Canon And Multiple Counterpoint

Transcript

'm\\v'. CORNELL UNIVERSITY LIBRARY MUSIC Cornell University Library MT 55.B85D7 3 1924 021 750 934 Cornell University Library The tlie original of tliis book is in Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924021750934 SIXTH THOUSAND. NOVELLO, EWER AND MUSIC PRIMERS. JOHN STAINER. Edited by Sir Double CO.'S Counterpoint AND CANON BY J. FREDERICK BRIDGE HUS. DOC, OXOM,; ORGANIST AND MASTER OF THE CHORISTERS OF WESTMINSTER ABBEY; PROFESSOR OF HARMONY AND THE ORGAN AT THE NATIONAL TRAINING SCHOOL FOR MUSIC, KENSINGTON, AND AT THE CRYSTAL PALACE SCHOOL OF ART; LATE ORGANIST OF THE CATHEDRAL, AND LECTURER ON HARMONY AND MUSICAL COMPOSITION AT THE OWENS COLLEGE, MANCHESTER; EXAMINER IN MUSIC TO THE UNIVERSITIES OF OXFORD AND CAMBRIDGE (x888). PRICE TWO In Paper Boards, Two SHILLINGS. Shillings and Sixpence. loo LONDON & NEW YORK NOVELLO, EWER AND CO. LONDON KOVELLO, EWER AND -PRINTERS. CO., INTRODUCTION. Those who propose to study Double Counterpoint and Canon should already have acquired the art of writing the various species of Simple Counterpoint in four or five parts, together with a There seems no reason why the good knowledge of harmony. who has been through student this preliminary work, should debarred the use of the resources of modern harmony writing his examples. Counterpoint, with mony, he far as is many he has diligently worked will not fail to feel its at when Simple progressions of melody and har- good influence, and consistent with the greater ireedom he to apply, as now enjoys, its valuable precepts. The application of Double Counterpoint and writing will, in student will choose many Although is all make With the art. point If its restricted be probability, be the the first this in view the Author has thought references to it well to of his examples from works of a fugal character. it is in to fugal which the use of his knowledge of this branch of in this style of composition that Double Counter- most used and most necessary, yet employed Canon direction in it has often been music not of a fugal character, examples of and which are g^ven many opportunities for those who its in the course of this work, happy introduction will be and found by take the pains to master a subject so necessary and so useful to the true musician. iv INTRODUCTION. An rules; justify same but at the necessary, him made has been effort all useless and pedantic time, for the student, rules are absolutely he -has acquired the until in to avoid departing from the knowledge which strict letter while he is will observing the spirit. The Author's best thanks are due to Miss Smart, for kindly allowing him to insert the interesting canon by Mendelssohn, hitherto unpublished (No. ip of Appendix) ; to F. Locker, Esq., for bringing to his notice and permitting him to copy from the ginal MS., the canon by J. S. Bach (No. 9 of Appendix) ; and to to many valuable James Higgs, Esq., Mus. Bac, for kind Dr. Gladstone for Example 128, together with suggestions ori; assistance and most useful advice which his well-known acquire- ments and special studies in this branch of the musical art rendered invaluable. The Cuoistees, Westmifstbf Aensr. Septemoer, ibSi. hav; CONTENTS. CHAPTER — PAOB I. — Double Counterpoint General rules Double Counterthe octave Examples Double Counterpoint in the fifteenth Examples Subjects to which Double Counterpoints may be added Examples of models derived from simple phrase Definition of point in — — — — — . CHAPTER in the tenth Double Counterpoint in the twelfth CHAPTER thirds , - • . • . l6~a4 III. — Examples CHAPTER Added — 15 II. —Examples Double Counterpoint i 25 — ^33 IV. —Examples —3S 34 CHAPTF" " Counterpoints invertible in various intervals — Examples CHAPTER Triple and quadruple counterpoints point Example — — and Strict — Examples— Quintuple counter- — — — CHAPTER — Examples— Chorales imitation imitations Partial —5a —57 VIII. — — 46 53 CHAPTER ^45 VII. — Examples free — — — — Free Examples Strict by contrary movement By diminution By Imitation by augmentation Examples augmentation and contrary motion By diminution and con. . . trary motion With reversed accents Examples Imitation — 39 VI. CHAPTER Imitation . . on — 58 —63 IX. vifhich are constructed 64 CHAPTER X. Canonicalimitation— Origin of term— Examples .... —75 76—79 CONTENTS. VI CHAPTER XI. PAOE —Infinite— Finite by augmentation — Infinite by augmentation — By diminution— Retrograde — Circular— Examples Canons : Finite CHAPTER Polymorphous canon CHAPTER 80 —gi . 92 —96 97 — 100 XII. —Examples— Sequential canon—Example Methods of exhibiting canons . XIII. —Open—Close—Canon four in two Round CHAPTER Hints to the Student XIV. —To compose a canon— Modulation in canon . loi — 102 io'> —12a APPENDIX. Examplef) of Double Counterpoint INDEX. Paraoraph. free parts to model for Double Coun. terpoint in tenth . . . | Added thirds to models for Double Counter- \ . point . j Addition of accidentals in inversion of model Addition of accidentals in inversion in the] Added . . . „ circular (per tonos) „ close „ by diminution „ enigmatical ,, finite , . by augmentation infinite by augmentation infinite or perpetual „ „ open polymorphous „ retrograde sequential . • . . . . . . 107, . 136, 14a 137 '33 124, 125 129 130. 131 126, 127 128 99. .... .... 117 no to . 103 to 105 137 to 143, 133 to 135.. "5 H3 I 13 9329. progressions . . . ..... .... Clefs prefixed to a close canon Contracted parts subjects ,, 118, 124 3 (notes to Sec. i) 3 (Sec. 3) . ! oblique motion generally 1 employed f Contrary in Double Counterpoint at the) Contrary and tenth ,, 39. c; 40, e . Canoni Chromatic notes „ • • 108 117 to 124 102 109 96, 97 100 lOI with coda ' ' 30 29. (g6 (note ,106, . .... . finite „ 68 to 74 80 91 Canon „ „ 42; 51,6 59, a, b, c; 60, 61, 62, 63, 64 J Antecedent „ „ „ „ 35- 43 tvirelfth - EXAMPLB. .... 34 • J motion 3 (Sec. 3) Counterpoints invertible. in various intervals Consequent Crossing of parts . . Double Counterpoint . Double Counterpoints most used 3 (Sec. 3) 65 to 71 81 3 (Sec. 2) • 1 . . 2 . 75 to 81 INDEX. VI 11 Paragraph. 15 to 24 Double Counterpoint in the octave „ „ „ „ „ „ „ „ „ II 11 1, iifteenth Example. 25 to 30 7 (note), 21 . octave displayed 1 at the doubleSve J octave inverted I at the fifteenth J 19. tenth 3 (notes to Sec. i),] twelfth- 3 (notes to Sec.i),] 25 . .1 I. II „ „ „ „ „ „ tenth,modeland' I, inversion at the time. thireleventh, 41 ( tenth combined with thatintheSve . 461050; 76,4 62 to 69, 78, 79 59- 40. same „ ,, ... and fourteenth Example of simple model elaborated Expansion of parts Fourth, augmented Fifth, dimmished or minor Figures denoting the interval in which a) canon is made J teenth, 58. 37, u, b, . .... .... Fugue in epidiapason Fuga ligata . . . „ „ by augmentation „ .... .... .... .... and diminution,! combined with contrary motion J by diminution ,. canonical . . on a chorale by contrary motion „ „ free or irregular in two parts, with independent) „ „ accompaniment „ partial or periodical > . . . . . . 34 (Sec. 41 144, u, b 119 122, b i2g (Sec 126 (Sec, I, 2 3.4) 127 4), 76. 83- III 85, "3. 84. 88,91 90. 112 81 . 79 • "4 iig to 121 105 to no 96 to 99 100 to 104 J 88, 8g, g . ... 87. .... 86. 87. 77.78 89. retrograde {per rede ei retro} or cancrissans J reversed accents (per arsin ei tkesin) „ reverse retrograde ,, strict or regular ,, on a theme or canto fermo „ Methods of exhibiting canons when written „ d, t 93>94 . „ 8, 10, . General rules Hints to attain clearness in canonic writing How to avoid modulation in a canon Imitation c, 3 (note to Sec 8, 10, 34 (Sec. . Model Modifications of terminations in Double) Copnterpoint in tenth and twelfth J Octave on gccented beat Qniission of accidentals in inversion ofmodel for Pe»ble ConjiteFpoipt in tenth / .... . 117 3 (Sec. "5 90 to 95 116 to iiS i) 29 (note) 14. 29. 39. 6 INDEX. !x Example. Paragraph. Origin of the term " canon " . . Partial or periodic imitation. Preparation and resolution of seventh in Double Counterpoint at the twelfth Progressions by similar motion in Double Counterpoint at the tenth PiOposition ..... Quadruple Counterpoint Quintuple Counterpoint Reversed clef and time signature Riddle Canon Round 93 51,52 58,59 . 34 (Sec. 41 I, 2, 3) 80 72 to 74 . 88 8g 133 75 103 log 126 .... Rule for discovering the inversion of any| interval (Sir J. Goss) Seventh diminished Simple model from which others are derived 16 . . Sixth augmented Sixths in Double Counterpoint at the tenth twelfth ,> >, » I. Solution Stretto Subjects to which counterpoints may be added Suspension of the second . fourth „ ,, seventh . „ „ ninth ,, ,, Table of inversions in the octave tenth . „ „ twelfth ,, „ Third, diminished Thirds in Double Counterpoint at the tenth . Triple Counterpoint To compose a canon Two ways . ..... .... of inverting in the tenth Unessential note Unprepared discords Use of three staves in inverting exercises Usual method of describing canons . i2> 13.34 (Sec, 1.3 24. 11,34 (Sec. 2, 31 to 33 47. 48, 51 log 116 36. 36. 37. 53.54 3). 50 41 37, a, b, 41. 57 c, 32 to 36 43 44, 60, 61 37 44. 47. 49 38,54 16. 45,61 27 d, . 43.44 31 to 33 72 to 74 126 28,30 81 to 87 (38, a,b,c; 40, a. 6, c \ 7 • 4 22 . 9a. DOUBLE COUNTERPOINT & CANON. i^se;^-! CHAPTER I. A TWO-PART phrase is said to be in double counterpoint admit of double employment, i.e., when either act as upper or lower part in other words, when they when both may I. subject's ; will invert : F*^=r= Ex. I. DOUBLE COUNTERPOINT AND CANON. General Rules. for inversion, which together model a convenient term which will be used henceforth in this work must never be separated by a greater interval than that into which fhey are to invert. The two phrases intended (i.) — constitute the — In Ex. I the phrases are never more than an octave apart, because they are designed for double counterpoint in the octave. If this interval were exceeded the parts would not invert. In Ex. 3, a, the interval of an octave is exceeded, and at b is given what should be the inversion of the same. Ex. 3. a =PI n i <;r-:J**- ^SiP^ 10 II 13 ^ S P^3 ^ m It will be seen that at Ex. 3, i, * * * no inversion takes place ; the parts are merely contracted, and the effect of both passages, so far as the last two chords are concerned, is essentially the same (Ex. IZ3Z 4, a, b). ma Ex.4. m10 II ' m 13 3 4 Ex. 5, a, is a model for double counterpoint in the tenth (see page 16), in at T * this interval (a tenth) is exceeded. An inversion of the model is given at b. It will be seen that the faults in the model result in the parts being merely contracted, not inverted, at the places marked * •. which Ex. N 3. Model for a d.c. in tenth Hi \- rj *-# \ II la m m -•- ^ GENERAL RULES. Inversion. b m -^2 Lower >!-- part of model a tenth higher. '^J JjJJN^^ij.jjL a I For a corrected form of the above example see page i8. Ex. 6, a, is a model for double counterpoint in the twelfth (see page 25) witK similar faults. At b it is inverted with the same results. Ex.6. M a Model for d.c. in twelfth. * • ' --. y J=¥=f Q ^. ^. 13 14 :$=&: 6 ^m^=^^ :t=E Inversion. pr^r i :$: Lower ^ (2.) The ^P It part of -»-f^ model a twelfth higher. &c. ^ ' -.° o <-J - parts should not cross in the model. It will be seen- in Ex. 7, a, b, that the effect of the -intervals marked * * • is rpractically the same. In this case the intervals marked * * ' in the model a are expanded, not inverted, at b. Ex. 7. gS m g^=^ n a^ T^"jyr — rs* »!- ^Si ^^B * I I DOUBLE COUNTERPOINT AND CANON. 4 subjects forming the model should be well conas to length of notes and melodic progression, contrary motion being always preferable to similar motion ; the two parts will thus possess individuality and be easily distinguished from one another. It is well that they should not begin together, but that one should enter after a short rest (see The two (3.) trasted both preceding examples). of course, be understood from the Introduction is not confined to the progressions and chords used in simple counterpoint in the strict style. While, however, chromatic progressions and unprepared discords are available, it must be remembered that the model will probably be heard alone {i.e., without accompanying parts), and therefore a somewhat strict rather than free use of such discords is advisable. It 4. to this will, work that the student DOUBLE COUNTERPOINT IN THE OCTAVE. 5. The intervals of the fifth and fourth are those which will most require the student's care when constructing the model. 6. The perfect (or major) fifth, although consonant in the This model, becomes by inversion a discord, viz., a fourth. condition must therefore be provided for, and as a fourth will seldom appear upon the accented beat without preparation, the Upon the unacfifth must conform to this usage (Ex. 8, a, b). cented beat fifths and fourths are of course often taken without preparation, especially when they occur as passing notes (Ex. 8, c), or by conjunct movement in at least one of the parts (Ex. 8, d). Ex.8. a i 3±L uaz =pzz ^C2= The bar marked d is =g= =r T=^ not very good in two-part writing. Even upon the accented beat cases may occur where these maybe used without preparation, particularly when one of the notes forming the interval is an unessential note. At Ex. 9. a, is an unprepared fourth upon the accented beat, the E in the upper of the two parts being clearly an unessential- note,— 7. intervals an appoggiatura. INVERSION IN THE OCTAVE. ^^^1 Ex. ^ g. The above is double counterpoint in the fifteenth or double octave (see par. 2i). 8. The augmented fourth (Ex. lo, a, b,c) and its inversion, the diminished (or minor) fifth (Ex. lo, d, e, /), may be freely used on either accented or unaccented beats. Inversion. g. The avoidance of consecutive major fifths is of course necessary, and the student will understand that consecutive major fourths are equally objectionable. lo. Some authors allow a major fourth, followed by an augmented fourth (Ex. II, a), resulting, when inverted, in a major fifth, followed by a minor (or diminished) fifth (Ex. ii, b); but these fourths should be avoided unless the model is accompanied by another part, which renders such harmony unobjectionable (Ex. II, Ex. II. c). gfF^; ll f_tf-H=^^-ljl l ;'-<^; ll were dotted, all objection would would then be a passing note (Ex. ii, d). If the first note of the lower part at Ex. ii,b, be removed, as the G The augmented sixth (Ex. 12, a) cannot be used because inversion, a diminished third (Ex. 12, 6), must be avoided in • two-part writing. II. its a Ex. 12. "^ h -P" jlBSl DOUBI-E COUNTEJlPOmX AND C^NON. 6 The diminished seventh may be used 12. if care be taken in resolution, as, for example, if one of the notes forming the interval be resolved before the other (Ex. 13, a b), or if, resolving on a fifth, such resolution falls on the unaccented beat ; but this is not recommended (Ex. 13, c). its Ex. 13. r^rW^fZ 'I iri- "p^^^~p" I i The diminished seventh should 13. fifth H A=[^A i on the accent (Ex. 14, a), not be resolved upon a because in its inversion a fourth results (Ex. 14, b). Ex. •'$ -W=^ 14. The octave becomes by inversion an unison, and in this species of double counterpoint should be .used sparingly, except at the beginning and end of the model, or perhaps occasionally as an unaccented note. It should not be taken by a skip on the accented beat, especially by similar motion. 15. With the exception of the fourth and fifth, to which special attention has been called, those intervals which are discords in the model (the seconds and sevenths) are discords in the inversion (becoming sevenths and seconds respectively), and the concords in the model (the thirds, sixths, and octaves) are concords in the inversion, becoming sixths, thirds, and unisons respectively. The 16. octave following table ..shows the result of inversion in the -. Model ... Inversion It may Goss perhaps be useful to mention the rule given by Sir J. Rudiments of Harmony," for discovering the inver- in his " sion of any interval [in the octave] by referring to the number g, " since each interval when added to its inversion will make up that number." This rjile may, of course, be expanded to apply to inversion in other intervals, the principle being to add one to the number of the interval in which the inversion is to be made. Thus, for inversion in the tenth (see par. 27)- each interj^al added to its inversion will make 11, and for inversion in the twelfth INVERSION IN THE OCTAVE. (see pars. 43 and 44) each interval added to its inversion will the addition of one is necessary, because the central 13 make ; note on which the inversion turns is counted twice, thus : i f3 + 6 = g. Examples of double counterpoint in the octave are give»' of the inversions do not appear in the compositions from which they are extracted, in the keys here given. The inversions of the first few examples which follow are, however, given in the same keys as their respective models, in order that each counterpoint and its inversion may be more readily seen by the student. It is not thought necessary to adhere to this plan throughout the work. 17. Some below. Ex. 15. Handel, Model. a i r=^ i s^ ^'--L^r ^m • d * ^ Inversion. b $ I^E t=^ p=s= 16. Handel. Model. $m ie^ 6 PH * P gjj -2_g= ^i tr Te Deum ^ in B|?. ^ atl^i^p^z^izhzi T3i Inversion. T^Tm ? ^ #-»- E^ Ex. a Oboe Concerto, s ?3= ^ izi: ^ DOUBLE COUNTERPOINT AND CANON. Ex. 17. a lit: ^ 3^ ^^ s i^ lit « i i GusTAV Merkel. Model. • -a 3z^ :e =PP 1:!?::?^: Leo. t^* & Ex ^± ig. a Kyrie. ^ Model. fe^ .WIl p &^ g Ex. 18. ^ ^ .JTJPrl^^J M^ a Organ Fugue. "rrrcriTi =t= Inversion. 6 * • Model. ^^kmxTjVj ~7rr f frn* ^S i 1=4 ^ ?^^^^ ^ f-> • n r? Haydn. =^ # ^^4 r o i Creation, i JNVERSIDN IN THE OCTAVE — •jg Inversion. 6 : -\i m^ m ^^ s ^,-r-n- 35ES ^^^ f=w^ SI i8. The inversions of the models which follow are given as they stand in the compositions from which they are extracted. Ex. 20. a Model. h KiRNBERGER. Inversion. i» :t- The skip of a third at * * is necessary for " tonal " reasons. See Primer on " Fugue," par. 34. The C at is replaced by B in the movement from which this is taken, for contextual reasons. ig. The following model is also double counterpoint in the octave, although it is, so to speak, accidentally displayed at the double octave, but that it is not truly in the .fifteenth: is evident from the fact that the upper part maybe brought down an octave; In or vice versd, without involving any crossing of the parts. practical composition it frequently happens that double counter^ point, essentially in the octave, is exhibited both in the model and its invfersion at the distance of two or even -three octaves. The difference between this and double counterpoint in the fifteenth will be seen further on. DOUBLE COUNTERPOINT AND CANON. 10 Ex. 21. a Model. pig From PoRPORA. r rjcsz \ \ u^ \ f^i±^ #r-=^^^rcr^nr'' M " H '1 Inversion 6 ^^ Sfe r? iR ^ aii f7t:frrir-G^f-|f ii 20. Still more often, when the model is within the octave, the inversion is exhibited at the double octave (fifteenth), the upper part being transposed two octaves lower, or the lower part two octaves higher, or both parts an octave in opposite directions. The following (Ex. 22 to 24) are inverted on the latter plan. Ex. 22. a Model, , |iS -P — —^-F^ ^ % P r f i f :t j^r, ^ i m Inversion. M^ b ^ From an Organ Fugue by Albrechtsberger. ;C_i: f I r r-^^F " INVERSION IN THE FIFTEENTH. Ex. 23. a Bach. Model. 6 6» Ti :ii>^ Inversion. ^^m ^ a ^^Jf¥=^ ^ W^^Si^ Ex. Z4. a GusTAv Merkel. Model. ^ b - -ti I Organ Fugue in A minor. ^m Inversion. • -<' Art of Fugue. ^^M ^rrmrr-n^m I ^^ ^ i ^E II i- I*. f =B: ^g^ i S^^ F yi t DOUBLE COUNTERPOINT IN r THE FIFTEENTH. 21. Double counterpoint in the fifteenth (double octave) is essentially the same as double counterpoint in the octave, except that the wider interval (two octaves instead of one) allows Although, as greater scope for the two parts forming the model. was said in par. 20, double counterpoint in the octave is often inverted at the double octave (fifteenth), the upper part of the model being transposed two Octaves lower, or the lower part two octaves higher, or both parts an octave in opposite directions, it DOUBLE COUNTERPOINT. fz ANt> CANiON. should be observed that a model for double countei point in the fifteenth cannot be contracted so as to invert in the octave^ Some examples of double counterpoint in the fifteenth are given below : Ex a 25. 000 i te^SE ^ o \i r} :Phe: 3E^ r f f f f \' m-^W^ fi fi f-i Arv ff ^ r I M r 1^^ ^^ Ex. 26. M ^^ ^i> ; -J-h Requiem. f=r=mi ¥=F^ Inversion. J :k JOMELLi. Model. a I D. F4=4=± i^# J in -rj- Inversion. b m Et vitam, Mass Beethoven. Model. ^^ ^F=F=*: i ^^ ss 32= =t=F ^ °v_^ * ' g> - =pz; fefc^ Ex. 27. a Model. Marthji. INVERSION IN THE FIFTEENTH Inversion. 6 J -•i. I i I3k 1 • * ! :ft . i T =F+=F Pi^^ s m pn^^t--^ 'r t=i=t * i -ftr t=& ^a =t=t= &c. ^ ^ ^rrrl^"-^ D The rest at • takes the place of the note in the model, Martini evidently regarding the figure given in the inversion as the real counter-subject. The appears in another part when the model is inverted.^ • D Ex. 28. Model. a , Handel. $ g^ m ^^r^rif-H &c. 42- s- b y> r -* ^ pc i Inversion. 6 :?2Z =k i :^ :^E :?2- ^ &ci ^^ r fe^ r- 'h^Um r Ex. 2g. ^ o i Haydn. Model. -f3- n^^rf ^^"X^ fr^^^j:^ r-rr( J Inversion. ^b''(M,rjj-^feff^^^ ^^ ^ ^^ Hrufc :^ ^£^ 3 H DOUBLE COUNTERPOINT AND CANON. Ex. 30. a Model. ^ n ^^ -^- , Martini. . .rjj . I a i B^a i ^fe 1^ b ^^^^ffil r""£r^-'^' Inversion. ^el^g ^ At * a slight alteration of the counter-subject leads to a contraction of the paits, the lower being brought an octave nearer the upper than its proper position by inversion in the fifteenth. The possibility of this arises from the fact that the model was at this point within the limit of an octave. 22. The Student should now construct models of double counterpoint in the octave and fifteenth by the aid of the precepts and examples already given. It will be found advisable to use three staves in the way indicated in Ex. 31, as we are thus enabled to see readily what the intervals in the model become when inverted. The two uppier staves of Ex. 31 contain the model the two lower its inversion in the octave : ; i EE Model. ^^ Intervals ] in the Model. i ^S 3 ^ =F7=P Inversion. Intervals inverted. 4 7 Subjects to which Double Counterpoints may be added. 23. For those who at first find it difficult to construct 6o• aid of passing and auxiliary upper part, and introducing by exceeding the limits of by modulating to the subfor inversion in the octave, CHAPTER DOUBLE COUNTERPOINT II, IN THE TENTH. Although taken next in order, this counterpoint by itself by no means next in value, inversion in the twefth being used far more frequently. There is, however, an incidental variety of double counterpoint in the tenth, combined with that in the octave, of considerable value and interest, which will be fully, treated of further on. (See par. 59.) 26. The general ruleson pages2,3,and4 must be borne in mind. 27. When the subjects are inverted in the tenth above or below, the consonances in the model change into other consonances, thus 25. is : Model 8 3 10 Inversion i and the dissonances 6 5 3 I 5 6 8 10 into other dissonances, thus Model g 7 4 Inversion 2 4 7 : 2 g 28. By the use of three staves as suggested in par. 22, the student will easily discover the inversions which the intervals in the model involve (see also par. 16). This method, however, will show only one inversion, whereas there are two ways of inverting a model for double counterpoint in the tenth, the two This will be inversions differing considerably in their effect. best seen from an example. Ex. 38, a, is a model b shows the inversion of the upper part a tenth below, c the inversion of the lower part a tenth above, both inversions being rendered in accordance with the signature of the model. ; Ex. 38. M a ^ b i i; Albrechtsberger. Model. t sr dLi^ ) I* ^ 3 t Inversion. E Upp^ paTt a*ten^ bllow^ i1 i INVERSION IN THE TENTH. i J7 ^ 14;=^ Lower part a tenth above. i =e=q^- E =p=i= ii;;^ ^ 29. Such inversions will often be satisfactory enough, but if the model contains chromatic notes, or notes inducing modulation, the result in the inversions will generally be that some modification of one or other of the parts will be necessary. In some cases this may be by the omission of an accidental employed in the model, in others by the addition of an accidental. Ex. 39, a, is a G by the F model commencing in C major and modulating to, 6 is one of the inversions, the accic is another inversion containing an sharp marked * dental being omitted at * ; additional accidental at *. Ex. 39. a Model. ^^ ; DOUBLE COUNTERPOINT AND CANON. i8 At par. 28 30. it was said there were two ways of inverting a higher part being But .put down a tenth lower, or the lower part a tenth higher. these inversions may be arrived at by other processes, some subjects inverting more agreeably in one way than in another. Ex. 40, a, is a model for inversion in the tenth model for double counterpoint in the tenth, the : Ex. 40. P«-r 3=P ' » s » ^Jlj^ -*-»- i ^ ^g -i-r-r At h the model (a) is inverted by taking the lower part an octave higher and the upper part a third lower : h s fs » » Lower ^^ part an octave higker. Upper part a At t the £= third lower. ^^ t-^-^ * d same model third higher K is inverted by taking the lower part a and the upper part an octave lower : ^^ Lower part a third higher. Upper part an octave ¥ m lower, ^ W^ s fe ^ F=^ Notice the numerous accidentals necessary to render the inversion satisThe usefulness of this method of inversion for the purposes of factory. modulation in fiigal writing is obvious. 31. As thirds become octaves when inverted, they must not be used consecutively. Sixths become fifths and follow the same rule, but in some cases (see par. 34 (3), and Ex. 41, A, t, f) consecutive sixths are possible. INVERSION IN THE TENTH. '9 Even single thirds and sixths must be used with judgment, in the inversion they become octaves and fifths respectively, and, however taken, they of necessity render the harmony somewhat bare. reference to Ex. 40 will show 32. remembering that A this. 33. in We should not approach these intervals by similar motion if by inversion objectionable hidden octaves and are produced. two fifths parts, 34. It is apparent from par. 31 that contrary and oblique motion must be generally employed. A few progressions, however, where the parts niave by similar motion may be used, viz. (i) A wwyB i fourth, followed by an augmented fourth (Ex. 41, a), becoming in the inversion, by the aid of accidentals (see par. 29), a minor seventh, followed by a diminished seventh (Ex. 41, b, c). A perfect «)Mttfi^r fifth, followed by a diminished owiminor (Ex. 41, d), becoming in the inversion a major sixth, followed by an augmented sixth (Ex. 41, e), or a minor sixth, followed by a major sixth (Ex. 41,/) : (2) fifth Ex. 41. ^Lower U '^ ^ part a tenth above. Model. Upper part a tenth below. ^m ^-l^lMs^jp r Observe the different effect T l f- produced by the two inversions (see par. 28). (3) It is obvious that a minor seventh, followed by a diminished seventh (Ex. 41, b and c), producing the fourths at a, and the sixths at e and/, producing the fifths at d, are equally allowable. 35. In a two-part phrase these progressions, particularly the fourths, should be avoided. If, however, other parts are pro- ceeding at the same moment with the counterpoint, they may niore readily be admitted, their imperfections being at least hidden if not made good. The questionable progressions in Ex. 41 are given in Ex. 42 with an added free part. DOUBLE COUNTERPOINT AND CANON. 20 Ex. 42 Fifths with lower Fourths with lower Sevenths with inner free part free part. free part. 36. The suspensions of the second and fourth occur only in the lower part, i.e., the note causing either discord must be prepared and resolved in the lowest part. The second must not be prepared by a third as at Ex. 43, a, or hidden octaves \yill be produced when the passage is inverted (b). The second may be prepared by the unison (c), fifth (rf), or sixth {e). The hidden octaves produced by the inversion of d and e could be softened (See small in effect by suitable accompanying harmonies. notes.) Ex. 43. m m^m Inversion. i ^ 1 <^ Model. i 3E ^ ^ 37. As has been seen in Ex. 41 certain fourths and sevenths are admissible without preparation, particularly the dominant and diminished sevenths, with their inversions the major and But a suspension of the fourth takes place fourths. only in the lower part (as was said in par. 36), and is generally resolved into a fifth or sixth (Ex. 44, a, b, c). The suspension of the seventh will occur in the upper part, and will resolve into a sixth or fifth (Ex. 44, d, e,f): augmented ^ ,6, . — ... -^Q-ljT^ujm^j f^rn^rj^rr1 4 5 4 & 4 76 73 & 75 38. The progressions contained in the two upper staves of Ex. 43, c, d, e, show the preparation and resolution of the suspended ninth. It should be added that when the ninth falls to its note of resolution, the lower part may rise a third {i.e., to INVERSION IN THE TENTH. 21 inversion of the chord on which the ninth would resolve, a), or a fourth {i.e., to another chord a triad on the fourth above Ex. 45, b): the first Ex. 45, — — — Ex. 45. ± zpz^-b r T r 9 39. The the tenth following are examples of double counterpoint in : Ex. 46. Schneider. W'T'~=rf^~w~i Model. \ T T \ ^ T ^ r~r DOUBLE COUNTERPOINT AND CANON. 22 Ex. 48. A. F. C. KoLLMAtW. Model. O -e- a ^i I [ &c. ^^ > ^^ r*^^ Inversion. =FFF= BS Lower L In Ex. 49, I ?gi ^h^^^^trf-ra j;j»**'*^ frri-s - I — S^^^ # Greene. m-teB ^v *^-A-. < p ^ * Ex. 74. ^ Dr. o —A-^ W hF 1, frfe