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/ 



GRAMMAR OF MUSICAL HARMONY: 



©lie Sbtrbstamt of ^kiuks * 



ST. MARTINS HALL 



THE TRAININO INSTITUTIONS OF THE NATIONAL SOCIETY. 



JOHN HULLAH, 




LONDON: 
JOHK W. PARKER AND SON, WEST STRAND. 



— 

174. h ■ 



5M. 



London: 
savill and kdward8, printer8, chand08 street, 

cotbnt garden. 



PREFACE. 



There are some terms belonging to every art or science which, though 
convenient or indispensable to adepts, are a source of embarrassment to 
beginners. 

In music, the distinctions between harmony and melody, and between 
melody and counterpoint, are among these. A succession of individual 
sounds, and a succession of combinations of sounds, ate obviously different 
things, and as such they require different designations, — the very ex- 
istence of which makes it difficult to appreciate the fact that the things 
designated, though different, must never be considered separately. 

For, a succession of sounds can hardly be recognised as melody, unless 
it be capable of proof^ by the addition of that harmony of which it is only 
one part; while a succession of combinations of sounds will be un- 
worthy of the name of harmony, unless the various parts of which it 
is composed be individually melodious. Certain it is that a musician 
never conceives melody without associating it with harmony, as he 
never hears harmony without being able to trace out more or less of the 
melody which it must of necessity contain. 

The line of demarcation between harmony and counterpoint being less 
strongly marked than that between melody and harmony, their dis- 
tinction by different names is attended with much greater inconvenience. 
For that distinction would seem to imply that the arrangement of in- 
dividual parts was something over and above, or even different from, 
making the chords in which they are contained succeed one another pro- 
perly. Now, no one could be considered as a harmonist who could not 



iv PREFACE. 

connect one consonant combination with another, prepare and resolve 
discords, and reconcile the frequently conflicting interests of combination 
and progression. And yet by the term counterpoint is understood little 
more ; for the treatment of iuere passing notes can hardly be brought 
altogether under those strict rules to which a science is generally sup- 
posed to be amenable. 

The musician who may have the curiosity to look into the following 
"Grammar of Harmony" must therefore be prepared to find that it 
contains much that relates to those parts of musical science which are 
commonly treated under the heads of Melody and of Counterpoint; and 
that many things usually reserved for subsequent explanation are intro- 
duced, as it may seem, prematurely. 

Should it be found, also, that some points on which musical theorists 
are not agreed, are put in a dogmatic form, it may be hoped this will 
be attributed, not to ignorance of, or indifference to, the opinions of 
others, but to a very decided conviction that beginners should not be dis- 
tracted by the consideration of opposite theories, and that, as a conse- 
quence, all discussions on disputed points should be kept out of elementary 
books. 

The student who is desirous of mastering the contents of the follow- 
ing pages should come prepared for the task, not only by the possession 
of some theoretical knowledge, but also of some practical skill. He must 
be familiar at least with the treble and bass staves ; with the construction 
of major and minor scales, and the relations of one scale to another ; with 
the nature and names of the various musical intervals ; and, in short, 
with whatever may be classed under the name of the " accidence " of 
music. Moreover, he must have some idea of, or some means of ascer- 
taining, "the sound of what he sees;" or — inverting the process — some 
power of expressing the effect of what he imagines. It is difficult to 
conceive any means by which this sympathy of eye and ear can be 
attained excepting singing, or playing in concert with others, or the 



PREFACE. V 

practice of an instrument like the pianoforte, from which many different 
sounds can be produced at the same instant. 

Considerable proficiency in the art of music has been often attained by 
persons who have had little or no knowledge of the science ; or, more pro- 
perly speaking, to whom the absence of study has been partially supplied 
by favourable organization, or that indirect culture which, being uncon- 
sciously received, and therefore never taken into account, is often mis- 
taken for it. But to pursue the science of music without reference to the 
art would seem, if not altogether a profitless occupation, certainly a very 
laborious and uninteresting one. The musical student must begin — as 
he should go on — with the consideration of what is practical; he must 
collect his facts before he can theorize upon them* Of what avail can it 
be to inquire why this combination or that progression is pleasing to the 
ear, unless he have ascertained, or can ascertain, for himself that it is, or 
that it is not so ? — It is from the neglect of this preliminary training of 
the ear (hardly possible without training of the voice or the hand) that 
so many, especially of those who begin its study late in life, fail in 
acquiring any real acquaintance with, or living interest in music* Deal- 
ing with symbols of whose powers he knows nothing, the mere theorist 
in music is in a position akin to that of an artist painting on porcelain — 
ignorant of the fact that his colours will come out of the furnace other 
than they went in. Music has a body as well as a soul; and we shall 
form but an imperfect acquaintance with her whole being, if we study the 
one without reference to the other. 

»»»»»» 

The publication of this Grammar will be immediately followed by 
that of a series of Exercises in Musical Harmony. These Exercises will 
be accompanied by references to the Grammar, and ample directions as 
to the best modes of using them. 



. * 



CONTENTS. 



CHAPTER PAGE 

I. The Harmonic Chord 1 

II. Intervals — Consonant and Dissonant 3 

III. The Triad and Common Chord 4 

IV. Arrangement of the Triad 6 

V. Figured Basses 8 

VI. Motion of Parts 10 

VII. Connexion of Chords 14 

VIII. Sequences 17 

IX. Resolution of Dissonances 18 

X. Discords by Suspension 20 

XI. Inversions of the Triad 23 

XII. Suspensions on Inversions of the Triad 27 

XIII. Fundamental Discord of the Seventh 30 

XIV. Resolution of the Fundamental Discord of the Seventh 33 

XV. Suspended Resolution 37 

XVI. Discords by Suspension on Fundamental Discords 40 

XVII. Inversions of the Discord of the Seventh 41 

XVIII. Licences in the Resolution of the Seventh 47 

XIX. Interrupted Resolutions of the Seventh 51 

XX. Changes of Root on a Single Bass Note 53 



Viii CONTENTS. 



CHAPTER PA0E 

XXI. Fundamental Discord of the Ninth 55 

XXII. Chromatic Intervals 57 

XXIII. Discord of the Diminished Ninth 59 

XXIV. Inversions of the Discord of the Ninth and Seventh 60 

XXV. Chromatic Intervals 66 

XXVI. Chromatic Harmony 63 

XXVII. Pedal Points . 71 

XXVIII. Progression of Fundamental Basses 72 

XXIX. Rhythm 75 

XXX. Harmonizing 77 



GRAMMAR OF MUSICAL HARMONY. 



CHAPTER I. 



The Harmonic Chord. 



1 . All sound results from vibrations communicated to the air by some disturbing 
force. Sound is musical or otherwise according to the regularity with which such 
disturbing force is exercised. 

2. The modes by which musical sounds are produced and controlled, though 
susceptible of infinite modification, may be classed under two heads: — 1st, wind 
instruments — pipes through which air is forced, and which produce grave or acute 
sounds as the pipes are large or small; 2ndly, instruments of percussion, the gravity 
or acuteness of whose sounds depends on the size, weight, or tension of the material 
of which they are composed. 

The single law of sound which for our present purpose it is necessary to understand, is 
best explained by reference to a string fastened at both ends. 

3. A simple, unmixed sound can never be maintained for more than an instant. 
Every principal sound generates others which, though often inaudible, and never 
heard with the same force as their generator, no less certainly exist, and that in 
infinite number. 

Fig. i. 

4. Suppose a string of a certain length and thickness gives a 
sound called Do. For an instant after it has been set in vibration, 
it sounds that Do only; then, in addition, though more faintly, 
the 8 ve above; then the (perfect) 5 th to that 8 ve ; then the double 8 TO ; 
then the (major) 3 rd , the 5 th , and the (minor) 7 th to that double 8 TO ; 
then the triple 8 ve ; then the 9 th to the double 8™; then the 3 rd and 4 th 
to the triple 8™; and so on, ad infinitum. _^_ 

So that when a violoncello player draws bis bow across the lowest string of his instrument, 
he produces not only the sound literally due to that string, but all the sounds in fig. 1. 

5. Subordinate sounds, thus unconsciously produced, are called harmonics to 
the prime, or lowest sound. The combination of a prime and its harmonics is 
called an harmonic chord. 

6. Now it is found that sounds identical with those in an harmonic chord 
may be produced artificially, by dividing the string which gives the same prime 
into aliquot parts. For if a string thirty inches long gives the lowest Do in fig. 1, 

G. M. H. b 




p 



m 



2 THE HARMONIC CHORD. [Chap. I. 

£ of it (fifteen inches) will give Do, the 8 ve ; f of it, Sol, the (octave) 5 th ; ^, Do, 
the double 8 ve ; •*-, Mi, the 3 rd ; £, So/, another 5 th ; -f Sib, the minor 7 to ; i, Do, the 
treble 8 ve ; £, Be, the 9 th ; -rV, Mi, the 3 rd ; -jV, Fa, the 4 to ; and so on. (Compare 

figs. 1 and 2.) 



Fig. 2. 



IP 6 <2 

f J 1 



I I I I I I I 



X X 

The notes and fractions marked x are not mathematically in strict accordance ; i.e., the 
sounds recognised by universal consent as the minor 7 th and perfect 4 th to Do, are not 
produced by precisely \> and precisely -^ of the string. 

7. This artificial arrangement partially accounts for the phenomenon of har- 
monics. It is evident that while a string produces one sound (the prime), it 
vibrates during its whole length, and that as soon as the octave is heard, each half 
of the string vibrates separately; in fact, that divisions like those indicated above 
are made by Nature, ad infinitum. 

Fig. 3. 
.... -- —- - — ..-————— -.—.-. — - ....._. m 

The ruled line in fig. 3 represents a string at rest; the dotted lines indicate the directions 
which the string would take when sounding the prime, its 8", and octave 5 th . 
The points of intersection (marked in fig. 3) are called nodes. 

8. Harmonics, up to a certain point, are imitated in the construction of the 
organ, the peculiar fulness in the quality of which instrument results chiefly from 
this imitation; the term "full organ" being applied to the combination of various 
harmonic "stops" with those producing primary sounds. 

The further consideration of this Bubject belongs rather to natural philosophy than to 
music; but the necessity for the foregoing explanations will be found in their practical 
application to what immediately follows. 



CHAPTER II. 



Intervals — Consonant and Dissonant. 



9. Sounds are consonant (capable of being sounded together) with one another, 

according to the order in which they are generated in the harmonic chord. As the 

relations of harmonics with their prime become more remote, they become less 

perfectly consonant; then, dissonant; and, finally, they cease to form part of our 

musical system. 

10. The relation of two different sounds one to another is called an interval. 
Musical intervals are consonant or dissonant. 

11. The consonant intervals are the octave, the fifth, and the third; with the 
inversions of the two last, the fourth and the sixth. The dissonant intervals are the 
seventh and the ninth; with the inversion of the former, the second. 

12. The ninth does not admit of inversion. 

13. The imperfect fifth and its inversion the pluperfect fourth are anomalous; 
being, though essentially dissonant, sometimes treated like consonant intervals. 

14. Consonant intervals are farther divided into perfect and imperfect. 

15. The perfect consonances are those found between the sounds ./&**/ generated 
in the harmonic chord — viz., the octave, the fifth, and its inversion, the fourth. The 
imperfect consonances are the third, and its inversion the sixth. 

16. Examples of all these intervals are contained in the harmonic chord. 

Fig. 4. 



( f) 




Consonant. 




: 


DlSBONANT. 




Anomaloub. 


1 y 














/^fc 




c > 


1 A 








i i 


ir - ^ 


ir^ > 


*. 7 


ir - "^ 


7r~^ 


lavm—m 






/— X 




\/K^> 


i/^_-j 




i/*— ' 


1/vJ 


kUUHHHfl 






_^^>3 


r~"^ *^~\ 








f^ 




fj 




o- -^-^ 


K^J *^> 


-O- 


-o- 


^-/ 


/ V 


c > 


< ■> 




i > 












t J* 




















< > 


c ■> 






































I 





















& 



Octave. Fifth. Fourth. 
Per/eefc 



MaJ.&Min. Maj.&Min. 
Thirds. Sixths. 

Imperfect 



Seventh. Second. Ninth. 



Imperfect Pluperfect 
Fifth. Fourth. 



17. In the harmonic chord the consonant intervals are generated before the 
dissonant, and the perfect consonances before the imperfect. (Compare Jigs, i and 4.) 



CHAPTER III. 



The Triad and Common Chord. 



18. From the three notes of different names first generated in a harmonic chord 
is formed the simplest of musical combinations, the triad — a bass note with its 
3 rd and 5 th . When the 8™ is added, the combination is called a common chord. 

By the term bass is here meant the lowest part, whatever be its pitch, or on whatever stave 
it may be written. 



Fig. 5. 



Fig. 6. 





3=1 



or 



i 



^ 



-O- 



19. A common chord contains none but consonant intervals. 



Fig. 7. 




m 



JZL 



3ZE 



J3l 



-O- 



-Q- 



^ 



O 



^ 



o 

Major. Minor. 
Sixths. 



OcUve. 



-©- 



Fifth. 



Fourth. 



Major. Minor. 
Thirds. 



20. When the 3 rd of a chord is separated from the bass by two tones (a major 
third) the chord is said to be major. 

Fig. 6 is a major chord; as is the harmonic chord, (fig. 1,) whence it is derived. 

Fig. 8. 

21. Only three notes of the natural scale bear major 
chords: viz., the tonic, (the 1 st ,) the dominant, (the 5 th above,) 
and the ^dominant, (the 5 th below.) 




I 



Bi 



22. A major chord on Re (the 2 nd of the natural scale) would require Fa to be 
made sharp. A major chord on Mi (the 3 rd ) would require Sol%; and on La 
(the 6 th ) JDo#. While a perfect major chord on Si would require not only Re§, 
but Fa ft; since Fa t| is an imperfect fifth from Si. 



Jfy. 9. 






m 



A 



3 



r> 



6 



The scale of Do (the natural scale) admits neither of sharps nor flats. 



Chap, m.] 



THE TRIAD AND COMMON CHORD. 



23. So that in treating each note of the natural scale (or any scale of like 
construction) as the bass of a triad composed only of such sounds as are found in the 
scale itself y we produce three major chords, and four minor chords; one of these 
latter being also imperfect, i.e., having an imperfect fifth. 



Fig. 10. 




Perfect Chord*. 



Imperfect. 



§ 



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



Minor. 



24. A bass note bearing a triad is called also a root, or radical bass. 

The term prime is restricted to rootB which bear harmonic chordB ; consequently, neither 
the 2 nd , 3 rd , 6 th , or 7 th sounds of a scale can be a prime; nor, indeed, (as will be shown here- 
after) can the l 1 * or the 4 th . 

25. In the triads of the 1 st , 4 th , and 5 th , (the tonic, dominant, and subdominant,) 
are contained every note of the scale to which they belong — viz., Do in the tonic 
chord, Re in the dominant, Mi in the tonic, Fa in the subdominant, Sol in the 
tonic and dominant, La in the subdominant, and Si in the dominant. 



Fig. 11. 




26. From these three chords the scale is, by some theorists, said to be derived. 
Practically it is worthy of remark that one or other of these three notes (the 1*, 4 th , 
or 5 th ) will serve as a root to any note of the scale. (Compare figs, n and 12.) 




-& 



Fig. 12. 



rr? 



1 



(7^ 



"O" 



HE 



*& 



HE 



^ 



XIE 



-& 



-O^ 



-O- 



HE 



HE 



HE 



HE 



"W/* ^ASNA *V* «* 



CHAPTER IV. 



Arrangement of the Triad, 



27. The sounds of a triad (and still more of a common chord) admit of much 
variety in their arrangement. Since, so long as a combination consists only of 
3*te 5^ gj^ gvee t a jjagg no te, it is still a common chord, let those notes stand 
in what relation they may to the bass or to each other, or be their number ever 
so great. 

Fig. 13. 
HL 




s 



HI 



HE 



HE 



H 



HE 



he 



HE 



he 



-& 



^ 



-© 



^ 



n 



& 



& 



-o- 



I 



HE 



-©- 



-O- 



HX 



nx 



he 



3d 



HE 



HE 



HE 



HI 



HE 



HI 



HE 



HE 



H 



HE 



HE 



Of the chords in fig. 13 some consist of four notes, some of more, and some of less; 
moreover, some are well arranged, some badly, some indifferently ; but they are all equally 
common chords (or triads) of Do. 

The principles which guide us in our judgment of these chords must be deduced from the 
harmonic chord. 



Fig. 14. 




¥ 






28. As the eye passes up fig* 14, (the harmonic chord,) it 
will be perceived that the notes lie nearer together; that the 
largest intervals are at the bottom of the chord and the smallest 
at the top; moreover, that this diminution of the intervals is 
gradual, and that there is nowhere any disproportionate hiatus. 
We have first an octave, then a fifth, then a fourth, then a major 
third, then two minor thirds in succession, then two major seconds, 
and then a minor second. * z&. 

29. In writing chords, of whatever kind, the arrangement of the harmonic chord 
should be imitated as far as possible. The lower notes should be separated by the 
largest intervals, and the diminution of the intervals should be gradual. 

In fig. 15 this rule is more or less strictly observed; in fig. 16 it is altogether disregarded. 



Fig. 15. 



Fig. 16. 




I 



© 



HI 
HI 



HL 



HE 



-O- 



HE 






HE 



-O 



HL 



HE 



§ 



HE 



S 



HE 



HE 



HI 
HI 



H 



HE 



-Q- 



HE 
HE 



i 



HE 
HE 



1 



Chap. IV.] 



ARRANGEMENT OP THE TRIAD. 



m 






30. Again, a common chord must contain only 8**", 5 th8 , and 3 1 * Fig. 17. 
to a bass note. In arranging chords for more than four voices, 
(and from other causes,) we must of necessity double (i. e., write 
more than once) this or that note or its 8™. The harmonic chord 
gives us a law in this case; since within the limits of the common 
chord it contains no less than three Dos (the prime and two 8™), 
two Sols (5 th8 to the prime), and only one Mi (3 rd to the prime). 
Whence we derive the following rule : 

31. Double the 8™ (to the root) rather than the 5 th , and the 5 th rather than the 8 rt ; 
especially when the 3 rd is major. 

In fig. 18 this role is observed ; in fig. 19 violated. 

a b c a b c 

zoz 




Fig. 18. 



3ZE 



-O- 



a 



H 



-©- 



-©~ 



© 



g 



Fig. 19. 



£ 



t 



3ZZ 



3ZE 



1ZL 



23 



3ZL 



n 



JZL 



HL 



X3T 



H 



Compare severally a, and 6, and 0, in figs. 18 and 19. 

32. Lastly, in arranging chords for fewer than four voices (and occasionally from 
other causes) we must of necessity omit some of the notes due to a complete common 
chord. In the choice of these notes Nature will not assist us; but experience gives 
the following rule^ which, though apparently contradictory to the last, will be seen 
eventually to be perfectly consistent with it, and founded on the same principle. 

33. Omit the 8™ (to the root) rather than the 5 th , and the 5 th rather than the 3 rd . 
In fig. 20 this rule is observed ; in fig. 21 it is violated. 




Fiy. 20. 



^ 



3ZL 



-& 



^ 



*&■ 



m 



JZL 



JZL 



S~L 



JZL 



33 



a 


b 


c 


d 
















C > 


< > 








f-x 




f^->% 




—t~~*% 


S^-S 




\^J 




Fig. 21. 






















t > 


i > 


i > 


< > 















Compare severally a, b, c, and d, in figs. 20 and 21. 



8 



CHAPTER V. 



Figured Basses. 



34. To indicate the chords due to bass notes, musicians use a kind of " short- 
hand/' wherein the intervals which the notes of a chord form with its bass are 
expressed by figures. A bass so accompanied is called a figured bass, or thorough 
bass; i. e., a bass written throughout a composition, in such a way as to indicate 
(partially) the general effect. 

35. Thus a bass note which is to be accompanied by a common chord, (its 8 ve , 

5 th , and 3 rd ,) is figured 5 or | or even 5 ; the highest number usually at the top. 

The common chord, however, as its name would imply, is so much more often used 
than any other single chord, that, save to contradict other figures before them, the 
above are seldom written ; it being understood, in thorough bass, that a bass note 
without figures is to bear a common chord of any number of notes in any position. 

Thus fig. 22, or any other form of the chord of Do, is implied by fig. 23, _. 
fig. 24, or fig. 25, and still more often by fig. 26. **' ' 

< > 



Fig. 23. 



m 



JJl 



3 



Fig. 24. 



"IT 
3 



Fig. 25. 



HE 



Fig. 26. 



rz 




-&- 



-©- 



m 



S^L 



The figures may be placed over as well as under the, bass notes, indifferently 



36. When accidentals are to be introduced into the chords, the figures must be 
preceded by accidentals (or otherwise modified) accordingly. In the case of a 
common chord, the interval to be altered is often the only one marked at all. More- 
over, the 3 rd requires alteration so much more often than any other interval, that 
the accidental is usually put without the figure to which it refers* 



37. Thus f, or b, or ty, under or over a bass 
note, means #3, or b3, or tj3; that the 3 rd (firom 
the bass note) is to be made sharp, or flat, or 
natural. {Fig. 27.) No interval but the 3 rd is ever 
thus implied by an isolated accidental. 




Fig. 27. 



P^ 



■fro-flo 



T3 — CF 



7" 



i 



-o — ^ 



< > 



# H b H 



Chap. V.] 



FIGURED BASSES. 



38. A short line drawn obliquely across the 
right extremity of a figure indicates that the note 
corresponding with it is to be raised a semitone. 
Thus J? is a contraction of 1 5, (Jig. 28), or, contra- 
dicting a flat, of t) 5 (fig- 29.) 



Fig. 28. 



Fig. 29. 



■^ 



7ZF 



^ 



£f 



i?n Ho 
< > 



-©- 



t 



In old figured basses, the elevation of a note a semitone is often indicated by a sharp, 
although the particular note referred to is really to be made natural — in contradistinction to 
a preceding flat. 



Fig. 30. 



39. It is not usual to express alterations in the 
8 ve , which must be made perfect 0^.30), unless 
expressly marked otherwise (fig. si.) 




ribzter 



b5 



Fig. 31. 



< > ftc ? 



^ 



JZL 






— •W^./V./S.-.,/ 



0. Iff. H. 



C 



10 



CHAPTER VI. 



Motion of Parts, 



40. Continuous harmony may be produced either by the combination of several 
instruments capable of sounding but one note at a time, (such as the human voice, 
the oboe, and others,) or from one instrument capable of sounding many notes at a 
time, (such as the organ and the pianoforte.) In a series of chords arranged for voices, 
the particular notes sung successively by each individual voice are said to form a 
part; and although with equal propriety we might speak of the individual parts in 
continuous harmony performed on the organ or pianoforte, such parts are less 
easily discriminated by the ear or the eye. The science of harmony is most con- 
veniently studied, by supposing, at first, all successions of chords to be intended for 
performance by voices. 

The examples which immediately follow are in four parts, which parts, for the present, 
will severally be spoken of as the Soprano, the Alto, the Tenor, and the Bass. 

41. When two or more voices sing the same notes in two or more following 
chords, they are said to sing in unison. The unison of two or more different voices 
is forbidden in music of any definite number of parts; since if two out of four 
voices sing the same notes in following chords, not only are the (supposed) four parts 
reduced to three, but an undue prominence is given to the one part thus doubled. 

Thus fig. 32 begins and ends in four parts, but at * * there are only three; because the 
Bass and Tenor sing the same notes in two following chords. 




Fig. 32. 



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42. The motion of any two real parts in respect one to another must be contrary, 
oblique, or similar. 



43. Two parts are said to be in contrary motion, when one rises and the 



Chaf. VL] 



MOTION OF PARTS. 



11 



other falls C^. 33); in oblique motion, when one rises or falls and the other stands 
still (Jig. 34); in similar motion, when both parts rise or fall, {fig. 35.) 



Fig. 33. 



Fig. 34. 



Fig. 35. 




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Contrary. 



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Oblique. 



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Similar. 
Fig. 36. 



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44. The mere iteration of the same 'notes, (fig. 36,) 
sometimes termed " parallel motion," is motion only 
as respects time, not tune: consequently, the union 
of the Tenor and Bass on the same notes (see ^ t fig. 32,) 
does not violate the laws of motion or progression, 
though it should be used sparingly, for the reasons given in par. 41 . 

45. Contrary motion, or oblique motion, may be made under almost any cir- 
cumstances, but similar motion is subject to many restrictions and liable to many 
rules. 

46. The first chord in fig. 37a (as has already been shown) is in a good, indeed, 
a perfect position. The position of the second chord is of necessity equally good, 
since it is identical with that of the first. Nevertheless, the second chord, in its 
present position, must not follow the first; because the Bass and the Alto keep an 
octave apart in similar motion, thereby making consecutive octaves (fig. 376); while 
the Bass and the Tenor keep a fifth apart in similar motion, thereby making con- 
secutive fifths , (fig. 37c) 



Fig. 37 a. 




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Fig. 38 a. 



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47. If it be required to make the chord of Re follow the chord of Do, the latter 
being in the position of fig. 37a, the parts must move as in fig. 38a, or at least in 
such a way as to avoid consecutive fifths or octaves. 

48. In fig. 38 the Alto, instead of rising from Do to Re, in consecutive octaves 
with the Bass (which also rises from Do to Re), falls to La (fig. 386), thereby making 
contrary motion with the Bass; and the Tenor, instead of rising from Sol to La, in 
consecutive fifths with the Bass, falls to Fa (fig. 38c), thereby making contrary motion 
with the Bass. 

49. It is true that in fig. 38, La and Re still remain in the second chord; but 
the bad effect of consecutive fifths is avoided by those notes being sung, not by the 
Alto and Tenor voices, (as in fig. 37,) but by the Soprano and Alto. 

From the above we deduce the following important rule: 



12 



MOTION OF PARTS. 



[Chap. VI. I ( 



50. Two parts in unison, or separated by an octave or a perfect fifth in one 
chord, must not be in unison, or separated by an octave or by a perfect fifth in the 
next; or, to use the accustomed formula, consecutive unisons, octaves, and perfect 
fifths are forbidden, and must be avoided. 



Fig. 39. 



51. Consecutive fifths, when not of the same kind, are allowed; 
i. e., two parts separated by a perfect fifth in one chord, may be 
separated by an imperfect fifth in the next, especially in descending. 
(See fig. 39.) This licence should, however, be used sparingly. 



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52. Consecutive octaves and fifths between notes which move by skips (see 
figs. 40 and 41) are equally to be avoided with those between notes which move, as 
in fig. 33, by degrees. 

Fig. 40. Fig. 41. 




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53. Octaves or fifths following one another, even by contrary motion, (see figs. 42 
and 43,) are objectionable in a small number of parts. 



Fig. 42. 




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Fig. 43. 



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54. The interdiction of consecutive perfect fifths and octaves is founded on the 
same principle as that of consecutive unisons. The relation of two notes an octave 
apart is the simplest possible; viz., that of 1 to 2; and that of two notes a fifth 
apart is the next to it; viz., that of 2 to 3. Successions of intervals so consonant 
one with another tend both to diminish the number of parts, and to give undue 
prominence to the passages between which they lie. Consecutive perfect fourths 
are, under certain circumstances, as objectionable as consecutive fifths; while the 
agreeable effect of consecutive thirds arises from their imperfect consonance, and 
their variety as major and minor. 

Consecutive major thirds were in many cases forbidden by the old masters. 



Chap. VI.] 



MOTION OF PARTS. 



13 



55. Moreover, two parts moving for any length of time in consecutive intervals 
of exactly the same kind, be they what they may except octaves, give an impression 
of, and often are in two different scales. 



/ty.44. 




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Fig. 45. 




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The upper part of fig. 44 is the scale of Sol; that of fig. 45, of Fa; that of fig. 46, of Mi; 
while the lower part of all three is the scale of Do. 

More convincing than argument will be any attempt to sing or play these passages, the 
effect of which (of the last especially) is abominable. 



14 



CHAPTER VII. 



Connexion of Chords, 



It will be remarked that the two chords in fig. 37 have no notes in common; not one note 
in the first chord is repeated in the second. Mi, Sol, and Do are the 3 rd , 5 th , and 8 th to Do; 
Fa, La, and Re, to Re. 



Fig. 47. 




56. The chords which follow one another with the 
best effect are generally those which contain one or 
more notes in common; such common notes being 
said to connect together the combinations of which 
they form part. Thus, in fig. 47 the 8 th of the first 
chord serves as the 5 th of the second ; and 8 th and 3 rd 
of the second chord as 3 rd and 5 th of the third, &c. 
The common notes are tied. 



57. Successions of unconnected chords (as of the chord of Do by that of Re in 
fig. 37) are exceptional; being peculiarly susceptible of consecutive fifths or octaves, 
always somewhat harsh, even when free from positive error, and generally difficult 
to sing in some one or more progressions. 

58. When two notes of the same name and pitch occur in two following chords, 
it is desirable that they be in the same part, (£. e., be sung by the same voice,) in 
both chords. 

In fig. 57 nearly every one of the chords is connected with that next to it by a common 
note. The connexion in each case is indicated by a tye. 



59. When two notes of the same name but of different pitch occur in two 
following chords, it is necessary that they be in the same part — i. e., be sung by 
the same voice in both chords. 



Fig. 48. 



Fig. 49. 




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60. In fig. 49 the Mi b of the Soprano part of the second chord is said to stand 
in " false relation" to the Mi t| of the Alto part in the first. 

False relations of this kind were allowed by the old masters ; possibly from the difficulty 
found in singing the chromatic semitone. (See Jig, 48.) 



Chap, VII.] 



CONNEXION OF CHORDS. 



15 



61. Harmony of which any individual part contains many large intervals has 
always an effect more or less disjointed; large intervals, too, in rapid succession 
are more difficult to sing than small ones. As a rule, therefore, — 

62. In continuous harmony, the parts should move mostly by small intervals; 
large intervals being introduced sparingly, and generally in not more than one part 
at a time. 

63. Figs. 50 and 51 consist of the same two chords. The effect of the former, 
though consecutive octaves and fifths are avoided, is disjointed, and the parts 
(especially the Alto) are difficult to sing. On the contrary, the effect of the latter 
is good, and the progressions are easy; because each part moves to the note of the 
second chord which is nearest to the note it has just quitted in the first. 




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Fig. 50. 



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Fig. 51. 



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Fig. 52. 






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64. In a mere change from one position to another of the same chord (Jig. 52), 
little difficulty will be found in singing large intervals. They should, however, be 
used sparingly, even in this case. 

Large intervals are found more often, and are generally used with better effect, in the Bass 
than any other part; indeed, in successions of common chords they are unavoidable. 

65. The pluperfect fourth or tritone, though not a very large interval, should be 
avoided in the progression of parts, on account both of the difficulty of singing it, 
and of its somewhat harsh effect. Its inversion, also, the imperfect fifth, should be 
used sparingly. 

Fig. 54 is to be preferred to fig. 53; and the progression of the Tenor part in fig. 55 
is objectionable. 




Fig. 53. 



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Fig. 54. 



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Fig. 55. 



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16 



CONNEXION OF CHORDS. 



[Chap. VE 



66. Parts are allowed to cross one another; i. e., the Tenor may rise above the 
Alto, or the Alto above the Soprano. {See fig. 56.) No part, however, must fall 
below the Bass; unless, indeed, the part so falling is qualified to take the place of j 
the Bass — the lowest part. 



Fig. 56. 




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In fig. 57, the various rules and recommendations given in the foregoing chapter are 
generally observed. 



Fig. 57. 




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67. The laws which regulate the influence of accidentals on the stave, apply 
equally to figuring. In bar 5 of fig. 57 the minor 3 rd to the second bass note (Do) 
is not expressed in the figuring, because it has been already made flat as the 8 th to 
the first note of the same bar (ilfib). 

" It is not usual to express alterations in the 8 ve ." (Par. 39.) 



17 



CHAPTER VIII. 



Sequences. 



68. By the repetition of the same succession of intervals on different notes a 
sequence is produced. 

In each part of fig. 58 every alternate note rises or falls by the same interval; the Bass 
by fourths and fifths, the Tenor by seconds, the Alto by seconds and thirds, and the Soprano by 
thirds and seconds. 



Fig. 58. 




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69. A sequence may be tonal or raz/. 

70. In a tonal sequence the intervals are perfect or imperfect, major or minor, 
as they present themselves in the scale. 

Fig. 58 is a tonal sequence; the progression of the Bass in the first complete bar is by 
an imperfect fifth; in the next bar by a perfect fifth. The first interval in the Soprano part 
is a minor third; the next but one a major third, &c. 

71. In a real sequence the respective intervals are exactly alike, involving 
generally very rapid modulation. 

By making fig. 58 into a real sequence (fig. 59), we shall modulate in four bars from Do 
into Do b. 



Fig. 59. 




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Tonal sequences are much more frequently used than real. 



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72. When a bass part or any portion of a bass part moves in sequence, every 
other part should move in sequence also. 



o. M. H. 



18 



CHAPTER IX. 



Resolution of Dissonances, 



" The dissonant intervals are the seventh and the ninth; with the inversion of the former, 
the second." (Par. 11.) 

" The ninth does not admit of inversion." {Par. 12.) 

" The imperfect fifth and its inversion the pluperfect fourth" are also " essentially dissonant" 
intervals. {Par. 13.) 

73. By a dissonant interval is not meant anything of necessity harsh, or dis- 
agreeable to the ear; but, technically, a combination on which the ear cannot rest, 
and which therefore suggests another. 

74s. The progression of two sounds separated by a consonant interval is, to a 
certain extent, a matter of taste or choice; in general they may make contrary 
motion, oblique motion, or similar motion. But a dissonant interval must h 
resolved; the notes composing it must make certain definite progressions in relation 
-one to another, in order that the ear may be relieved from the feeling of suspense 
•uniformly attendant on the sounding of a dissonance. 

75. Dissonant intervals are mostly resolved by contrary or oblique motion, one 
-of the notes invariably moving one degree. 

76. Of two notes a seventh apart the upper note should fall one degree, while 
-the lower may keep its place (Jig. 60), rise a fourth (fig.'ei), or descend a fifth (fig. 62). 

Fig. 60. Fig. 61. Fig. 62. 

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As a fifth is the inversion of a fourth, figs. 61 and 62 are theoretically identical. 

77. Of two notes a second apart the lower note should fall one degree, while 
the upper may keep its place (fig. 63), rise a fourth (fig. 64), or fall a fifth (fig. 65). 

Fig. S3. Fig.te. Fig. 65. Fig. 66. 

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The last rule is but a repetition of the one before it, since a second is the inversion of ft 
seventh. I 

Another mode of resolving a seventh will be shewn hereafter. 



Chap. DL] RESOLUTION OP DISSONANCES. 19 

78. Of two notes a ninth apart, the upper note should fall one degree, while the 
lower note may keep its place (Jig. 67), rise a fourth (fig. 68), or fall a fifth (fig. 69). 

Fig. 67. Ify. 68. Ity. 69. 

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79. The mn/A must be carefully distinguished from the second; since though 
produced by notes of the same name, those intervals are not inversions of each 
other. "The ninth has no inversion " (Par. 12.) This caution is the more necessary, 
because the second is sometimes, like every other interval, made compound, (i. e., 
increased to an octave second,) (fig. 66,) while a ninth can never with propriety be 
reduced to a second, since two dissonant notes cannot be resolved by melting into one. 

Fig. 70. 
Compare the resolution of the compound (< 





with that of the ninth (figs. 68 and 69.) Also the resolution of the /A \ ^y 
ninth (fig. 67) with fig. 70, the first interval in which is not a ninth, 
but a second improperly resolved. 

80. A second can always be made compound, (i.e., increased to an octave 
second;) but a ninth must never be reduced to a second. 

81. A dissonance should always be resolved; it must sometimes, also, be pre- 
pared; i. e., the note which causes it must form part of the combination imme- 
diately preceding. 

82. A dissonant interval is therefore liable to three processes — preparation, 
percussion, and resolution. 

In figs. 71 to 76, the dissonances are prepared, as well as sounded and resolved. 
Fig. 71. Fig. 72. Jtg. 78. 






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Fig. 74. Fig. 75. JRg. 76. 

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20 



CHAPTER X. 



Discords by Suspension, 



83. A combination in which is contained a dissonant interval is called a discord; 
as one composed only of consonant intervals is called a concord. 

84. By prolonging a note not common to two following chords from the first 
into the second, we produce a discord by suspension. A discord by suspension (as 
its name might imply) must he prepared (par. si), as well as sounded and resolved. 



85. In fig. 77, the chord of Fa is followed by the 
chord of Sol; but in the Tenor part the note Do (not 
common to the two chords) is maintained during half 
of the time due to the chord of Sol. Thus a dissonant 
interval (a second) is produced between Do and Re; 
whereby the Bass note Sol is made to bear a discord by 
suspension; the dissonant note (Do) being prepared in 
the chord of Fa, sounded in the first half of the chord 
of Sol, and resolved in the second half. 

86. Again, in fig. 78, the chord of Fa is followed by 
the chord of Sol; but in the Soprano part the note La 
is maintained during half of the time due to the chord 
of Sol. Thus a dissonant interval (a ninth) is produced 
between this La and the Bass note {Sol), which, therefore, 
bears a discord by suspension; the dissonant note (La) 
being prepared in the chord of Fa, sounded in the first 
half of the chord of Sol, and resolved in the second 
half. 




Fig. 77. 



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Fig. 78. 




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87. A double discord by suspension is produced by 
prolonging two notes not common to two following 
chords, from the first into the second. Thus, in fig. 79, 
the two suspensions in figs. 77 and 78 are combined. 



9 

Fig. 79. 



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8 
3 



88. A discord by suspension is distinguished from any other species of discord 
by its place in a bar; being sounded on an accented beat, and resolved on an 
unaccented beat. 

89. The resolution of a discord by suspension is usually made by the dissonant 
note taking the same progression it would have taken had there been no suspension. 
Thus, in fig. 77 the progression of Do is only delayed, not altered. This rule, 
however, explains nothing: for the Do does not fall to Si, because it would probably 
have done so had there been no suspension, but because the ear requires relief from 
the dissonance formed by Do and Re. 



Chap. X.] 



DISCORDS BY SUSPENSION. 



21 



90. The pleasurable effect of a discord by suspension results from the delay of 
the dissonant note in making the progression expected of it. A dissonant note, 
having been prepared, must be sounded and then resolved. It is manifestly absurd 
that percussion and resolution take place at the same instant. 

91. A dissonant note and the note by which it is resolved must never be 
sounded together: for, irrespective of the harsh effect of such a juxtaposition, and 
various minor errors consequent thereon, suspense and certainty cannot be felt at 
the same instant. 

92. In writing discords by suspension, omit the note by which the dissonance 
is to be resolved; and, except in the case of the ninth, even the 8™ to that note. 

Fig. 80. 



Compare fig. 77 with fig. 80, where, in addition to the 
intolerable harshness of the beginning of the second chord, the 
latter half of it contains two major 3 rd " from the Bass. 




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93. In order to prepare a discord by suspension (as well as from other causes) 
it becomes necessary sometimes to alter the position of the chord immediately 
preceding it. This may be done by writing two chords to a single bass note, instead 
of one {see fig. 81), but more elegantly by writing two notes instead of one in a single 
part (see fig. 82), which is made to cross the other. (Par. 66.) 



Fig. 81. 




Fig. 82. 






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9 



8 



The relations of the upper parts of a musical combination to their bass are expressed by 
figures placed under or over that bass. (Chap. V.) 



94. A straight line 



after a figure indicates that the note due to that 



figure is to be continued, whatever changes may be made in the other parts or even 
in the bass of the combination in which it first appeared. 

The passages in figs. 77, 78, and 79 are folly and exactly expressed as follows. 



Fig. 88. 

3 8 — 

8 5 — 

5 .4 3 



Fig. 84. 

3 9 8 

8 5 — 

5 3 — 



Fig. 85. 

3 9 8 

8 5 — 

5 4 3 



95. Of these figures, all that refer only to the notes of the triad are superfluous 
(par. 35); those only which express the suspended notes being essential: viz., 4 3 to 

O ft 

the second bass note in fig. 77; 9 8 to that of fig. 78; and 4 3 to that of fig. 79. 



22 



DISCORDS BY SUSPENSION. 



[Chap. X. 



Fig. 86 contains examples of the suspensions treated of in the foregoing pages: the rules 
laid down are strictly observed. 




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Fig. 86. 

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23 



CHAPTER XI. 



Inversions of the Triad. 



96. The different arrangements of which the upper notes of a chord are 
usceptible are generally described as changes of position. These changes, as we 
Lave seen, are numerous, and afford much variety of effect to the chords in which 
hey are made. This variety is greatly increased by inversion; wherein one or 
ther of the upper notes of a chord being substituted for the root, becomes the bass. 

Thus, of a combination containing no sounds but those found in the triad of Do, Mi or 
)ol may be the lowest. (Compare jigs. 90, 91, and 92.) 



Fig. 90. 




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97. The prime or root of a chord is therefore not, of necessity, the bass. 

The bass of fig. 91 is Mi, of fig. 92, Sol; the root of both chords is Do. Of fig. 90, Do is 
>oth bass and root. 

98. When the 3 rd from the root of a chord becomes the bass (as in fig. 91), the 
Irst inversion is said to be used. 




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99. It is " understood that a bass note without figures F & & 8 - F *9- M» 
s to bear a common chord." (Par. 35.) Were the bass 
>f fig. 93 presented alone, the common chord of Mi would 
S)e due to it. Some indication, therefore, is wanted to 
show that the chord in fig. 93 is to be written or played, 
ind not the chord of Mi. On comparing fig. 93 with 
ig. 94 (the triad of Mi) } it will be found that the differ- 
;nce between them lies in one note ; that in fig. 93 there 
s Do, a sixth to the bass, and in fig. 94, Si, & fifth. " ?j 

100. This difference is expressed under fig. 93 ; 3 implying that instead of the 
>* and 3 rd to Do, the 6 th and 3 rd are to be written. 

101. As the chord of the Sixth differs from the triad only in one interval, it is 
generally sufficient to express that interval oniy, in the figuring. The 3 rd to the 
)ass, being common to both chords, is seldom marked. 



24 



INVERSIONS OP THE TRIAD. 



[Chap. XI. 



102. Thus when we find a 6 under a bass note, we know at once that the bass 
is not the root ; and, in the present instance, that it is the third to the root. 

103. For the arrangement of chords with the root in the bass, two rules have 
been given : — 

"Double the 8 ve rather than the 5 th , and the 5 th rather than the 3 rd , especially when the 
3 rd is major." (Par. 31.) 

u Omit the 8 Te rather than the 5 th , and the 5 th rather than the 3 rd ." (Par. 33.) 

104. These rules, apparently contradictory, are based on the same principle : — 
that the notes of a chord may be multiplied or omitted in proportion to their 
importance, or effectiveness. The 8™ is the least effective note in a chord, and 
therefore when doubled is less obtrusive, and when omitted more easily spared than 
any other note. Whereas the 3 rd (especially when major) is the most effective note 
in a chord, and therefore when doubled is more obtrusive, and when omitted is less 
easily spared than any other note. 



105. Of the chord of the Sixth, the bass is itself the 3 rd from the root ; and the 
3 rd and 6 th from the former are 5 th and 8 th to the latter. 



Fig. 95. 



See fig. 95, where Mi, the bass, is the 3 rd from the root Do (indicated 
by a dot). While Sol, the 3 rd , and Bo, the 6 th from the bass, are the 5 th and 
8 th from the root. 



The rules above, therefore, slightly modified, may be applied to the first 
inversion of the triad, thus: — 




^ 



106. In writing the chord of the Sixth, omit the 8™ to the bass, (especially if 
the bass be a major 3 rd from the root,) and double the 6 th rather than the 3* 1 . 

Of the three following chords fig. 98 is preferable to fig. 97, and fig. 97 to fig. 96. 



Fig. 96. 




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107. " The chords which follow one another with the best effect are generally 
those which contain one or more notes in common." {Par. 56.) The triads of two 
bass notes occupying following degrees of the scale in no case contain a common 
note, and the progression of radical basses by seconds is consequently to be avoided. 
For this reason the chord of the Sixth is often introduced, instead of the common 
chord, on the subdominant, when that note, being in the bass, moves to the 
dominant ; a note common to the two chords being thus introduced. 



Chap. XL] 



INVERSIONS OF THE TRIAD. 



25 



Compare figs; 99 and 100, in the former of whieh the subdominant (Fa) bean a common 
chord, in the latter a chord of the Sixth— of which Re, also the 5 th to the dominant, forms part. 



Fig. 99. 



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Fig. 100. 



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108. The chord of the Sixth on the subdominant is sometimes called "the 
chord of the added Sixth." In this work it will be treated as the first inversion 
of the chord of the 2 nd of the scale, even in the minor mode, where the 2 nd bears 
an imperfect 5 th . 

" The imperfect fifth, though essentially dissonant, is somotimes treated like a consonant 



interval." (Par, IS.) 



Fig. 101. 



The root of the first chord in fig. 101, as in fig. 100, is Re, 
the tonic of fig. 101 being Do minor. 

Lab is the imperfect 5* to Re. 




In fig. 102, several chords of the Sixth are introduced ; the 8** to the bass is omitted from 
all of them. 

Fig. 102. 




109. When the 5 th from the root of a triad is the bass, the second inversion 
is said to be used. Fig. 103 is an example of the second inversion of the chord 
of Do. 

110. Were the bass of fig. 103 presented without 
figuring, the chord of Sol would be due to it. On com- 
paring fig. 103 with the triad of Sol (fig. 104), a difference 
of two notes will be found. In the latter there are Be, 
a 5 th , and Si, a 3 rd to the bass; in the former, Mi, a 6 th , 
and Do a 4 th to the bass. 



111. This difference is expressed under fig. 103; 
I implying that instead of the 5 th and 3 rd , the 6 th and 4 th 
to the bass are to be written. 



Fig. 103. 




Fig. 104. 



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26 



INVERSIONS OF THE TRIAD. 



[Chap. XI 



112. Thus when we see £ under a bass note, we know that the bass is not tM 
root, but the 5 th to the root. 

Fig. 105. 

113. Of the chord of the Sixth and Fourth, the bass is itself 
the 5 th from the root ; and the 4 th and 6 th from the former are the 
8 th and 3* to the former. 




See fig. 105, where Sol, the bass, is the 5 th from the root Do (indicated by 
a dot). While Do, the 4 th , and Mi, the 6 th from the bats, are the 8 th and 3 rd 
from the root. 






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6 

4 



The rules repeated in par. 103 may therefore be applied to the ueond inversion of the 
triad thus:— 

114. In writing the chord of the Sixth and Fourth, omit the 8™ to the bass 
rather than any other note, and double the 4 th rather than the 6**. 

Of the three following chords, fig. 108 is preferable to fig. 107, and fig. 107 to fig. 106. 

Fig. 106. Fig. 107. Fig. 108. 






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115. The omission of the 8™ to the bass in the chord of the Sixth and Fourth 
is recommended, not, as in the case of the chord of the Sixth, enjoined. (Compare 

par. 106 and 114.) 

116. 4 is often followed on the same bass by 3 . When two 

sets of figures are placed under the same bass note, half the time 
of that note should be given to one chord, half to the other. 
Moreover, it is generally understood that the 5 th is to follow the 
6 th and the 3 rd to follow the 4 th in the same parts. In this pro- 
gression, too, the 8™ to the bass, being the only note common to 
the two chords, is generally added. 



i^. 109. 






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In fig. 110 several chords of the Sixth and Fourth are introduced ; 
the 8™ to the bass is omitted from most of them. 

Fig.110. 



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27 



CHAPTER XII. 



Suspensions on Inversions of the Triad. 

117. "By prolonging a note not common to two following chords from the 
former into the latter, we produce a discord by suspension." {Par. 84.) 

118. A note may be thus prolonged or suspended not only when the root is the 
bass, but when any of the inversions of a chord are used ; the suspension itself 
being occasionally thrown into the bass. 

119. Fig. Ill is the suspension (4 3) on a root {Sol), explained in Chap. X. 
Fig. 112 is the same suspension on, or rather of, the first inversion of Sol; the 
suspended note and that by which it is resolved being the bass. Fig. 113 contains 
the same suspension on the tecond inversion of the same chord. 



Fig. 111. 



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5 6 
2 8 



7 6 
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These three examples differ from one another only in the relative positions of the notes ; 
the notes being, in all, of the same names, and making, in all, the same progressions. The 
figuring, as usual, expresses the relations of the upper parts to the bass; consequently, though 
the notes in each example are the same, as the bass in each is different, so are the figures. 

120. Inverted suspensions are subject to the same rules as suspensions in a 
direct form; the dissonant intervals they produce being equally liable to pre- 
paration, percussion, and resolution. {Par. 82.) 

Observe, that in fig. 112 there is but one chord to two bass notes, each of which is figured. 
This arises from the fact that the notes which are the 5 th and 2 nd to Do are likewise the 
6* and 3 rd to 8%. 



Fig. 114 contains examples of the suspensions explained above. The suspension on the 
second inversion of the triad (Jig. 113) is not much used. 



28 



SUSPENSIONS ON INVERSIONS OF THE TRIAD. [Chap. XII. 




121. Kg. 115 is the suspension (9 8) on a root (Sol), explained also in Chap. X. 
Fig. 116 is the same suspension on the first inversion (of Sol); fig. 117, on the 
second inversion. Fig. 118 is the same suspension of the root (Sol), the suspension 
being in the bass. 



Fig. 115. 



Fig. 116. 



Fig. 117. 



Fig. 118. 




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The figuring expresses the relations of the upper parts to the bass. The retolution of the 
second chord in fig. 118 shows that the interval between La and Si is a compound second, not 
a ninth. (Compare par. 79.) 

122. " In writing discords by suspension, omit the note by which the dissonance 
is to be resolved, and, except in the case of the ninth, even the octave to that note/ 1 

(Par. 92.) 

123. From all inverted discords by suspension it is desirable to omit the 8™ to 
the note by which the dissonance is to be resolved. 

In figs. 116, 117, and 118, the places of these notes are indicated by black dots, to show 
that they are sometimes introduced, though better omitted. The inversions of 9 8 are, 
perhaps, more elegantly used in harmony of three parts than of four. The following example 
is treated in both ways. 



Fig. 119 (a.) 




Chap.XIL] suspensions on inversions of the triad. 



29 



Fig. 119 (*.) 







124. Fig. 120 is the double suspension (J §) on a root (Sol), explained also in 
Chap. X. AIL its inversions are shown in figs. 121, 122, and 123. 



Fig. 120. 



Fig. 121. 



Fig. 122. 



Fig. 123. 




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The inversions of 4 9 may be elegantly used in three parts. {Compare Jig. 124, a and 6.) 

Fig. 124 (a.) 




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30 



CHAPTER XIII. 



Fundamental Discord of the Seventh. 



125. In the harmonic chord of Do (Jg. 1), immediately above the second 5 th (Sol), 
is found the minor 7 th (Si b). 

126. The seventh is a dissonant interval. {Par. n.) "A combination in which 
is contained a dissonant interval is called a discord." {Par. 83.) A discord com- 
posed only of sounds found in the harmonic chord is called a fundamental discord; 
that under consideration is called the discord of the Seventh. 



Fig. 125. 




or 



ip 



127. In fig. 125 are combined Si b and Mi fcj. The former of these notes 
indicates a scale of at least one flat; the latter proves a scale of not more than one 
flat ; i. e. y the scale of Fa. 

128. The root of the harmonic chord (of which the fundamental discord of the 
Seventh is but an extract) is therefore not the tonic of the scale to which the notes 
composing it belong. A major common chord, indeed, may be formed on the 
dominant or subdominant of a major scale, as well as on the tonic; but the minor 
seventh can only be combined with the common chord on one of these notes — the 
dominant. 

129. In treating each note of the natural scale (or any scale of like construction) 
as the bass of a discord of the Seventh composed only of such sounds as are found m 
the scale itself we shall produce but one chord exactly like fig. 125, i. e., combining 
a major 3 rd with a minor 7 th ; this one chord will be formed on the dominant. 



Fig. 126. 

Perfect Chords. 

3 4 



6 




Imperfect* 

7 





Mqjor S** 

7th 



» 



Minor 3 rd 



Minor 8 1 * Mqor 3 rd 
7 th 7 * 



» 



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Major 3 rd 
Minor 7* 



Minor 8** 

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Minord 14 
7* 



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130. In fig. 126 are exhibited no less than four different kinds of discord : — 



On the 1 st and 4 th 



„ 2 nd , 3 rd and 6* „ minor 
„ 7 th an imperfect „ 



» 



5* (only), 



a perfect major chord with a major 7 th 

minor 7 th 

a perfect major chord with a minor 7 th 






39 
33 



Chap.XHL] FUNDAMENTAL DISCORD OF THE SEVENTH. 



31 



131. This last combination governs, or decides the scale; which none of the 
others are competent to do. Since of fig. 126— 

Chord 1 may be formed on the 4 th of the scale of Sol, 



» 2 , 


y 99 


99 


6* 


99 


99 


Fa, 


» 8 , 


9 99 


99 


6 th 


99 


99 


Sol, 


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9 99 


99 


1* 


99 


99 


Fa, 


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99 


99 


» 7 , 


9 99 


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2 nd 


9$ 


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La minor. 



Whereas Chord 5 can only be formed in the scale of Do, and that on the 5 th 
sound ; which in all scales is called the dominant, because the discord peculiar to it 
contains two sounds (its 3 rd and 7 th ), which, being combined, decide, beyond the 
possibility of doubt, what the scale is. 

182. The variable 7 th of the minor mode arises from the need of a true dominant, 
which the minor scale in its original form would not furnish. The minor scale is 
simply another mode qf arranging the sounds of its relative major. La minor 
consists of the same sounds as Do major; t. e., of natural sounds exclusively; the 
order alone is changed; that which was the 1 st in the latter, becomes the 3 rd in the 
former. 

133. •Of such a scale unaltered the dominant would bear a minor 3 rd . 

Fig. 127. 





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6 



134. By railing Sol to Soli, on the 5 th of the scale, a true dominant is produced, 
inasmuch as it has a major 8™, and perfect 5 th , and will bear a minor 7 th . 




/ 



Fig. 128. 
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135. Remark, that the 2 nd of the minor scale (V) bears an imperfect chord, as 
does likewise the 7 th (a), when made a leading note. 

The following are all major chords with minor 7 th *, and consequently the roots are all 
dominants. The first of Fa, the next of Sol, &c. (See fig. 129.) 



of Fa. 



of Sol. 




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Fig. 129. 
Dominant Sevenths. 
of La. of Do. 



of Be. 



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of Mi. 



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32 



FUNDAMENTAL DISCORD OP THE SEVENTH. [Chap-XEL 



figured I 

3 



186. The epithet "fundamental" is not confined to discords of the dominant 
Seventh, but is applied also to those quasi-harmonic chords which consist of a baa 
note with its &*, 5% and 7 th , even though the 3 rd be minor, the 7 th major, or the 
5 th imperfect. 

The discords in fig. 126 are "fundamental." 

137. A bass note note bearing a 7 th in addition to a common chord is Jvttj 

Q 

But it has been shown that * are seldom used save to contradict other 

3 

figures. A single figure 7, preceded by any accidental that may be wanted, is in 
general enough. 

138. In writing common chords, the student has been recommended (where the 
progressions admit) to double and omit certain notes rather than others. (Chap. IV.) 
The same rules, drawn from Nature, are generally applicable to the discord of the 
Seventh; save that in the latter, the 3 rd to the root is not of such vital importance 
as in the former; since if the 3 rd to the root be omitted from the common chord, it 
then contains no imperfect consonance (fig. iso>, whereas if the 3 rd be omitted from 
the discord of the Seventh, there still remains an imperfect consonance between 
the 5 th and 7** sounds, whatever be their relative positions (Jig. i3i> 




Fig. 130. 



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In fig. 130 there is no imperfect consonance (third or sixth) ; in fig. 131 there is a third 
between Be and Fa, or a sixth between Fa and Be. 

139. In no case can the 7 th be omitted from the discord of the Seventh ; but 
any other note may. 

Other considerations are, however, mixed up with the doubling or omission of notes in 
dissonant combinations which can only be treated in connexion with their resolution." 



CHAPTER XIV. 

Resolution of the Fundamental Discord of 

the Seventh. 



u A dissonant interval must be resolved; the notes composing it must make certain definite 
progressions in relation one to another, in order that the ear may be relieved from the feeling 
of suspense uniformly attendant on the sounding of a dissonance." {Par. 74.) 

140. The fundamental discord of the Seventh in its complete form includes at 
least two dissonant intervals — the seventh or its inversion the second (sometimes 
both), and the imperfect fifth or its inversion the pluperfect fourth (seldom both.) 

* Of two notes a seventh apart, the upper note should rail one degree, while the lower may 
keep its place, rise a fourth, or descend a fifth." {Par. 76.) 

" Of two notes a second apart, the lower note should fall one degree, while the upper may 
keep its place, rise a fourth, or descend a fifth." (Par. 77.) 

141. Of two notes an imperfect fifth apart, the upper should fall and the lower 
rise, each one degree. (Fig. isa.) While of two notes a pluperfect fourth apart, the 
lower should fall and the upper rise, each one degree. (Fig. iss.) 




Fig, 132. 

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Fig. 133. 



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142. By making the bass of a discord of the Seventh rise a fourth or descend a 
fifth, all the dissonant intervals which it may happen to contain will be properly 
resolved in the following chord. 




Fig. 134. 



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In fig. 134 there are three dissonant intervals — a seventh between the Alto and the 
Soprano, another between the Bass and the Soprano, and an imperfect fifth between the Tenor 
and the Soprano. In fig. 135, there are a pluperfect fourth between the Tenor and the 
Soprano, a second between the Tenor and the Alto, and a seventh between the Bass and the 
Tenor. In fig. 136, there are an imperfect fifth between the Alto and the Soprano, a seventh 
between the Tenor and the Soprano, and another seventh between the Bass and the Soprano. 
Each of these intervals is properly resolved on the following chord. 

6. M. H. F 



34 



RESOLUTION OF THE 



[Chap. XIV. 



143. With one exception, the progression (or more properly, resolution) of every 
note in the fundamental discord of the Seventh is defined. 

Fig. 137. 
( f\ 

144. The bass usually rises a fourth (or descends a fifth); 
the 8™ keeps its place; the 3 rd rises, and the 7 th falls; each 
one degree. The 5" 1 alone, not forming a dissonant interval with 
any note in the combination, may rise or fall. It generally 

falls; because, by rising, it produces two &** in the next chord. 

(See fig. 137.) 




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I 



145. It must be obvious that the resolution of the upper parts of a discord of 
the Seventh entirely depends on the progression of the radical bass; since if the 
latter were to move to any note but the 4 th above or the 5 th below, the former 
could not make the progressions due to them. 

146. Thus if Sol (the bass of fig. 137) moved to Re, the 7 th {Fa) could not fell 
one degree (to Mi), because Mi. is not a note of the chord of Re. Neither for the 
same reason could Si (the 3 rd ) rise to Do, nor Sol, the 8™, keep its place. On the con- 
trary, progressions would have to be made intolerable to the ear. (See figs. 138 and 1S9.) 




Fig. 138. 



Fig. 189. 



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147. To only one note besides that a 4 th above or a 5 th below 
it, can a bass note bearing a 7 th move with any propriety, viz., 
to the next note (or 2 nd ) above it. (See fig. uo.) This progression, 
however (which involves the omission of the 8™ from the chord 
of the 7 th and doubling the 3 rd in the following chord) will be 
separately treated in its place, the chapter on the fundamental 
discord of the Ninth, of which the first chord in fig. 140 should 
more properly be considered an inversion. 

It has been shown (in Chap. XIII.) that a scale contains only one note (the dominant) which 
will bear a true fundamental discord, but that that combination may be imitated, more or less 
imperfectly, on every note of the scale. (See fig. 126.) The term " fundamental discord" is 
extended to these gwaw-harmonic chords ; which are, for the most part, treated in the same 
manner as the combination distinguished as the fundamental discord of the dominant Seventh. 

148. Besides resolution, a dissonant interval admits of preparation — that the 
dissonant note be first heard in the preceding chord, and in the same part. "A 
discord by suspension (as its name might imply) must be prepared, as well as 
sounded and resolved." (Par. 84.) A fundamental discord may be prepared, but its 
preparation is not indispensable. 

149. A discord by suspension is invariably sounded on an accented beat and 
resolved on an tmaccented beat — the resolution being almost always made on the 



Chap. XIV.] 



FUNDAMENTAL DISCORD OF THE SEVENTH. 



35 



same root as the suspension. A fundamental discord is generally sounded on an 
i/waccented beat and resolved on an accented beat; the resolution being always 
made on a different root from the suspension. (Compare fy*. u\ and us.) 



Fig. 141. 
by Suspension. 



Fig. 142. 
Fundamental Discords. 



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150. " The triads of two bass notes occupying following 
degrees of the scale in no case contain a common note, and 
the progression of radical basses by seconds is consequently 
to be avoided/' (Par. 107.) By the addition of the 7 th to 
the latter of two chords thus related, a note common to 
both may be introduced, the 7 th of the second chord being 
prepared by the 8™ of the first. The 7 th on the dominant 
is often thus prepared by the 8™ of the subdominant. 



i 



Fig. 143. 
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See the first bar of fig. 143, where -Fa, the 8™ to the subdominant, prepares the 7 th to Sol, 
the dominant. 

151. The 7 th may be agreeably introduced after the 8 th "in passing" (Jig. 144); 
or we may rise to it from the 5 th (Jig. 145), or from the 3 ri (Jig. 146), or the 8 th Ufy. 147). 
The progression of the Soprano part in fig. 146 is a little difficult to sing; but that 
in fig. 147, though by a large interval, is easy. 




Fig. 144. 



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Fig. 146. 



Fig. 147. 



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Great variety may be afforded, especially in harmony of only three parts, by the intro- 
duction of such progressions as the above. 

152. In the doubling or omission of notes, regard must be had, in the case of 
a discord, not only to the effect of those notes in themselves (as in a concord), but to 
the possibility of resolving them, and to their influence on the following chord. It 
is obvious that certain notes of a discord if doubled could not be regularly resolved 
without consecutive octaves, while the omission of others would impoverish the next 



36 



RESOLUTION OP THE DISCORD OP THE SEVENTH. [Chaf. XIV. 



chord. And although various licences (to be explained hereafter) are admitted in 
the resolution of discords, they are to be regarded rather as last resources than 
legitimate means. For the present, therefore — 



153. In writing discords of the Seventh (and their 
inversions) double only the 8™ to the root, which " keeps 
its place" {par. 144); for though the 5 th may rise as well as 
fall, by doubling it we produce two 3** in the next chord. 

(Fig. 148.) 




Fig. 148. 



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154. Omit the 5 th rather than the 3 rd , and the 3 rd rather than the 8 Te ; for the 
omission of the 8 Te deprives the next chord of its 5 th . 



Fig. 149. 



Fig. 150. 



Fig. 151. 




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In fig. 149, the 5 th is omitted from the discord of the Seventh ; in fig. 150, the 3 rd ; and 
in fig. 151, the 8". The last chord of fig. 151 has three Dos and no Sol. 

" In no case can the 7 th be omitted from the discord of the Seventh." (Par. 138.) 

Fig. 152 (a> 





Fig. 152 (6). 



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37 



CHAPTER XV. 



Suspended Resolution. 



155. The resolution of a fundamental discord is often delayed by the suspension 
f any, or all of the notes composing it, on the bass of the following chord. 

In fig. 153, Fa, the 7* to Sol, instead of falling at once to Mi, forms a discord by suspen- 
on (4 3) on Do. In fig. 154, Be, the 5* to Sol, forms a discord by suspension (9 8) on Do. 
i fig. 155, Si, the 3 rd to Sol, forms a discord by suspension (7 8) on Do. 




Tig. 153. 



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:o: 



7 8 



From the last example, we deduce a rule ; that — 

156. In a discord by suspension, of two notes separated by a 
tajor seventh, the upper rises one degree, and the lower keeps 
te place. 



Fig. 156. 




Ol 



£ 



tt 



In writing discords by suspension, omit the note by which the dissonance is to be resolved ; 
ind, except in the case of the ninth, even the 8" to that note." (Par. 92.) From fig. 155, 
he black notes are better omitted. 



157. The last suspension (7 8) is most commonly used in combination with one 
>r both of the two first (4 3 and 9 8.) 



Fig. 157. 




^ 



Fig. 158. 



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9 8 

7 8 



The suspension in fig. 159 is sometimes improperly figured |. 



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Tig. 159. 



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7 
4 



8 
8 
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38 



SUSPENDED RESOLUTION. 



[Chap. XV. 



158. Occasionally, an entire fundamental discord (bass 
as well as upper parts) is treated as a discord by suspension; 
i. e., sounded on an accented and resolved on an tmaccented 

beat. (Fig. 160.) 



Fig. 160. 




J TcJ ,1 



«a 



& 



< >l< >^Q 




159. As a general proposition it may be asserted, that in passing from one 
combination to another, any note of the former may be suspended provided the 
conditions of the latter admit of that note being properly resolved. 



Fig. 161. 



160. For example, the 8 Te to one bass note can never 
be suspended as the 9 th to the next, since its resolution 
would involve hidden consecutive octaves. 

Though the bass Be in fig. 161 does not move to Do at the 
same instant as the Soprano, the effect is that of consecutive octaves. 




dsi 



■e> 



161. Thus, occasionally, combinations are produced not 
in themselves dissonant, which it is still convenient to class 
as discords by suspension ; applying to them the rule in 
Chap. X., which says that, "the resolution of a discord by 
suspension is usually made by the dissonant (in this case, 
the suspended) note taking the same progression it would 
have taken had there been no suspension/ 1 



3 



Kg. 162. 




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< » Q 



i 



^ 



162. Even the suspension 4 3 ceases to be dissonant when the 5 th to the root 
is omitted (fig. 164); or the 6 th is substituted for it (fig. 165); for the dissonance 
is not between the suspended note and the root, but between the suspended note 
(the 4 th ) and the 5 th . The treatment is in no way altered by the omission of 

the 5 th . (Compare figs. 163 and 164.) 



Fig. 163. 




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1 



Fig. 164. 



312 



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Wig. 165. 



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6 

4 



5 
3 



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Fig. 166 contains examples of most of these suspensions; a in four, and b in three parts. 



.XV.] 



SUSPENDED RESOLUTION. 



Kg. 166 («.) 



39 




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3^ 



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1 'Mil 



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XX 



b7 4 3 |96 6— 6 5*7 81 7 98 798 6 98 7 7 8 

5 4 ft— 4 3 4 3 4 3 



Jty. 186 (*.) 




=mp , i M e irTTp 

7 4 3 h6 6— 6578 7 98 7 I 9 8 

5 4 fl — ' 4 3 4 3 



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8 6 9 8 7 7 8 
3 4 3 



r« /vvvvvvw* 



40 



CHAPTER XVI. 



Discords by Suspension on Fundamental Discords, 



163. The discords by suspension of the Fourth or the Ninth (Chap. X.) may be 
made on the fundamental discord of the Seventh as well as on the common chord: 
the presence of the 7 th in no way interfering with their resolution, nor their resolu- 
tion with that of the 7 th . 



Kg* 167. 



Kg. 168. 



Fig. 169. 




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pt^Ts 



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r-f 631 



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7 — 
4 3 



3 



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9 8 

7 — 



3 



9 8 

7 — 

4 3 



H 



164. These examples demand no explanation; they speak for themselves. So 
long as the distinguishing characteristics of the two kinds of discord are kept in 
mind (par. 149) no difficulty about their treatment need occur, however they may he 
intermixed in composition. 




I 



F^ 



%. 170. 



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,°i "c, ifhh" ' v' iffi ^ 






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rx 



b7 4387 43 7— 9856 7 1—7— 4 
$5 — 43 7823 4 3 4| 



3 — 
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4 3 



41 



CHAPTER XVII. 



Inversions of the Discord of the Seventh. 



165. The discord of the Seventh contains four notes of different names : it is 
therefore capable of three inversions. When the 3 rd from the root is the baas, the 
first inversion is said to be used ; when the 5 th is the bass, the second inversion ; 
when the 7 th is the bass, the third inversion. 

Fig. 172 is an example of the first inversion of the chord of Sol, with its resolution on Do; 
fig. 173 of the second inversion; fig. 174, of the third. Fig 171 is the discord in its direct 
form. 



Ify. 171. 




n§. 172. 



d=^ 



Fig. 173. 



^C 



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A 



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Kg. 174. 



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33 



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4 
3 



6 

4 
2 



6 



166. On examining fig. 172, it will be found that the upper parts form in 
relation to the bass, the intervals of a 6 th , a 5 th , and a 3 rd — not a 6 th instead of a 5 th , 
as in the first inversion of the triad, but a 6 th in addition to a 5 th . As in the first 

inversion of the triad, the figure 3 is superfluous ; so that when we see 5 under a 
bass note, we know that the bass is not the root, but the 3 rd to the root, and that 
the root bears a discord of the Seventh. 

167. The resolution of the discord of the Seventh in the fundamental position, 
»". e. 9 with the root in the bass, was fully explained in Chap. XIV. The resolution of 
a discord in an inverted form is in general similar to that of the same discord in 
its fundamental position : i. e., the several parts make the same progressions, what- 
ever may be their place in the chord in relation one to another. 

168. Thus, in fig. 172 one 8 ve to the root (and 6 th to the bass) rises a 4 th , while 
the other keeps its place; the 3 rd to the root (the bass), Si, rises one degree; the 
5 th to the root (the 3 rd to the bass), Re, falls one degree ; and the 7 th to the root 
(the 5 th to the bass), Fa, falls one degree. (.Compare figs. 171 and 172.) 

169. In writing chords of the Sixth and Fifth, double the 6 th to the bass (the 
8 ve to the root), rather than the 3 rd (the 5 th to the root); and omit the 3 rd to the 
bass rather than the & h . The 5 th to the bass (7 th to the root) is indispensable. 



o. M. H. 



o 



42 



INVERSIONS OF THE DISCORD OP THE SEVENTH. [Chap.XVIL 




Txg. 176. 



A 



Ot 



Fig. 177. 



Or 



^ 



Fig. 178. 



^r 



X3 



6 i 
5 



-O 



i 



A A 



6 
5 



?F3 



Fig. 175 is preferable to fig. 176, and fig. 177 to fig. 178. The omission of the 6* firas 
the first chord of fig. 178 deprives the neat of its 5 th . 

170. " The triads of two bass notes occupying following degrees of the scale ii 
no case contain a common note, and the progression of radical basses by seconds is 
consequently to be avoided." (Par. 107.) 

171. The discord of the Sixth and Fifth is often substituted for the common 
chord on the subdominant of the scale, when that note, being in the bass, moves to 
the dominant ; a note common to the two chords being thus introduced. 



Comparo figs. 179 and 180. 

Fig. 179. 




212 



*y 



i u:i ^ i o i 



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Fig. 180. 



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r^- r j t -J- 



m 



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-tHy 




The root of the second chord of fig. 180 is Re, even in the minor mode, when the La k bU 
(Compare par. 108.) 

172. Although the 7 th can be added to any of the triads to be formed on the 
notes of a major or minor scale (see Chap. XT//.), it is for obvious reasons more often 
added to the dominant triad than to any other. The inversions of the " dominant 
seventh" are, therefore, more often used than those of any other fundamental 
seventh. This has naturally led to the use of contractions in the figuring of some 
of the inversions of the dominant Seventh. 

178. A single figure 5 on any of the first six notes of a scale would indicate s 
common chord — that the bass was also the root. Now, the 7 th of the scale when it 
rises directly to the 8 th (its usual progression), is very rarely, if ever, used as a root, 
because " the progression of radical basses by seconds is to be avoided." (Par. 107.) 

174. Wherefore, 5 on the 7 th of a scale means not 3 , but 5, — not that the 

bass is also the root, as of any other note so figured, but the 3 rd from the root; 
in fact, that thejirst inversion of the dominant Seventh is to be written, and that 
the root is a 3"* below the bass, bearing a 7 th . 



Chap.XVII.] INVEBSI0N8 OF THE DISCORD OF THE SEVENTH. 



43 



# 



(fiV 
kKf 



Kg. 181. 



Kg. 182. 



fig. 19$. 



fig. 184. 



« 



£ 



r-R 



t 





3^ 



m 




175. No difficulty can occur in recognising the bass notes figured 5 in the above 
examples as leading notes, since their fifth* are all imperfect. Fig. 181 is in Do; 
fig. 182 in Sol; fig. 188 in Fa; fig. 184 in La minor. 

176. The progressions described in par. 151 may be made with equally good 
effect in the first inversion as in the discord of the Seventh in its direct form. 



Tig. 185. 




Jty. 18*. 



Fig. 187. 



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O 



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m 



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Fig. 188. 



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XI 



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6 — 
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fFr 



n 



xt 



o 



xx 



6 



6 — 
6 5 



6 - 



Fig. 185 is marked 6 5; the 5 being a contraction of g. The full figuring would be • « 

1 77. The discords by suspension of the Fourth and of the Ninth may be made 
(together or separately) on the first inversion of the fundamental discord of the 
Seventh, as well as in the direct position. 



fig. 189. 




3 



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Jig. 190. 



X2 



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Fig. 191. 



X2 



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6 

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5 



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5 
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i' "q < ti y 1 01 ,. w m *i< > q 



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5 6 5 56 b 5 ! I 6 5 65 57 



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5 

4 5 
2 3 



4 5 
2 3 



44 



INVERSIONS OF THE DISCORD OF THE SEVENTH. [Chap.XTO 



178. When the 5 th from the root is the bass of a chord, the 
second inversion is said to be used. 

Fig. 193 is an example of the second inversion of the discord of the 
Seventh on Sol, with its resolution on Do. 

179. On examining fig. 193 it will be found that the upper 
parts, in relation to the bass, form the intervals of a 6 th , a 4 th , and 
a 3 rd ; not a 4 th instead of a 3 rd , but in addition to it. So that 
on seeing % under a bass note we know that the bass is the 5 th 
to the root, and that the root bears a discord of the Seventh. 




Fig. 193. 

2 



B 



m 



i >: U I 



W 



8 



180. " The resolution of discord in an inverted form is in general similar to that 
of the same discord in its fundamental .position." (Par. 167.) Thus in fig. 193, one 
8 ve to the root and 4 th to the bass rises a fourth ; the 5 th to the root (the bass), ife, 
falls one degree; the 7 th to the root (the 3 rd to the bass), Fa, falls one degree; 
the 3 rd to the root (the 6 th to the bass), Si, rises one degree. 

181. As of the figuring of the first inversion of the dominant Seventh (par. m), 
certain contractions are used, so of the second ; and for the same reason. 

182. A single figure 6 on the 1 st 3 rd 4 th 5 th 6 th or 7 th note of the scale raft 
indicate the first inversion of the common chord — that the root was a 3 rd below. 
But 6 on the 2 nd of a scale means not the first inversion of the leading note, which 
"is very rarely used as a root," but the second inversion of the dominant Seventh; 
in fact, that the root is a fifth below the bass, bearing a 7 th . 




lig. 194. 



-& 



-ei 



m 



Fig. 195. 



Mg. 196. 



Rg. 197. 



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183. The sharpened 6 in fig. 195 proves that the note above it (La) is the 
2 nd of a scale ; since Fa § can only be combined with Do ty in the scale of Sol 
The root is, therefore, Re, with a major 3 rd (Faty, and a minor 7 th (Do). 

The elevation of a note a semitone is sometimes indicated by "a short line drawn 
obliquely across the right extremity of the figure corresponding with it." {Par. 38.) 

184. By similar investigation, we ascertain the root of fig. 196 to be not Mi, to 
which Si fiat is an imperfect fifth, but Do, with the minor 7 th . Neither can the 
root in fig. 197 be Sol%, the third below the bass, but Mi, the fifth below it. 



6 



185, Therefore 6 on the 2 nd of the scale means 4. 

3 



iap.XVIL] INVERSIONS OF THE DISCORD OF THE SEVENTH. 



45 



186. The progressions described in par. 151 may be made with good effect in 
le second inversion, as in the discord of the Seventh in its direct form. 



Fig. 198. 



SZ1 



j. 



^ 



:o: 



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Ifg.lW. 



O 



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O 



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Kg. 200. 

Jo. 



3 



Kg. 201. 



-C * 



S 



XD. 



^ 



-©- 



HE 



iDL 



^> 



6 — 
4 3 



3 



-©r 



HE 



< > 












^* * 


a 











JCL 



LQI 



6 4 
4 2 



6 



6 3 

4 — 



6 — 
4 3 



187. The discords by suspension of the Fourth and the Ninth may be made on 
lie second inversion as well as on the discord of the Seventh in its direct form. 



Kg. 202. 



Eg. 203. 



Fig. 204. 




^ggfp 




^^ 



el^U^ 



J- 



-O- 



7 6 

4 — 

3 — 



4 k 



I 



-©r 



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j- j^j 



^ 



6 — 

5 4 

3 — 



2fy. 205. 



3 



-©r 



-e> 



X3 



7 6 4 

5 4 

3 — 



188. When the 7 th from a root is the bass of a chord, 
he third inversion is said to be used. 

Fig. 206 is an example of the third inversion of the discord of 
be Seventh on Sol, with its resolution on Do. 

189. On examining fig. 206, it will be found that the 
Lpper parts, in relation to the bass, form the intervals of a 
I th , a 4 th , and a 2 nd . So that seeing I under a bass note, we 
mow that the bass is the 7 th to the root. 



Fig. 206. 



&=n 



T3 



X3 



-©- 



^SE 






3=5 



6 
4 




46 



INVERSIONS OF THE DISCORD OF THE SEVENTH. [Chap. XVII. 



190. " The resolution of a discord in an inverted form is in general similar to 
that of the same discord in its fundamental position. 1 ' Thus, in fig. 206, one 8 Te to 
the root (and 2 nd to the bass) rises a 4 th , while the other keeps its place ; the 7 th to 
the root (the bass), Fa, falls one degree ; the 3 rd to the root (the 4 th to the bass), 
Si, rises one degree ; the 5 th to the root (the 6 th to the bass), Re, falls one degree. 

191. The progressions described in par. 151 may be made with good, effect on 
the third inversion of the discord of the Seventh, as in the fundamental position. 



Kg. 207. 



Fig. 208. 



Fig. 209. 




Fig. 210. 



^ 



-O- 



33 



-& 



© 



O- 



-O- 



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33 



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m 



rs 



43 



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-^ 



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33 



3=5 



©r 



5 — 
3 — 



6 



6 

4 



4 
2 



6 



6 ■ 



33 



6 



3 — 



33 



192. The /w// figuring of the second note in the first bar of each example 
above is I ; this may be contracted to \ (Jig. 208), and even % (fig- 209) ; the lowest 
figure never being omitted, unless the sign — be substituted for all the figures, 
which it generally is when the preceding bass note is a degree higher (or a seventh 
lower) than that which bears *. (See fig*. 207 and 210.) 

193. The discords by suspension of the Fourth and Ninth may be made on 
the third inversion of the fundamental discord of the Seventh, as well as on the 
discord in its direct form. 



Fig. 211. 




J. 



Fig. 212. 






J 



Kg. 213. 



^ 



A 



XT-fo 



\ 



■el^l J -J 



J. 




<& 



^ 



13 



j- 



:§: 




<stel J J 



S 



:§: 



6 — 5 6 

4 — 2 3 

3 2 



S 



6 — 5 6 

5 4 2 3 

3 2 







2fy. 214. 



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}( "6 {- 6 4 
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5 6 6 
2 3 



47 



CHAPTER XVIII. 



Licences in the Resolution of the Seventh. 



194. " In the doubling or omission of notes regard must be had, in the case of 
a discord, not only to the effect of those notes in t/temselves (as in a concord), but 
to the possibility of resolving them, and to their influence on the /allowing chord." 

(Par. 152.) 

195. The regular resolution of the discord of the Seventh treated in the fore- 
going pages, includes the best progressions of the notes composing it, i.e., the 
progressions most easy to sing and most satisfactory to the ear when sung. The 
desire to sound or hear sounded, the 8 th of the scale after the 7 th , the 3 rd after the 4 th , 
the 1 st after the 2 nd , and (in the bass) the tonic after the dominant, is, if not a 
th&tural feeling, certainly one which use has made part of our " second nature." 

196. In this regular resolution, only one note (the 8 th ) can, without more or 
less inconvenience, be doubled {par. 153); but, by licence, certain other progressions 
are admitted, which may be made not only in addition to those heretofore treated, 
but even instead of them. Of these progressions some are peculiar to certain 
inversions, and some can be used in all. 

197. In progressions of many parts, octaves and fifths by contrary motion are 

allowed. (Compart par. 58.) 



Fig, 215. 




^t 



Fig. 216. 



Fig. 217. 






T^ 




Kg. 218. 




198. In a discord of the Seventh of which the root is the bass, one of two 3 rd * 
may fall two degrees {fig. 219); or a single 3 rd may make this progression for the 
sake of enriching the next chord with a 5 th {fig. 220). 



Kg. 219. 




-& 



T± 



T^ 



^ 



Fig. 220. 



33 



rv 



1 



•d 



IT 



33 
XT 



A 



d 



Fig. 221. 



JCX 



JZZ 



or 



r\ 









n 






48 



LICENCES IN THE RESOLUTION OF THE SEVENTH. [Chap. XI 



199. In the first inversion of a discord of the Seventh, an 8™ to the bass (J 1 ! 
the root) may fall two degrees. (Fig. 222.) 



Fig. 222. 



Kg. 223. 




-Ql 



n 



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A 



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or 



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33 



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200. In the second inversion of a discord of the Seventh, 
two 3 rd8 to the bass (7 th * to the root) may be written, one of 
which must rise one degree. (Fig. 224.) From this combination, 
the 4 th to the bass (8 Te to the root) is usually omitted. 



201. In the third inversion of a discord of the Seventh, an 
8 ve to the bass (7 th to the root) may rise one degree. (Fig. 225.) 
From this combination, the 2 nd to the bass (8 ve to the root) is 
usually omitted. 



4 
2 










202. The dissonant note in a discord of the Seventh, whether in its direct form 
or in any inversion, may be deprived of its regular resolution by the motion of 
some other part to the note to which the seventh ought to falL In this case, the 
latter rises one degree. 



Fig. 226. 




m 



Fig. 227. 






-©> 



33 



Fig. 228. 



m 



US 



3=* 






:o 






Fig. 229. 



-er 



I 



Tf 



5 



3 

6 



X3 



6 



m 



1 

TT 



4 
2 



6 

4 



In figs. 226, 227, and 228, the Bass falls or rises to Mi, the note to which Fa (the 7 th to 
the root of each) ought, by rule, to fall. While in fig. 229, the Alto falls to 3ft, the note 
to which the Bass should fall. 

Of these progressions, fig. 228 is that in most common use. 



<.XVHL] LICENCES IN THE RESOLUTION OF THE SEVENTH. 



49 




t' 



203. The upward progression of a tingle 7 th to the root is always made to 
id an effect still more objectionable ; e. g. y doubling the 8™ in the chord of the 
th (Jigs. 231 and 232), or hidden consecutive octaves (Jigs. 230 and 233.) 



Fig. 230. 



^M 









rr-~r 



m 



e 



m 



6 



Fig. 231. 



ifei 



rr 



p 



4 



j 



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5 



6 



fly. 282. 



ifei 



*} 



P 



JJ 



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3 



6 



%. 233. 



^ 






■^ 



Ti 



4 6 

2 



204. A discord of the Seventh may be formed on any bass note which rises 
a fourth or descends a fifth, since its resolution is provided for in the next chord. 
When a bass part moves thus by a sequence of fourths and fifths, a 7 th may 
be added to every triad; one discord being resolved by another. In such case, 
each 3 rd (from its root) prepares the 7 th of the next chord (fig. 234) ; unless the 
7 th be preceded by the 8 Te (fig. 235.) 



Fig. 234. 




d 






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ts 



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3ZS 



&c. 



315 



3 



Fig. 235. 



^#ti 



° I < >< > 



*3 



87 87 8 17 87 



^ 



RTF 



&c. 



205. By making the sequence real (par. 71), the discords all become dominant 
Sevenths. In this case, each 3 rd (from its root) must fall a chromatic semitone 
(fig. 236) ; unless the 7 th be preceded by the 8 ve (fig. 237.) 



s? 



J 



3 



i 



Fig. 236. 




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b? 



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Rg. 237. 



fl< r I m 



u 



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° I < 1< > 



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8 7 8 7 8 

i 



fr 



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b7 8b7 



&c. 



Figs. 235 and 237 explain figs. 234 and 236 ; the two former containing in every pro- 
gression an ellipsis of the two latter. 



6. M. H. 



50 



LICENCES IN THE RESOLUTION OP THE SEVENTH. [Chap. XVm. 



206. The above sequence of sevenths may be treated on any inversions of the 
discord of the Seventh. 



Fig. 238. 



* 






I 



U 



$ 



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4 6 4 

2 5 2 



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/fy. 242. 



F^. 243. 



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Several of the Kcence* explained above are resorted to in the following example. 




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2ty. 244. 



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6 4 6 #4 6 467 — 

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51 



CHAPTER XIX. 



Interrupted Resolutions of the Seventh. 



207. The resolution of a discord of the Seventh, both in its direct and in its 
inverted forms, may be delayed, or interrupted, by the interpolation of one or more 
notes or chords between the dissonant note and the note or chord by which it is 
eventually to be resolved. 



£*st 



1.1 



Fig. 245. 

o 



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Fig. 246. 



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5 



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4 



ffy 247. 




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3 

/fy. 248. 
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ff 4 3 



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d d d d 



tf 2 



5 
3 



6 



Of these examples,, fig. 247 is that in most common use. In all, the 7 th from the root of 
the first chord is sustained until it is resolved on the 3 rd of the next chord hut one. 

208. " The dissonant note in a discord of the Seventh may be deprived of its 
regular resolution by the motion of some other part to the note to which the 7* 

Ought to fill." (Par. 202.) 

Fig. 249. 



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4 



5 
3 



3 



The dissonant note in the first chord of fig. 249 (Do) is in the Tenor ; it is resolved 
evertiucdly (in the last bar but one) by the Soprano, which falls from Do to Si. 



52 



INTERRUPTED RESOLUTIONS OF THE SEVENTH. [Chap. XIX. 



209. The 8 Te to the root is often introduced between a 7 th and the note by 
which it is afterwards resolved. 



Fig. 250. 




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ity. 252. 



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*fy. 253. 



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£3 



33 



4 

2 — 



— 6 



210. The discord of the Seventh, containing in its complete form four sounds 
of different names, cannot be fully expressed in less than four parts. By judicious 
omission of the least important notes, it may be indicated, especially in its inverted 
forms, beyond the possibility of mistake, in three, and even in two parts, especially 
with the help of the licences just explained. 



In fig. 254 a, b, the discords (suspended and fundamental) are all regularly prepared, 
sounded, and resolved. 




d 



.«' o i l , J 



Fig. 254 (a.) 

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53 



CHAPTER XX. 



Changes of Root on a Single Bass Note. 



211. Two or more sets of figures are often found on the same, or a repetition of 
the same, bass note. In some cases, they merely indicate changes in, or additions 
to, the upper parts ; the root, as well as the bass, remaining the same ; as in 8 7 
and its inversions, and in all discords by suspension. More often, however, they 
imply a change of root; since every note forms part of more than one chord — a fact 
recognised in all good average progressions. (Par. 56.) 

212. The possible number of changes of root on the same note (whether in the 
bass or not) depends on the number of combinations of which that note may form 
part. This number is great: e. g., Do is not only the 8 Te in the common chord of 
Do, but the 5 th in that of Fa, the minor 3 rd in that of La, the major 3 rd in that of 
La\>. Over and above these, it may form part of various discords fundamental 
and suspended, several of which have already been explained. (See fig. 255.) 



Fig. 255. 




< > cJ I < > fc i> 



^S 



&c. 



213. In the treatment of different chords on the same bass, the Student may, 
for the most part, be safely left to the guidance of the general principles of musical 
progression laid down in the foregoing pages. Some few cases, however, require 
special consideration. 



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fj 



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Fig. 256. 



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Fig. 257. 



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214. " 6 on the 2 nd of the scale means %" (par. 185.) In the first bar of fig. 256, 

the root changes from Re to Sol with the 7 th ; two chords with but one common 
note being due to the bass. But "in the second inversion of a discord of the 
Seventh, two 3 rd8 to the bass (7 th * to the root) may be introduced, one of which 
must rise one degree " (par. 200.) This would give another note common to the 

two chords (see fig. 257.) 



54 



CHANGES OF ROOT ON A SINGLE BASS NOTE. [Chap. XX. 



215. When a bass note figured 5 6 rises one degree, its 8 ve usually forms part 
of the chord, and its 3 rd (the 7 th to the second root) rises also, to avoid the 8™ to 
the bass in the next chord of the Sixth. (Compare figs. 258 and 259.) 



Fig. 258. 




212 



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Fig. 259. 

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In fig. 260 the progression 5 6 is treated in various positions, and resolved in various 
ways. In bars 6 and 7 the resolution is interrupted in one of the modes shown in Chap. "XTK- 
(Comparefig. 247.) 

Fig. 260. 



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tel 






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5 6 6 



5 6 5 

b 



4 3 #6 — 
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6 5 — 
4 3 — 

8 7 



55 



CHAPTER XXL 



Fundamental Discord of the Ninth. 



216. In the harmonic chord, "immediately above the triple 8** to the prime is 
found the 9 th ," which, being added to the discord of the Seventh, produces a com- 



bination of six sounds of different names, fully figured * (.Fig. 26i.) 

a 

3 

217. From the fundamental discord of the Ninth and Seventh, the 8 Ye to the 
root is usually excluded (Jig. 262); of the other sounds, the 5 th should be omitted 
{fig. «6S) rather than the 3 rd (fig.***) The Ninth and Seventh are, of course, 
indispensable. 




Fig. 261. 



Fig. 262. 



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Fig. 263. 
O 

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Fig. 264. 

O 
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218. "Of two notes a Ninth apart the upper should fall one degree; while the 
lower may keep its place, rise a fourth, or fall a fifth." (Par. 78.) 

219. In the resolution of the discord of the Ninth and Seventh, the sounds 
which form dissonant intervals one with another take the same progressions as in 
the discord of the Seventh ; i.e., the bass rises a fourth, or falls a fifth, the 3 rd rises 
one degree, the 7 th falls one degree, and the 8 ve , if retained, keeps its place. The 
5 th alone, not forming a dissonance with any sound in the combination, may rise 
or fall, and when doubled takes both progressions. In certain positions, however, 
it must rise, or form consecutive fifths with the 9 th . (Compare figs. 265 and 266.) 




m 



Fig. 265. 



Fig. 266. 



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33 



220. When the 5 th of the discord of the Ninth rises, two 3 rd8 are produced in 
the following chord (fig. 265); a lesser evil, however, than consecutive fifths (fig* 266.) 



56 



FUNDAMENTAL DISCORD OF THE NINTH. 



[Chap. XXL 



221. From fig. 265 we gather that of two notes a seventh 
apart, the lower may rise one degree ; and from fig. 266, that 
of two notes a second apart, the upper may rise one degree. 

(Figs. 267 and 268.) 

The latter resolution is the inversion of the former. 





Fig. 267. 



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Fig. 268. 



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222. The Ninth is sometimes used as a fundamental discord without the 
Seventh; the combination, however, is somewhat harsh, from the comparative 

paucity of imperfect consonances. (Compare figs. 269 and 270.) 



Fig. 269. 




3 



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Fig. 270. 




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Fig. 271. 



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Fig. 272. 



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223. When the 7 th is omitted from the discord of the Ninth, the 5 th must rise, 
or the next chord will be deficient in a 3 rd . (Compare figs. 271 a«rf 272.) 

224. The fundamental discord of the Ninth and Seventh is less used in its 
direct than in its inverted forms. In the former case, the preparation of the 
dissonant notes (the 9 th and the 7 th ) is very desirable — if not indispensable. 

In fig. 273 most of the dissonances are prepared. 



Fig. 273. 




57 



CHAPTER XXII. 



Chromatic Intervals. 



Fig. 274. 




225. The semitone between two notes of the same 
name but of different pitch, is called chromatic. 



226. A chromatic interval is larger or smaller, by a chromatic semitone, than 
any interval including the same number of diatonic positions. 

227. Thus, the imperfect fifth and the perfect fifth, being both found in the 
diatonic scale, are diatonic intervals (Jig. 275), but the augmented fifth, which is a 
chromatic semitone larger than the perfect fifth, is a chromatic interval. (Fig. 276.) 



Imperfect Fifth. 
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Fig. 275. 




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Perfect Fifths. 



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Diatonic. 



Augmented Fifth. 



Fig. 276. bo 



Chromatic. 



228. Every diatonic interval can be either augmented or diminished by a 
chromatic semitone ; being called augmented or diminished accordingly. 



229. Thus, by flattening the upper of two notes a ninth 
apart, the interval of a diminished ninth is produced 
between them. 




Fig. 277. 



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W 



In figs. 278 and 279 are contained all the chromatic intervals within the octave ; those in 
the latter being inversions of those in the former. 

For the sake of classification, the chromatic semitone is sometimes called the augmented 
unison; although, of course, the unison is not an interval. 



Unison. 



Fig. 278. 
Second. Fifth. Sixth. 




biolE 



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Augmented. 



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Fig. 279. 

Octave. Seventh. Fourth. 
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Third. 



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Diminished. 



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58 CHROMATIC INTERVALS. [Chap. XXII. 

230. The second, fifth, and sixth cannot be diminished, nor ^Fig. 280. 
can the seventh, fourth, or third be augmented. The unison, of 
course, cannot be diminished ; but the octave can be augmented, — 
or rather the chromatic semitone (augmented unison) can be made *j q 
compound. 

231. Achromatic interval is essentially dissonant; it is " a combination on 
which the ear cannot rest satisfied, and which therefore suggests another/' {Par. 73.) 

232. "A dissonant interval must be resolved" {par. 74); and "sometimes also 
prepared." (Par. 81.) 

Fig. 281. 

233. Two notes separated by a diminished ninth are resolved n \>i 
in the same manner as when separated by a. perfect ninth; the 
upper note falls one degree, while the lower note may keep its 
place, rise a fourth, or descend a fifth. (Fig, 281.) 

"The ninth does not admit of inversion" (par. 12); neither must it be confounded with 
the octave (or compound) second, an interval requiring altogether different treatment. 
(See par. 79.) 

234. Of two notes separated by an augmented second, the upper note should 
rise one degree; while the lower may fall (also one degree) or keep its place. 

(Figs. 282 and 283.) 

235. Of two notes separated by a diminished seventh, the lower note should 
rise one degree; while the upper may fall (also one degree) or keep its place. 

(Figs. 284 and 285.) 

Fig. 282. Fig. 283. Fig. 284. Fig. 285. 

bo. ^ \>^ 





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n< >q 14 Moo a ao * * 3E 



HE 



The last rule is but a repetition of the one before it ; since the diminished seventh is the 
inversion of the augmented second. 

The remaining chromatic intervals will be treated hereafter. 



59 



CHAPTER XXIII. 



Discord of the Diminished Ninth, 



236. " Every diatonic interval can be either augmented or diminished by a 
chromatic semitone, being called augmented or diminished accordingly." (Par. 228.) 



237. The ninth in the fundamental discord of the Ninth and Seventh is especially 
liable to this treatment ; the chromatic form being as often used in modern music 
as the diatonic. 



238. The resolution is in no way affected by the 
change; whether the 9 th be perfect or diminished, it falls 
one degree, and the other parts take the progressions 
assigned to them in Chap. XXI. {See fig. 286.) 




Fig. 286. 



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A. A 



f 



^ 



239. These progressions are even more imperatively demanded in the discord of 
the diminished, than in that of the perfect Ninth; since the former contains always 
either a diminished seventh or an augmented second — chromatic intervals which 
must be resolved according to the rules given in the last chapter. {Pars, 234 and 235.) 



60 



CHAPTER XXIV. 



Inversions of the Discord of the Ninth and Seventh. 



240. The discord of the Ninth and Seventh contains five sounds of different 
names; it admits, therefore, otfour inversions. 

Fig. 288 is an example of the first inversion of the discord of the Ninth and Seventh on 
Sol, with its resolution on Do; fig. 289, of the second inversion; fig. 290 of the third; 
fig. 291, of the fourth. The second chord of each example shows the resolution of each. 
Fig. 287 is the discord in its direct form. 



Fig. 287. 




Fig. 288. 



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Fig. 289. 



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Fig. 290. 



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Fig. 291. 

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7 



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5 



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3 



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6 
4 
2 



6 

4 



241. The upper parts of fig. 288 form, in relation to the bass, a 7 th , 5 th and 3 rd ; 
figured 5 or merely 7. 

242. Now this is the figuring of the discord of the Seventh in its direct fcrm; 
and in the case of a single bass note figured 7, there would be no means of knowing 
which chord was intended. The following bass note in all cases removes the doubt, 
since the root of a discord of the Seventh rises a fourth or descends a fifth; 
whereas the 3 rd from the root of a discord of the Ninth rises one degree. 

{Compare figs. 292 and 293.) 



Fig. 292. 




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Fig. 293. 






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Chap. XXIV.] DISCORD OF THE NINTH AND SEVENTH. 



61 



243. The distinction between the 7 th on a root and the 7 th on the 3 rd from a 
root, is not only of great importance theoretically, but practically; since when the 
bass is also the root, its 8™ may form part of the chord (leefig* 292); but when the 
bass is the 3 rd from the root, neither the 8™ to the bass nor the 8™ to the root 
can with propriety appear in the chord; the former, because it could not be resolved 
without consecutive octaves, apparent or hidden {figs. 294 and 295) ; the latter, on 
account of its very harsh effect. (Fig. 296.) 




Fig. 295. 



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I 



Fig. 298. 



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a 




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244. From the first inversion of the discord of the Ninth, omit the 8™ to the 
root and the 8™ to the bass. 

245. The first inversion of the discord of the diminished Ninth is called the 
discord of the diminished Seventh. The treatment is the same as in the diatonic 
combination. {See fig. 297.) 



Fig. 297. 




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or 



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l 



l 



33 



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b7 7 

246. "The resolution of a fundamental discord is often delayed by the sus- 
pension of any, or all of the notes composing it, on the bass of the following chord/' 

(Par. 155.) 

247. In resolving discords of the Ninth, direct or inverted, suspensions are 
often introduced, not only for the sake of effect, but to avoid error. In bars 
6 and 7 of fig. 298, consecutive fifths between the Tenor and Alto are avoided by 
deferring the resolution of the latter, half a bar. 

Fig. 298. 




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4 



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3 



62 



INVERSIONS OF THE DISCORD OF 



[Chap. XXIV. 



248. When the 5 th from the root is the bass of a chord, 
the second inversion is said to be used. Fig. 299 is an 
example of the second inversion of the discord of the Ninth 
and Seventh on Sol. 

249. The upper parts of fig. 299 form, in relation to the 
bass, a 6 th , 5 th and 3 rd , figured 5 or merely |. 






V 



TIT 



Fig. 299. 



F^ 



cU 



3 

6 



TX 



250. Here, as in the case of the first inversion, we have 

figuring belonging to another chord ; since g expresses also 

the first inversion of the discord of the Seventh. The 
following bass note, however, again removes all doubt; 
since the 3 rd of a chord of the Seventh rises one degree, 
the following bass note bearing a common chord; whereas 
the 5 th of a chord of the Ninth rises one degree, the 
following bass note bearing a chord qf the sixth. (Compare 

fig*. 200 and 299.) 




J 



<y* 



Fig. SOO. 



Ef5ES 






a 



251. From the second inversion of the discord of the Ninth, omit the 8™ 
to the root, and, in general, the 8 ve to the bass; the former, on account of its 
harsh effect; the latter, because it adds little to the harmony, and is liable to 
cause both consecutive octaves and fifths. 



252. The treatment of the second inversion of the 
diminished Ninth is the same as that of the diatonic 
combination. (See fig. soi.) 





u 



Fig. 302. 



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^ 



, pQ-Jbri , Jfr-J , J -^, rl J' 



XX 






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6 
5 



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5 



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5 



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6 
5 



rx 



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*On*r. XXIV.] 



THE NINTH AND SEVENTH. 



63 



253. When the 7 th from the root is the bass of a 
chord, the third inversion is said to be used. Fig. 803 is 
an example of the third inversion of the discord of the 
Ninth and Seventh on Sol. 

254. The upper parts of fig. 803 form, in relation to 
the bass, a 6 th , 4 th and 8* figured 4. 






7HF 



I 



Fig. 303. 



d-rrl 



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J_A 



§ 



255. Here again we have figuring belonging to another 
chord ; but, as before, the following bass note removes all 
doubt; since the 5 th of a chord of the Seventh falls one 
degree, the following bass note bearing a common chord; 
whereas the 7 th of a discord of the Ninth falls one degree, 
the following bass note bearing a chord of the Sixth. 

(Compare fig* 304 and 303.) 



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1 



Fig. 304. 



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2=5 



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6 

4 
3 



3 



256. From the third inversion of the discord of the Ninth, omit the 8™ to the 
root and the 8™ to the bass. 

Fig. 305. 



257. The treatment of the third inversion of the 
diminished Ninth is the same, as that of the diatonic com- 
bination. (See Jig. 305.) 




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a j. 



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6 

4 

b 



6 



ify.306. 



,P,I. ' ', ol I , d l <' dl o l l*J | d|,'Jl d . o l l.l J | ,, | | 

Art ^ i fe, i ■ n" 1 gji 1 1 yi I « ]"■ 1 1 -cj d r i - II 



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*4 6 4,4 6 4 6 6 — 

*b *b b 4 3 



64 



INVERSIONS OP THE DISCORD OP 



[Chaf. XXIV. 



258. When the 9 th from the root is the bass of a chord, 
the fourth inversion is said to be used. Fig. 307 is an 
example of the fourth inversion of the discord of the 
Ninth and Seventh on Sol. 

259. The upper parts of fig. 807 form, in relation to 
the bass, a 6 th , 4* and 2 nd , figured 4. 

A 




Fig. 807. 



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s 

4 
2 



4 



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6 

4 



Fig. 308. 



260. Once again we have figuring belonging to another 
chord; but distinguished as before by the following bass 
note. Since the 7 th of a chord of the Seventh^ falls one 
degree, the following bass note bearing a chord of the 
Sixth; whereas the 9 th of a chord of the Ninth falls one 
degree, the following bass note bearing a chord of the 

Sixth and Fourth. (Compare figs. 308 and 307.) 




261. From the fourth inversion of the discord of the Ninth and Seventh, omit 
the 8™ to the root and the 8™ to the bass. 



262. The treatment of the fourth inversion of the 
diminished Ninth is the same as that of the diatonic com- 
bination. (See fig. 809.) 



Fig. 309. 




d 



i v l>o (nl 
« J« — 



6 

4 

s 



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6 

4 



Fig. 310. 




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Ph 1 ] |B 



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33E 



&tt^ — — br^r 




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6 #4 

4 *2 



6 4 6 7 
4 2 4 



Chap. XXIV.] 



THE NINTH AND SEVENTH. 



65 



263. From every inversion of the discord of the Ninth and Seventh, omit the 
8* to the root and the 8™ to the bass. 

264. The discord of the Ninth and Seventh, containing in its complete form 
five sounds of different names, cannot be fully expressed in less than five parts. 
As in the case of other chords, by judicious omission of the least important notes 
it may be indicated, especially in its inverted forms, beyond the possibility of 
mistake, in Jour and even in three parts. 



9 



In fig. 311 the discords 7 are regularly prepared, sounded, and resolved. 



Fig. 311. 




G. M. H. 



66 



CHAPTER XXV. 



Chromatic Intervals, 



265. The chromatic intervals were all exhibited in Chap. XXII. (figs. 278 jr 279); 
and the treatment was explained of those in most common use ; viz., the diminished 
ninth, the diminished seventh, and its inversion, the augmented second — the last 
two intervals forming part of the discord of the diminished ninth. The remaining 
chromatic intervals are, the augmented unison, fifth, and sixth, with their inver- 
sions, the diminished octave, fourth, and third. 

266. Of two notes separated by an augmented unison, the upper should rise one 
degree; while the lower may keep its place (Jig. 312), or fall one degree (Jig. sis). 

267. Of two notes separated by a diminished octave, the lower should rise one 
degree ; while the upper may keep Us place (fig. 3U), or fall one degree (fig. 315). 



Fig. 312. 



Fig. 313. 



Fig. 314. 



Fig. 315. 







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The last rule is but a repetition of the one before it ; since the diminished octave a the 
inversion of the augmented unison. 

268. Of two notes separated by an augmented fifth, the upper note should rise 
one degree, while the lower note may keep its place, rise a fourth, or fall a fifth. 

(Fig. 316.) 



269. Of two notes separated by a diminished fourth, the lower note should rise 
one degree, while the upper note may keep its place, rise a fourth, or fall a fifth. 

(Fig. 317.) 



Fig. 316. 



Fig. 317. 




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The last rule is but a repetition of the one before it. 



Chap. XXV.] CHROMATIC INTERVALS. 6? 

270. Of two notes s ep arate d by an augmented sixth, the upper note should rise 
and the lower fall— each one degree. (F9- sit.) 

271. Of two notes s ep arate d by a diminished third, the lower note should rise 
and the upper fall — each one degree. (F9- sis.) 

Fi§. SIS. Fif. SIS. 

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The last role is but a repetition of the one before it. 



272. In the resolution of an augmented interval the upper note always 
rises, and the lower note, when it moves, falls; while in the resolution of a 
diminished interval the lower note always rises, and the upper note, when it moves, 
falls. 

273. In an augmented interval, the tendency of the two notes is to separate ; 
in a diminished interval, to approach one another. 



68 



CHAPTER XXVI. 



Chromatic Harmony. 



274. The augmented unison, fifth, and sixth, with their inversions, chiefly arise 
from the introduction of passing notes into harmony otherwise diatonic; audi 
passing notes being considered to give variety or smoothness to the progressions 
from one chord to another. 



275. A chromatic interval may be thus introduced into any chord, provided 
the conditions of the next chord admit of its being regularly resolved. 

276. Neither the augmented unison nor its inversion the diminished octave, 
are much used in their original forms. (Figs. 320 and 321.) 




3 



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277. But the compound augmented unison 
(or augmented octave) is more common, 
especially in inversions. (See Jig. 322.) 



Fig. 322. 




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Chap. XX VL] 



CHROMATIC HARMONY. 



69 



278. The augmented fifth or its inversion the diminished fourth, may be intro- 
duced with good effect into any chord the root of which rises & fourth (see Jigs. sas, 
4>#5), or falls a third. (See figs. 8S6, 7, £ a.) 



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279. The augmented sixth may be introduced on the^rsf inversion of the chord 
of the subdominant minor (see fig. 329), or on the second inversion of the discord of the 
dominant seventh. (See fig. 330.) 



Fig. 329. 



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280. In fig. 329, the chromatic interval is produced by the augmentation of the 
8™* to the root Fa; in fig. 330, by the diminution of the 5 th to the root Re. 

The second chord in fig. 329 admits also of another interpretation — that the root changes 
from Fa to Re with an imperfect fifth. 



281. The augmented sixth may also be introduced on either of the foregoing 
chords (figs. 329 and 330) when they are accompanied by a 5 th (from the bass.) 



70 



CHKOMATIC HAEMONY. 



[Chap. XXVL 



282. In this case, the immediate resolution of the 5 th , which forms an augmented , 
second with the (augmented) 6 th , cannot be made without consecutive fifths. By . 
deferring the resolution, the fifths are avoided, and a single or double discord by 
suspension introduced at the beginning of the next chord. {See figs. 331 and 332.) ■ 




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283. The 5 th is also allowed to rise a chromatic semitone before being resolved. 
The progression in fig. 333, though of late somewhat vulgarized, is certainly one of 
the most beautiful in music. 

284. The root of the chords in the first bar (of each fig.) may be considered to 
be either Re, with 7 , the 5 th being lowered a chromatic semitone in the latter part 
of the bar; or Fa, with b 7, and then Re, with *> &c. 

285. By inverting the progressions in figs. 331 and 332 the dimmished third 
is introduced. 



Fig. 334. 




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286. These inversions are rarely used. It is even laid down as a rule in some 
treatises that "the diminished third must never be used in harmony, nor its 
inversion the augmented sixth in melody." There appears to be more ground for 
the latter than the former rule. 



CHAPTER XXVII. 



Pedal Points. 



287. Appended to every complete organ is a set of keys for the feet, called 
pedals — as the keys for the hands are called manuals. From a very obvious and 
effective mode of using these (foot) keys has arisen the term pedal point, by which 
ii understood a note maintained during several successive changes of chords, or 
passages of melody. In the course of these changes, not only is it allowable to 
introduce all the combinations of which the sustained note might possibly form 
part (compare par. 212), but various other combinations with which it could never 

otherwise accord; — provided always that they be properly adjusted in relation to 

one another. 

288. A pedal note is not of necessity confined to the bass, though the bass is, 
more often than any other part, the seat of it. 

289. The 5 th of the scale in which a pedal point begins and ends is the note in 
most common use as a pedal note, especially when it is in the bass. The termina- 
tion of a passage is often protracted by a pedal point on the last tonic. 



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72 



CHAPTER XXVHL 



Progressions of Fundamental Basses. 



The number of progressions possible to a fundamental bass note is only limited by the 
number of sounds in the chromatic scale of which it forms part. It cannot be said, with 
safety, that there is one radical progression of which an example might not be adduced from 
a good writer. 

To lay down any laws by which the progressions of fundamental basses may be regulated 
would therefore seem of little use. Such, however, is not the case ; since, though it is idle to 
say of any progression that it must never be made, an examination of the least regular com- 
position of any good musician will show that, on the whole, he has been guided by a few great 
principles; nay, that all the most agreeable and popular melodies — the offspring, in many 
instances, of uncultured genius— are conformable to certain laws of which their composers 
possibly may have been ignorant. 

290. The harmonic chord contains many dissonant intervals, — a $eventh, an 
imperfect fifth, a second, a, pluperfect fourth, &c. On such a combination "the ear 
cannot rest satisfied;" "it suggests another," the root of which experience ahows 
to be the fourth above or fifth below. This second root has also its own harmonic 
chord, and consequently its own dissonances ; which require, equally with those 
on the first root, to be resolved — on the chord of the fifth above or fourth below 
it. So that, continuing this process of resolving harmonic chords, we should 
produce a succession of roots each alternately a fourth above or a fifth below the 
other, which, by the help of an enharmonic change, would become a circle, in 
traversing which we should return to the root whence we started. (Setfy. 338.) 




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291. The most natural fundamental progression, therefore, consists in ascent by 
fourths and descent by fifths ; because the dissonances generated by each root can 
be resolved on the next ; whence we derive the law so often referred to, — that the 
root of a fundamental discord must rise a fourth or descend a fifth. This law givei 
rise to another : — 

292. A fundamental discord may be formed on any bass note which rises a 
fourth or falls a fifth. 

293. But in artificial or practical harmony, the harmonic chord is by no means 
perfectly imitated on every bass note; on the contrary, combinations into which 
dissonances do not enter are as much or more used than those into which they do. 



Chap.XXVIIL] PROGRESSIONS OF FUNDAMENTAL BASSES. 



73 



Bat as harmonic or natural chords afford us models for the arrangement of 
artificial chords {see Chap. IV.), so do natural progressions suggest to us principles 
far the regulation of artificial progressions. 

294. It has been shown {Chap. VII.) that the " chords which follow one another 
with the best effect are those which have one or more notes in common." This is 
strikingly exemplified in the natural fundamental progressions of fig. 338, where 
the 8™ and 5 th of one chord are the 5 th and 9 th of the next. Whence we derive 
mother law; that, — 

295. One root may be followed by any other whose chord contains a note 
common with it. 

296. Under this law a fundamental bass note may be followed, in the same 
scale, by the 3 rd the 4 th the 5 th or the 6 th above it, and by the 8™ of those notes, 
the &* the 5 th the 4 th or the 3 rd notes below it. {See figs. 339, 340, S4i, and 342.) 






2^^339. 

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297. Rapid though agreeable modula- 
tion is produced by the ascent of a root a 
minor 3 rd or 6 th ; or by its descent a major 

3 ri OT 6 th . {Figs. 343 and 344.) 



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298. The progression of a root one degree up or down, is objectionable {par. 107), 
chiefly from the want of connexion between their triads. {Figs. 345 and 346.) 

299. Two chords, however, standing in the relation of those in fig. 345, may 
be connected by the addition of a 7 th to the latter; provided, of course, it can be 
resolved afterwards. {See fig. 347.) 



Fig. 345. 




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74 



PROGRESSIONS OP FUNDAMENTAL BASSES. [Chap. XXVIII. 



800. And the harsh effect of the progression in fig. 345 may be considerably 
ibated by the introduction of a 7 th on the first chord. {Figs. 348.) 

Fig. 348. 




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801. The inverted forms of all these progressions may be used with as good, 
and often better, effect than the direct forms. Indeed, many progressions in- 
tolerable in their original shape become agreeable, and even beautiful, by inversion, 
and a judicious introduction of dissonant intervals. 

302. It would hardly be possible to devise any progression more revolting to 
the ear than that in fig. 349 ; and yet fig. 350, though essentially the same, must 
be received as an example of good though rapid modulation. 



Fig. 349. 



Fig. 350. 




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The art of connecting chords together is generally used subserviently to some musical 
idea — to some melody, or passage of melody, which is to be clothed with harmony, combined 
with some other passage, or otherwise musically treated. 

In the mind of a practised musician, melody and harmony may be said to be insepusNe: 
it is hardly possible for him to exercise his invention in the one, without some reform* to 
the other. Nevertheless, he is often called upon to harmonize melodies or passages of melody 
not of his own invention ; and, indeed, the power of doing this is indispensable not *uKj ss 
a means of study but as an accomplishment. 

No law of universal application exists, no recipe can be given for "putting a bass to* a 
musical passage. The progressions of melody are infinitely various; nay, each individual 
melody may be grafted on a great variety of roots and fitted with a far greater variety of 
basses; and the selection from these must depend on the experience and taste of the 
harmonist. Certain general principles, however, exist, by which this selection may be ren- 
dered more easy. 

The consideration of these must be preceded by a few brief explanations on the subject 
of Rhythm, 



-\ x v» *. * 



75 



CHAPTER XXIX. 

Rhythm. 

Of the pleasure afforded by music, time is an element no less important than time; the 
lays* and aoetnt of a note are as much worthy of consideration as its pitch. A succession of 
wmeasured, unaccented musical sounds may hare (irrespective of their timbre or quality) a 
certain Tague beauty ; such sounds, howorer, take little hold on the attention or the memory. 
Whereas the measured reiteration even of the same sound (as in the case of the drum, tam- 
barina> triangle, &c.) is always heard with satisfaction and even pleasure. When strains, 
witbotat any very obvious rhythm or measure, do produce a pleasurable effect, it will generally 
b# fatad to arise from the hearer imagining for himself some law, and making allowance for 
departures from it ; as in those well known effects, rattentando, aeceUerando, tempo 
Sec. The ear has been elegantly compared, in estimating music professedly un- 
fiiytfcmical, to an elastic rule, in which the absolute sizes of the divisions may yary infinitely, 
imt their proportions remain always the same. 

808. The word "passage" is used in much the same sense in relation to Music 
aa to language; being understood generally to mean a succession of notes (as of 
words) presenting, in their connexion with, and dependence on, one another, some 
idea more or less complete in itself. 

304. A succession of musical passages, connected together according to certain 
principles, is said to form a movement. 

305. A movement is divisible into periods; a period into sections; a section 
into phrases ; and a phrase into feet. 

306. In a long-metre psalm tune we have an example of the most simple and 
symmetrical form of "movement." Fig. 367 is divisible into two periods, four 
sections, eight phrases, and sixteen feet. 

307. Musical notes, in respect to rhythm, are distinguished as accented and 
unaccented ; and they take their places in a bar, or measure, accordingly. Every 
bar is divisible into times or beats ; the accented notes occupying the strong times 
or down beats, — the unaccented, the weak times or up beats. 

308. A bar of music may consist of alternations of down and up beats (strong 
and weak times), or of one down beat followed by two up beats — literally, a side 
beat and an up beat. In the former case, the bar is in duple time; in the latter, 
in triple time. 

Quadruple or common time of four beats is essentially the same as duple. 

309. A foot is generally, though not always, of the same length as a bar, but 
rarely corresponds with it in accent. Every bar begins with a down beat; almost 
every phrase begins with an up beat ; so that a bar rarely contains an entire foot, 
but consists usually of the end of one foot and the beginning of another. 

See fig. 367, where the letters ft. mark the limits of the first foot. 

The first foot begins before the. first, and the last foot ends after the last complete bar. 



76 RHYTHM. [Chap. XXIX. 

310. A musical foot differs from a poetical foot in the fact, that whereas the 
number of syllables in the latter is small, and the modes in which they can be 
arranged not very various, the number of notes in the former is unlimited, and the 
modes in which they can be arranged, infinitely various. 

311. A. phrase consists generally of two, sometimes of three feet. 
See fig. 367, where the letters ph. mark the limits of the first phrase. 

312. A section consists of at least two — generally of more than two — phrases. 
See fig, 367, where the letters sec. mark the limits of the first section. 

313. A period consists of at least two — often of many more than two — sections. 
See fig. 367, where the letters per. mark the limits of the first period. 

314. In the higher classes of musical movement, the rhythmical divisions are 
much less strongly marked than in simple melody, like fig. 367 ; since a phrase 
may be extended, a section contracted, or one phrase or section be made to begin 
before another is ended. Nevertheless, some law of proportion will be found to 
prevail in all well constructed movements, the section having generally a relation 
to the phrase similar to that of the phrase to the foot ; such relation being per- 
ceptible even between the period and the section, and between the entire move- 
ment and the period. 

It may be convenient to caution the student that he will sometimes find the word pforatt 
used in the sense ascribed above to the word section, and even to the word foot. 



77 



CHAPTER XXX. 



Harmonizing. 



315. It has been already remarked, that "the possible number of changes of 
root to the same note depends on the number of combinations of which that note 
may form part ;" and that " this number is great." {Par. 212.) 

316. Thus, an individual note Do may form part of the following combinations, 
and of the various inversions of which they are susceptible ; all in the scale of Do, 
or some scale easily connected with it, — such as its relative minor, dominant, or 
nbdominant. 



Fig. 351. 




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317. Here we have four distinct fundamental basses to Do, and one on which 
it forms a discord by suspension ; three of these basses, (Do, Fa, and La) will bear a 
common chord with or without a 7 th , the 7 th in two (Do and Fa) being either major or 
minor; while another bass (Re) to which Do is itself the 7 th , may bear a major or a 
minor 3 rd . Of each of these bass notes there are at least two inversions ; making 
upwards of fifty combinations of which this single note Do may form a part. 

318. But as a single note does not constitute melody, so a single chord cannot 
be said to make harmony: harmony results from a succession of chords ; and unleps 
it can be known by what note or notes Do is followed, or preceded, whether it is 
at the beginning, middle, or end of a phrase, it will be impossible to select the 



78 



HARMONIZING. 



[Chap. XXX. 



root most fitted to it. And as in harmonizing a single note reference must 
be had to the phrase of which it forms part, so in harmonizing a single phrase 
we must consider its relation to the section, period, and even the entire melody or 
movement to which it belongs. 

319. It is usual to accompany the last foot of a period or of a section (some- 
times even of a phrase) by an harmonic figure, called a cadence or close. 

320. A cadence may be perfect, imperfect, or plagal. 

321. A perfect cadence is formed by the progression of the chord of the 
dominant (with or without the 7 th ) to that of the tonic. (See figs. 356 and 357.) 

322. An imperfect cadence is formed by the progression of the chord of the tonio 
to that of the dominant. (See fig. 358.) 

323. A plagal cadence is formed by the progression of the chord of the nit- 
dominant to that of the tonic. (See fig. 359.) 

The plagal differs from the imperfect cadence only by its place in the scale. (Compart 
figs. 35S and 359.) 

324. The first chord of a cadence should be sounded on an unaccented beat, 
the second on an accented beat. (Compare par. 149.) 



Fig. 356. 



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325. The term cadence (from cado f to fall) refers to the root of the first of the two 
chords of which it is composed, which (see the above examples) falls a fourth or fifth. 
A cadence is said to be interrupted when the ear is disappointed of the progression 
or resolution natural to the first chord. An interrupted cadence, therefore, is a cadence 
910/ made ; since the root rises (one degree), instead of falling. (See fig*, zoo and XL) 




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Another derivation of cadence is suggested by the motion of the hand, which in beating 
time to a cadence, falls at the second chord. 

326. It rarely happens that all the sections of a melody end with the same 
cadence, or in the same scale. Almost every melody, however simple, contains or 
suggests modulation. 



fJmr.XXX.] 



HARMONIZING. 



79 



827. The most common modulation, from a major scale, is that into the scale 
jf the dominant, the luMominant, or the relative minor ; also, into the scale of the 
dative minor of the dominant and ^dominant. 

328. Modulation may be made in an almost infinite variety of ways ; especially 
ital, or transient modulation. But when a section ends in a scale different 

from that of the whole melody to which it belongs, it is usual to accompany the 
list foot by a perfect cadence in that (different) scale, whatever it may be. 

329. Some of the most obvious and short ways of conducting the common 
modulations named above (par. 327) are exhibited in figs. 362, 363, 364, 365, and 366. 
Each modulation terminates with a perfect cadence. 



Fig. 362. 




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880. The most obvious bass notes with which to accompany a phrase within the 

Units of any particular scale, are the 1 st , 4 th and 5 th of that scale, and, of course, 

their inversions; since "in the triads of" those notes "is contained every note of the 

scale to which they belong" (par. 25); and " from these three triads the scale" is 

even said to be derived. Practically, it is worthy of remark that one or other of 

theft notes (the 1 st , 4 th or 5 th ) will serve as a root to any note in the scale." 

(See par. 26 and fig. 12.) 

331. In the use of these or of any other notes as roots, regard must be had to 
the order in which they follow one another, — a subject on which much has been 
said in Chap. XXVIII. In respect to the choice of inversions, two points have to 
be considered; the combination of each particular bass note with the note or 
notes of the melody to which it is to be set; and the progressions of the notes 
of the bass itself considered as a melody. 

332. As respects the former of these considerations, no rules or directions will 
supply the place of judgment and taste, the result of careful study of good models: 
.as respects the latter, the bass differs from any other part only admitting a greater 
number of large intervals ; if, however, those intervals follow in too rapid succession, 
the bass will be difficult of execution and disjointed in effect. 



80 



HARMONIZING. 



[Chap. XXX.: 



An examination of the three different basses under fig. 367 will show how far the principles - 
laid down in the foregoing pages have been carried out in practice. 

333. Fig. 367 ends, as it begins, in Do; the last foot forms the perfect cadence 
of Do. » 

334. The first period ends in Sol (the dominant of Do); the last foot is the^ 
perfect cadence of Sol. 

335. The first section of the first period ends in Do; the first section of the 
second period in Re (minor); the last foot of each is the perfect cadence in each of 
those scales. 

336. We are thus far assured of certain points to which the progressions in 
each individual section must necessarily tend, and have reference. Let us examine 
each individual section, with reference to the roots. 

The notes are numbered 1, 2, &c, and the basses lettered A, B, &c, for reference. 

337. Of the first section — 

Note 1 may be treated either as the 5 th to Do, or the 8 TO to Sol. Note 2 is the 
8™ to Do; 3, the 5 th to Sol; and 4 the 3 rd to Do. Note 6 may be treated as the 
5 th to Fa (see B) or the 4 th to Sol (see A and C); in the latter case it forms a discord 
by suspension, being resolved by note 7, the 3 rd to Sol, and prepared by note 5, 
considered either as the 5 th to Fa (see A), the 3 rd to La (see B); or the 8™ to Do Caee C.) 




Fig. 367. 
1 2 3 



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HARMONIZING. 



81 



838. Of the second section — 

Note 1 is the 3 rd to Do; 2, the 5 th to Sol; 3, the 3 ri to Sol (see B and C), which 

the next bar becomes the tonic, or the 5 th to Mi (see A) (the relative minor of 

?.) On note 4 commences (m A and B) the modulation with which the section 

a -; it is first the 3 rd to La and afterwards the 7 th to ite, being resolved on 

5, which is the 3 ri to SW. Notes 7 and 8 form the perfect cadence in Sol; 

dominant Re, being preceded (in A and C) by the subdominant, Do, with the 

|ftt-called) added Sixth and Fifth (par. 108), the dissonant note of which (Sol) is pre- 

in the harmony to note 5. 

339. Of the third section- 
Note 1 is the 5 th to Sol, which can be distinguished at once as the dominant of 

___ original scale by the introduction of the 7 th (Fa %) (see C). Note 2 is the 8™ to 
Do, or the 3 rd to La: and note 3, the 5 th to Sol, if note 4 be the 3 ri to Do (see A 
miC); or the 8™ to Re, if note 4 be the 8™ to Mi (see B). Note 5 is best accom- 
panied by the chord of the (added) Sixth on Sol the subdominant to Re minor, 
with the perfect cadence of which the section ends. 

340. Of the fourth section — 

Note 1 is the 5 th to Sol; 2, the 3 rd , and 3 the 8™ to Do; note 4 is the 3 ri to Re, 
and afterwards the 7 th to Sol (see A and B), being resolved on note 5, the 3 rd to Do. 
The fourth section, second period, and entire melody end with the perfect cadence 
to Do. 



2 3 4 5 



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INDEX. 



PARAGRAPH 

Accidentals in Figuring 36 

Cadence or Close 319,326 

Cadence, imperfect 322 

interrupted 325 

perfect 321 

plagal 323 

Common chord 18, 19, 27 

arrangement of. 29, 31, 33 

Concord 83 

Consecutive fifths 46 

when allowed 61 

octaves 46 

Chords, connexion of 66 

Discord 83 

by suspension 84, 88 

double 87 

resolution of 89 

Fundamental 126 

of the Seventh 126 

■ different kinds of 130 

Dissonances, percussion of 82 

preparation of 81, 93 

resolution of 74, 75 

False relations 60 

Fifth, augmented 268, 278 

imperfect * 141 



PARAGRAPH 

Figured basses 34 

Fourth, pluperfect 141 

diminished 269, 278 

Foot 309, 310 

Fundamental basses, progression of, 291, 295, 

296, 297, 298 

Harmonics 5,8 

Harmonic chord 4 

Intervals 10 

—-anomalous 13 

augmented 228 

chromatic 225 

consonant 11, 14 

diatonic 227 

diminished 228 

dissonant 11, 73 

Inversions of the Triad 96 

Licences in resolution of Seventh, 194, 198, 202 

— — — first inversion of 199 

second inversion of 200 

third inversion of 201 

Line after a figure 94 

Modulation 326, 327, 328, 329 

Motion, contrary 43 

oblique 43 



84 



INDEX. 



PARAGRAPH 

Motion, similar 43 

parallel 44 



Movement 304, 305 

Ninth 78, 79 

Ninth and Seventh, fundamental discord of 216 

first inversion of 241 

second inversion of. 248 

— — — third inversion of 253 

fourth inversion of. 258 



diminished, resolution of 233 

diminished, fundamental discord of 236 

Notes, accented and unaccented 307 



Octave, diminished 267, 276 

Parts 40 

crossing of 66 

motion of 42 

Passage 303 

Pedal points 287 

Period 313 

Phrase 311 

Prime 5 

Radical bass 24 

Bhyfchm 314 

Root 24 

changes of, on one bass note 211 

Scale, derivation of 26 



PARAGRAPH 

Section 312 

Second 77 

augmented 234 

Sequence 68, 69 

tonal 70 

real 71 

Seventh 76 

major 156 

diminished 235 

discord of dominant 131 

figuring of 137 

■ resolution of 143 

preparation of 148 

interrupted resolutionof 207 

first inversion of 165 

second inversion of. 178 

■ third inversion of 188 



diminished, discord of 245 



Sixth, augmented 270, 279 

added 108 

Sound 1, 2, 3, 4 

String, division of 6,7 

Suspensions on inversions 118 

Time, duple and triple 306 

Third, diminished 271,285 

Triad lft HI 

first inversion of. 98 

second inversion of 109 

Unison 41 

augmented 266,276 



EDITED BY JOHN HDLLAH. 



Part Music. Class A. 

For Soprano, Alto, Tenor, and Bass Voices. 

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

Secular Pieces. 



COKTADIIHG 



damfc. 



National Anthem, God save the Queen. 

Full Anthem, Lord for Thy tender, Farrant. 

The Hundredth Psalm, With one content. 

Full Anthem, OLord theMmker. Kixo HbnbtYIII. 

Sanctus, Holy Lord God of Host*. Tallis. 

Responses to the Commandments. Talus. 

The Hondred and Forty-ninth Psalm. 

Motet, I will gire thanks. Palestrina. 

Chorale, Since on the Cross. Martin Lutsbr. 

Fall Anthem, God is gome up. Dr. Croft. 

Psalm, JFhen as we sat in Babylon. 

Motet, be joyful. Palestrina. 

Psalm, Ye Gates, lift up four heads. 

Evening Hymn, The Dag is past. John Hullas. 

Hymn, Thou that from Thy Throne. Haydn. 

Psalm, Venite, exultemus Domino. Tallis. 

Motet, Thou art beautiful. Giovanni Crocb. 

Hymn, Lord ! another Day isjlown. M. Haydn. 

Psalm, The Lord I will for ever bless, H. Lawks. 

Anthem, Praise the Lord, Jerusalem f J. Clarks. 

Canon, Gloria Patri. Purcbll. 

Sanctus, Holy, holy. Crkyqhton. 

Motet, Be not Thou far from me. Palestrina. 

Anthem, Hide not Thou thy Face. R. Farrant. 

Hymn, Jesu, Lord of Heavenly Grace. CLbjunb. 

Quartette, Give ear, God. Himmbl. 

Anthem, Praise the Lord, my Soul ! W. Child. 

Motet, Blessed be Thou. Antonio Lotti. 

Hymn, Forth from the dark, Rousseau. 

Psalm, Almighty God, who hast. Fords. 

Anthem, I will arise. Robert Crbyghton, D.D. 

Motet, Sing to the Lord in joyful strains. Dr.Tyb. 

Chorus, Hear my prayer. Michael Haydn. 

Psalm, King t eternal and divine / Dr. Croft. 

Hymn, Oh, God of Truth. B. Rogers, Mas. Bac. 

Qaartette, remember not the Offences. Rossini. 

Hymn, Give to us Peace. Russian Mblody. 

Anthem, Thou knowest, Lord. Purcbll. 

Chorus, Amen. Dr. Cooks. 

Hymn, Sweet day, so cool, so calm. H. Dumont. 

Motet, Go not far from me, O God. Zingarslli. 

Anthem, how amiable. Richardson. 

The Hundred and Forty-Eighth Psalm. J. Clarks. 

Anthem, Almighty and everlasting God. Gibbons. 

Canon, Awake, thou that steepest. W. Horslby. 

Chorus, Hallelujah. Dr. Boycb. 



dtcular. 



Dm. Arnb. 

MadrigaL Alt ye vena Music sssc Donato, 
MadrigaL Bard by a FmnUsmn, Waklbrxt. 
Glee, 1> Spa tted Snakes (Shakspeaxe). Stsybns. 
Madrigal, Flaw, O my Tears. Brnnbtt. 
MadrigaL IV Waits. Sat ills, 16Q7. 
Glee, Coma lei us all a Maying go, Lcffman 

Attbrbury. 
Song in Honour of Peace, Freemen, rejoice! 

Purcbll. 
Part Sons;, Lang may Life. 
Glee, Hail, hollowed Fane, Lord Morninotox. 
Glee, CraUed Age and Youth. R. J. S. Stbybn*. 
MadrigaL In going to mylomeiy Bed. R. Edwards*. 
MadrigaL Ah, me! Fsucb Anrrio. 
MadrigaL Nymphs of the Forest. W. Horslbt, 

Mas. Bac. 
Fireside Song, O never fear, though Rain bo 

fulling. 
Holiday Songs. No. I May Dam. Nbithabd. 
Solfeggio. Scarlatti. 

MadrigaL Lady, see, on every side. Luca Marbnbio. 
Glee, Howsleep the Brave ! Dm. Brnjamin Cooks. 
Choras, Hark, the Village Maids. Csbrubini. 
MadrigaL All hail, Britannia J Antonio Lotti. 
Glee, Upon the Poplar Bough. Stbphbn Paxton. 
Madrigal, Since first I saw your face. T. Fords. 
Choras, How glad with smiles the Vernal Memt 

Gluck. 
Grotesque Madrigal, Sing a Song of Sispenee. 

G. A. Macfarrbn. 
Glee, Happy are they. Stephen Paxton. 
MadrigaL See, from his Ocean bed. V. Ruffo, 
Part Song, Day-break. I. Moschblbs. 
National Song, The hardy Norseman. Pbarsall. 
Madrigal, Come again, sweet Love. J. Dowland, 

Mus. Bac. 
Glee, In Paper Case. Dr. Cooks. 
Holiday Songs, No. II. Harvest Time. 
Glee, Thy Voice, Harmony. Samuel Webbr. 
Glee, Awake, Eolian Lyre ! John Danby. 
Part Song, My Lady is as fair as fins. J. Bknnbt. 
Choras, Sing loud a joyful Strain. Gluck. 
Madrigal, April is in my Mistress* Face. Thomas 

Morlby. 



Score, 9#. each Volume, cloth. Sacred or Secular. 

Voice Parts (Soprano, Alto, Tenor, and Bass,) 8#. each. Sacred or Secular. 

Ditto ditto 5s. each. Sacred and Secular, bound together. 

In Numbers (1 to 6) Score, 2^. 6d. ; Voice Parts, Sd. each. 



EDITED BY JOHN HULLAH. 



Part Music. Class A. 

For Soprano, Alto, Tenor, and Bass Voices. 

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

Secular Pieces. 



CONTAINING 



dacrefc. 



Hymn, King of King* I Kreutzer. 
Double Chant, Magnificat. Dr. B. Cooke. 
Responses, Kyrie eleeiton. Dr. W. Child. 
Christmas Hymn, come, ye FaithfuL 
Canon, Hotanna in excelsis. George Bero. 
Chorus, Amen. Neukomm. 
Anthem, Lord, grant the King. Dr. W. 

Child. 
Canon, Ut queant laxis. Harrington. 
Sanctos, Holy Lord God of Hosts. Rogers. 
Motet, Why do the Heathen rage ? Palestrina. 
Chant, Exatiabo Te, Domine. Humphrey. 
Motet, Plead Thou my cause. G. Cboce. 
Motet, Ponder my words. Zinqarf.lt J. 
Hymns for Morning and Evening. Clarke. 
Canon, Thou shatt show me. Dr. Calloott. 
Anthem, My God, look upon me. Reynolds. 
Anthem, Wherewithal shall. Alcock. 
Hymn, Saviour, is thy promise fled ? HORSLEY. 
Introit, most merciful God. John Hullah. 
Hymn, Praise the Lord of Heaven. Gossec. 
Sanctus, Holy Lord God of Hosts I Bassanl 
Anthem, We wiU rejoice. Dr. Croft. 
Canon, Lord, in Thee have J trusted. Paxton. 
Anthem, Try me, God. Dr. Nares. 
Canon, Lord, teach us to number our days. 
Chorus, Praise ye the Lord. Brassettl 
Motet, J wiU remember. Giovanni Croce. 
Hymn, Peace. M. Hadyn. 
Canon, Hallelujah. Elway Bevtn. 
Psalm, AU People. Old Hundredth Tune. 
Canon, Praise the Lord. J. W. Calloott. 
Anthem, Behold, now praise. Rogers. 
Anthem, The Lord hear Thee. Dr. J. BLOW. 
Canon, Hotanna. T. F. Wat.mtbt.ey. 
Motet, Help us, God. F. Durante. 
Chorale, The Day must come. N. Decius. 
Canon, Hear me. W. Horsley, Mus. Bac. 
Sanctos, Holy Lord God. O. Gibbons. 
Motet, Let all the people praise thee ! Palestrina . 
Chorus, Blessed be God! Dr. Greene. 
Anthem, God, Thou art my God 1 H. Purcell. 
Motet, Mock not God's name. Dr. Tye. 
Motet, The voice of joy and health. JANNACONI. 



Secular. 

Madrigal, The joyous Birds. Bast. Spontone. 
Glee, Here in Cool Grot. Lord Morntngton. 
Grotesque Madrigal, Girls and boys come out to 

play. G. A. Macfarren. 
Glee, Swiftly from the Mountain's brow. Webbs. 
Part Song, Our Native Land. G. Rbxchabdt. 
Part Song, Like to the Grass. J. Benedict. 
Glee, Ode to Spring. Stephen Paxton. 
Madrigal, Come, Shepherds. Bennett. 
Glee, Hark, the Lark. Dr. Cooke. 
Haymakers' Glee, Come, my friends. Horsley. 
Glee, Oh i how sweet. Sir John Rogers. 
Canon, Long live the Queen. Dr. Boyce. 
Ranz des Vachez, Come, Shepherds. Grast. 
Dolce Domom. [Lat. & Eng.] Reading. 
Glee, Thyrsis, when he left me. Dr. Calloott. 
Glee, Which is the proper est day to sing? Abne. 
Glee, Albion, thy sea-encircled isle. Dr. Cooke. 
Part Song, The Good Morrow. Hullah. 
Glee, Breathe soft, ye winds. S. Webbs. 
Chorus, Amid the din. Gluck. 
Madrigal, Who wiU bring back to me my heart f 

Giaches de Vert. 
Part Song, Hark, hark, a merry Note J hear. 

German Part Song. 
Madrigal, Thyrsis, steepest thou? J. Bennbt. 
Part Song, Unto the merry. Italian Air. 
Part Song, Dance we so gaily. F. Schubert. 
Glee, Blow, blow, thou winter wind. B. J. 8. 

Stevens. 
Part Song, Awake, sweet love / J. Dowland. 

Part Song, 'Twos on a bank of daisies sweet. 

John Hullah. 
Glee, From Oberon in fairy land. R. J. S. 

Stevens. 
Madrigal, Thus saith my Chloris bright. JOHN 

Wilbye. 
Part Song, Now, now, I needs must part, John 

Dowland. 
Glee, Happy are we met S. Webbe. 



Score, 9s. each Volume, cloth. Sacred or Secular. 

Voice Parts (Soprano, Alto, Tenor, and Bass,) 3*. each. Sacred or Secular. 

Ditto ditto 5*. each. Sacred and Secular, bound together. 

In Numbers (7 to 12 Score,) 2s. 6d. ; Voice Parts, Sd. each. 



EDITED BY JOHN HULLAH. 



Part Music. Class B. 

In Score for the Voices of Women and 

Children. 



dacrttt. 

National Anthem, God save the Queen. 

Bound, Hallelujah. Dr. BoYCE. 

Motet, Show me Thy wag*. Palestrina. 

Quartet, Not unto us, Lord! Saliebi. 

Twenty-third Psalm, My Shepherd is the Lord, 

Hound, Come, let us strive to Join. 

Motet, Behold, now praise. BlENAlHS, 

Psalm, It is a good. St. John's Tune. 

Hymn, Lord, dismiss us with Thy blessing. 

Round, Absalom, my Son. Charles Kino. 

Motet, Servants of God. CONSTANT Barbice. 

Canon, From everlasting. 8. WEBBS. 

Motet, Hear my crying, God. PALESTRINA. 

Psalm, Jehovah, Thou. St. James's Tune. 

Motet, Prostrate before Thee. CARAFA. 

Bound, all ye works of the Lord, 

Hymn, Stand up and bless the Lord. IMMLER. 

Verse, He hath put down. PALESTRINA. 

Double Chant, Benedictus. 

Psalm, My voice went up. St. Mary's Tune. 

Hymn, Christ, whose glory Jills the skies. 

Chorale, Great God I Luther. 

Hymn, The Midnight Cry. G LASER. 

Canon, Be merciful unto me, God I JACKSON. 

Canon, Unto Thee, God. Hayes. 

Hymn, Great God of hosts. Pleyel. 

Trio, And His mercy is on them. PALESTRINA. 

Hymn, Thee wiU I love. HOFMEISTEB, 

Bound, sing unto God. Six Voices. 

Bound, I will always give thanks. Six Voices. 

Bound, Be glad, ye righteous. Four Voice*. 



Secular. 

Bound, May-Day. W. Horsley, Mrs. Bac. 
Glee, Huntsman, rest! Dr. Arne. 
Fugato. From Les Solfeges fltalie. 
Madrigal, Why do you sigh I John Bennet. 
Part Song, Child of the Sun ! Ebeutzeb. 
Bound, Hot Cross Bunns I L. Attebbuby. 
Glee, Though I soon must leave Thee. G. Bebo. 
Bound, Hail, green Fields. Dr. Green. 
Solfeggio. From Les Solfeges d*Italie. 
Glee, The Load Stars. W. Shield. 

Bound, Prythee, do not chide me so. Mozart. 

Madrigal, Dear Pity. Wilbye. 

Part Song, The Sun-beams streak. Pohlenz. 

Bound, When the rosy Morn appearing. 

Bound, Weep o'er his Tomb. HAYES. 

Bound, See where the Morning Sun. MOZART. 

Glee, Come, follow me. Danby. 

Part Song, Gentle Moon. 

Bound, Go, Gentle Breezes. 

Canon, The flowers their buds are closing. Mo- 
zart. 

Madrigal, Come, sprightly Mirth. John Hilton. 
Canon, Heigh oh, to the Greenwood. W. Bybd. 
National Song. Rule, Britannia. Dr. Arne. 
Bound, Three blind Mice. 



One Volume of Sacred, and One of Secular, Pieces (3«. each, cloth). 

In Numbers, I. to VI., Sd. each. 



EDITED BY JOHN HULLAH. 



Part Music. Class C. 



In Score for the Voices of Men, 



dacrett. 

National Anthem, God save the Queen. 

Canon, Non nobis, Domine. W. Byrd. 

Canon, Amen. Dr. Cooke. 

The First Psalm, How blest the man. 

Bound, Jerusalem / Bosingraye. 

Sanotus, Holy Lord God of Hosts. J. CLARKE. 

Hymn, And now the Sun*s. Berner. 

Psalm, My soul. St. Bride's Tune. 

Bound, Glory be to God on high. Dr. Botce. 

Hymn, God I that modest. Hullah. 

Bound, Hallelujah. Dr. Hates. 

Verse, Jehovah, Jehovah ! Spaeth. 

Chant, Cantate Domino. 

Hymn, In sleep*s serene oblivion laid. FRECK. 

Canon, Gloria in excelsis. 

Psalm. Buckxersbury Tune. 

Hymn, Soft Slumbers. Hxller. 

Canon, Haste thee, God. Cirri. 

Hymn to the Creator, Heaven and Earth. 

Trio, He hath filled the hungry. Palestrina. 

Bound, Lord! how are they increased. 

Canon, I will praise. Dr. Hates. 

Bound, / will be glad. Byrd. 

Chorale, Thou, to whose all-searching sight. 

Hymn, Who are these. Naegeli. 

Motet, Draw nigh unto my soul. Palestrina. 

Canon, Not unto us, Lord. Dr. Hates. 

Trio, Let Hymns of praise to Heaven ascend. 

Hymn, Lord, now we part. Bolle. 

Anthem, Make a joyful noise. Carissdu. 

Evening Hymn, Glory to Thee, my God. 



Secular. 

Part Song, The Smith. Kreutzer. 

Bound, Past Twelve o'clock. For Six Voices. 

Bound, Row the Boat. For Three Voices. 

Bound, Lets have a Peal. For Nine Voices. 

Glee, St. Martin's Bells. Lidarti. 

Part Song, How exquisite. De Call. 

Glee, Halcyon Days, Dr. Cooke. 

Bound, With Horns and Hounds. L. Atter- 

burt. 
Bound, Half an hour past Twelve. Marella. 
Part Song, The Wa/fcry is sounding. H. Wer- 
ner. 
Glee, Come, come, all noble souls. Sogers. 
Glee, Fairest Isle. PuRGELL. 
Catch, To the old long life. Webbe. 
War Song, Clad in spring tide beauty. 
Glee, When for the world's repose. Earl of 

MORNINGTON. 

Bound, Come, let us aU a maying go. Hilton. 
Duet, How sweet in the woodlands. Harrington. 
Catch, Would you know my Celia's charms. 

Webbe. 
Glee, How sweet, how fresh. Stephen Paxton. 
Bound, Well done and quickly done. Six voices. 
Bound, Come, let us sing. Seven Voices. Buffo. 
Bound, White sand and grey sand. Three Voices. 
Bound, Hot mutton pies. Three Voices. 
Glee, The cloud-capt towers. B. J. S. Stevens. 
Glee, You Gentlemen of England. D. Callcott. 
National Song, Rule, Britannia. Dr. Arne. 
Yawning Catch. Dr. Harrington. 



One Volume of Sacred, and One of Secular, Pieces (8*. each, cloth). 

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