

Tone, division of into two semitones, 92. 

Tonic, 73, 81 ; triad of the, 90 ; any note 
may be made a, 107 ; the tonics in 
actual use, 110, 111 ; how ascertained 
from the signature, 134; how ascer- 
tained in ancient music, 211. 

Transposition, 238 ; how effected, 239 ; 
examples of, fig. 163 ; practised by 
the Old Masters, 210. 

Tremolando, 255. 

Triad, 86 ; of the tonic, 90. 

Triplet, 49 ; marks a change of time, 242. 

Iwrn, 252. 

Voices, of men, 283 ; of women, 283. 

THB E2n>. 



Works by John HuUah, 

JPrq/vMor of Voood Mune in King^$ College^ and QueerCs CoUege, London ; 

Published by 

John W. Parker and Son, West Strand, London. 

"VTEW EDITIONS, " Revised and Reconstbucted m 
SINGING, adapted to English Use, under the Superintend- 
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together, in cloth, 6s, 

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For the Use of Pupils. 

LARGE SHEETS, contaming the Figures in Part I. of 

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%* The above New Editions, " Bbyisbd jlnd Ebconstbucted ik 1849," are 
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seven years' experience (the Second Edition having been published in 1842) has 
shown to be desirable. 

<9* The Editions of Wilhem's Method by Hullah, published in 1S4Q, are now 
out of print. 


Part Music, Class A. 

For Soprano, Alto, Tenor, and Bass Viices. 

The First Volume of Sacred Pieces, and the First Volume of 

Secular Pieoea 



National Anthem, GM $av« the Quetn. 
Foil Anthem, Lord for Thy Under. FAXiAirf. 
The Hundredth Psahn, WUk one eonaont. 
Fall Anthem, O Lord the Maker. Kiiro Hbitst YIIL 
Sanctofl^ Solg Lord Ood qfSoate, Talus. 
BeepouMs to the Conmiandments. Tallib. 
The Hundred and Foity-nlnth Psahn. 
Motet, I wiU give ikanJn. Palsstsiva. 
Chorale^ SiHce on ihe Cron. Mabtot Luthib. 
Full Anthem, Chd U gone up. Bb. Cbor. 
Psalm, When euweeaiin BdbyUm, 
Motets O bejogfuL Palsstbxka. 
Psalm, Te ChUee, Ijfl up gour heade. 
Evenmg Hymn, The Dag ispatt. Jour Hullak. 
Hymn, Thou thai/¥om Thgf Oitone. Hatdv. 
Psalm, Venite, exuUemue Domino. Tallis. 
Motet, I7u>u art beautiful. GiovAirari Cbocb. 
Hymn, O Lord I another Dag i$ flown. M. HATim. 
Psalm, I%e Lord I wUl for ever bleu. H. Lawbs. 
Anihaca, Praiee the Lord, OJeruealem/ J. CxiABU. 
Canon, CHoria Fatri. Pubcsll. 
SsnetuB, Holgt Holy. Cbbtshtov. 
Motet, Be not Tkoufarjhm me. Palsstbxva. 
Anthem, Hide not Thou thy Face. B. Fabbakt. 
Hymn, O Jeeu, Lord qf Heavenly Orace. C. Lbjuvb. 
Quartette, Give ear, O Chd. HiHiaeL. 
JkJDi\uaai,TredeafheLord,OmyBoulI W.CsnA. 
Motet, Bleeeed be Thou, Ajnovio Loxn. 
Hymn, Forth fiwn the dark. Boussbav. 
Psalm, Almighty Ood, who haet. Fobdb. 
Atifhgm iwiU ariee. Bobbbx Cbstohtov, DJ). 
1IL(Xtet,8ingtofheLordin^oyfia9trainM. DB.Tn. 
Chorus, ITsar My jMMjr«r. MicIBCabl Hatdv. 
Psalm, O Kingl eternal and divine/ Db. Cbor. 
Hymn, Oh, Ood qf Truth. B. BpQBBS, Mus. Bao. 
<)atrtett^ Oremember not fhe <jffbnee». BoSBin. 
Hymn, Oive to u$ Feaee. Bubsiak Mblodt. 
AnfJ^gni l%ou knoweet. Lord, Pvbcxll. 
Chorus, Amen. Db. Cooxx. 
Hymn, Sweet day, §o eoU, §o ealm. H. DuicoHT. 
Motet, Oo ntttfarfnm me, O Ood. ZorOABBLLt. 
Anthem, O horn amiabU, BxCKABDseir. 
The Himdred and Forty-eighth' Psalm. J. CLiBXX« 
Asi^Aam, AUm^My amd everUMMHng Ood. GnBom. 
Canon, Awake, thou thai eleepeet. W. Hobsut. 
Chorust HalMi^ah, Db. Botcb. 

SOOBE, One Volume^ Sacred 

„ „ Secular 

YoiobPabts, Soprano^ Alto, 

Tenor, or Bass. Sacred or 



National Song, Bute, Britannia, Db. Abitb. 
Madrigal, All ye who Mueie love. Doitato. 
Madrigal, Hard by a Fountain, Wablbbht. 
Olee, Te Spotted Snake* (Shakspeare). SiBTXira. 
Madiriga]^ Flow, O my Teare. BsBirBn. 
Madrigal, The WoUe. Batillb, 1667. 
Glee^ Come, lot ue all a Haying go, LumcAV ArpiA' 


Song in Honour of Peace, Freemen^ r^foieel Pub- 


Part Song, £011^ may Uife, 

Olee, HaiX, haUawed Fame, Lobs MoBBUraroir. 

Olee, Crabbed Age and Touth. B. J. S. Stbtbhb. 

Madrigal, In going to my lonely Bed. B. Edwabdbb. 

Madrigal, AJt^ met Fbucs Abbbxo. 

Madrigal, Nymphe qfthe Foreat. W. Hobslbt, Mus. 

Fireside Song, O never fear, though Bain be fall- 

HoUd^y Songs. No. I. May Day, Nbixkabd. 

Solfeggio. SCABXiAnx. 

Madrigal, Lady, eee, on every eide. Luoa Mabbvzio. 

Glee, How eleep the Brave I Db. BairJAXiir Cookx. 

Chorus, Hairk, the Village Meade, CsBBUBiiri. 

Madrigal, AU hail, Britannia ! AmeoBio Lom. 

Glee, Upon the Foplar Bough, Stbpbbv Paxtov. 

liadtigMltSinaeJtretlBawyourJ^tee, T. Fobdb. 

Chorus, How glad with entile* ihe Vernal Mom I 


Grotesque Madrigal, Sing a Song qf Siagpenee, O. 

A. Mactasbbit. 
Glee, Happy are they. Sisphsit Paximt. 
Madrigal, 8ee,Jlrom hi* Ocean bed. V. Bwfo. 
Part Song, Day-break. I. Moschbiao. 
National Song, The hardy Noreeman, Pbabsall. 
Madrigal, Come again, eweet Love, J. Dowlavb, 

Mus. Bao. 
Glee, In Paper Cam, Db. Cooxb. 
Holiday Songs. No. n. Harveti Time, 
OAee, Thy Voice, O Harmony. Saiotbl Wbbbb. 
Glee, Awake, Jtolian Lym t Jonr Dabbt. 
'BwtQoihg, My Lady ieaa fair Q» Jim. J« BsBirnc. 
Chorus, Sing loud a joyful Strain. Glvck. 
Madrigal, J^^ k in my Muiret^ Ftice, Tkokm 


In Printed ^^rappers, it, each. 
In Cloth, 6$, each. 

In Printed Wrappers, Is, each. 
In Qoth, U, 9d. each. 


Part Music, Class A. 
For Soprano, Alto, Tenor, and Bass Voices. 

The Second Volume of Sacred Pieces, and the Second Volume of 

Secular Pieces. 



Hymn, O Xing tffXingM I Ksbutzbb. 
Doable Quuxt^ Magnifieai, Db. B. Cooxa. 
Responses, Kyrie tleeiton. Dr. W. Child. 
Christmas Hymn, O eome^ ye Faii^ful. 
Canon, So$anna in exeeUii. Gxobox Bsso. 
Chonu, Amem. Nsuxoxic 
Anthem, O Zord, grant the Xing. Db. W. Child. 
Canon, Ut queant laxia. HxBBiir&TOir. 
Sauottts, Holg Lord God ^fKoeU. Ro&SBB. 
Motet, Whg do the Heathen rage t Palxstbuta. 
Chant, ExaUabo 2V, Domine. Huicphxbt. 
Hotet, Plead Tho« my Cause. G. Cbocb. 
If otet. Ponder mg worde, Zixoabbllx. 
Hymns for Morning and Evening. Claxkb. 
Canon, Hkou thaU ehow tne, Db. CALLCon. 
Anthem, Hy Gkn^ look upon me. Bbtkoldb. 
Anthem, Wherewithal $haU. Alcock. 
Hymn, O Saviour] is thy promise Jledf Hobslst. 
Introit, O most merciful Chd. JoHir Hullah. 
Hymn, Praise the Lord qf Heaven. Gossbc. 
Sonctas, Holy Lord Chd qf Hosts 1 Bassakx. 
Anthem, We will r^oiee. Db. Cbott. 
Canon, O Lord, in Thee have I trusted. Paxtoit. 
Anthem, Try me, O Qod. Db. Nabbb. 
Canon, O Lord, teach us to number our days. 
Chorus, Praise ye the Lord. Bbabsbttz. 
J&.ot^ I wtU remember. GioTAVin Cbocb. 
Hymn, Peace. M. Hatsit. 
Canon, HcMelv^ak. Blway Bsmr. 
Fsahn, AU People, Old Hundredth Tune. 
Canon, Praise the Lord. 3. W. Callcott. 
Anthem, Behold^ now praise. Boobrs. 
Anthem, The Lord hear Thee. Db. J. Blow. 
Canon, Hosanna. T. F. Walmislbt. 
Motet, Help us, O God. F. Dubaktb. 
Chorale, The Day must come. N. Dbciits. 
Canon, Hear me. W. Hobblbt, Mus. Bac. 
Sanctus, Holy Lord God. 0. Gibboitb. 
Motet, Let all the people praise thee ! Falbbtbdta. 
Chorus, Blessed be God! Db. Gbbbitb. 
Anthem, O God, Thou art my God, H. Pubcxll. 
Motet^ Mock not God^s name, Db. Tyb. 
Motet, The voice qfjoy and health. Jabtvacoitl 


Madrigal, The joyous Birds. Babt. Spoktoitb. 
Glee, Here in Ck)ol Grot. Lobd MoBBiirGTOB. 
Grotesque Madrigal, Girls and hoys come out to play, 

Q. A. Maofabbbb-. 
Glee, Swiftly from the Mountain's brow, Wbbbs. 
Part Song, Ouf^NoHve Land. G. Bbichabdt. 
Part Song, Like to the Grcus. J. Bbitbdics. 
Glee, Ode to Spring. Stbpkxit Paxtov. 
Madrigal, Come, Shepherds. Bbkitbtt. 
Glee, Hark, the Lark. Db. Cooxb. 
Haymakers' Glee^ 0mm, my friends. Hobbixt. 
Glee, Oh I how sweet. Sib Johh Bogbbb. 
Canon, Long Uoe the Queen, Db« Botch. 
Banz des Vachez, Qnne, Shepherde. Gbabt. 
Dulce Domnm. [Lat. & Eng.] Bbadiho. 
Glee, T^frsis, when he Irft me, Db. Callcor. 
Glee, Whic^ is the properest day to sing t Abhb. 
Glee, AtbioTi, thy sea^eneireled isle. Db. Cookx. 
Part Song, The Good Morrow. Hullah. 
Glee, Breathe sqft, ye winds. S. Wbbbx. 
Chorus, Amid the din. Glvcx. 
Madrigpal, Who will bring back to me my heart t 


Part Song, Hark, hark, a merry Note I hear. Gbb- 

Madrigal, Thyrsis, sUepest thout J. Bbithbt. 
Part Song, Unto the merry. Italxah Aib, 
Put Soog, I>anee we so gaily, F. Schubbbc. 

Glee, Blow, blow, thou winter wind, B. J. S. 

Part Song, Awake, sweet love! J. Dowlakd. 

Part Song, 'Twos on a bank qf daisies sweet. Johh 

Glee, IHm Oberon in fcury land, R. J. S. 

Madrigal, Thue saith my Chloris bright. Joas 

Part Song, Ifow, O now, I needs must part, Johh 


Glee, Happy are we met, S. Wbbbx, 

ScoBE, One Yolumei Sacred, ) In Printed Wrappers, is. each. 

Secular. ) In Cloth, 58, each. 



Voice Pabtb, Soprano, Alto, 

DICK Faets, Soprano, Alto, ) , ^ . , , ^ , , 

Tenor, or Bass. Sacred or In Pnnted Wrappers U ea<.h. 

Secular. ) ^ ^""^ ^'' ^^- ^^ 



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