xxiv

SUBSCRIBERS.

Watts, Mr. Cirencester Place

Webster, Mr. R. Professor of Music, Glasgow

Weekes, Mr. T. E. Professor of Music, Stonehouse,
Plymouth

Weiss, Mr. Music-seller, Liverpool

Wellard, Mr. Music-seller, Canterbury

Wellman, Mr. Professor of Music, Southampton

Wells, Mr. Professor of Music, Poplar Cottage, Brent-
ford Road

West, Mr. Henry, R.A.M.

2 Copies

West, W. A. Esq. Paris

Westervelt, Mr. Amateur, New York

Whall, Mr. B. Organist, Lincoln

White, Messrs. Music-sellers, Bath

White, Mr. Professor of Music, Wakefield

Whitehead, Mr. Organist of St. Mary de Crypt,
Gloucester

Wholmes, Mr. J. Organist, Charlton, Kent

Wickens, Mrs. Music-seller, Oxford

2 Copies

Wicking, Mr. W. C. Professor of Music, London

Wilder, Charles, Esq. Eton College

William, Mr. Professor of Music, Glasgow

Williams, Miss, Organist of St. Ann, Limehouse

Wilkins, Mr. Organist, Ilfracombe

Wilkinson, Miss E. M. Professor of Music, 21, Old
Cavendish Street, Cavendish Square

Wilkinson, Mr. James, Professor of Music, 3, Theberton
Street, Islington

Willis, Mr. Brewer Street, Golden Square

Wilson, Mr. William, Organist, Unitarian Chapel,
Leeds

Wilson, Mr. M. C. 22, Connaught Square

Wilson, Mr. W. Organist of St James's, Garlick Hill

Wilson, Mr. W. B. 21, Stepney Causeway; Organist of
St. Mary, Greenwich

Wilson, Mr. Walter, Organist of St. Mary's and of
Christ Church, Scarborough

Windsor, Mr. J. W. Bath

Winter, Mr. Organist, Long Sutton

Woakes, Mr. Professor of Music, Cheltenham

Wolff and Co. Messrs. Cornhill

Wood, Alfred, J. Esq. Surgeon, Gloucester

Wood, Mr. T. Music-seller, Cambridge

Wood and Co. Messrs. Edinburgh, 3 copies

Woodward, Mr. Music-seller, Cheltenham

Wright, Mr. Organist, Sunderland

Wright, Mr. T. Professor of the Harp, 15, Norton St.

TRANSLATOR'S PREFACE.

COUNTERPOINT may be described as the art of adding one or more parts to a given melody or subject, so as by these additions to form a correct and harmonious whole. It is to musical composition what grammar is to language: and, as it is impossible to understand a language without a knowledge of the principles which regulate the combination of its words, and sufficient practice in the application of these principles; so it is impossible to make any considerable progress in composition, without a knowledge of, and a sufficient practice in Counterpoint.

Counterpoint and composition resemble grammar and poetry;—the contrapuntist is not necessarily a composer, any more than the grammarian is necessarily a poet; but as the poet must of necessity understand grammar to write with any degree of correctness, so must the musical composer necessarily understand Counterpoint, or he will, at every moment, encounter difficulties which he will be unable to vanquish, and fall into errors which will consign his productions to contempt and oblivion, whatever may be their occasional merit.

By the study of Counterpoint, the composer obtains a fulcrum, or point of support, upon which he may at all times safely repose; and, without the help of which, he cannot to give his productions

XXvi

PREFACE.

unity, regularity, nor intrinsic and lasting import-
ance; while, by this study, he will ensure to himself
an inexhaustible treasure of musical forms, analo-
gous in their very nature to the principles of unity
and variety combined.

That the English musical public at length begin
to perceive the paramount importance of the study
of Counterpoint, as the key to composition, is suffi-
ciently obvious from the extensive encouragement
they have given to the magnificent edition of
Albrechtsberger's Theoretical Works, in two vols.
8vo. published by Messrs. Cocks and Co. and to the
series of little Musical Catechisms on Harmony,
Counterpoint, and Fugue, by Hamilton, as well as
from the splendid and almost unprecedented list of
Subscribers prefixed to the present work; a list
which contains no fewer than from six to seven
hundred names, including, besides six ROYAL
PERSONAGES, nearly all the principal Composers,
Organists, Professors, and distinguished Amateurs,
throughout the three kingdoms, as well as many
eminent Foreigners. The conviction of this fact
has led to the translation of the present work by
CHERUBINI,—a name known and venerated where-
ever music has found cultivators and admirers;
a name, in short, which is in itself a sufficient
guarantee of its extraordinary merit.

Emanating from the pen of so distinguished a
composer, so profound a theorist, and so practised
a teacher of his art, every page is, as might be
anticipated, distinguished by lucid and systematic
connection of ideas; and, considered as a whole,
the work is so complete, so well digested in all its
details, and so surprisingly rich in classical and
beautiful examples, that we do not hesitate to place

PREFACE.

xxvii

it among the brightest ornaments of musical lite-
rature, and to predict that it will be universally
looked upon as an imperishable monument of glory
to its illustrious Author.

This translation will, it is hoped, be found a
faithful transcript of the original. Nothing has
been omitted, nothing essentially altered, nothing
transposed. The only changes which have been
made consist—*first*, in the distribution of the work
into books and chapters, for the sake of greater
convenience of reference, and the more easy compre-
hension of it as a systematic whole; and, *secondly*,
the *total omission of the three C clefs*, which are to
be met with in almost every page of the original.
Much experience in teaching Counterpoint has con-
vinced the Translator that these clefs oppose the
greatest obstacle to the progress of students in
general; and that more of the practice of Counter-
point may be acquired by a pupil in three months,
when taught through the medium of the treble
and bass clefs only, than he could acquire in as
many years, if embarrassed from the outset with
these additional clefs. Not that they are to be
considered as useless:—after some little progress
has been made, the pupil should learn them one by
one; and this he will then be able to do with ad-
vantage and facility.

The place of the notes in the great scale of
sounds, or, in other words, their absolute pitch, has
no where been altered; the sounds indicated are
exactly the same as in the original examples;
the translator has only expressed those notes by
means of the treble clef, which, in the original,
were written in the soprano or in the contralto clefs;

xxviii

PREFACE.

and in the bass clef, those which originally stood in
the tenor or C clef, on the fourth line of the stave.
These changes, it is hoped, will render this edition
much more generally useful and acceptable to the
musical public, than if the notation of the original
had been scrupulously retained.

J. A. HAMILTON.

London,
1st May, 1837.

CONTENTS OF VOL I.

---o---

BOOK I.—COUNTERPOINT.

<table><thead><tr><th>CHAPTER</th><th></th><th>PAGE</th></tr></thead><tbody><tr><td>I.</td><td>Introduction.</td><td>1</td></tr><tr><td></td><td>Preliminary Notions.</td><td>3</td></tr><tr><td></td><td>Concords which may be used in strict Counterpoint</td><td>3</td></tr><tr><td></td><td>Discords to be employed in strict Counterpoint.</td><td>3</td></tr><tr><td></td><td>Different kinds of movement, as conjunct, disjunct, similar, contrary, and oblique.</td><td>4</td></tr><tr><td>II.</td><td>Counterpoint in two Parts.</td><td>6</td></tr><tr><td></td><td>First Species—Note against note.</td><td>6</td></tr><tr><td></td><td>False Relations.</td><td>13</td></tr><tr><td>III.</td><td>Second Species in two Parts—two notes against one</td><td>20</td></tr><tr><td>IV.</td><td>Third Species in two Parts—four notes to each semibreve.</td><td>30</td></tr><tr><td>V.</td><td>Fourth Species in two Parts—Syncopations.</td><td>40</td></tr><tr><td>VI.</td><td>Fifth Species in two Parts—Florid Counterpoint.</td><td>49</td></tr><tr><td>VII.</td><td>Counterpoint in three Parts.</td><td>54</td></tr><tr><td></td><td>First Species—note against note.</td><td>54</td></tr><tr><td>VIII.</td><td>Second Species in three Parts—two minims to one semibreve.</td><td>61</td></tr><tr><td>IX.</td><td>Third Species in three Parts—four crotchets to one semibreve.</td><td>70</td></tr><tr><td>X.</td><td>Fourth Species in three Parts—Syncopations</td><td>76</td></tr><tr><td></td><td>Syncopations on a pedal-note, with examples.</td><td>82</td></tr><tr><td></td><td>Second and fourth and third and fourth Species mixed, with examples.</td><td>87</td></tr><tr><td>XI.</td><td>Fifth Species in three Parts—Florid Counterpoint.</td><td>89</td></tr><tr><td></td><td>Examples of the second and fifth Species combined</td><td>90</td></tr><tr><td></td><td>Ditto of Florid Counterpoint in two of the three parts.</td><td>91</td></tr><tr><td>XII.</td><td>Counterpoint in four Parts.</td><td>92</td></tr><tr><td></td><td>First Species—note against note.</td><td>92</td></tr><tr><td></td><td>Examples of the first, second, and third Species in four parts, and various combinations of them</td><td>98</td></tr><tr><td>XIII.</td><td>Fourth Species in four Parts—Syncopations.</td><td>110</td></tr><tr><td></td><td>Examples on Pedal Harmonies in four Parts.</td><td>116</td></tr><tr><td></td><td>Combinations of the second, third, and fourth Species.</td><td>122</td></tr></tbody></table>

XXX

CONTENTS.

XIV. Fifth Species in four Parts - Florid Counterpoint..124
Examples of Florid Counterpoint in two and in
three of the four Parts..126

XV. Counterpoint in five, six, seven, and eight real Parts.127
Example for five voices—note against note..131
Ditto.. florid counterpoint in
four of the parts..132
Ditto in six Parts—note against note..133
Ditto.. florid counterpoint in five of
the parts..134
Ditto in seven parts—note against note..136
Ditto.. florid counterpoint in six
of the parts..138
Ditto in eight parts—note against note..140
Ditto.. florid counterpoint in seven
of the parts..142
Examples of the sixth struck together with the
seventh, and the eighth with the ninth..145
Example for two Choirs in Florid Counterpoint
without any given subject..146

BOOK II.—IMITATION.

XVI. On Imitation generally..150
Imitation in two parts, in similar motion..152
Examples in all Intervals..153

XVII. Imitation by contrary motion..159
Strict or regular imitation in contrary motion..162
Retrograde imitation in contrary motion..163

XVIII. Several other sorts of imitation : as
Imitation by augmentation..167
— diminution..168
— with reversed accents, or by arsin
and thesin..169
Interrupted imitation..170
Convertible imitations..171
Periodical imitation..172
Canonical imitation..173
Example of finite canonical imitation..174
— infinite canonical imitation..175

XIX. Imitations for three and four voices..176
Inverse contrary imitation..186
Example of ditto in eight parts, for two choirs..192

xxxii

CONTENTS.

CONTENTS OF VOL. II.

—o—

EXAMPLES ON FUGUE WITH A PERPETUAL
ANALYSIS.

<table><tbody><tr><td>1. Strict Fugue in Two Parts</td><td>1</td></tr><tr><td>2. Tonal Fugue in Two Parts</td><td>6</td></tr><tr><td>3. Strict Fugue in Three Parts</td><td>13</td></tr><tr><td>4. Tonal Fugue in Three Parts, with One Countersubject</td><td>26</td></tr><tr><td>5. Ditto</td><td>34</td></tr><tr><td>6. Ditto</td><td>50</td></tr><tr><td>7. Chromatic Fugue in Four Parts, with Three Countersubjects</td><td>66</td></tr><tr><td>Remark on the Plagal Cadence</td><td>87</td></tr><tr><td>8. Tonal Fugue, much developed, in Eight Parts, for Two Choirs</td><td>88</td></tr><tr><td>9. Strict Fugue in Eight Parts, for Two Choirs, composed by Joseph Sarti</td><td>168</td></tr></tbody></table>

APPENDIX.

Fifty-three Subjects of various lengths and in different Keys, to serve for Lessons on Strict Counterpoint</td><td>200</td></tr></table>

Twelve Basses for Counterpoints in Eight Parts, and for Two
Choirs</td><td>211</td></tr></table>

2

I therefore recommend the pupil who devotes himself to composition, to read, and even, as often as possible, to copy out with attention and reflection the works of classical composers, and, occasionally, even of those of an inferior grade; to learn from the former how to compose well, and, from the latter, how to avoid falling into their errors. By these observations, often repeated, the pupil will accustom himself to exercise the ear through the medium of the eye, and will progressively form his style, his sentiment, and his taste.

The young composer, who shall have followed the instructions contained in this course of study, when once arrived at fugue, will no longer have occasion for lessons; he will be able to write with purity in any style, and, by studying the forms of the different kinds of compositions, he will easily express his ideas with propriety, and produce whatever effects he may desire.

3

# PRELIMINARY NOTIONS.

## CONCORDS WHICH MAY BE EMPLOYED IN STRICT COUNTERPOINT.

Ancient composers, from Guido d'Arezzo, have admitted only two *perfect* concords, the octave and the perfect fifth; and two *imperfect* concords, the third and sixth.

The former are called perfect, because they do not admit of any alteration without losing their consonant character.

The latter are called imperfect, because they are subject to be altered; that is, they may be major or minor.

### DISCORDS TO BE EMPLOYED IN STRICT COUNTERPOINT.

Discords are the second, the fourth, the seventh, and the ninth. These discords can only be used when prepared by one concord, and resolved by another; unless they are used by transition, of which we shall treat farther on.

The imperfect fifth, and the superfluous fourth or tritonus, were rejected by ancient composers; we must therefore not use them in strict counterpoint, except as passing discords.

*Observation*.—I repeat, once for all, that in saying strict *modern* counterpoint, I only intend to apply the term *modern* to the nature of the modes which are to be employed; but, as to the chords themselves, I have only used those which are met with in ancient authors; that is, the chord of the third and fifth, and that of the third and sixth, and the discords which we have just enumerated. It is only in treating fugue, that the pupil may allow himself a greater degree of latitude.

### ON THE DIFFERENT KINDS OF MOVEMENT.

By the word *movement* we intend to define the progression from one sound or note to another,

B 2

6

Of these three movements, the most elegant is the contrary movement; oblique motion holds the second rank; direct motion ought to be used but little, because it produces inconveniences which we shall explain in the sequel.

We shall here add, that in all the species of counterpoint of which we are going to treat, as well as in Fugue, the pupil should write for voices, and not for instruments. He must therefore conform to the natural compass of the different kinds of voices. He will thus learn to produce effects by voices only —a study of considerable difficulty, and perhaps but too much neglected; and he will afterwards find himself more at his ease when he shall write for instruments, and when, of course, he will no longer be obliged to confine himself within the limits of the voice.

## CHAP. II.

### COUNTERPOINT IN TWO PARTS.

COUNTERPOINT in two parts is the most rigorous of all, either in the ancient system or the modern. The reason of this is simple: the fewer the difficulties to be overcome, the more strict must be the observance of the rules. Two parts only do not present so many trammels as a greater number of parts moving together; so that the severity of this kind of composition diminishes as the number of the parts augments.

#### FIRST SPECIES—NOTE AGAINST NOTE.

##### RULE I.

We must begin with a perfect concord, and also terminate with one; so that the first bar may be either a fifth or octave (or unison), and the last bar

7

must be simply an octave or a unison. We shall here observe, once for all, that by a fifth we also mean a twelfth, and by the octave, a fifteenth, according to the relative distances of the voices which we employ: the same must be understood of all the intervals which may be doubled or even tripled.

RULE II.

The parts must always proceed in concords, avoiding the unison, if possible, except in the first and last bars.

*Observation*.—The production of harmony being the end chiefly aimed at in counterpoint, the unison is prohibited as not producing any. The same objection does not apply to the octave, though it is nearly in the same case as the former; but the difference of effect, which is perceptible between grave and acute sounds, renders it somewhat less devoid of harmony than the unison.

RULE III.

The upper part may sometimes be allowed to cross below the bottom part; this must always be done by means of a concord, and must not last for any considerable time; indeed, this means is only allowed, either to enable us to escape from some case of embarrassment, or to improve the melody of the parts; since, as we have already said, the pupil should at first write for voices only. Ex.

8

The * indicates the places where the upper part crosses below the under part. I advise the pupil, however, to employ this license with reserve.

RULE IV.

Several perfect concords of the same denomination must never succeed one another; consequently, two fifths or two octaves, in succession, are prohibited.

This prohibition is applicable to all kinds of strict composition, whether in two parts or in more.

*Observation*.—A series of octaves renders the harmony almost a nullity; a series of fifths forms a discordance, because the upper part moves in one key, while the lower part proceeds in another.

For example, if to the scale of C we add an upper part which shall form a perfect fifth in each bar, thus:

One part will be in the key of C, while the other is in G. It is from this concurrence of two keys that the discordance of the passage originates; and hence the prohibition of using several fifths in succession—even when the movement of the parts, instead of being conjunct, is disjunct, for the discordant effect will still exist.

Such is one of the inconvenient results of similar motion, which we have before promised to explain.

Consecutive fifths have been and are still tolerated in contrary motion; because, though their nature is the same, the movement causes them to change their species.

9

By this example, we perceive that one is a twelfth and the other a fifth, which changes their nature. Still, however, this license is not allowed in counterpoint in only two parts, particularly in note against note; it is only tolerated between the middle parts, in composing for four voices, when we are embarrassed to find a good progression for the parts.

The pupil may, in works written in the free style, as operas, symphonies, &c., occasionally meet with consecutive fifths; but these licenses are only to be tolerated in such kinds of composition.

## RULE V.

We are not allowed to proceed to a perfect concord in similar motion, except in that particular case where one of the two parts moves only a SEMITONE. This exception is permitted.

### EXAMPLE I—FORBIDDEN PROGRESSIONS.

11

case is different; for, in filling up in the same way by crotchets the spaces marked by the intervals, though there will still result two fifths, one is *imperfect* and the other perfect.

EXAMPLE II.—WITH CROCHETS.

These two fifths are allowed, because they are not of the same nature, and because the discordance, of which we have spoken as resulting from a succession of perfect fifths, does not occur in the present case. The old authors, however, have generally avoided this license in counterpoint in only two parts; and it is only in composition for several parts, that they have employed it in one or other of the middle parts, to escape from some embarrassing progression.

RULE VI.

All progressions ought to be natural or diatonic, as far as melody is concerned; and conjunct movements agree better with the style of strict counterpoint than disjunct progressions. Hence, progressions of a major and a minor second, a major and minor third, a perfect fourth, a perfect fifth, of a minor sixth, and of an octave, are allowed both in ascending and descending. Skips of a superfluous fourth or tritonus, of an imperfect fifth, of a major and minor seventh, are expressly prohibited both in ascending and descending.

*Remark*.—This is a prudent rule; and the ancient masters had the more reason for conforming themselves to it, as they wrote for voices only, without accompaniments. They thus obtained a flowing and correct melody, which the intervals and progressions disallowed would have rendered difficult as to intonation. However, at the present day, this rule is not much regarded in modern compositions.

14

EXAMPLE I.

False relation of superfl. 8ve.

EXAMPLE II.

False relation of dim. 8ve.

The C natural in Ex. I, placed in the upper part of the first chord, is discordant with the C sharp placed in the lower part of the second chord. If on this subject we consult the ear, we must acknowledge that nothing in this case can destroy the impression which the ear has received from the C natural; because it still remains, even at the moment when the sound of C sharp strikes upon it, and thus produces nearly the same effect as if those sounds were heard simultaneously. If we consult reason in its turn, we shall come to the conclusion that the discordance of these two sounds is derived from their want of coherence, and from the false relation which exists between them; since C natural and C sharp belong to two different keys, and the chords in which they are separately included cannot succeed one another, arranged as they are here arranged, unless other intermediate and relative chords, by connecting them together, cause the false relation to disappear. What I have just said with respect to the first example may equally be applied to Ex. II.

To render the effect less harsh in the succession of these two chords, since it is impossible to destroy it altogether, we must endeavour to find some means of weakening it without employing other chords. The means is simple: we must so manage that the part which sounded C natural shall also sound the C when chromatically altered by the sharp or flat.

EXAMPLES.

or else

or else

16

By the assistance of these corrections, the false relation is in part or altogether eclipsed. In the other species of counterpoints, as we shall see, it is still more easy than in this to avoid the false relation of the tritonus.

It now remains to demonstrate how and why the tritonus is a false relation in harmony. What I am about to say applies equally to counterpoint in two or in several parts; and I insert the demonstration here, that I may not again be obliged to speak of it with so much detail.

To explain the cause of this false relation, I shall take the major common chord of G, and cause that of F major to immediately follow it.

The succession of these two chords instantly gives birth to the false relation of the tritonus.

1st. Because the first chord, supposing that it is considered as belonging to the key of C, naturally tends to proceed to the tonic, or to A, its relative minor, and not to the subdominant.

2ndly. Supposing, on the other hand, that this same chord belongs to the key of G, the chord of F natural, which follows it, becomes altogether foreign to it, because the F ought to be sharp, in order that any analogy may exist between these two chords; besides that the F, if it were sharp, ought naturally to carry a chord of the sixth, if taken as a bass note.

3rdly. For the same reason, if we should consider the second chord as belonging either to the key of C, or to that of F, on the first hypothesis it would require to be followed and not preceded by the chord of G; and, in the second case, the B natural, in the chord of G, necessarily and evidently becomes foreign to it; for, by analogy, the B ought to be flat. Thus, therefore, the F and B, being in open contradiction to one another, and through one another, the relation which results is false.

Consequently, all successions of chords, of which one includes F natural, and the other B natural, or *vice versa*, will undoubtedly introduce the false relation of the *tritonus*. We shall give a series of chords which always produce this relation, and which, therefore, produce a very harsh effect upon the ear.

17

RULE VIII.

Except in the first and last bars, we ought, in
the course of the composition, to employ as much
as possible imperfect concords, rather than perfect.
The drift of this rule is to produce harmony rather
by the means of imperfect concords, which are more
harmonious than the others. Still, however, many
imperfect concords of the same sort would plunge
us into the abuse which I have hinted at in Rule VI.
We must therefore learn to intermix with taste and
discernment both perfect and imperfect concords,
in order to give sufficient harmony to the counter-
point. Example:

Subject.

c

18

These examples are conformable to the rules of strict counterpoint of the first species. The imperfect concords are employed with the requisite variety, and more frequently than the perfect concords. The direct, contrary, and oblique motions are properly managed; the false relation of the tritonus is avoided, and the melody always proceeds diatonically, and with facility and elegance.

*Remarks*.—In order to reduce to practice all the rules which we have laid down, the pupil will receive from his teacher a *Melody* or *Subject*, which he will place first in the bass, and on which he will then compose as many different melodies as he can; sometimes writing for a *Soprano* voice, sometimes for a *Contralto* or a *Tenor*. He will then place the same subject in the upper part, and compose several different bases to it.

The melody which the pupil receives from his teacher is sometimes called a *plain chant*, or *Canto firmo*; the part written by the pupil is called the *Counterpoint*.

At the end of this Treatise will be found various *subjects*, suited to all the different species, which will afford the student the means of employing all the resources of Counterpoint.

In placing the *given subject* in the upper part, the pupil must employ that species of voice which is best adapted to it, and sometimes he will be obliged to transpose the subject into some other

* Those who are unacquainted with the compass of the different voices, may consult the Translator's *Catechism on Singing*, published by Messrs. COCKS AND CO.

19

key, if he wishes to use all the different kinds of voices without exceeding their natural compass.

The two last bars of the *subject* ought always to proceed from the second note of the scale or key to the key-note itself. For example, in the key of C, the two last notes must stand thus :—

In the last bar but one, the part which forms the Counterpoint must always be the *major sixth*, and the last note itself the *octave*, if the subject be in the bass; but, if it be placed in the upper part, the last bar but one of the Counterpoint must be a *minor third*, and the last bar itself the *octave*. For example:

Counter-
point.

Given subject
placed in the
upper part.

Subject
given.

Counterpoint.

Before I conclude the first species of Counterpoint, I will add a few words respecting *modulations*; and my observations on this subject will equally apply to every sort of strict Counterpoint.

In any piece we must only modulate into such keys as coincide as to their tonics with the notes of the scale belonging to our primitive or principal key.

Let us first suppose that the original key is C major; we can only modulate in G major, into A, the relative minor, into F major, and into D minor; and even then the key of F must be touched upon in a merely transient manner, because it weakens the impression of the principal key on account of the B♭, which destroys the leading note; the key of D minor must be treated like that of F, and for the same, or even stronger reasons, because it destroys the tonic by introducing the C♯, the leading note of this new key. We may also modulate into E minor, but only in a still more transient manner than into the two former keys, because of the F♯ and D♯, which it introduces. The key of B is prohibited, because the fifth is not perfect.

c 2

25

I shall nevertheless observe, that this way of avoiding either two consecutive fifths, or two consecutive octaves, in two-part Counterpoint, was considered reprehensible by the ancient masters. I am of the same opinion, and think that when two successive strong times are occupied by two fifths or two octaves, no intermediate note placed on the weak time will totally destroy the impression produced by these two fifths or octaves; at least unless the movement be very slow; for then, each time being taken as an entire bar, the weak times may be accounted by the feelings as so many strong times. This reasoning, however, is merely specious, and ought not to be made into a law.

I conclude, therefore, that the present rule can only be employed when we compose in more than two parts, or, at least, that we must but seldom have recourse to it in this species, and then merely to escape from some still greater embarrassment.

I have introduced these remarks and experiments with regard to two fifths and two octaves, less to prove by my examples that they may be saved in some positive way, than to demonstrate the weakness of this rule, which I consider as merely foisted among the strict rules of the ancient classical authors. Notwithstanding this imperfection, however, it may occasionally prove of some utility.

## RULE IV.

In Counterpoint of the present species, we may either have one chord in each bar, or we may introduce two. Consequently, when we have only one chord, though each minim forms a different concord, yet both belong to the same chord.

27

RULE VI.

In this species, whether the counterpoint be placed in the upper part or in the lower part, we may, in lieu of the strong time of the first bar, place a minim rest, provided that the weak time is a perfect concord.

This way is considered as more elegant than if both parts were to begin at the same time.

RULE VII.

In the first species, the skip of a minor sixth is allowed; in this second species it should only be used when the parts, by the nature and elevation of the given subject, come too close together; and we find ourselves embarrassed to separate them otherwise than by this skip. In such cases we are allowed, as in the first species, to cross the parts; that is, to cause one part to pass above or below another.

All other progressions allowed in the first species are so likewise in the present species.

*Remark*.—Here the skip of a minor sixth is in some degree prohibited, because this interval, being more difficult in respect to intonation than any other allowed interval, particularly in ascending, it becomes still more so in this species, where the notes

35

EXAMPLES OF ONE CROTCHET.

EXAMPLE OF TWO CROTCHETS.

EXAMPLE OF THREE CROTCHETS.

RULE IV.

If, in the preceding species of counterpoint in
two parts, we have forbidden the skip of a major
sixth or even of a minor sixth, and those of a tritonus
and false fifth; they are still more strictly prohibited
in the present species, because of the short duration
of the notes, and the little time which is allowed to
the voice to prepare and seize the intonation of
such difficult intervals.

We must also avoid, as difficult in point of intonation, and disagreeable to the ear, the interval

D 2

56

on account of the diapason or compass of the voices,
or because of the bar which follows, instead of
using the common chord in the form 3, we are
5
1

3
obliged to introduce the form 5, or even to omit
1
altogether some member of it. In this latter case,

3 8 5
we may use the following forms: 8, or 3, or 8, or
1 1 1

8 8

5, or 8. As this last form everywhere offers the
1 1
same sound, it produces the same effect as the
unison. We are only allowed to begin in this
manner.

With respect to employing the common chord
in the last bar, these are the forms which we may
1 8 8 5 5

introduce: 1, or 8, or 5, or 8, or 1, as often as pos-
1 1 1 1 1

sible; but it is often difficult, and sometimes im-
possible, to employ any one of these forms when
the subject is in the bottom part; for, in this case,
we must almost always finish by the third and oc-
tave. The ancient composers always ended with
the major third, whatever the principal mode might
chance to be; and the reason which they assigned
for so doing, was that the minor third being much
more imperfect than the major third, the latter was
more proper as a close.

RULE III.

The parts ought always to be at a proper dis-
tance from one another; and the nearer they are
together, the better the effect which will result.

57

There are cases in which this rule admits of excep-
tions; but they ought to occur but seldom, and
should be avoided, unless it becomes impossible for
us to do so. To facilitate the observance of this
rule, in a position of difficulty, we may occasionally
allow an upper part to cross below an under part.

RULE IV.

In counterpoint for three parts, we are not al-
lowed, any more than in two parts, to use hidden
octaves or fifths, either between the extreme parts,
or between an intermediate and one of the extreme
parts.

Sometimes, though very seldom, we may infringe
this rule, as far as regards the intermediate part
only, when the strict observance of the prohibition
would clog the progression of the two parts, or
else give birth to some other still more serious in-
convenience with respect to the next bar.

No exception is allowed with regard to the
extreme parts as compared with one another.

*Remark.*—It is unnecessary to mention here the rule which forbids two *consecutive* fifths or octaves, since this rule is common to every species of composition.

The prohibition of using two *hidden* octaves or fifths between the two extreme parts, also applies to every species of *strict* composition.

In using incomplete chords, we must not intro-
duce the third or sixth in two parts at the same
time. We are not allowed to double either, on ac-
count of their imperfection, and because they would
render the harmony too thin and poor. The double
octave or fifth is permitted in incomplete chords
because of their perfection. This rule is, however,
subject to numerous exceptions; and many cases
occur where, for the sake of good harmony, or a

58

good progression of the parts; or, lastly, to avoid graver errors; we may double the imperfect cords, when we have, without success, tried all possible means of acting otherwise.

EXAMPLES OF THIS RULE STRICTLY FOLLOWED.

RULE VI.

Neither of the upper parts must ever stand in the relation of a fourth to the bottom part; consequently, we can never employ the chord of the fourth and sixth. The fourth between the intermediate part and the upper part is allowed; as, for example, in the chord 3, or in the incomplete common 1, 8 chord in the form 5, such as it may be used in the first and last bars.

RULE VII.

The chord contained in the last bar but one ought always to be complete.

65

RULE VI.

In the present species, or in any of those which follow, we may, in embarrassing situations, as was remarked in the preceding species, occasionally cross the parts; that is, let an upper part pass below an inferior part. This kind of transposition, however, must not last longer than one or two bars at most.

RULE VII.

In the second species of counterpoint in two parts, we were forbidden to immediately repeat the same note in the part which contains the two minimis. This prohibition is continued in the present species, though the rule is subject to an exception, and one which is authorised by the example of classical composers. The exception can only take place in the last measure but one, and no where else; it is allowed, to obviate the inconveniences which would otherwise result from the nature of the given subject, as may be seen in the following example:

The counterpoint arranged in the manner shewn in these two examples, offers on the one hand, at *, the unison on the strong time with the upper part, and the same on the other hand at * * with the bottom part. To avoid these two faults, we shall exhibit two examples in which these inconveniences are not to be found, and yet all the prescribed rules are strictly fulfilled.

F

81

EXAMPLES.

The discord of the NINTH must be accompanied by the third and resolved on the OCTAVE; it may be placed either in the middle or the top part.

EXAMPLES.

RULE III.

When, from the nature of the given subject, from the progression of the harmony, or from the disposition and melody of the parts, it would be impossible to syncopate either with or without a discord, without falling into proscribed inconveniences, we may omit syncopation altogether, or employ a minim rest in the middle of the piece; and, at the beginning, even a whole bar rest.

EXAMPLES.

92

CHAPTER XII.

COUNTERPOINT IN FOUR PARTS.

IF the rules of counterpoint in three parts are not so strict as those of counterpoint in two parts, they naturally are still less rigid, with respect to the counterpoint of which we are going to treat. Indeed, we meet with examples even among the classical composers, PALESTRINO for instance, such as, at the first glance, we are tempted to consider absolutely incorrect, or, at least, as exhibiting too great a degree of license; but the various difficult positions in which these passages occur, and the frequent introduction of them by such great masters, prove that these passages are thus combined under favor of a relaxation in the severity of the rules, a mitigation which, as we have said, is allowable in proportion as the number of the parts increase; hence those examples, which at first appeared incorrect, eventually become authorities.

RULE I.

5 6

The chords 3, 3, being composed of only three members, it is necessary to double one of these members in counterpoint in four parts; thus, in the chord 3, we may in turn double all these members according to the position of the parts; but we should double the octave and the third more often than the unison or the fifth. If we employ either of these chords incomplete, which is allowed, and at times even indispensable, we are compelled to double two or to triple one member—an expedient,

96

These two chords will have more or fewer different aspects, according to the pitch or elevation of the lower or bass note. For this reason, and because of the particular movement in each part, it is difficult to employ the chords complete in every bar.

### RULE II.

We must contrive so that the parts may neither be too distant from, nor too near to one another, particularly in the lower parts; we must therefore avoid, as far as possible, using several successive thirds between the tenor and bass. Endeavour, that the parts may preserve a moderate and fitting distance from one another.

*Remark.*—When the parts are too close, particularly the two lower parts, they produce a dull and indistinct effect; when they are too much dispersed, being at a great distance from one another, the effect which results is vague.

### RULE III.

As we have done before in counterpoint in three parts, we may also in this, from time to time, particularly when the case absolutely requires it, allow an upper part to cross below an inferior part, during one or two bars at most. This means enables us to avoid many faults, and often favors an easy flow of melody in the parts.

### RULE IV.

Two octaves or two fifths in succession, and by similar motion, are always prohibited between any of the parts. But we are allowed to employ two fifths in contrary movement among any two of the three upper parts, or in the two mean parts with respect to the bass. They are sometimes allowed between the two extreme parts, but not too frequently; it is only after we have, in vain, tried all other means to avoid so doing, that we may employ them.

129

three, or four parts: it is only when the five, six, seven, or eight parts really move together, that the above mitigation of the rules is allowed.

There are two ways of composing in eight parts: the first is that which places the two TREBLES directly after one another, and the CONTRALTOS, the TENORS, and the BASSES, in the same order; the second way is that in which the eight parts are divided into two choirs, each composed of four parts, viz. one SOPRANO, one CONTRALTO, one TENOR, and one BASS. These two isolated choirs must be contrived so that each of the two may occasionally proceed alone, and that they may alternately interrogate and respond to one another. In this case, it is necessary that the choir which is silent, while the other proceeds, should resume its proposition before the other shall have terminated its period; and that ultimately both should proceed together. In this sense, the two BASSES enjoy the privilege indicated in the two preceding examples of skipping from the unison to the octave.

Ancient authors, when they wrote for a double choir, carried their attention so far as to render the harmony complete in each chorus; so far, at least, as the nature of the subjects which they treated, and the arrangement of the parts, would allow. They imposed this obligation on themselves on account of the distance which often separated the two choirs; and, in order that such of the audience as might chance to be placed nearer to one choir than to the other, might, by hearing a complete harmony, receive the more agreeable sensation. However, this condition is not absolutely indispensable.

Ancient masters have written compositions in which they have combined as many as six choirs at a time*. It requires much address and atten-

* They often exceeded this number; in Marpurg, may be seen an example of a canon for twenty-four choirs; that is to say, ninety-six voices.

K

130

tion to vanquish all the difficulties which result from
the junction of so numerous an assemblage; but
every thing may be obtained by labour and a
flexible organization.

When the student has sufficiently practised
counterpoint in four parts, he may progressively go
forward to counterpoint in five, six, seven, and
eight parts, beginning with note against note in a
given subject, and afterwards introducing, on the
same melody, florid counterpoint in all the parts,
without passing through the intermediate sorts with
minims, crotchets, and syncopations. In writing
for five voices, he must sometimes compose for two
TREBLES, sometimes for two CONTRALTOS, or two
TENORS, or two BASSES; for six voices, let him
sometimes employ two TREBLES and two CON-
TRALTOS; sometimes with two TREBLES, two
TENORS, or two BASSES, &c. &c.; for seven voices,
he must observe the same arrangements, till he ar-
rives at eight parts, in which each kind of voice is
naturally doubled.

We shall now give examples of subjects filled
up to five, six, seven, and eight parts; first, with
note against note, then in florid counterpoint. The
given subject may be placed in any part at plea-
sure; still, in the aggregation of so many parts,
the melody would be eclipsed if it were to be placed
in one of the middle parts: for effect, therefore, it
will be best that it should be situated in one of the
two extreme parts; but the student should also ex-
ercise himself in placing it in one or other of the
middle parts, that he may habituate himself to
conquer all sorts of difficulties.

146

EXAMPLE FOR TWO CHOIRS IN FLORID COUNTERPOINT
WITHOUT ANY GIVEN SUBJECT.

149

The examples which we have here given, afford an idea of the manner in which counterpoint must be treated, according to the number of parts intended. We see, in counterpoint of note against note, that, in certain cases, we cannot avoid unisons or similar motion between the extreme parts in passing to a perfect concord. Such also is the case in florid counterpoint; but as, in this species, we have it more in our power to arrange the parts as we wish, than in the former species, we must manage, when unisons are inevitable, so as to attack them on the unaccented times of the bar.

This caution was always observed by the ancient classical composers, particularly in their compositions in more than four parts.

151

EXAMPLE.

Imitation may be made in various ways. It is called *regular or strict*, when we reply exactly to the nature of the intervals proposed by the **ANTECEDENT**; that is, when we observe an exact correspondence of tones and semitones. In this kind of imitation, we reply to a minor second by a minor second; to a major third by a major third; and so on.

This imitation is obtained naturally when the **CONSEQUENT** imitates the **ANTECEDENT** in the unison or in the octave; imitations in the fourth and fifth approach, in some degree, to the exact correspondence of intervals; but here and there accidental sharps or flats are required to render them perfectly so: it is almost impossible to obtain this identity, if we commence on any other degrees of the scale.

152

Imitation is called FREE or IRREGULAR, when this correspondence is not observed, and when we assume the liberty of replying arbitrarily, and according to the key in which the intervals of the CONSEQUENT takes place: in this kind of imitation, we may reply to a major second by a minor second; to a minor third by a major third; &c.

Imitation in SIMILAR motion is that in which, as its name indicates, the melody ascends or descends as in the ANTECEDENT. The preceding examples are in similar motion.

The imitation is in CONTRARY motion when the CONSEQUENT replies by ascending progressions to the descending progressions of the ANTECEDENT, and the converse. This imitation, like the preceding one, may be either REGULAR or IRREGULAR.

Imitation in RETROGRADE movement is that which imitates a period, or a member of a period, by taking it backwards; that is, when the CONSEQUENT commences at the last note of that period of the ANTECEDENT, which it is about to imitate, and returns back to the first note.

Retrograde imitation may be either REGULAR or IRREGULAR; it may also be treated either by similar or contrary motion.

There are several other kinds of imitations, which we shall mention in the sequel.

We shall treat on each of these species, beginning with imitations in two parts.

## IMITATION IN TWO PARTS.

### FIRST SECTION.—IMITATION IN SIMILAR MOTION.

Any imitation, of what nature it may be, can only be made in as many ways as there are intervals in the scale; that is, in the UNISON, SECOND, THIRD, FOURTH, FIFTH, SIXTH, SEVENTH, or OCTAVE, above as well as below the tonic.

180

In this last example, there is one part which, though it belongs to the whole, has no analogy to the imitation; for this reason it is said to be *ad libitum*. The same thing must be done if we wish to have four parts, and content ourselves with writing on the given subject an imitation only between the two other parts. If we wish to have on the subject three parts in imitation, there will be two consequents, both of which will imitate the subject proposed by the antecedent, either in the same or some different interval.

After the student has sufficiently practised writing imitations on the given subject in two parts only, with or without a fourth part *ad libitum*, from imitation in the *unison* to that of the *octave* inclusive, he may undertake the practice announced above; that is, the introduction of two consequents, by which means he will have a double imitation.

182

Before we proceed farther, it is necessary to observe that this subject may, if thought necessary, be written in semibreves, thus :

instead of its being written in breves.

When the student has sufficiently practised imitations between two and three parts on the given subjects, he may exercise himself in treating imitation in three and then in four parts, without any subject being given. On this head, he will do well to consult the work of Marpurg, in order to see all the combinations of intervals by which imitations may be effected. It is to place under his eyes a great number of examples, that we recommend him to consult the work of Marpurg.

We shall give two examples of imitations; the first in three parts, the second in four; which will suffice to give an idea of this kind of practice.

186

The student must also exercise himself in treat-
ing imitations for five, six, seven, and eight voices,
either on given basses, or without any part being
given; in which latter case the composition will be
wholly by himself. *Ad libitum*, or accompanying
parts, may be introduced when he cannot succeed
in finding regular imitations in all the parts.

Before we terminate this chapter, we shall ex-
plain another kind of imitation, which may be
practised in eight parts, by means of two choirs.
This imitation is called *inverse contrary* imitation.

EXPLANATION.

A theme in four parts is proposed by one of the
choirs; the reply must be made by the other.

That the reply may be *inverse*, the bass of the
theme must be placed in the soprano part in the
reply, and the soprano part placed in the bass; simi-
larly the contralto part must be given to the tenor,
and the tenor part to the contralto.

That the reply may be in contrary motion, each
part of the reply must answer, in contrary move-
ment, to the parts which proposed the theme, and in
the order above explained.

To obtain this artifice, we must observe the
following rule: none of the lower parts must ever
stand in the relation of a fourth to the soprano

191

Inverse contrary reply, according to Scale IV.

Before we give an extended example of this
kind of imitation, it is necessary to state that it is
indispensable that the reply in inverse contrary
motion should commence before the period of each
theme is concluded, or at least towards its termina-
tion; the succeeding theme, in its turn, must enter
either before the reply or towards the end of it.
According to this rule, we must combine the harmony
and the parts so that they may lend themselves to
this arrangement with regard to the entries. An
example will perhaps better explain what we have
just said.

219

BOOK III.

ON DOUBLE COUNTERPOINT.

CHAPTER XX.

DOUBLE counterpoint is a composition in which the parts that are added are so artificially combined, that they may, without inconvenience, be transposed from ACUTE to GRAVE, if they are placed above the theme or subject; or from GRAVE to ACUTE, if they are placed below; while the theme undergoes no change in its melody, whether it be placed in one of the extreme parts, or in one of the intermediate parts.

Inversions may be effected in seven ways: there are, consequently, seven species of double counterpoints; viz. in the NINTH or SECOND; in the TENTH or THIRD; in the ELEVENTH or FOURTH; in the TWELFTH or FIFTH; in the THIRTEENTH or SIXTH; in the FOURTEENTH or SEVENTH; and in the FIFTEENTH or OCTAVE.

Before we proceed to speak of each of these seven species separately, it is necessary to observe in general: first, that for any double counterpoint the parts must be distinct from one another, as far as can be, by the value of the notes: that is, if the theme is composed of semibreves or minims, we must, in the counterpoint, oppose to it crotchets or quavers; still, however, in that varied manner practised in florid counterpoint. Secondly, that the part which contains the counterpoint must commence after the theme. Thirdly, that we must not, without

225

CHAP. XXII.

DOUBLE COUNTERPOINT IN THE NINTH.

WHEN the inversion of a counterpoint takes place in the NINTH, either above or below, it is called a DOUBLE counterpoint in the NINTH or SECOND. The combinations of this species of counterpoint are obtained by means similar to that already employed for counterpoint in the octave; in other words, by opposing to one another two series of figures, each of which series is bounded by the figure indicated by the name of the counterpoint. Hence, as each series in the counterpoint in the OCTAVE is composed of eight figures, so in the counterpoint of the NINTH, of which we are now treating, each series must be composed of nine figures. It is the same with all the counterpoints which follow these, and for each of which we must employ its proper progression; viz. for counterpoint in the TENTH, ten figures; for that in the ELEVENTH, eleven figures; and so on. We give this explanation here, that we may not be under the necessity of speaking of it again, when we treat of the subsequent species.

This, then, is the series of figures which belong to double counterpoint in the NINTH:

1 2 3 4 5 6 7 8 9
9 8 7 6 5 4 3 2 1

From this scheme we see that the UNISON is changed into a NINTH; the SECOND into an OCTAVE; and so on. The FIFTH is here the principal interval. It merits the most attention, either to prepare or to resolve, not only dissonant intervals, but also such as become so by inversion. The discord of the

Q

253

The other manner of practising TRIPLE and QUADRUPLE counterpoint in the octave, consists in so combining the parts that they will admit of being inverted with respect to each other; that is, so that each part may be placed either high or low without requiring any change in the melody, and without there resulting from these changes any inconvenience or infraction of the strictest rules. For this purpose, it is indispensable that the parts should never stand in the relation of a FOURTH or of a FIFTH with regard to one another, except when the melody moves by degrees, or when we use the prepared discords of the SECOND, FOURTH, and SEVENTH. The discord of the NINTH is impracticable in this species of counterpoint, as we have already said in double counterpoint in the OCTAVE.

EXAMPLE OF TRIPLE COUNTERPOINT IN THE OCTAVE.

274

CONCLUSION.

These examples give rise to an important remark, which is, that, notwithstanding the denomination of TRIPLE and QUADRUPLE counterpoint in the TENTH or TWELFTH, there is not, in reality, any true TRIPLE or QUADRUPLE counterpoint but that in the OCTAVE.

In effect, the combinations of this species of counterpoint alone, will allow us to compose a piece for three or four voices (or even a greater number), in which all the parts equally lend themselves to a complete inversion.

In a correct QUADRUPLE counterpoint in the OCTAVE, the parts may without difficulty be displaced, and thus furnish a crowd of new aspects by transposing some parts from acute to medium or grave, while the grave parts ascend to the medium or acute.

But it is, as we may say, impossible to compose for three or four voices, with the condition that any of the parts may, in turn, be transposed to the THIRD or TENTH above or below, or to the FIFTH or TWELFTH above or below, without ever ceasing to be in correct harmony with the other three parts: we are therefore obliged to use artifice to obtain the counterpoints called TRIPLE or QUADRUPLE counterpoints in the TENTH and TWELFTH.

In composing, as we have said, a DOUBLE counterpoint in either one or other of these intervals, in contrary or oblique motion, so as never to have two successive THIRDS, and avoiding all prepared dissonances, it becomes possible to add to each of the two parts another part in THIRDS, and the counterpoint becomes TRIPLE or QUADRUPLE by the junction of one of these parts, or both at the same time.

But in QUADRUPLE counterpoint in the TENTH, obtained by this proceeding, no inversion in the TENTH is possible; because it is these very inversions themselves which proceed with the principal part

275

to make up the four parts: but this counterpoint
may be inverted in the OCTAVE; that is, we may
change the place which the divers parts occupy, if
we have taken care to observe the rules of DOUBLE
counterpoint in the OCTAVE.

QUADRUPLE counterpoint in the TWELFTH is
more real and varied; that is, among the four parts
thus combined there are always two which may be
transposed, one a FIFTH above, the other a FIFTH
below; these are the two principal parts, and which
do not on that account cease to be capable of pro-
ceeding in THIRDS with the two added parts.

Before we conclude this section, we shall exhibit
a series of examples by the learned Father MARTINI,
relative to those counterpoints, in which we shall
see the use which may be made of them.

EXAMPLES.

FIRST SPECIES—Counterpoint in the upper part.

Lower part.

Counterpoint an octave lower.

T 2

285

BOOK IV.

CHAP. XXXI.

ON FUGUE.

THE word FUGUE (*Fuga*) is ancient; it is met with among the old composers, but they did not affix to it the signification which we attach to it in the present day. They gave this name to those counterpoints in imitation, of which the melodies of plain chants formed the subjects, and in which we now and then meet with canons. At present, we apply the name of FUGUE to a composition of considerable development and regularity, which was unknown to the ancient classical composers, and which indeed they could not know, because their system of tonality did not lend itself to what we call a tonal *fugue*, as we shall presently see.*

The fugue then, notwithstanding the ancient origin of the word, is a creation of modern times, which has only been introduced in church music since we have thrown off the obligations, which contrapuntists had imposed upon themselves, of always writing on plain-chants.

Such as it exists at the present day, fugue is the complement of counterpoint. It ought to include

* See what Padre Martini says on the subject, in his Treatise on Counterpoint.

286

not only all the resources which are furnished
by the study of the different species of counter-
point, but also many other artifices peculiar to itself,
and of which we shall speak farther on.

Fugue may be considered as the transition be-
tween the systems of strict counterpoint and of free
composition; we therefore forewarn the student that
he will find, in the examples on fugue which we shall
give, several chords that we have not hitherto em-
ployed.

All that a good composer ought to know may
find its place in a fugue; it is the type of every piece
of music; that is to say, whatever piece we com-
pose, if it shall be well conceived, very regular, and
conducted with intelligence, it must at least have
the spirit of fugue, without having precisely its
peculiar character and form.

There are two principal kinds of fugue, from
which emanates a third species; and from this latter
spring all the rest. The two principal kinds are
the TONAL FUGUE and the REAL FUGUE; the other
is the FUGUE OF IMITATION. All the rest, children
of caprice, are IRREGULAR FUGUES OF IMITATION,
or merely pieces in the FUGUE STYLE.

The indispensable conditions of a fugue are the
SUBJECT, the ANSWER, the COUNTERSUBJECT, and
the STRETTO. To these conditions we may add the
PEDAL, which is almost always introduced in a fugue
of any considerable development.

All the artifices which we can introduce in a
fugue depend on the knowledge, the address, and
the will of the composer, and at the same time also
on the nature of the SUBJECT and COUNTERSUBJECT,
which may be more or less susceptible of lending
themselves to these artifices.

Such artifices consist, first, in the employment of
imitations, formed by detaching portions of the
SUBJECT or COUNTERSUBJECT; secondly, in the
transposition of the SUBJECT into different keys,
and in the advantages which, in this respect, may

287

be derived from double counterpoints; thirdly, in the inversion of the **SUBJECT** by contrary motion; fourthly, in a new **SUBJECT** which may be introduced, and which will admit of being combined with the first **SUBJECT** and the first **COUNTERSUBJECT**: fifthly, in the manner of combining the **STRETTO** in various ways, each time drawing closer and closer together the **SUBJECT** and **ANSWER**; sixthly, in the means which may be used to simultaneously unite the **SUBJECT** and its inversion in contrary motion; seventhly, and lastly, in the manner of combining the **SUBJECT**, **COUNTER-SUBJECT**, and **STRETTO**, on the **PEDAL**, and in the address and the taste which we may employ in the connection and the introduction of these artifices in the course of the fugue.

We may employ all these combinations, and even various others, in a fugue merely intended for study; but, in one which is to be given to the public, we must make a choice, and not introduce them all: without this precaution, the fugue would be too long, and consequently become tiresome.

We shall now proceed to the explanation of each of the denominations which we have enumerated above.

## CHAP. XXXII.

### ON THE SUBJECT, ANSWER, AND COUNTERSUBJECTS OF A FUGUE.

#### § 1. *Subject.*

THE **SUBJECT** or theme of a fugue ought neither to be too long nor too short; its length should be such that it may be easily engraved on the memory, and that the ear may seize on and recognize it with facility in the different parts and in the different ways in which the composer may introduce it.

288

The following is an example of a subject of
a proper length.

The **SUBJECT** being once well imagined, the whole
fugue ought to be, as it were, included in its extent;
and that of the **COUNTERSUBJECT**, which serves it,
as an auxiliary.

The **SUBJECT** may also be called the **PROPOSITION,**
**ANTECEDENT,** and **GUIDE ;** and the parts which suc-
ceed it may be called **ANSWERS** or **CONSEQUENTS.**

The composer is at liberty to choose any part in
which to propose the subject. Ancient composers
were, however, in the habit of observing the follow-
ing method: when the subject commenced by the
octave of the **TONIC,** and afterwards descended to
the **DOMINANT,** they took the most acute part to pro-
pose it, in order that the answer, which was to
descend from the **DOMINANT** to the **TONIC,** might be
made by the lowest part.

Padre Martini.

300

It is needless to say, that, in a fugue in five, six,
seven, or eight parts, we shall be obliged to have
several parts AD LIBITUM, because of the difficulty,
and even impossibility, of finding a sufficient number
of COUNTERSUBJECTS, that is, of parts in double
counterpoint, for so great a number of voices.

The COUNTERSUBJECTS in a fugue may be placed
immediately and simultaneously with the SUBJECT.
To me, this disposition does not appear the best; and
I think we shall obtain the greatest variety in the
ensemble of the parts, by managing the COUNTER-
SUBJECTS so that they shall only come in succes-
sively; first allowing the subject to be heard iso-
lated, or at most accompanied by a single COUNTER-
SUBJECT, if the fugue is in three parts, or by two,
if it is in four parts.

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To convince ourselves more thoroughly that this ought to be the case, let us suppose that these different *subjects*, instead of being heard at once and simultaneously with the principal subject, were only introduced successively by the parts, as they enter one by one; these different accompaniments of the *subject* or the *answer* which we named subjects, when employed at the commencement, would in this case be called *COUNTERSUBJECTS*; now, as we might have caused all these *countersubjects* to have been heard at the same moment that we proposed the *principal subject* for the first time, it does not, by any means, follow that, merely on the former account, we change their denomination.

We must however observe, that, in case we so plan our fugue as to introduce several countersubjects at the same time that we propose the *principal subject* for the first time, these countersubjects must remain invariable in their inversions throughout the whole course of the *fugue*.

On the contrary, when these different countersubjects are only introduced afterwards, either during the *subject* or the *answer*, and that they have not been proposed at the very commencement of the *subject*, we are then free either to preserve their identity as often as they occur, or to slightly modify them by changing some notes, according to the wants and the situation of the parts.

In all cases, it is important and indispensable that we should always combine these *countersubjects* according to the laws of *double counterpoint*, that they may be applicable under all circumstances, and freely lend themselves to the different artifices which we wish to employ.

## CHAP. XXXIII.

### ON THE STRETTO.

STRETTO is an Italian word which signifies CLOSE; it has been adopted into our musical language, and is employed to indicate an artifice which consists in bringing, as close as possible together, the entry of the answer to that of the subject.

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The STRETTO is, as we have already observed, one of the conditions indispensable to a fugue; we shall indicate the place which it ought to occupy, when we speak of the entire contexture of a FUGUE. The art of employing the STRETTO to advantage consists in the manner of varying its aspects, and in seeking the means, each time that we introduce the STRETTO, to draw closer and closer together the commencement of the SUBJECT with the entry of the ANSWER. The effect which this produces is very piquant and exciting.

We are sometimes permitted, when we can do no otherwise, in order to bring closer together the entries of the ANSWER and the SUBJECT, to change some notes of either; or, if we do not change the notes, to alter the duration of them; but these variations cannot take place in the SUBJECT till after the entry of the ANSWER, nor in the latter, till after the entry of the SUBJECT, and so on. All this, however, is subject to many exceptions, which are allowed according to the circumstances in which we are placed, as we shall see in our examples on FUGUE.

When the SUBJECT, by its peculiar nature, is not properly disposed so to combine in forming the STRETTO in a manner altogether natural, we are allowed to commence the STRETTO by the ANSWER; but, if neither the one nor the other are adapted to obtain all the aspects which we desire to give to the STRETTO, we must then content ourselves with causing the ANSWER to enter after the SUBJECT, or the SUBJECT after the answer, in whatsoever place we can, employing afterwards the allowed changes

X

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either in the notes or in their relative values. For
the rest, practice will still better teach the means by
which we may extricate ourselves in difficult cases.

A good subject for a fugue ought always to admit
of an easy and harmonious stretto; in composing
it, therefore, we should, before-hand, think of the
different combinations of the stretto.

## CHAP. XXXIV.

### ON THE PEDAL.

THE PEDAL is a note prolonged and sustained
during several bars. It may be placed in the ACUTE
part, in one of the MIDDLE PARTS, or in the BOTTOM
PART; it can only occur, whatever its position, on
the TONIC or on the DOMINANT; but that kind from
which we can draw the greatest advantage, and
which is most generally employed in fugue, is
the DOMINANT placed in the LOWEST PART.
The property of the PEDAL is to free the composer
from the severity of the rules; that is, during its
duration, he may introduce discords not prepared,
and even modulate, provided, however, that the
parts which proceed thus are combined with respect
to each other according to rule, and as though
the sustained note of the PEDAL did not exist, ex-
cept in the first and last bar, which ought always to
harmonize with the note of the PEDAL.

From what we have said, we may cause the
SUBJECT, the ANSWER in STRETTO, the COUNTER-
SUBJECTS, and, if we can, some of the artifices which
we may have introduced in the course of the fugue,
to be heard on the PEDAL.

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The D which ends the first phrase, belonging naturally by its descent on the DOMINANT to the KEY OF G, the ANSWER ought to change into G, the first note C of the subject, in order to conform to the law of a *tonal fugue*, and to replace the D of the subject by a G which will descend on C in the key into which we shall transpose all the rest of the subject to construct the ANSWER.

It would be superfluous to instance a greater number of SUBJECTS; with the means which we have explained, and a little consideration, we shall be enabled to find the ANSWER to any subject for a TONAL FUGUE which may be offered.

## CHAP. XXXVI.

### OF THE REAL OR STRICT FUGUE.

THE *strict* or *real* FUGUE is more ancient than the TONAL FUGUE. It is that in which the SUBJECT begins by the TONIC, and directly proceeds to any other chord than that of the DOMINANT, and of which the ANSWER, which must be made in the FIFTH of the principal key, is in all respects *similar* to the SUBJECT.

Ancient composers recognized two sorts of REAL FUGUE, the FREE and the LIMITED; that was called FREE in which the ANSWER, which must be in every respect similar to the part which it imitated, was not continued beyond the duration of the SUBJECT or COUNTERSUBJECT.

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But if the ANSWER was similar, not only to the
SUBJECT, but to all the notes of the *antecedent* part,
from the beginning of the FUGUE to its end, the
REAL FUGUE then assumed the denomination of
LIMITED; and this kind of FUGUE was no other than
that piece of music which we now call a CANON, as
we have already said in the introduction to a former
chapter.

At present, these denominations are no longer
used; and what the ancients call a REAL and FREE
FUGUE, is the only REAL FUGUE cultivated.

It may chance that the SUBJECT of a FUGUE
offers, in the first bars, all the characters of a REAL
or STRICT fugue, and, suddenly modulating towards
the close, terminates in a *tonal fugue*. The ANSWER
must then follow the conditions of the SUBJECT; that
is, beginning like a STRICT FUGUE, it must conclude
as in a TONAL FUGUE.

EXAMPLE.

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CHAPTER XXXVII.

FUGUE OF IMITATION.

THE FUGUE OF IMITATION is that of which the ANSWER is nearly, but not altogether, similar to the SUBJECT, the composer having the liberty of introducing some changes, and of curtailing it if he thinks fit.

The FUGUE OF IMITATION has also another privilege, which is that the CONSEQUENT or ANSWER has neither a fixed time nor a fixed interval in which to reply to the ANTECEDENT or SUBJECT, and we are, therefore, at liberty to cause it to enter at the most favorable moment, and in any interval.

Thus, the ANSWER may be made, not only in the UNISON, the FIFTH, the FOURTH, and the OCTAVE, but also in the THIRD, the SIXTH, the SECOND, the SEVENTH, and their compounds; by these means, we produce that variety so desirable in music, and so highly appreciated by the hearer.

We have said above, that the SUBJECT of a FUGUE ought to be of a proper length, neither too long, nor too short; but, in the species of fugue of which we are now treating, the subject should always be very short, that the ANSWER may speedily make its appearance.

In treating the SUBJECT of a FUGUE OF IMITATION, we have the power to change, into a fugue of this name, even a TONAL FUGUE, by replying to a SUBJECT of the nature of this latter FUGUE with the freedom of a FUGUE OF IMITATION.

EXAMPLES.

Subject of a tonal fugue.

Answer as a fugue of

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In modern fugues it is usual to prolong the Codetta of the **ANSWER**, before the **SUBJECT** reappears. This disposition is wise, and ought to be followed; it has the double advantage of causing us to wish for the reappearance of the subject, and of throwing variety into the composition, by preventing the monotony which would arise from the too near repercussions of the subject and answer; it contributes therefore to give elegance to the conduct of a fugue, and may also furnish an additional **THEME** for imitations and episodes: this remark applies to every species of fugue, whatever be the number of the parts.

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modulates, for the purpose of introducing in other keys the PRINCIPAL SUBJECT, the ANSWER, and the COUNTERSUBJECTS.

The EPISODE may be long or short, at will; and in the course of the FUGUE there ought to be more than one EPISODE, varying our choice of the means made use of in treating it. When we come to the question of the entire composition of a FUGUE, we shall point out the situations which these EPISODES, called by the Italians ANDAMENTI, naturally occupy; and we shall shew, at the same time, the manner of constructing them. The short explanation which we have here given of the EPISODES, will serve the purpose for the present moment.

## § 2. Modulation.

The means which for a long period has been used to direct us in the choice of modulations, consists in regulating ourselves according to the DIA-TONIC SCALE of the key in which the piece is to be written, so as not to modulate into chords which are foreign to this same scale. According to this rule, we may modulate into the DOMINANT and SUBDOMINANT, of which the modes are naturally MAJOR; and into the SECOND, the MEDIANT or THIRD, and the SIXTH, of which the modes are naturally MINOR. We cannot modulate into the SEVENTH or LEADING NOTE, because its FIFTH IS NOT NATURALLY PERFECT. What we have said applies to the scale of the MAJOR MODE. If we desire to compose a piece in a MINOR KEY, these are the keys into which we may modulate: into the SUBDOMINANT and the DOMINANT, of which the modes are naturally MINOR; into the MEDIANT and the SIXTH, of which the modes are naturally major. We cannot modulate into the SECOND, because its fifth is not naturally PERFECT; we must also avoid modulating into the SEVENTH.

Modern composers in their compositions have broken through this simple and rational law of modulating, replacing it by a manner much more free,

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and often crude and incoherent; but if their deviations from the beaten path be tolerated in modern works, it is essential, and it is expressly recommended to the student, not to follow their wanderings in respect to a composition so strict as FUGUE.

Thus, when a FUGUE is in the MAJOR MODE, the key into which we ought first to modulate is that of the DOMINANT with its THIRD MAJOR; we may then modulate into the SIXTH, the relative MODE MINOR of the PRINCIPAL KEY; we may afterwards modulate into the major mode of the SUBDOMINANT, to the MINOR MODE of the SECOND, and to the MEDIANT also MINOR; we may then return to the KEY of the DOMINANT, to arrive afterwards at the conclusion, which must be made in the principal key.

In the course of a FUGUE in a MAJOR KEY, we are allowed to change into minor the mode of the principal key; but this permutation of mode can only be employed for a few moments, and then merely to lead to a repose or suspension on the DOMINANT, in order afterwards to attack the MAJOR of the principal key.

When a FUGUE is in a MINOR KEY, the first modulation is into the MAJOR MODE of the MEDIANT, which is the RELATIVE MAJOR of the PRINCIPAL KEY; afterwards, we modulate by turns, either to the MINOR MODE of the DOMINANT, or to the MAJOR MODE of the SIXTH, or to the MINOR MODE of the SUBDOMINANT, or the MAJOR MODE of the SEVENTH; and, lastly, from one or other of these keys, we must return to the PRINCIPAL KEY itself to conclude. Like the FUGUE in a MAJOR KEY, we may transform the mode of the PRINCIPAL KEY from MINOR to MAJOR, under the same conditions as were explained in speaking of FUGUE in a MAJOR KEY.

Such are the laws of modulation in a regular composition. What makes the difficulty in the art of modulating, is the choice of chords and their succession, so as to pass from one KEY to another, in a manner at once natural and analogous to the

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key into which we desire to proceed, and that without shocking the ear or the feelings by these transitions. Experience, which practice alone can give, will smooth the difficulties which the want of both may cause the student to meet with.

## CHAPTER XL.

### ON THE ENTIRE COMPOSITION OF A FUGUE.

AFTER having passed in review what concerns the elements of a FUGUE, there now only remains for us to treat of its entire composition. We have already said that the indispensable conditions of a fugue are the SUBJECT, the ANSWER, the COUNTER-SUBJECT and the stretto; the ACCESSORY or EPISODICAL conditions are IMITATIONS formed by FRAGMENTS of the SUBJECT, or of the COUNTERSUBJECT, with which we compose the different EPISODES or ANDAMENTI that take place in the course of the FUGUE. All these elements suffice to construct a short or ordinary FUGUE. But if, in any composition of this species, we proceed to introduce other combinations and other artifices, we shall produce an ensemble more varied and developed. It is difficult to determine the number of these artifices which we may introduce into a FUGUE; their choice, their quantity, depend mainly on the nature of the SUBJECT and the COUNTERSUBJECTS, and on the more or less practised address of the composer. There is no FUGUE but what differs from every other, either by the manner in which it is conducted, or by its combinations: this difference and this variety are the effects of caprice, or of an imagination more or less fertile; practice, the habit which it gives,

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There is no absolute necessity to employ a pause, or point of repose, before the entry of the stretto; but when we do use it, it is in order to give greater brilliancy and effect to its appearance, by isolating it from what precedes; and this means produces a very good effect. In introducing this repose, it is not absolutely indispensable to practise it in the previously established *key* of the *dominant*; it depends upon the fancy of the composer to make it, either on this *dominant*, or on the pre-established *relative minor mode*: or on the *dominant harmony* of this same *minor mode*; or on the *established minor mode* of the *mediant*; or, lastly, on the *dominant* of the *principal key* changed into *minor*; for here, after having prepared for it some bars beforehand, is the proper place to introduce the *minor mode* in a *fugue*. What we have just laid down relative to the repose in question, may be applied to every sort of fugue, whatever may be the number of parts of which it is composed.

GENERAL REMARKS.

On examining the preceding example, we shall be convinced that the development of the FUGUE is entirely drawn from the SUBJECT and COUNTERSUBJECT. This it is which forms the unity of a piece of music of this kind.

As it is necessary to give occasional rests to the parts, in order to vary our effects, we must observe that such rests ought to take place in those parts in which the SUBJECT or ANSWER is to re-appear, and just before their entrance. When these rests are employed under other circumstances, the part which has been silent ought never to recommence without reason, nor with a mere idle motivo, nor with notes merely serving to fill up; but it should re-enter either to reply to some IMITATION already proposed, or to propose one in its turn.

We must also avoid monotony in our choice of ideas, and in that of the design and melodic figures. This fault is blameable in any piece of music: we shall easily fall into it in writing a FUGUE, if we draw all the ideas which compose the ensemble either from the SUBJECT or the COUNTERSUBJECTS, in order to preserve too strongly the unity of character of which we have spoken above. To avoid these faults, observe, in combining an episode, not to employ those fragments drawn from the SUBJECT or COUNTERSUBJECT, which we have already made use of in the preceding EPISODES. With this precaution, and by varying with address our modulations, and the aspect of the imitations by inverting them, we shall avoid becoming monotonous and tiresome.

Another remark which remains to be made, is, that in a FUGUE, either STRICT or TONAL, the ANSWER is always in the FIFTH of the TONIC, and all the imitations in the course of the FUGUE ought to be made in the same interval as the ANSWER itself, or else in the FOURTH, which is only a FIFTH inverted.

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As to FUGUES of IMITATION, if the ANSWER is in the FIFTH,
or the FOURTH of the SUBJECT, we must observe, with regard to
the imitations, the law which serves as a guide to STRICT and
TONAL FUGUES; but if the ANSWER be in the SECOND, THIRD,
SIXTH, or SEVENTH, and their compounds, the imitations through-
out the FUGUE must always be made at that same distance which
the ANSWER shall have indicated at the commencement. We
may add, that, in any FUGUE whatever, we may also practise
imitations in the UNISON or OCTAVE, at whatever degree or in-
terval the ANSWER to the subject may originally have been made.

According to these observations, we may continue our examples
without being obliged to add any thing more to what we have
already said on the subject of FUGUE.

END OF VOL. I.

PRINTED BY J. MALLETT, WARDOUR STREET, SOHO, LONDON.