Chiuubaii ^rcs^ Utiles COUNTERPOINT, CANON, AND FUGUE OUSJELEY ILonbon HENUY FROWDE OXFOHD UNIVERSITY PRESS WAREHOUSE 7 PATEENOSTEli HOW Clareniroit IBttSB Scnts A TREATISE ON COUNTERPOINT, CANON AND FUGUE BY THE Rev. Sir F. A. GORE OUSELEY, Bart., M.A., Mus. Doc. PROFESSOR OF MUPIC IN THE UNIVERSITY OF OXFORD Second Edition at the clarendon press M.DCCC.LXXX ^ \^ All rights reserved ] TO JOH¥ STAII^ER ESQ., M.A., MUS. DOC, IN ACKNOWLEDGMENT OF MUCH VALUABLE AID GIVEN IN THE PREPARATION OF THIS WORK FOR THE PRESS, THE FOLLOWING PAGES ARE DEDICATED, WITH EVERY AFFECTIONATE REGARD. BY HIS OLD FRIEND THE AUTHOE. 601373 PREFACE. The present work is intended as a companion rather than a sequel to the author's " Treatise on Harmony." There is a great difference of opinion in different countries as to the method and order in which Harmony, Counterpoint, Fugue, Form, and Musical Aesthetics should be studied. In Italy, for example, it has been (till quite recently) the custom to study Counterpoint first, then Fugue, then Harmony ; whereas, in Eng- land, Germany, and France Harmony has always been taught before any other branch of the subject. But upon a careful consideration of the whole matter, it seems more reasonable to study Harmony and Counterpoint simultaneously. The principal reasons for adopting this course are stated in the body of this work, and both the author's Treatises have been written with a view to this method of treatment. Many persons conceive that the restrictive rules of Simple Counterpoint are of no great value, inasmuch as they are never followed in all their rigour in the works of our best composers. But this opinion arises from an erroneous idea of the object which these rigorous restrictions are intended to attain. For a course of Elementary Counterpoint is chiefly useful, as giving facility in combining many melodies into one harmonious whole ; as engendering habits of smooth part-writing, by successively vanquishing the various technical difficulties which ever stand in the way ; and as making free composition comparatively easy afterwards 1)y contrasting it with what must be acknowledged to be the drudgery of the earlier processes. viu PREFACE. By tlu; caruful study of Kcstrictcd Counterpoint the t\'ro acquires the use of the tools of his art; and without such drilling he will never have them well under his command. Let him then not grudg-c the lahour he bestows on such exercises, for they will stand him in good stead at a later period of his progress in the art. The student who has carefully mastered the elements of Counterpoint and Fugue, at the same time studying the laws of Harmony, is recommended to follow up this course by carefully setting out the Organ-Fugues of J. Sebastian Bach in open score, in the proper clefs, at the same time analysing their construction, and noting any peculiarities they may present. He will also find much benefit from the opposite process of condensing into an organ arrangement the open scores of good Motetts, Anthems, and ]\Iadrigals, by the best masters of the sixteenth and seventeenth centuries. He will still have to learn Instrumentation, Form, and General Com])osition, before he can be said to have completed his musical studies. The present work does not pretend to any great originality of design. The only advantage which the author hopes he has been able to secure in it, consists in the methodical arrangement of its various parts, and the character of the Examples \\ith which it is illustrated. Some apology is due for the size of the volume. It has indeed swelled to somewhat larger dimensions than was originally expected or intended. But this could not be avoided without sacrificing some of the best Examples at the end of the book, and such a sacrifice the author was loth to make. Marc/t, 1869. TABLE OF CONTENTS. CHAPTER I. General Observations. 1. Harmony and Counterpoint distinguished. 2. Definition of Counterpoint ; Counter- point divided into Simple and Compound ; Simple Counterpoint divided into Five Species. 3-^5 . Restrictions as to Intervals and Progressions 1 CHAPTER II. Of Simple Counter^yoint of tJie First Sjyecies, or "note against note,'' in Two Parts. 1 — 3. Concords and Discords allowed. 4. The different sorts of Motion. 5. The rules against Consecutive Octaves and Fifths. 6. Hidden Fifths and Octaves. 7. Consecutive Thirds and Sixths. 8. False Relations. 9. The Augmented Fourth or Tritone. 1 0. Examples of Counterpoint on a " Canto Fei-mo " of this Species, and in Two Parts. 11, 12. Additional Eules, &c 6 CHAPTER III. Second Species. Two notes to One, in Two Parts. 1. Description. 2 — 7. Rules, Exceptions, and Precautions. 8. Examples of this Species. 9. Peculiar Licence allowed. 10, 11. Counterpoint of Three notes to One 12 b X CONTEXTS. CHAPTER IV. Third Species. Four notes to Oiie, in Two Parts. page 1 — 4. General Rules. 5. Ancient Licence not recommended. 6. How to save Consecutive Octaves or Fifths. 7. How to avoid the Tritone. 8, 9. Additional Rules. Examples of this Species 18 CHAPTER V. Fourth Species. Syncopated Counterpoint, in Two Parts. 1. Admits only of Minims. 2. Definition and Example of Syncopation. 3. Discords prepared. 4 — 9. Rules and Examples. 10— 12. Additional Rules. 13. Examples of this Species. 14. Syncopated Counterpoint in Triple time 23 CHAPTER VI. Fifth Species, or Florid Counterpoint, in Two Parts. 1. Elorid Counterpoint defined. 2 — 4. Rules and Restrictions. 5. Examples of this Species. 6, 7. Additional Remarks 28 CHAPTER VIT. First Species. Note against note, in Three Parts. 1, 2. General Rules. 3. Licence allowed as to Hidden Octaves. 4 — 8. More Rules and Explanations. 9. Examples of this Species 31 CHAPTER VIII. Second Species. Ttvo notes to One, in Three Parts. 1. Ancient way of saving Fifths not recommended. 2—4. Rules and Restrictions. 5. Examples of this Species. 6. Triple time 34 CHAPTER IX. Third Species. Four notes to One, in Three Parts. 1, 2. Rules and Relaxations. 3. Examples of this Species. 4. Combination of Second and Third Species 38 CONTENTS. xi CHAPTER X. Fourth Species. Syncopated Counterpoint, in Three Parts. page 1, 2. General Rules. 3. To guard against Hidden Consecutives. 4, 5. Rules about Dissonances. 6. Pedal Bass; Rule exemplified. 7. Consequent Remarks. 8. Additional Rule. 9. Examples of this Species. 10, 11. Concluding Remarks 43 CHAPTER XI. Fifth Species, Florid Counter2)oint, in Three Parts. 1. General Remarks. 2. Examples from Fux. 3. Florid Counterpoint in Two Parts at once 51 CHAPTER XII. First, Second, and Third Species, in Four Parts. 1. Relaxation of Rules. 2. Doubled Notes. 3 — 5. General Rules and Relaxations; Examples of eacb Species. 6. Combinations of the Three Species 54 CHAPTER XIII. Fourth and Fifth Species, in Four Parts. 1 — 4. Rules, Explanations, and Cautions. 5. Resolution of Dissonances on a dif- ferent Bass, and new efifects thus obtained. 6. Use of the Pedal ; Palestrina's method. 7. Diminished Fifth ; when allowed. 8. Examples of Fourth Species. 9. Example of Four Species combined. 10. Examples of Florid Counterpoint. 11. Florid Counterpoint in Three Parts at once 66 CHAPTER XIV. Of Counter2)oint in more than Four Parts. 1. Relaxation of Rules. 2. What is meant by "Real Parts." 3, Certain Licences allowed. 4. Introduction of Rests. 5. Examples of Counterpoint in Five Parts. 6. Examples of Counterpoint in Six Parts. 7. Progression of Basses in Coun- terpoint of more than Six Parts. 8. Peculiar Licence allowed. 9. Curious b 2 xii CONTENTS. PAGE Combination found in old compositions. 10. Tlie two ways of writing in Seven or Eight Parts. 1 1. Additional advice, and Exuniple of Counterpoint of the First Species in Seven Parts 84 CHAPTER XV. Of Imitation. 1, 2. Explanation and Description ; Examples of Imitation analysed. 3, 4. Definitions and Directions; Examples of Imitations at the Fourth and Fifth. 5. Free, or Irregular Imitation at other Inten'als ; Examples from Sala. G — 10. Imi- tation by Contrary Motion, with Rules and Examples. 11. Imitation "per recte et retro," witli Example by Dr. Crotch. 12. Imitation by Augmentation. 13. Imitation of Diminution. 14. Other kinds. 15. Of Canon, with Example. 16, 17. Canons in Three or in Four Parts; Azopai'di's Bass Themes; various Examples. 18, 19. Various Examples of Canons 94 CHAPTER XVI. Of Double Counterpoint. 1. Definition and Examples. 2. Various kinds. 3 — 6. Rules for Double Countex-- point at the Octave, 7. Examples from Fux. 8, 9. Rules for Double Counter- point at the Tenth. Examples from Fux and Cherubini. 11. Example from Fux of a Subject in Counterpoint both at the Octave and at the Tenth. 12 — 15. Rules for Double Counterpoint at the Twelfth. 16, 17. Examples from Fux, and Observations 117 CHAPTER XVII. Of Trijyle and Quadruple Counter2)oint. 1. Definition. 2. Examples of each kind. 3, 4. Other sorts of Counterpoint. . .135 CHAPTER XVIII. Of Fugue. 1, 2. Explanation and Definition. 3. Various kinds of Fugue. 4. Constituent parts of a Fugue 251 CONTENTS. xiii CHAPTER XIX. Of the Subject and Ansiver. page 1. Definition of the "Subject." 2. Definition of the "Answer." 3. Eules and Examples from Reicha 153 CHAPTER XX. Of the Counter subject of a Fugue. 1. Definition and General Rule. 2. Certain Variations sometimes necessary. 3, Some- times the Countersubject must be considered as a Second Subject. 4. More than One Countersubject 3 Rules. 5. The "Codetta" or "Conduit"; Example 163 CHAPTER XXI. Of the Stretto. ,1 . Definition of the word ; of the thing ; Example. 2 — 4. Various Rules for making Strettos. 5. Canonical Stretto, or " Stretto Maestrale." 6. Strettos by Inversion 167 CHAPTER XXII. Of Episodes, the Pedal, and the Coda. \, 2. Object and Use of Episodes ; how constructed. 3. Examples for Contrapuntal Episodes. 4. Other kinds of Episode. 5. Fugues of Imitation. 6, 7. The Dominant Pedal. 8. The Tonic Pedal. 9. The Coda 170 CHAPTER XXIII. General Structure of a Fugue ; its Modulations. 1. General Form and Arrangement. 2. Exposition. 3 — 6. Rules and Examples of the Exposition. 7. The Counter-Exposition. 8, 9. Fugal Modulation ; Rules. 10, 11. Additional Rules. 12, 13. How to introduce the Subject or AnsAver. 14. How to introduce the Pedal. 15. Additional Caution. 16. Inverted Pedal. 17, 18. How to make a Fugue interesting. 19. Instrumental Fugues. 20. Ex- ample of a Four-Part Fugue. 2 1 . Analysis of the foregoing Fugue, bar by bar. 22. General Advice to the Student. 23. Conclusion 179 xiv CONTENTS. LIST OF THE EXAMPLES. PAGE Twelve Canto Fermos to be used in every Species of Countei-point 197 No. 1.— Eight-Part Florid Counterpoint. By Perti 199 No. 2.— Eight-Part Anthem for Two Choirs. By F. A. G. 202 No, 3. — Canonical Harmonizations of the Scale. By Zimmerman 210 No. 4. — Miscellaneoiis Examples. By Zimmerman 214 No. 5. — Examples of Canon. By A. Scarlatti 220 Xo. 6. — Example of a Canon Four in Two. By Marcello 226 No. 7. — Example of a Canon Four in One, by Inversion. By Purcell 228 Xo. 8. — Example of a Canon Eight in Four. By F. A. G. 231 No. 9. — Example of a Canon Nine in One. By Travers 236 No. 10. — Example of an Infinite Canon, which ascends a tone in pitch at each i-eturn. By Martini 248 No. 11. — Examples of Infinite Canons at Various Intervals. By A. Andre .... 249 No, 12. — Example of a Canon by Triple Augmentation, By A. Andr6 252 No, 13. — Example of a Canon by Ketrogi-ession, or "Canon Cancrizans." By A. Andr6 253 No, 14. — Examples of Subjects in Double, Triple, Quadruple, and Manifold Counter- point 254 No, 15. — Examples of Subjects and Answers for Fugues 263 No. 16, — Example of a Fugue for Three Voices, and One Subject, By F. A. G. 0, ,273 No. 17. — Example of a Four-Part Fugue. By Cherubini 278 CONTENTS. XV PAOH No. 18. — Example of a Four-Part Fugue, with Three Subjects, and an Answer by Inversion. By J. Sebastian Bach 302 No. 19. — Example of a Four-part Fugue with One Subject, containing Diminution. By J. Sebastian Bach 325 No. 20. — Example of a Choral Fugue with Two Subjects and in Five Parts. By L. Leo 334 No. 21. — Example of a Five-Part Choral Fugue, containing Augmentation. By Dr. Croft 361 No. 22. — Example of an Eight-Part Fugue with Two Subjects, containing Inversion and Augmentation. By F. A. G. 377 THE PEINCIPLES OF COUNTERPOINT AND FUGUE. CHAPTER I. General Ohservafions. Eeicha, in his excellent " Traite de Haute Composition Musicale" (vol. i. p. 87), says : — " Les mots Contrepoint et Harmonic sont syno- nimes." This statement is surely incorrect ; for although they are correlative terms, yet Harmony and Counterpoint differ completely, as shall be soon explained. The chief difference between the two consists in the point of view from which it is regarded. When we look at a piece of harmonized music from the harmonic point of view, we confine our attention to the chords of which it is composed, to their preparation, resolution, and derivation, as is explained in our " Treatise on Harmony." We look at each mass of harmony as it were perpendiculady, up and down the paper, referring each note of which it consists to its proper bass. But when we look at a piece of harmonized music from the contra- puntal point of view, we mostly direct our attention to the melodies B 2 THE PRI>X'IPLE8 OF of whicli each part should consist, to their combinations one with another, to their fitness for singing, and to their adaptability to further contrapuntal development. We look at these melodies as it were liori- lontally, along the paper, from left to right ; and tlie harmonic deri- vation of the chords they may jointly produce is kept out of sight. The two aspects then of all harmonized music are perfectly distinct and complementary to each other. But, on the other hand, it is per- fectly true that to a certain extent the one involves the other ; for the preparation and resolution of discords according to the rules of harmony necessarily involve a progression of the parts, and thereby form melodies which are used concurrently, and therefore contrapuntally ; while, at the same time, no combination of melodies for contrapuntal purposes can exist without forming chords (consonant and dissonant), which chords necessarily include harmonic considerations. Therefore Harmony and Counterpouit are, in one sense, intimately connected together. 2. Counterpoint then may be called the " art of combining melodies." Such, at least, is a correct definition of it as it exists in modern times. And it is divided into two kinds. Simple, and Double. These must be considered in order, beginning with the former. Simple Counter- point is divided into five species : — (1) Note against note ; (2) Two notes to one ; (3) Four notes to one ; (4) Syncopated counterpoint ; (5) Florid counterpoint. Of the subdivisions of Double Counterpoint we will speak hereafter. 3. The older writers on Counterpoint imposed very strict and rigid rules as to the employment of intervals, many of which rules were derived from the mcomplete notions of harmony which were prevalent at that date ; others had their origin in the imperfect scales in which ecclesiastical melodies had been composed before the introduction of harmony. In modern music, of course, most of these restrictions should COUNTERPOINT AND FUaUE, 3 be modified or discarded. But still it will be a valuable exercise to the student of counterpoint to subject himself, in the first instance, to some at least of tliese old rules, as it will give him the habit of economizing his resources, and making the most of small materials ; and then, when he comes afterwards to write in a freer style, he will have acquired a facility in the mechanism of the art of composition not otherwise attainable. The rules in question will therefore now be laid down. 4. No melody may proceed by any of the following successive inter- vals — angmented diminished aug-mented diminislied augmented seeoncb fourth, fourth^ fifth, fifth^ major sixth, -f^- -!S>- =1^ ife: :S^= -&' 1?^ :ar^=j$d: diminished seventh. minor seventh, major seventh. augmented third. diminished second, except in certain cases, when the major sixth and augmented fourth are tolerated ascending, and the diminished seventh allowed in descending only. The allowable progressions in melodies of this style, then, are — g * 3 -(Sh- -Gh id: -(S>- :32^ -G)- G>- }&- ^21 -S' -G>- -Gh minor major minor major perfect perfect minor major second, second, third, third, fourth, fifth, sixth, octave, and these may all be used cither ascending or descending. B 2 ^ THE PRINCIPLES OF The case in which the augmented fourth is tolerated is in this jjrogression — No. 1. ni: ^m ^^^^^^^= tl,P !Ir '"''! '° '"'''* *' ^o^-^ding major .ixth k tolerated is when all tl.o other notes are stationary, and the harmony remains unaltered ; thus- -G>- •y -Gh- I 22: :z2: i COUNTERPOINT AND FUGUE. The case in which the diminished seventh is allowed is when it is in the minor mode, and then only descending ; thus — 122: V -' 3^ 'jr^: Z2: s>- -«s>- jC^ -G^ 5. The reason for the severity of these restrictions is, that counter- point in this style is meant solely for vocal performance, and therefore only the easiest intervals are admitted. Note.— The four vocal clefs now in use, viz, treble, alto, tenor, and bass, ^Yill be freely employed in this treatise, as every student of counterpoint ought to render himself thoroughly familiar with them. They are explained in the first chapter of our " Treatise on Harmony ; " also, more completely, in Hullah's admirable " Treatise on the Stave." It will be very serviceable to the student to write out in what is called " short score " (i. e. two staves, treble and bass) the examples in this treatise, which will be given in " open score " and in their proper clefs. CHAPTEll 11. Of simple counterpoint of the first species, or ''note against note," in two parts. 1. This is the most rigorous, difficult, and uninteresting of' all counterpoints. And as the contrapuntal rules concerning concords and discords are observ^ed without any mitigation in this most severe species, this appears to be the proper j)lace for their enunciation. 2. The only concords recognized in strict coimterpoint are the per- fect octave (or unison), the perfect fifth, the major and minor thirds, the major and minor sixths, and their compounds. 3. The discords admitted are the second, the seventh, the ninth, and lastly the fourth, which in strict counterpoint is always treated as a discord. The diminished fifth, and the augmented fourth, can only be used in strict counterpoint as passing discords. All these discords require preparation by one concord, and resolution on another (except wdien treated as passing chords, which never occur in the first species of counterpoint), as will be more fully shewn here- after. 4. There are three kinds of motion : — similar, oblique, and contrary. Similar motion is when two parts move upwards or downwards at the same time. Example — THE PRINCIPLES OF COUNTERPOINT AND FUGUE. ~F' 71 ms i"^ ^ /<-j VM/ ^- rj '^ r> f^Zi -O ^—^ tii' ^J . ^_ rj (S (S rj rj G) L Oblique motion is when one part moves and the other is stationary. Example — y A TTj f(\) r^ V^\) <^ rj <& J Gt ^ /^' l*^- rj \^ rj rj rj c^ Contrary motion is when the parts proceed in opposite directions. Example — -f 1 r n vl rj \(^ '^ <--i V ; '— ^ f ^ «y Cm^: t<*J- rj» v^ ■"" rj - -- -Gt- :q: -«S'- _"?:> -- r^ ' ' 122: 'JTJl 'JOl — s>- 1^21 :zz2: — - :^2: -o- -(S»- -s*- Very bad. Very Lad. Not allowed in less Tolerated occasionally, than six parts. hut very rarely. The student should beware, however, of availing himself of this licence of using fifths by contrary motion in the present species of counterpoint. The old writers always disallowed it. 6. It is forbidden to proceed to a perfect concord by similar motion, except when one of the parts moves only a semitone, and not even then if hidden consecutives are produced. For the ear or imagination of the hearer will supply intervening notes which are not actually sounded, and may thus produce the effect of consecutive octaves or fifths, even when not actually written. These imaginary octaves or fifths are called " hidden consecutives." For example — i :c2: -Gf- 'Gh ~rJL -O- -^-^ -G*- 122: -Gh- -- ~nr -^Sr 6 5 When, however, one of the parts only moves a semitone, it may happen that the hidden fifth may be a diminished fifth, in. which case hidden consecutives would not arise ; thus — COUNTERPOINT AND FUGUE. -O' ^ -«s>- ^^ -^&- -o- -(S»- -&-:s- '^2zzza z:^: 3 4 05 5 3 4 C5 5 This would be tolerated. But it is best to avoid even this licence in counterpoint of the first species in two parts. 7. A long series of consecutive thirds or sixths produces a very monotonous effect. It is better not to have more than three in imme- diate succession ; and these should be, if possible, alternately major and minor. 8. False relations are forbidden. By a false relation is meant the simultaneous, or immediately successive, sounding of a note of the same name, but accidentally altered pitch. Example — J=d= d=g^ t^- t^ ttp= -Gi- t^- J S=^^F -& r--r~Y ^ "tt^ These false relations are avoided by altering one of the notes chromatically, as thus — J^d=d: B p flp - r -- l&- ife^ -~ -- -(S?- 10. The first species of counterpoint is called " note against note," because every note of the "Canto fermo" (or given melody) is accom- jDanied by one note only, of equal length, in the counterpoint added to it. Usually all the notes are semibreves. For exampile* — Counterpoint. '-& Z2: 22: -s^ 1^21 -s>- -&- Z2: IZLZ :^z: 4f^ -&- Canto fermo. Z2: -&- :^: ^3 -- Z2: -<&— - 5 n 3 5 ;5 G 3 3 6 B or with the canto fermo given in the upper part, thust — Canto fermo. n?- 1 Ak i i ((\) ^l'' ^--) rj (^^ V y ' r' ^ ,*— > — ^ r^ ^'^ ^,_^ Counterpoint. 1^^ CJ hS- ^^ ' /»)' y ,*--> S^' i * ^-~i r' J '^-^ \ J '^ * From Fux, " Gradus ad Parnassum," fol., Vienna, 1725, p. 47. t Ibid. p. 48, COUNTERPOINT AND FUGUE. 11 11. The first note of the counterpoint must be an octave to, or in unison with, the canto fermo ; or, if the counterpoint be in the upper part, it may also begin with the fifth. In either case the conchiding note must be either the unison or the octave. The last note but one of the canto fermo should always be a whole tone above the concluding notes, and the counterpoint should always rise to the final by a semi- tone. 12. The student will now take some of the subjects or melodies given at the end of this treatise, using each as a canto fermo, first in the lower, and then in the upper part, and adding counterpoints to them according to the rules laid down in this chapter. c 2 CHAPTER III. Second species. Tivo notes to one, in two parts. 1. This species of counterpoint is easier to manage than the last. In it there must be two minims in each bar, if the canto fermo con- sists of semibreves. In the last bar alone the counter^Doint ends with a semibreve also. Every bar contains two beats, one down-beat, and one up-beat ; or, as Cherubini and others name them, a strong or accented time, and a weak or unaccented time. They were respectively called "Thesis" and "Arsis" by Fux and the older contrapuntists. 2. The down-beat must be a concord, except in certain cases which shall be explained hereafter. The up-beat may be either a concord or a discord. If a discord be thus placed, it must be preceded and fol- lowed by concords, and the melody must not proceed by a skip. Such discords are called "passing discords." Examples from Cherubini — Note airainst note. Two notes to one. -s>- -.^±± -- -s»- -- H^- m -jzL THE PRINCIPLES OF COUNTERPOINT AND FUGUE. 13 i^z: 1^2: -^- 1221 HE^Eg^ 'JTU. -«S- Z2zzi: -s*- -^- :iz?2: 1 -1^- -(S*- ^2: 12:2: - — Ci ■^ -?- -1 — ^ — 1 u 3. Fiix and others give a rule by which consecutive octaves and fifths between the "strong times" may be saved by allowing the counterpoint to skip an interval greater than a third, so as to come to the succeeding concord by contrary motion, the " weak time" in this case being also a concord ; thus — -y- rj ni A rj -^ rj frn f^ r- l^ J 1 8 8 8 8 5 8 5 8 1 1^-^ J c^ r^ r^ ^ -I Faulty consecutives. Said to be saved by this rule. But not only are the octaves equally offensive when thus treated, but consecutive fifths also are created on the up-beats. This rule is there- fore a bad one, and should be rejected by the student. 14 THE PRINCIPLES OF 4. The false relation of the tritone, described in the preceding chapter, can be easily avoided in this species of counterpoint, thus — False relation Another case avoided thus avoided thus 5. The student is advised to avoid a skip of a minor sixth in this species of counterpoint, as it is less easy to sing than the other allowed intervals, and can be easily got rid of with two notes to one. 6. It is considered elegant to put a minim rest at the beginning of the first bar, letting the counter23oint commence at the up-beat ; thus — ■ d-'-i Ml . 1 1 ^ -^ ^ -ts^- ■f^- p -T 7. The correct way of terminating a counterpoint of this species, when in the upper part (sujiposing the canto fermo to fall to the final regularly by a whole tone), is by a fifth on the down-beat of the last bar but one, followed by a major sixth on the weak time, leading thus up to the octave of the final ; thus — :^== "CT" 122: and if the counterpoint be in the lower part, it should properly have a fifth on the down-beat of the last bar but one, followed by a minor third on the weak time ; thus — -="- ^lo~ i^f^ -%-^ ^- COUNTERPOINT AND FUGUE. 8. We will now give examples of this species — Counterpoint. ^ — , — ^_ 15 gEl^^ ^2: fS>- (S» ^21 Canto fermo. 4t- I! 122: Z2: -G>- 3 4 (S _CZ_ Counterpoint. y r^ ^ "J J. /f r^ rv —^ 1 /-^ 5 f ^ ff ^ ^- rJ p> « V yl ' 1 6 3 3 4 6 3 Canto fermo. 6 3 5 6 8 U '^ ■^-^ rJ rj i^ -1 — 1 1 . il Canto fermo. ^ :^2_ Counterpoint. 1^2: -- 221 ZijL »_ :2i= Z2. ^ :?2: ^ i^ --^^=^ 1^=^ 'B O- Canto fermo. i^ i^ :^2: Z2: hS*- -o- 122: b6 3 8 7 3 C 5 COUNTERPOINT AND FUGUE. 17 #^^^-^ fS> 1 J 1 — . — 1 E^I^pz - o4p — f- :q: Q . 122: Counterpoint. 13 =2: -^- S^ o—f^- =g^-^[^:^E^^gp=F=r 8 6 3 8 7 -J (•> 8 6 5 4 6 7 :S2: -£2_ -S>— T- 1:2 ' _: -(S>- xz: & @Eg=^=g=^ ^^E^Eg C^ (S>- ^=P= i^: :tt^ -o- 678663876687553 « D CHAPTER IV. Third species. Four notes to one, in two parts. 1. In this species of counterpoint every bar except the first and the last must contain four crotchets against the semibreve of the canto fermo. 2. Skips should be avoided as much as possible, especially intervals greater than a fifth. 3. Every bar should commence with a concord. The three suc- ceeding crotchets may be alternately consonant and dissonant ; but every discord must be preceded and followed by a concord, and no discord may be attacked by a skip. Examples — -y 1 A 1 1 \(^ ' rz> ^ ■> \ J M ^ * * - _ _c-^ __. ^^^^ rj tJ -J-^ • ' * ^ f^ 1 ^,_, — —.—. — r^-r- ^ f ^ v^ — ^ — — ^ — rj c^. ^^T' —o—- ' y m f^:t ^ A -> ^ ^ ^ <"^ (c\ » ^ r rj> VMJ 1 J fm\' ^-^ l^- ^^ 1— :> TD " I v^^ S ^ ^ 1 THE PKINCIPLES OF COUNTERPOINT AND FUGUE. 19 4. The unison is allowed in this species, except on the first note of the bar. 5. Zarlmo, Fux, and other old contrapuntists allow a licence in this species, when the second or fourth crotchet is dissonant, in which case they allow a concord to follow by a skip ; thus — -9- "C7" :?2: -s*- ^^rf :g: 5 "CT -''^3- is i ^i^^ f e^- i:=o: '-QT- -^s*- -&- "C7" 122: -«s>- ■rr and Fux explains it by reference to certain passages in florid counter- point of which it is a simplification, e. g. — -Try - simplified into -iS*- ^ -s»- But Cherubini demurs altogether to the use of this licence, and would rather write thus — i 1221 -&- XT ^^ On the whole, Cherubini's view seems to be the more consistent and reasonable. The student is therefore recommended to avoid such counterpoints as the above, although they have the sanction of great classical composers. 6. To save consecutive fifths or octaves, more than two, or even three, crotchets are required. All the following examples are faulty. D 2 20 THE PKINCIPLES OF i ^^ ■^s^. M ^t^^=i 5 ^-±jtJ^zst W -- 22 THE PPJNCIPLES OF COUNTERPOINT AND FUGUE. 11. It is sometimes necessary to allow the parts to cross. But this should never be done tHl every other mode of escape from a difficulty has been tried in vain. 12. The folloA\ing examples will serve as models. P^=?i --]= ^ ^5Pj ^^=^«=^ Canto fermo. ;3E i?:^: ^TT ~r2L -Gh ^^n^:^ 3^^^^S ^3F :£2_ -- -o- Z2 Canto fermo. i a xz: -- iq: -«s>- ;e^!3^ r ^-^ Sfe ?*=^- B^f J p f 'Z^iL. -^ i:2L -&>- t^i^H a=*: ^ £ K ^ Z2: CHAPTER V. Of the fourth species. Syncopated counterpoint, in tivo parts. 1. This species admits only of minims, and a concluding semibreve. 2. A semibreve is said to be syncopated when it is struck on the up-beat, and continued over the down-beat of the next bar ; thus — i ¥ -. ¥ 5 -- -Gt- :?2: 3± -G>- or, as it is now usually written — E!^ j^i z:^: iQ. 1?:^: rj; .e>- ^-s!= -Gh- 3. In the last example there were no discords. Nor must they ever occur on the up-beat ; but on the down-beat they are permitted, provided they are prepared and resolved according to the rules of harmony which refer to suspensions. See " Treatise on Harmony," Chapter VIII. Example — J i J_J q^ > - Z2: i^ — s>- -jzt -&- 7 6 i:± ~?2 -G>- -& 24 THE PRINCIPLES OF 4. Always let tlie dissonant note be heard as a concord in the pre- ceding chord. This is called preparing it. 5. Always resolve the dissonant note by letting it descend one degree to the succeeding concord. 6. The resolution of one dissonance may serve as the preparation for the next. See last example. 7. By leaving out the dissonances, the derivation of them will be made clear ; thus — i^ ^^- s > _ — i^ — 9 8 1^21 -Gh- -j^z -- 7 G Let us take this example, and leave out tlie dissonances, when it will become — S A i^^ -G>- 1^21 I ZIZL -&- 8. If we resolve a series of seconds by the unison, or of ninths by the octave, we shall produce hidden unisons or octaves. '-^=^ - ocJ^^^_^.^: or will produce, when analysed^- ffi^ -<& CJCJ or I! :^ -^ -G>- "O- i^ A -(S>- 'Tizr z:± 221 G>' COUNTERPOINT AND FUGUE. And in tlie same way the following succession — 25 J!Eig G>- ._C2- -S>- ~-T^4^^^^o- z- -^- 122: -iS"- -s*- /S'- P#" when analysed, is resolved into consecutive fifths; thus- :^: :z2: -s>- 1^21 -S>- iFE!^ &- :?^ -- -^s*- -s»- -^- -(S- 1^2: All counterpoint of this species should be tested in this way. 9. The dissonances of the fourth and ninth should be avoided as much as possible, when writing in no more than two parts. When the counterpoint is in the upper part, the best dissonance is the seventh ; and when it is in the lower part, the best dissonance is the second. 10. Every bar ought to be syncopated whenever it can be done without either going beyond the limits of the voice, or leading to frequent repetition of the same phrases, or involving liability to contra- puntal errors of a graver kind. Whenever such difficulties arise, the syncopation may be interrupted for two minims, but never more. 11. It is usual and elegant to begin the first bar with a minim rest, followed by a perfect concord at the up-beat. 12. In the last bar but one, if the counterpoint is in the upper part, the syncopation of the seventh should be invariably used ; and that of the second, if the counterpoint is in the lower part : thus — M -&■ -r± o- -^± ^- 7 6 22: or ::±:^i==g--g ^^j^ -- E 26 THE PRINCIPLES OF 13. The following examples"' are intended as models- '(', - -^ .^n :z2: ^ ^=^ P^=^^^ fS>- 3^ Canto fermo. i£! 221 :q: -s>- 12:2: -- 1!S>- 4r^ -- 22: Canto fermo. fcffi 2:2: 22: -- 22: -<^ I 1^=:^ ^21 22: 11 ^=^^=P :^r^:: =S 3 zz: .C2_ -- I^Z -- :?2: 1^=3? 22: _C2_ C2- g:]T~"r^ ^ ^^ 22: 5 3 3 2 3 * From Fux, " Gradus ad Parnassuin," p. 74. COUNTERPOINT AND FUGUE. 27 14. There is a variety of this species sometimes used, in which three minims are placed in every bar, against one dotted semibreve in the canto fermo. Of this an example or two will be a sufficient explanation. ^m -^ :£ ^2: (S>- :^ ^ =?:2: ■rJ — >- --^ ^~ -^± q=f Canto fermo. ffiEs: :?2: rzf . iq: -«s*- :^: W^ 6 76343a 766 ?2: :^=^ -f- — h :^=^ f^- -^=^: :^= :^: tSt- pzgp>-^|E^^ +ai=22=z: _C2- -S>— V- 122: -^— ; -7^- 76 43676 Canto fermo. 6 7 B - 1^21 :^z: -«&- 221 -<^ — - W^ Z2q~p: a :& e; r^=^:z:&z^ ■^==^ (S»- (S>- :^ 3 2 3 -Q. -S*— r 1^2: fe :q: -- (/3) Quavers should never be admitted in the first or third quarter of a bar, but only in the unaccented portions ; thus — Ko. 1. I ^ ^ -s* No. 2, Z2: No. 3 122: In the last example four quavers are introduced. This is, however, by no means recommended as a frequent practice. (7) Quavers should never move by a skip, but always dia- tonically, as in the preceding examples. 5. The following examples of florid counterpoint altered from Fux may serve as models — I S 'W=^ ^^- fS- H«=^ ■^— ^ rcz 5t^ Canto fermo. M S; xz: -«s»- -^- -ry 30 THE PRIXCIPLES OF COUNTERPOINT AND FUGUE. gg^£F=^-t^ :±g^j^ s C5: T^- -r^L -C2_ -s>- Z2: m- -Gh- 1^21 Canto i'ermo. 1 r-j J / ■h rj rj !»^-V / 7 (. -"v f^ m r^ ri r' i - \ a ^ r A r ^ M ^ M J * ^ r TT ^ ) S \ \ r • ^ r 1 <««j — 1 1 1 1 — 1 — . 1 _Q- -S>- -TJi -iS*- xz: cz c^ a^^ T^ T2L ^s^ 6. Before proceeding any further, the student is ad\ased to write counterpoints of each species, adhering strictly to all the rules, and taking for his subjects any of those which are appended to this treatise. CHAPTER VII. First species. Note against note, iyi three parts. 1. All the rules whicli have been given for two-part counterpoint, apply equally to the present kind, except where otherwise specified. 2. As far as possible every bar should contain complete harmony, i. e. a major or minor triad, or its first inversion. See " Treatise on Harmony," Chapter III. 3. If the canto fermo is in one of the upper parts, the rule about hidden octaves (Chapter II, sect. 6) is so far relaxed that the bass may descend to the final by a skip in similar motion ; thus — Canto Fermo. 1 1 ^ rj -^ L > rj r^ - a-_± y 7 1 J , '— ' -,. . . ^^ ^ — , -» r ¥ /"-:) <^->' ""Tit / C. ! II ni\' rj i^' (^ rv V.^ i J rj 5 3 6 6 5 But this license should only be used when absolutely unavoidable. 4. In the second and third bar of the foregoing example the chord is incomplete ; but it is a case in which this is tolerated in order to secure a melodious inner part, which could not otherwise be obtained. 32 THE PRINCIPLES OF In three-part counterpoint skips are always to be avoided, unless abso- lutely necessary. 5. The old contrapuntists generally avoided the third in the fin;J chord ; or if they used it at all, they always made it major. This major third, if thus introduced into the minor mode, was called the " Tierce de Picardie." To modern ears a concluding chord composed of octaves and fifths, without any third, sounds harsh and crude. In three-part counterpoints, therefore, the following positions are to be T Q Q Q •> •-! ^ *i preferred (the third being always made major): — i 8 i 3 s i :', -y These are placed in the order of merit. 0. Tlie third and sixth ought never to be doubled, i.e. neither of them must be heard simultaneously in two parts. This rule may be relaxed, however, in case of emergency. 7. In this species of counterpoint neither of the upper parts may be at the distance of a fourth or an eleventh from the bass part. But the interval between the two upper parts may be a fourtli, e.g. \?^ or \o S. The last bar but one must always contain a complete chord. 9. Never allow a part to be stationary on one note for more than tliree bars at most. 10. We now subjoin examples to serve as models. Canto fermo. II , \~^^ — 1 S>— n rj r:i r- 1 CJ^ T=*^T * ?:^ rv ^^ - blX " " / 1 /'—I rj <0 -4**^ r^ H J C/ . >'-> c (r-~^ /*^' rD 1 ICJ. / \ ^-. *^-^ 1 ^^ . ,^-) V^^l J ^^^ _ --■C-» r J "— ^ 1 . . '"^'''^ COUNTERPOINT AND FUGUE. 33 Canto fermo- P > fjr zzr~r^~ W^ -G>- :q: -«s- 1^21 -s»- L'^z: -^- Z2: 122: -G>- -^ -s» — ' :C2ZIL Z2: -- -o- r3 ,,._-, -■=t-^ ^-^ rj ^^-, f^ - r* *~-^ C2 J*/^ ■ n) -* V y -g r^ u ^ (a > <-> j??:> -/^-i J r-J ^.^ He? Canto ferm 0. i»y TD ^2" l^- / > r^* c-> r^ r^ v^-A^ <^ - These examples are from Fux, x\ third has, however, been inserted in the concluding chord of the last, in accordance with modern practice. Fux made his tenor end on the fifth. It will also be observed that in bars 5 and 10 of the last example a chord of the major sixth and minor third has been introduced by Fux. This may always be done under similar circumstances. F CHAPTER VIIT. Second species. Two notes to one, in three parts. 1. The old contrapuntists laid it down that it is allowable to save consecutive fifths by introducing contrary motion in the inner part ; thus — ■ 22: -(S»- --^- fS- -jTJL -G>- iq: e But the student is strongly advised not to avail himself of so question- able a licence. 2. The two minims must be placed exclusively in one and the same part throughout a piece, and the other two parts nuist contain nothing but semibreves. 3. The third may be doubled on the up-beat, but not on the down-beat, except in cases of absolute necessity. THE PRINCIPLES OF COUNTEEPOINT AND FUGUE. 35 4. The unison should be avoided generally on the down-beat, but is allowed on the up-beat. It is of course allowed also in the first and last bars. 5. A syncopation is allowed in the last bar but one, as in the fourth species. Examples — No. I. Canto fermo. fe^ 1^21 22: «s>- Z2: - k 17 ILl --■, -^ ' ' - f-* i'-n T-^ ^' ..^ 'TJ r> i*,^^ - -«s>- 2z: 1^2: :?2; PE^ --r ^ — (^ ^2: ^~ :& J p— fa -s»- ^ -o- 12:2: :zc2zz I -s>- - -e>- -•s*- No. III. 5E^ <^~ i^z: Z2: -(S>- -<^- Canto fermo. 3!==^- : ry -(S>- 1221 hS^ -li=t- ffi^J^ 1^5=1 -^ — O- -(S- -/S- -lS> X2: g; r:^—- 1 COUNTERPOINT AND FUGUE. 37 tr- ,^-~i r^ 1 rj ! ((^ r:j f^ 1 v^ ; 1 u^o «l - Z2: i-Qz Canto fermo. " ! rj e*- Z2: -s»- e^ iS^ :tf^ --S- i^i -^- #^ -s»- 1; -Gh- :^ -- 1^21 -— =Jf^: Canto fermo. -o- :i:2r. -o- 1221 I THE PRINCIPLES OF COUNTERPOINT AND FUGUE. Canto fermo. 39 U-H— + it^ 3? 'JTJL :fi^: -(S>- -^- icz: Canto fermo. I ' TTT -^- 1^21 1.^ J-|^ Canto fermo. %- 122: «s> -- U: :JIq: -- 3. The following examples are intended as models. No. I. EE!3: ^ £ ^^>--tfF^ Canto fermo. :z2: -cs- feEg 122: -~r"^»n^ 1 -l"^ — ^ ^ L -Vf-m, 1 — 2 eS* t^-f-^-^-- -r J r - 1 r f^r- J 1 Jg^- y J ^-i* V ; ' ' 1 1 ri J ^-^ rj J rj ^ 7 u /«^' ■-^^ l^' rj 4Q THE PRINCIPLES OF No. II. w~r » IS S=p: ;s WM -- -Gh- :?:2: 1221 =12 22: Cauto fermo. J! -s^- -- 1^2: -«s>- 1^2: i ^ssg ESSSfES I^ ^^^=^ -S*- 'It^~ -(S'- -s>- 122: 1^ e -s>- -- 1^2: -«s>- No. III. ±1 TT 1^2: -iS^ 122: -s>- Canto fermo. B^ IE 122: fefe^ ^ — "C2: 1*=^ -- :22: £E^ ^•^^ -- -r- | f r r f * COUNTERPOINT AND FUGUE. 41 1 r J " <^ 1 G> 1 ^^— i — &< - J- ^^ i— ^ -^ rj) ■« ^ ^ iB P- . ^ ^ f^— — -^ ^ ^ -^-r---K- i h^*- -A ^— ^- P^^-P ^- ^ » r » * pH — ^ — ^ *^^ «- -h— «-— P- —& 1 — 1 ' I ' ^ No. IV. Canto fermo. I ^^2L -j^2i ■- :q: -»s>- fc ^EaEg=^ =j=J;^ ^E^ ^=g=F:^=j^ E33 =^ ^^^ J=|=j:fe^=3i^ G- -- :q: :?2: 122- :3zzi22: hS>- :q: -<&>- 'j:j : 4t^-«-^-^ #: ^^ ^^ ^^=±=^ -I h -«s>- -^3- Z2: icz: -s'- -(S>- G 42 THE PRINCIPLES OF COUNTEPtPOINT AND FUGUE. 4. After taking the various given subjects at the end of this volume, and treating them according to the above models, the student will next combine the second and third species of counterpoint, treating each according to their respective rules. An example is subjoined — -f^^T-^^-^^- -d-i^ . ^ — 1 1 1 — ' /?^^-F— J i- ^' m~y^ m TV J *' J' 1 —1 \ — h \S ) ^ ' s ^ * S S J ^ S J ; 1 ! J 1 yi P - — o — -»-T Ss» — rj -b/^^ — ■7-f^ \ ~r — ^— 1 -i p — -A-^ rt— C, ^ "^ _L . Canto fermo. {^^7\i ^ ^ rj V^-f^ ^ G>- |E3^fe -p^ —m- ^- ? -«s»- fe 5p i^ -(S^ -fS>- T^- :p -fS>- z:2: i^- ^^~n -- -^s»- 1^2: -<^ 12:2: -G>~ CHAPTEE X. Of the fourth sjjecies. Syncoixded counterpoint, in three parts. 1. As flir as regards the canto fermo and the syncopated part, the same rules apply here as in the fourth species in two parts. 2. The third part, which consists of semibreves, must always form concords both with the canto fermo and with the resolutions of the syncopations. Thus, if the syncopations are removed, there will remain regular counterpoint in three parts of the first species. For example, take the following — -G>- 22: -(S>- 1^21 -Gh- I --^ fS>- ¥ - ^- T^ fS^ (S»- ^2: -&- i=^F='-^ :q: -«s>- Z2: :q: If we remove the syncopations, it will stand thus- G 2 44 THE PRINCIPLES OF m 3i -S>- T^ I hS>- ;22: -- iiz:;z S 32: -o- :c2: -