,J ^ I • Jadassohn Canon and Fu^ue CORNELL UNIVERSITY LIBRARY Gift of Professor and Mrs. Donald J. Grout Music CORNELL UNIVERSITY LIBRARY 3 1924 060 737 784 The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924060737784 A COiffiSE OF INSTRUCTION IN PURE HARMONIC WRITING IN THREE VOLUMES BY S. JADASSOHN. Volume third: Instructor in Canon and Fugue. LEIPZIG, BREITKOPF AND HARTEL. NEW YORK, G. SCHIRMER ENT? STA. HALL. 1887. A COUESE OF INSTRUCTION ON CANON AND FUGUE BY S. JADASSOHN, PROFESSOR AT THE ROYAL CONSERVATORIUM OF MUSIC, LEIPZIG. TRANSLATED INTO ENGLISH BY GUSTAV (TYSON-) WOLFF, MUS. DOC. CANTTTAB. LEIPZIG, BREITKOPF AND HARTEL' NEW YOKE, G. 8CHIRMER ENT? STA. HALL. 1887. Copyright 1887 hy O. Schirmer. PREFACE. Ihose who desire to profit by this book, ought to have thoroughly mastered all the studies in Harmony, simple and double Counterpoint, and the practice in exercises of more than four parts. A student, thus well prepared, will be enabled to follow this course of teaching of the Canon and Fugue, arranged in progressive order; and commencing with the easiest forms of imitation, to compose more elaborate compositions in the form of the Fugue. Although the composers of the present day make use of this conti'apuntal form comparatively seldom, we find its employment mostly in compositions for Organ, or in the choruses of Oratorios and Psalms ; nevertheless, the study of the Fugue is indispensible to every true artist, especially to him who desires to devote him- self to the cultivation of free composition. Also to non-composers , the study of Canon and Fugue will afford insight into the classical works of Bach, Handel and other important masters of the past. One need scarcely remark that the creations of art exist for every one, endowed with feeling; and that also the unpretending amateur will receive a deep and lasting impression, after hearing the Cantatas and Passion-music of Bach, Handel's Oratorios, or other contrapuntal master-pieces, without being able to understand all the ingenious combinations of them. This we are far from disputing, but on the other hand, we must admit, that the appreciation and understanding of a master-piece will very materially heighten the enjoyment of it, and that also the executive artist will be better qualified to in- terpret a work, the more he has learned to grasp the very innermost nature of it. VI PREFACE. The earnest study of contrapuntal forms, and the work in ,,pure harmonic writing" will awaken and strengthen the sense for polyphonic combinations in the composer. These combinations cannot be dispensed with in larger, more elaborate compositions, such as Sonatas, Symphonies etc. and they impart also an especial charm to smaller pieces of music. It was necessary to send forth as introductory the ca- nonical work, as the nature of the Fugue rests on imitation. This study treats just this part of the preliminary studies of the Fugue with especial care; it contains about 60 examples for all kinds of canon. To incorporate all these examples within this book, seemed absolutely necessary; for especial rules for the formation of Imitations in all the intervals, in similar and con- trary motion, can only be given in general. It has been the author's experience of many years standing, that examples, especially worked in all kinds of imitation, answer best for the direction of the student. Except those examples of the Fugue and its analysis, drawn from the works of the classics, the book contains a large number of examples for the study of the Fugue. These examples, written for the most part by the Author, for the practical guidance of the student, may be found suitable perhaps for tuition also in wider circles. May they facilitate the instruction for the teacher, and the endeavors of the student in this very difficult disciplin. Leipzig, October 1887. S. Jadassohn. TABLE OF CONTENTS. PART FIRST. The Theory of the Canon, Chapter I. Fag. 1—2], § 1. Canon in straight movement. § 2. Canon in two parts -with- out accompaniment The infinite Canon. Canon in the inversion (al rovescio). § 3. More difficult imitations in the third, in the sixth, in the octave, in unisons, in enlargement, diminution. Cancer or re- trograde canon. Chapter II. Pag. 22—30. § 4. Canon in contrary motion, in the octave, and in unison. Mirror canon (Canon inversus). § 5. Canon in contrary motion in other intervals. Chapter III. Fag. 30—50. § 6. Canon accompanied by another free contrapuntal part. § 7. Canon accompanied by two or more free contrapuntal parts in dif- ferent intervals and al rovescio. Chapter IV. Fag. 50—57. § 8. Canon in three- and four -parts. § 9. Double Canon in straight and contrary motion. Key- and Riddle-canon. Circle-canon. Chapter V. Fag. 58—68. § 10. Canon for singing- Voices in three, fotir and more parts, in unison or octave. § 11. Canon with free-harmonious accompaniment. PART SECOND. Chapter VI. Fag. 69—77. § 12. Fugue in general. § 13. The Theme of the Fugue. Chapter VII. Fag. 77—89. § 14. The Answer of the theme. § 15. The Answer of themes, which finish in the Dominant. vrn TABLE OF CONTENTS. Chapiep VIII. Pag. 89—100. § 16. The continuation of the theme as counterpoint to the an- swer. § 17. The conclusion of the themes. Chapter IX. Pag. 100—105. § 18. The Interludium in the Fugue. Chapter X. Pag. 105—113. § 19. The »Stretta« (Engfiihrung). § 20. Stretta, formed by enlar- gement of the theme. Chapter XI. Pag. 114—121. § 21. The Form of the Fugue. § 22. The Fugue in two parts. Chapter XII. Pag. 121—133. § 23. The strict Fugue in three parts. § 24. More elaborate fugue in three parts. Chapter XIII. Pag. 134—142. § 25. Free fugue in four parts. § 26. Various constructs of the Fugue. Chapter XIV. Pag. 142—166. § 27. Strict fugue in four parts. § 28. Fugue for singing-Voices; treatment of the words. § 29. The choice of theme in the vocal fugue. § 30. The strict vocal fugue for four parts with orchestral accompaniment. § 31. -More independent Figurated orchestral accom- paniment to the vocal fugue. Chapter XV. Pag. 166—178. § 32. Double-fugue. § 33. Double fugue for Orchestra. § 34, Very- elaborate Fugue for Chorus and Orchestra. § 35. Triple fugue and fugue with four themes. Chapter XVI. Pag. 179—191. § 36. Fugue in five parts. § 37. Fugue for Double Choruses in eight parts. § 38. Choral fugue. § 39. The Contra-Fugue. (Fuga al rovescio). Conclusion. PART FIRST. The study of the Canon. CHAPTER I. Canon in Equal motion. § 1. The Canon is a musical composition, in which the melody of one part or voice is imitated by another after the elapse of a cer- tain period of time, in the same or in another interval. The leading melody ought to be formed in such a manner, that the imitation be easily recognizable by the alternation of the rhythmical parts in the different bars. The sooner the imitation occurs, the more effective will be the Canon, as the ear can more easily foUow the leading and the imitating parts. Canons in which the imitation occurs only after eight or more bars, and those in which the imitation, though effected sooner, move in exactly the same rhythm, are not considered Canons from a contrapuntal point of view. Nobody would consider Example 1 as a Canon in the octave, although the imitation occurs in the second bar. i ^^=^ J ! J A- f^^ I I i Jma ^ End. r r ^ f ^ r r But if we develop the melody of Ex. 1 in such a manner, that there occurs a rhythmical contrast between the leading part and the Jadassohn, Canon and Fugue. 1 CHAPTER I. § !■ imitating one, we should get a Canon, while in Ex. 1 we heard only intervals in equal rythm. ^ ^j&T-^^r 3E ^ 2. ^^-j II ' ^^rffrrT^f^^ ^ [ i^i 1 End. -ST. 1=^ J— ^ We have to conceive the leading part as a cantus firmus, the imitating one, as a counterpoint to the cantus firmus. Now, as every good counterpoint should contrast to the cantus firmus in some way or other, and the imitating part cannot give anything, but what the leading part has just brought before, we shall have to give to the leading part, from the very first, such a melodious colouring and rhyth- mical construction that the imitating part be brought into contrast with the proportionate bars of the leading one. The imitation can be formed from each interval in similar, as well as in contrary motion. The imitation can also be given in half as many large, or double as many, small notes. In the former case one obtains a Canon in the enlargement, (per augmentationem) in the latter, in the diminution (per diminutionem) . It must be clearly under- stood, that an imitation, given in notes as long again, will reach only to half of the Canon, and that a part imitating another by diminu- tion, even at a much later entry, will have finished, long before the other part will have come to the end, and consequently the Canon will be finished. We would not have mentioned these "ingenious tricks" and artifices, any more than the Canon in reti-ograde motion, the Circle-canon, the Mirror and the Eiddle-canon , if the imitations in the enlargement and diminution did not find their application in the "Stretta" of the Fugue. Under certain circumstances the employ- ment of the imitation in the enlargement can be especially eflfective in the Fugue. We would not recommend the imitation in the enlar- gement on diminution for the Canon as an independant musical com- position. We would otherwise arrive at a standpoint, where the spe- § 1. CANON IN EQUAL MOTION. cnlative cleverness achieves every thing, and the creative genius avails nothing. Imitation can be effected from any interval; Canons exist in Unison, in the Second, Third, Fourth, Fifth, Sixth, Seventh and the Octave. One counts the interval of imitation always in an up- ward direction, immaterially, whether the imitating part is placed above, or below the leading one. The greatest master of Canon, August Alexandek ELlengel proceeds in this manner and marks all his Canons thus: Canone Y. alia Settima con parte libera nel Basso. 3. m etc. Canone VIII. alia Quinta per moto contrario. 4. ^S ^=P etc. P^0rf=^:^^ Canone XII. a 3 parti alia Quarta e Sexta, k ^^^=4i^ etc. etc. etc. e=s Imitation in Imitation in the Sixth. the Fourth. Canone XIII. a 3 parti alia Quinta e Seconda. fe^ Eg 5^ ^ ^m ^s X m etc. CHAPTER J. § 1. Canone XXI. Canone doppio alia Dominante a 4 parti. 7. { ^gTEcT etc. te( ^^ — 3.^ r tnr H The second canon in the second volume of Klengel's work alia Quarta e Settima, is marked in this manner, although the imitation is eflfected in the Fifth below and in the Second below. Likewise the third, sixth, fifteenth, seventeenth, twenty first, and twenty second canon. The old masters managed in the same way, and the deno- mination Canon in the lower second, lower third, lower fourth, are found scarcely anywhere, but in treatises. We must however lay stress on the importance of the system of notation, as different no- tations of one and the same interval, would only embarrass the stu- dent; he would fancy he perceives an imitation in another interval, at the change of parts in the Canon, while in reality it is exactly the same, as before. However such a change, or inversion of the canonic parts, occurs often in one and the same canon. The canon appears then "al rovescio" that is, in the inversion. Klengel, in his marvellous canon cromatico ed enarmonico, allows the parts to enter at first in this manner. I ^ mcit ^E^ jW ^ 4=fc:^=^= 1? ^-v> 8. { I I Wt ■* P-* ■#. KJ—X g^^£S= ^ ^^^^ i*: I felE u ^-\ i ^v etc. »* ^^^ r Later on, he presents the canon "al rovescio" with a free part in the soprano in the following manner: § 1. CANON IN EQUAL MOTION. ^^j I i_ J ^^p ^Eg 9. t^ t ^m I ^- m ar=F=^ The designation of the imitative parts is marked at the outset : Parte 1"* alia Secnnda, parte 3^* alia Qninta. The imitation in Unison and in the Octave must be always a perfectly strict one. The perfect intervals must be answered with perfect, the diminished with diminished. However, at imitations in the other intervals, a divergence from this strict manner is not only al- lowed, but even often absolutely necessary, otherwise the parts would encounter one another in different keys. Each interval, however with the exception of the octave, can therefore be imitated, either quite strictly, or only generally in such a manner, that the fifth be answered by a fifth, the second by a second etc., it being quite immaterial, whether the preceding fifth be a perfect, or the imitative one a diminished one ; or the second of the leading part be a major, or the imitative part be a minor second : Adagio. 10. gz^riil "ir -feL ^ W^^$ 9 ^=^ ^ t- CHAPTER I. § 1. The following Canon begins with a leap of an octave; the imi- tation appears in the second. The first three notes, of the leading part, are strictly imitated; bnt the diminished fifth, from the third note B, to the fourth F, is already answered in the bass by a perfect fifth C to G; G and G. are imitated by A (bars 3 and 4). Similarly the major sixth G — E. (bar 3) is answered by the minor sixth A — F (bar 4). The commencement of the canon might have been: 11. { ^Eg^n L^.^^ etc. i^ ^ Therefore the minor second C — B (from the second to the third note of the leading part) would be imitated by the major second B — C. The distance in which the imitating part follows the leading one, must always remain unchanged. In strict Canon one should not allow the imitation to enter anyhow, say now after two, and then again after three, or more or less beats, the interval of imitation dare also not be altered, and may not be formed alternately in the second, fourth, fifths, octave, or so on. Such arbitrary alterations of inter- val or distance belong to free imitation. Such a piece of music is only written in canonic style, but it is not a strict canon. The free parts accompanying the canon may on the contrary, relinquish their positions, and the same free part may become (as demonstrated in example 10) either middle part, or bass of a Canon, as is the case in example 10 from bar 3, 4, 5 and 6. The free part, which formed the tenor in the first three bars, changes its position with the fourth bar, and represents from there the bass, while the Canon-part, which gives the bass during the three first bars, overtakes the place of the tenor. Before we attempt however, to accompany the Canon with one or two free parts, we will endeavour to demonstrate it in two parts, in all intervals; in equal — and in contrary motion. These exercises are in reality more difficult, than if we try to form a canon in conjunction with free, accompanying parts, as we have to consider, not only the imitation, but also the constrained rules of pure two part-writing, and have to dispense with the assistance of the free parts to the canonic ones. The imitating parts have always to be subjected to the rules, relating to pure two part-writing. The diffi- culties connected with this undertaking are not small ; but the student could not very well adopt another course, as the formation of a Ca- non, accompanied by free parts, would embarrass him at the outset. X §2. CANON IN EQVAL MOTION. The Unaccompanied Canon in Two parts. § 2. We arrange the imitation in such order, as to show it at first in those intervals, in which it can be most easily managed, after which we shall proceed to more difficult intervals. It is impos- sible to give definite rules, by which one is able to succeed ab- solutely with the imitation. It is of no use to tell the student, (as is sometimes done) that he may at first denote the intervals of the major and minor scales, with an imitation, in that interval in which he desires to make an imitation, he would learn then, where to find con- sonances or naturally dissolving dissonances; and, resting on this observation, he may try to form a Canon. But as, according to the period of time by which an imitation is effected, the relation of in- tervals between the two parts to one another, will become different, every time, this procedure would only be embarrassing to the stu- dent, he fancies to find assistance in a rule, which in° most cases, cannot be relied upon. If we note down the scale of Cmajor with an imitation in the fifth, after two or six notes, we would have all imperfect consonances, such as thirds and sixths. i * ^ ^ ^^ ^ ^^^^ -s>~ ^ ^^ ^^ -• — p- t=^ In every other case, we would obtain either perfect consonances or dissonances, which would not afford any point of support whatever, for imitation. We can consequently only show, how the imitation can be pro- duced; the student must try to construct similar phrases by himself. He will see from the examples, what will be usable under the indi- vidual circumstances. 8 CHAPTER 1. Here follows a canon in the fifth. 12. §2. i P^^^^i^ i ^^^ 9»-d S^ I ^^ 1*^ ?cs=J Jma End. 3^5S ^ m ^ 3J^i- 4' i: The preceding canon contains a repetition, these kinds of canons are termed »Infinite Canons.a It is however not necessary to furnish a canon with a repetition. This would cause to the beginner unne- cessary difficulties. The end of the canon is formed in a free man- ner, otherwise the movement could not finish satisfactorily. Sequences of several chromatic notes should be avoided, as they require strict imitation. Example 12 could also be noted so, that the imitating part is placed above the leader. For instance : -P-» ^ m etc. 13. A free ending to canon 12 could be composed in the following manner : -^^ § 2. CANON IN EQUAL MOTION. 9 The student may now try to form some canons in the fifth ; he would do well to compose these little movements in diflferent keys, and to allow the imitating part to enter first after one, two, or three crotchets, (in 3 crotchet time) and then after the elapse of a whole bar (in four crotchet time), but never later, than after two bars, at the longest. The closer the imitating part joins the leader, the ea- sier the ear will be able to follow the imitation. Considering the limited means which the two part-phrase offers, it would be advisable not to extend the canons to too great a length ; one may however try to conduct the imitation at least through six or seven bars. After the student has worked three or four such little canons in the fifth, he may proceed to the canon in the fourth; canons should always be written down doubly, as shown in the succeeding Canon in the fourth. As the distance between parts often transgresses the compass of an octave, and the parts are allowed to cross one another, the appear- ance of the canon at the inversion will not be altered so much, as is the case in double counterpoint. 14. i 3^ ^==a=fcf Kr* m ISE^ i!Jjll=r i rrr^^^ ^^^fs^ f i Hf.f^ Ji i £ M^ -f-»- -^0 1^ ^ 1=q= ' . rrrjv zsi £^ JfeteMs^ ^^ e to CHAPTER 1. § 2. Jma f H :«= ^m Jma End. ^ m NB. Either parts may also te in- verted a double ootave ; for Instance : as ^ " i ^ — — - i^^ i^Mfe etc. If one had formed the "reprise" in the following manner, 15. ^^^ — ^fe^- #^ *■ — « r^k-^ ^ \^=^-^ii- 1 — ^ 1 -J-J-4- Ljji 1 U^ Jma ^S ^S ^ =t though very convenient, it would not have manifested a great amount of taste. The student may consider, that the imitation itself forms the commencement of a sequence. One should consequently take care never to bring into the leading part more than two similar figures in succession in order to avoid a monotonous sequence. This can easily be avoided, by an alteration of a few notes; and in writing out the repetition a §2. CANON IN EQUAL MOTION. 11 alight alteration is easily eflfected. We illustrate this in the following example ; it contains the same canon Nr. 14 with a few alterations, and with the employment of the sequence given in Nr. 15, taking care however, that the harmonious progression remains the same as in ex- ample 15, although the melodious formation shows material alterations. 16. ^^t-r- TM===^-^^^ ^ ^^IHt^^ ^^^ I jm ^ ^^^^ ^^- i ^^^ ^ g^a?^ ^ Jma a ^feE ^ i "^n^ ^ ^r^ End. i ^ Another variation of the sequence Nr. 15 can be given: n a. ) ij>[ii:r '^■\ idf T =t * ¥ *■ ^ m ^^S^^^^^^p ^^^^^^ 12 CHAPTER J. §2. In sucli a case the notes ^?-B, could be imitated with E. and in like manner G-Gf)[ with C|f. However it is better to avoid chromatic progressions and their free, inconsequent imitations, as in example lib. lib. M ^ ^=rm ^ f=^~ m ^fe^^ i ^ f ! ■ ! ' ! y— ^^'^^ m ^^^mm M ^■ "^^ In the inversion (al rovescio) example 16 would be shown in the following manner: 18. I ^i^=^ E^ :t g?=|?=^g^ m^s fe^^i^^^ ^^^^^^sS ^ . rrr^rf -C^ggS^^^^-^ I Jma ES^ *^- «ft ^ £E End. fe^^ g^ § 2. CANON IN EQVAL MOTION. 13 The following example shows an imitation in the second. 19. r =iji ^ ^ 1 i F==F«^ is ^ =^t 9^-ff •-s-#-|* ^^ ? i Ima I Ilda E^ ^5^ ^ ^£^ r^^^rrf The same canon follows here in the inversion. 20. i ^^E ^ 3t:nat 3^ -^^ S 2^ -^-•- :1^-^:t i i E^^ ^S _!.' aJ- ^ fe i Jma End. ^^ 5S=C 14 CHAPTER I. % 2. With few and unessential alterations this canon could be given in three crotchet time. 21. I ^ S m ^ 9^^ #-^s-=- mf£ i Jma End. i E^^ 3=^ .#• -^ •«>•• H=£ £:^ ^^g ^^e£ =t The inversion of Nr. 21 has to be done in the same manner, as has been shown in Nr. 20. More precarious is the entrance of the imitation in the minor second; after all the imitation would nevertheless have to take place, alternately, in the minor and major second, to re-establish the unity of the key, as has been the case in examples 19, 20, 21. At any rate the commencement of the imitation in the minor second is more awkward and less natural than in the major second. Here follows an example of an imitation commencing with a minor second. 22. I ^ ^ ^^ SE S X * ^ :£^ :£^ I h - §2. fe CANON IN EQUAL MOTION. I i^i I End. 15 ^ --^ t aig^^g^^ ^^hr^ p=g^=g More difficult than the imitation in the fifth, fourth, and second will show itself the imitation in the seventh. In this case the com- mencement of the imitation in the minor seventh will be found much easier and more natural, than that in the major seventh. The fol- lowing example has been worked in such manner, that the imitation commences (Nr. 23) in the minor seventh, and (Nr. 24) in the major. In the course of the canon however, both kinds of imitation will have to be used, as otherwise the two parts would encounter each other in keys devoid of all relationship. 23. a ^ f-p-^ ^=t?U=UdJ fe ^^^^^^r-^^ ^^ ' ' ' ' ^3=^ i^^ ^m^^=?^T^^ ^^i=^=^F ^ ^EE^ fe^ -^^^ i ^fefc i Jma ^ ■a- 16 CHAPTER I. § 3. We will alter the key to commence the imitation in the major seventh, and reproduce the canon in 5 minor. 24. PrrzCj^Cfl g ^^E^ m^- ^ m i Jma I ^ i Ie — I — I — ^^^~ § 3. We must consider canons in the third and sixth as belonging to the most difficult imitations. In both cases one will have to re- produce the imitation, as much as possible, in another key. It would produce disagreeable monotony, if the leading and the imitating parts remain for some time in the same key. The difficulty consists in forming the leading part, so as to contain suitable modulatory evasions, which are on the other hand, not only answered by the imitating part in such a manner, as to avoid the modulation leading too far from the original key, but, on the contrary return to it back again. The task will be the easier, the later the imitation enters; in these intervals let the student try at first, to bring the imitation § 3. CANON IN EQUAL MOTION. 17 after the elapse of, say, two bars. Care also must be taken, in the first bars, to point out at once through the leading part, (by the form- ation of melody), the possibility of using different harmonies. One can form the beginning of a canon in the third, for instance in the following way: 25. ^^^ =^ i^ ^ etc. I «: ^ i: -:B After all, the canon in the sixth, will be more easily managed, than that in the third. The succeeding example shows an imitation in the sixth. 26. < m ^- 5t^.*^ m^^^ ^ --^- fit^4^f:*^ ^f^m ^B^ ^§- t i ■^■^j EE (^ ^ Ima volta mi^ a a^=m^ ISC 5 ^^^^m K ^ M M 11^ volta m m m "W^ JadaB80]in, Canon and Fugne. 18 CHAPTFB J. § 3. The student will find the formation of canon in the third the easier, the more he has practised working it in the sixth. We add an example of imitation in the third. One will see that a frequent change of harmony and modulatory evasions are absolutely necessary in this kind of Canon. 27. ^ ^^ l~^T^ m ^^^^' w^ ¥ ^ ^^' $^m ^^ 3^^ w m 1^ I ima ^ 3!r i> tili^ -sz fW ^ m The imitation in the octave or in unison has always to be a perfectly strict one. Each note of the leading part has to be imi- tated by the other part in the perfect octave, or perfect unison. Through this a great difficulty arrises ; to return back again after modulations, into the original key. If the canon has to be formed without any free accompanying parts, it would be advisable to avoid all evasions into foreign keys, as well as chromatic progressions, and not to work the canon too elaborately, as the imitating part is obliged to repeat exactly, what the leading part has given just before. It would be quite different, if one or two free contrapuntal parts be added to the canon in the octave, or a free harmonious accompaniment be written to it. In this case the field for combinations is greatly enlarged, and modulatory evasions much more easily effected, by the help of the accompanying parts. Example 28 shows a Canon in the octave in two parts. §3. CANOlf IN EQUAL MOTION. 19 28. { ^^^ ^^ -:^ i m m fE^^ i ^ ifa ^ S^^^ Ei^^ i :^£=^ ^ jma ^^ 5* The Canon in two parts in unison is still more difficult; as in this case not even the change of the parts, (distant from each other an octave) can be efiFected, and therefore monotony must ensue, un- less free accompanying parts be added. Nr. 29 gives a short instance of this kind of imitation. 29. P^Tr^ ^- ^ ^^^^^^^ '^ ^ i Xma ^ -251- j Ilda ^= -ir^ 1^ We shall take cognizance of the canon in unison later on under the heading of "Vocal Canons". 2* 20 CHAPTER I. §3. As all kinds of imitation treated here, will have to serve as preliminary studies for the Fugue, respectively for its "Engftthrung" (stretta, climax) we may not leave out of consideration, the en- largement and diminution of imitation, especially, as the former will sometimes produce a very good effect. Later on in the instruction on the fugue, we shall have to return more minutely to this subject. At present, it will suffice, to show this imitation of enlargement in the following example, in double as long notes. 30. { :eeee :bee ^ -^^m:^^^ I & ^^^# i ^. ^■^- z—F- i *» — ^- EE w^- ^ Si=»: 2ti ^ -'J- m 3 =^ ^ ^^^m s ^r^^3^^ -^i»- =L^t 4: As the lower part is set at liberty already at the second crot- chet in the third bar, this sort of imitation is not difficult to produce. One need only manage the leading part in such a manner, as to suit the first five notes of the enlarged imitation, and to place after that a free counterpoint to the other notes of the enlargement. The imi- tation in the diminution is less often employed, than in that of the enlargement. It is also not very difficult to treat. One need only manage the second half of the leading part so, as to form a suitable counterpoint to the diminished notes of the imitating part, as shown in the succeeding example. § 3. CANON IN EQUAL MOTION. 21 31. N ^3E ^ m ^ i ^^^ pi^ ^ E fe^t^flrt In conclusion we have to take notice of the cancer or retrograde canon, although this trick will very seldom find application in the fugue, but very seldom, unless one has taken it into account at the invention of the theme, so as to employ it simultaneously in similar motion, (per moto retto) and retrograde motion (per moto retrogrado). The manner of procedure for this trickery is this : One forms a me- lody in such a way, that this same melody, beginning from the end, and returning to the beginning, note for note, may serve as a coun- terpoint to itself. 32. I ± l^P^ t ^ ^^ ^ i ^ ^ *: ^ lE^ To form such a little phrase, one has to avoid as much as pos- sible suspensions, ties, and dissonances. The notation for this kind of canon appears sometimes in this manner: 33. 4- rTfTT t ^m ^s m The student need not practise this kind of Canon, as it has neither value nor importance, for the practice of musical composition. 22 CHAPTER 11. §4. CHAPTER n. Canon in Contrary motion. 34. { m ^=^ =i= d: * -¥ etc. ^^^^^^^m r- ^^ % 4. We place the above commencement of the "Engfflhrung" of Bach's Fugue in B^ minor, (wohltemperirtes Clavier volume 11) as a Motto for this chapter, as a competent proof of the extraor- dinary effects obtained by the imitation in contrary motion. Although the Canon in contrary motion as an independant piece of music, will occur but seldom, still the practice of this kind of imitation in all intervals, is absolutely necessary as a preliminary exercise for the fugue. — It will be found that the imitation in contrary motion can be easily and most naturally formed in those intervals, in which it proved most difficult in similar" motion. We commence therefore with the Canon in unison, or, what would mean just the same, in the octave. The following little movement could be noted in twofold man- ner; commencing with the octave or in double octave, but it would show little difference from the beginning in unison. Already in the fourth bar, we would obtain the same effect in Nr. 36 as we have in Nr. 35. ^ 35. i Ef^5^3 :zti r^. g^ £ i^E^ ^« s^^ eS #53 ^F i^=5±l r^ •^ ■•■ ^ §4. CANON IN CONTBART MOTION. 23 36. I ^^ u m »' "^ m ^^T^b f^ 7T T f-»-!^ * etc. ^ If we scrutinise this imitation, we will find, that the dominant C is imitated by the dominant; and accordingly, the sixth D is ans- wered by the fourth li?, the seventh E, by the third A, the tonic by the second, the second by the tonic, the third by the seventh, and the fourth by the sixth. Perhaps it would be advisable for the be^nner to write down a scale in contrary motion^ by which he will see, how he can best manage his leading part in order to obtain — after the elapse of a desired period of imitations — the consonant intervals of the scale, as fixing the harmony, on an accentuated part of the bar, and the dissonant ones on the weak parts. We try to elucidate this in Nr. 37 o. I I 1 I 37 a. &^ ^ I I I This certainly is only but a very weak help, inasmuch as the relations of the intervals would become constantly different, by starting the contrary motion from another point, as shown in example 37 i. 37S. ^ i s I r ± zz^ L-J- ^ =f= I gj ^^=^ ¥ T r I In the meantime these representations will offer to the student a kind of support, in order to judge, after what elapse of time the imitation could enter, and which note would be a common one, in the leading and imitating parts, and how, consequently, consonants or dissonants would occur. The imitation can, and need not be quite strict, although it com- mences in unison. This however had to be the case in the canon in 24 CHAPTER II. §4. unison and the octave in similar motion, to preserve the unity of the key. For this reason the imitation in contrary motion must not be quite strict in unison and in the octave. Example 35 shows the minor second B — F (from the second to the third bar) imitated by the major second A — G (bar three to four) in the second part ; the minor third A — C (in the eighth bar) imitated in the second part by the major third JE—^C (in the ninth bar). Only the prime and octave have always to be answered by perfect intervals in contrary motion. Again the perfect fourth and fifth will have to be imitated, in most cases, perfectly strictly, although there are some exceptions. Thus, in the minor key m ¥-^T=^ the perfect fourth will have to be answered by the diminished, if one wishes to avoid modulation. For the same reason in Example 48 the diminished fifth has to be imitated by the perfect one. In both cases this had to be done, in order to preserve the unity of the key. Especial care has to be bestowed on all kinds of suspensions, as the suspension in the leading part would become in the other, only a simple tie. Seconds and sevenths have to be treated as passing notes. In canon for two parts, the rules demonstrated in two part-writing, have to be adhered to as to perfect intervals. Perfect octaves, fourths, fifths and unisons can only appear in passing. A Canon worked in this manner allows of a double representation. We can notate it as Canon inversus (Mirror-Canon) in placing the ori- ginally imitating second part, as the leading one, or by putting the originally first part as imitating one. We would receive thus the "image " of a canon , which we would see , if we held the canon, turned wrong side up, against a looking glass and read it with ex- changed keys. We note the mirror-image of example 35. 38 o.. a ^^s fnct ^ fe3.-^^^Htr-^f^tf5^t^^^=WtT-=l i ^?=P= ^tSt ^^ « l * ' ^ I -^-r- Etfrar § 5. CANON IN CONTRAST MOTION. 25 One notated such a canon with double keys, as shown in ex- ample 38 i. 385. ai 14 fc ^rfflnH-^ ^ I ^«: fe^tE^ etc. In this way, it was intimated, that the canon could be read in both ways. Sometimes one had to mark another key behind the re- versed key. If there were signs of transposition required in the middle of the canon, one marked them above or below the individual note. As different signs of transpositions were required with changed key, at the Mirror-Canon, one would sometimes find a | and i} or b and 4 under, or above the same note at ilae same time.*) § 5. All that has been said, concerning the imitation in contrary motion, finds appliance at the imitation in unison or octave, as well, as for those in any other intervals. But also here, we must remark that if the canon be written in a minor key, the perfect fourth has to be imitated often by a diminished one; for instance: 39. ^-^^ ' -^ 13^ t ^ — — I — ^ ^ m NB. The pause indicates the end after the repetition. In this case it was necessary to answer the F of the leading part by G^, because of the key of A minor not having G natural, and a modulation not being required. *) For the minute study of these "Mirror-canons", we draw attention to the 25 Alhum- canons hy Moeitz Hauptmann. This volume, which contains two- and four-part Canons appeared after the death of the celebrated Cantor of the "Thomas-Schule" at Fe. Kibtnbe, Leipzig, 1868. 26 CHAPTER 11. % 6. The reverse of this, viz: that a leap of a diminished fourth is imitated by a perfect one, can also occur. This will be the case, when we write out example 39 as canon inversus. 40. ^^^^=j^ ^ ^■* p=^=^^^^^ w ^^ ^ We would note as mirror-canon example 39 in the way, that old writers did, viz: 31 41. 1^ ^^=*=f ^ ?^ 9^= }==! ^33= F ti- My\^0^^^^ eCJ ^£=i^^ 1^=^ ^3^ The imitation in the examples 39 and 40 is in the fifth. Con- trary motion in that interval is the most difficult to form, while the imitation in the fifth is easiest in similar motion. As was ob- served before — the case is the same with the imitations in all other intervals; they are in the same degree difficult in contrary motion, as they are easier and more natural in similar, and vice-versa. We now continue our studies with that imitation in contrary motion, which is the easiest, after the imitation in unison. This is the one in the third. § 5. CANON m CONTRARY MOTION. 27 42. f^*^==r~ f^ m~Ftf~ rr~f~~\ h-? P=^ 1 — \M^ — ! — V — « -\- — r- B£Z ^t-^ =i^- "^i^ 3^^F i ^ =ti=3t ^ f^ t^^= This little movement will represent itself as Canon inversus thus: 43. EE -P3 ?at ^ -f^-^ ^ 1=^ i -^ —T-r-^ % ^^ ^ :!=* Example 42, held against a mirror, would show the canon in A major, granted that one imagines bass-clefs marked with three sharps, on both staves. One can easily develop a longer und more complicated movement out of the former short phrase. For the better information of the stu- dent we give such an example, which could be, at pleasure, still further developed. It is founded, in it's first four bars, entirely on the beginning bars of example Nr. 42. 44. ;e EBE -•-^ -•-f- St -*-^-#- ^^ E^^^ ■^^ 28 CHAPTER II. §5. {^^r=^^ r — r- -r-=F= ztf^ES- \=r-f-* 77=^^ \P — 1 v — TT\ \ 1 — ^ nTj-i — - — ^=1 ■ H ^S=P- >^»'J -t •3- — 1 -$=^=^ I iS j^crroirni^ *-'^- ^-rt ?3=ra^^S^g=p=MI Inversus. 45. ^ ^^ l^E^^P^ S^S i J ^ J « i * i =5^ ^ 3^ * jw *- s- * ^^ TTT Sil-^ * * 1 U— y==:j= -J-i:j^ t^^^^ ^^J The imitation in the sixth would offer but little difficulty. A short example may serve the student as a guidance. It can also be used as canon inversus, as well as the succeeding examples; the student may write out the mirror-reflections for his information. 46. I fe ^ ^3 ^ tf &^ ri I I - i^ § 5. CANON IN CONTRARY MOTION. 29 ^M &^ £fe :eS ^ ^ m m mm m u. The imitation in the seventh and fourth will prove nuich more difficult , but hardest of all, that in the fifth. We h^ve already- given an example for the last interval. We give further Jin imitation, in the seventh and fourth under Nr. 47 and 48. Alia Settlma. 47. { |ap±c ^ M^ £ i =? ■K— '— «^ i ^ i -^ — ^- U I I ^- Alia Qnarta. 48. ^ ?1= i*bt: 9^r?~.rT 77 -*=- ^ E^ ^ ^ ^S -^-» =i=p= ^fe^ 30 CHAPTER III. § 6. i ^s -^"-jXiJ '-^ 1P^ ^ ^ 3^ 11^ -#-•- ^; The student has to practise industriously all these various kinds of imitations ; he is, however, not obliged to work his canons, so that they repeat. It would do perfectly well, if he imitated a few bars and added after that, a free ending. But he should form several imitative movements in every interval, and denote these in different species of time; also the imitation should enter at different periods of time. It is evident, that one would not extend these little movements to too great a length, which are not only subject to the necessity of con- trary movement, but also to the strict laws of pure harmonic writing. The student must guard himself against artificiality; he should look upon these studies as a necessary course of preparation for the Fugue. Only in poly-part imitations, and those accompanied by free-parts, one will be enabled, in the strict form of the canon, to invent a congenial piece of music. CHAPTER III. Canon accompanied by Free-parts. § 6. After the student has practised the imitations in two parts, in similar as well as in contrary motion, he will not find it very difficult to compose a canon, accompanied by free-parts. Liberated from the narrow chains of two-part style, he will be able to make use in the imitating parts, of all imperfect consonances, all dissonances (partly prepared, partly passing) and all those, which had to be hitherto avoided. With one, or still better with two free-parts, one will be able to fill, harmonically, the perfect Consonance -intervals of the prime, octave, fifth and fourth, and to soften Dissonances in case they meet in the imitating parts. Herewith the opportunity is greatly enlarged for combinations in the Canon, and it is possible to com- pose a piece of music, which, according to the ability and the inventive power of the individual, may become a congenial and effective composition. Nevertheless the way to free creative work §6. CANON ACCOMPANIED BY FREE-PARTS. 31 will remain, in the canon, a long and irksome one. It is the pur- pose of this work to show the way and we will endeavour to try to elucidate to the student the most suitable manner for attaining it. For the commencement the student may invent the imitating part, regardless of the two-part style, and, after that, to form a free, contrapuntal part. Later on, he will very soon throw aside this merely formal procedure , and feel himself capable of inventing a movement in three parts, from the beginning. Let him choose at first only imitations of the simplest kind, in the intervals of the fifth, fourth, and second, in similar motion. The most natural way would be, to give the canon to the two upper parts, and to place a free part under them, as bass or tenor. We will now try to make clear to the student our method by practical examples, which however, we cannot carry as far as to musical composition, as the space within the limit of a treatise is too restricted. Example 49 shows a melodious sequel in the soprano, which is imitated in the fourth by the alto, after the elapse of one bar. Andante ^ ^ ^ ^ S I rr rrn To this we add a contrapuntal third part as bass in the fol- lowing manner. Andante. 50. J I S 30» ^^ ^¥ ^r ^^ -0—^- ^ -fi^ 32 CHAPTER III § 6. i Jma rrr End. 9^:4-^=^=^ In the following exercise we show how to develope a more com- plicated movement from this simple example. Andante. 51. m ^d= s ^^^ ^ r^ Se -•— P- 4r=C ^^ ^^ ^^ ^^e ^ ^^ r-rrf ^ ' •>-^:=- ^ - ^^ ^^£ ' r ff .*— »- f=Em-r F=i I ir: Ima volta End. iW if- r' ""^2- #* ^g = gjTiJ-^^=^=N ^E^^ If one desired to carry out such a little movement still further, one could give after the I"* volta — or instead of it — a II** volta and work the canon further. This would be done perhaps in the following manner. $ Ilda volta 5 ^- 4- J^ 52. r r-r . W-'^rm^ -^-f- § 6. CANON ACCOMPANIED BY FREE PARTS. 33 =J-ij- ^J=Jd: U * ^ prnr^- i, ^ :££ £ -f— •- ^^ &E^ =t=t E^ f'i^i b'^ '^^^ i: r^'^^^^"""!^ ^i,J-%;^ 1 '^JHj -jT = =£_^' — ffl fla. "L. 1— ^-^T- Dal segno § example 51 al Fine. We have chosen the imitation in the fourth for the two pre- ceding examples, as we desire to give the canon to the two upper parts: soprano and alto. A Canon between two outer, and a free middle part, would be less natural, and more difficult. Besides choosing the imitation in the octave, the difficulty is still augmented by this choice of interval. We commence such a canon and leave it to the student to work it further, leaving away the I""* volta. Allegro moderato. 53. ^- rs= f ^. T I §aE J^ 3^ Jadassoh.n, Canon and Fngne. 34 CHAPTER III. § 6. i m -M=±=^ I I I — -I ♦• - iS- ■ Tr f r :^^: t;=^ nCzt ^^^^ i=3: :^ ' " ^ Ima volta ■^1 ■r ?^ f r f-_f r f tt=1:: ---^ End. fe=^ I i r r It would appear still less natural to give the canon to tie lower parts, placing a free one above; the imitating parts would be much covered to the listener, by so doing and the charm of persueing the imitation would go lost to a great extent. But, as the exercise of these canons is of great value as a preliminary study for the "Stretto" to the Fugue, we cannot spare the student this work. If the canon is an independent piece of music, we should only in rare cases, make use of this kind of imitation. We commence a canon in the lower parts, with a free upper one, and, in order to give variety to our work, and also to practise the imitation in different intervals choose the answer in the second. The student may develope this commencement, leaving out the "reprise", and work later on little movements in other intervals. § 7. 54. CANON ACCOMPANIED BY FREE PARTS. Allegro moderato. ^J^^JJrt^B ^m %m St #. ?: «..- -1*—m- 35 ess eS ft "1 — ^1 — Inri — ~»'~ -4-^—- ] -1 9^ 1 — • ^ — \ — 1 — f=r= — «— * — 1- — fL. -(2^^ — ^ =^— - — [— • -f^ 1 fL. -I ^ T- \ — -^ f-, Ima Tolta End. =sc=4: F > t=t: ^ ^ z^ :t=t: Canon accompanied by two and more free parts. § 7. If we add two free parts to two imitating ones, the move- ment would gain in fullness and richness of sound, by being in four parts. At the same time the combinations would be enlarged in the parts, producing the canon. One will be enabled to allow the canon-parts to pause now and then, and to proceed with the move- ment by the free parts. Again one, or both of the free parts may be allowed to pause at intervals, only care must be taken, not to let them finish abruptly; this can only be done at a suitable place, in- asmuch as the free parts are independent and fully entitled parts of the whole, which cannot be thrown aside at will, when they begin 3* 36 CHAPTER III. § 7. to become troublesome, as will no doubt be the case to the unini- tiated beginner. It will give an especial charm to the movement, when the free parts also imitate one or the other motive, perhaps at the commencement of the canon ; this can be done in a free manner and need not be strictly canonical. The ear of the listener will be deceived by so doing, and he fancies he hears a canon of many imitating parts; and such imitations attract his attention. We will show this in an example a little further on; at present we intend to demonstrate to the student the method of working. In such Canons the most suitable would be, to form the two upper parts, soprano and alto, or soprano and tenor, imitatively, so that in the one case the two lower parts, — tenor and bass, in the other, — alto and bass, are free parts. To allot to the canon the two lower parts and to form a free soprano and alto, would be quite unpractical, because in most cases the free parts would entirely cover the imitating ones. One might, perhaps place the canon in soprano and bass, forming two free middle parts; this work would not be difficult, but the effect would be injured by the long distance of the imitating parts from each other. In working, the beginner would have to aim principally at the imitating parts in the first line. He may then avail himself in his first attempts — of the more mechanical procedure, mentioned above, to composing first, the two canon-parts and, then adding the two free parts. After the beginner has acquired some practise in this way (which we recommended only, not knowing of any better) he will soon learn to compose the movement altogether from the beginning, if he possesses sufficient power of imagination and invention. Example 55 shows the commencement of :a canon for soprano and tenor, which is concipated for the addition of two free parts. Avdante. 55. i2r ^^^^^m s)- ^. ^S^^Efe E^^S ^gg i te^s S: E^ d£ fe ^ §7. CANON ACCOMPANIED BY FREE PARTS. 37 i^ Xma ^ ^ End. 3 i«^ The free alto and bass for this little movement, will come almost by itself. We -will conceive it as simply as possible, so as not to cover up the canon. That the middle parts are allowed to cross in the eighth, ninth and tenth bar, does not matter, nay, on the contrary, it will serve to bring out the imitation in the tenor all the clearer. In order to mark duly the commencement of the imitation, the free parts enter after the canonic parts; the movement during the little composition is kept up, partly by the canonic, partly by the free parts. Andante. 56 a. ' ^E :1= ^ .t^^J T=^^=^ ^ :ttpf r fTT ^=^ ^ f^ f-^T tf f ^y^- ■-l^Ei - i ^ p 38 CHAPTER III. If, in a more elaborated canonic movement, the imitating parts exchange places one with the other, at a repetition, in such a man- ner, that the original leading part becomes an imitating one, -whilst the latter takes the lead, then this kind of Canon is called "Canone al rovescio" (canon in the reverse). The free parts are then added afresh in a suitable manner; but they can also remain, as they had been placed originally. We will make use of example 56 a (with a few unessential alterations) and show the canon "al rovescio" from bar 13*^. Andante. 56J. I J=* -e>- ^^^1 S^ ■»^T'#- E^ P=me: .f f ♦ -a- — t r r t4 9tit ZTJ "vr :2r. § V. CANON ACCOMPANIED BY FREE PARTS. 39 AJ ^^4^^^ ^ ^-J j I . -^^-^ d=d ^=r=^ ^ la^^^ ^i ii j-^ P^"^r rUr^ g If the canon lies in the two upper parts, it would be heard even more predominantly. "We give such an instance, and allow the free parts to enter, so as to imitate also the beginning motive of the Ca- non-parts. Andante. 57, =te ^W^. ^^- s^ ifcziH: i^z^-=4. ^3E -^— I* -& ^^ ^ ^^ =t=t^=t -P-F #— #- i^^^ w^^ H-*- ?S ^ ^ -T- r^ ^--^ : ^fete: - J l?-fe -(* s^ =^E=t: ?» — 1^- 5 i fe=:^^=i4^ -0—^—0- -r- rr 1^=^ ^^^ftMf^ ^i M/-f^:^^^Ei ^m ^ W=x=r^ - p » ^ T (From § to the pause, which maiks the end). Is one desirous of repeating the canon, it would be advisable, to alter the free parts at the repetition, (one obtains thus variation, which would be effective, especially when giving quicker movement to the free parts, the second time. Such a canon follows here; the imi- 42 CHAPTER 111. tation is in the octave, between soprano and tenor. The canon writ- ten for Piano (or Organ) will be found as prelude VIII in the Authors "Preludes and Fugues" op. 56, Vol: 3. Andante. 59. t S^ r ff=f^ ^ I S ^ ^ 5 m Sr^ 7nf doloe r? lit ^M ^^ m ^^ asfefe^ SS3 P p^ f- f g -b— jg- i g « i lEE^ crcse. con espr. - — « ff^ S ^^ g -a—^ trt cresc. con espr. ^^^^ ^^^=3 I Se ^ -tS* W t- 1^- dim. fe=^ -!•—»= E^ 1^ e =pef ffi^ :3li ^P^ =P=^ H= •--»■ dim. ^^^ ^^^ ^^ ^=^3^^^E^^i §7. CANON ACCOMPANIED BT FREE PARTS. 43 mE ^ ^rr^nnrw^^ ==E^^ cresc. con espr. I m^ -H- — — d — ^— f-»-s-»- ^ -\ ' — ' ' ' ' ' F=gi cresc. con espr. i^ ^ EBE I fe^i *-# 1=4 \Wt^ ^^ ^^ 1-^ ^^ -«^ ^ :^ -^-^ 333i ^ i^t^si ^ From here the imitating parts repeat with alteration of the free ones. ]=:r=± ^ '^ 3fe -«>-=- -«^ f ma dolce ^^ffi ^ - \> ' '■ J- f ma dolce ^^m -»-4- *r==ti=ii ^^m^ -;5iT =9^ -*-*- -»-* -4-^-^i>- i^ 44 CHAPTER III. §^■ ^m zxizzizz::^ ^ ^ =^3^ ^h^H-J-^^v^ ^-d-* m. s ES gfe^ ;e=^ -(S ^ ^^j^^ f—is>- I ^F>i I . ^^^^ ^^^^^^^ ^f=^ * ^E »3^^S^^^ E^ S P I ^==F=1= ^^¥f -jg w. , ^ f_J =dr p^-«^ 'bfc£j^E^ ^^^E^ s £E-f ^fc ^££ ?EBE feF^^ ^^~^^~\- ^ BE p^^^^^^ § 7. CANON ACCOMPANIED BY FREE-PARTS. 45 I fe m ^ »^-^- i^^ dimin. ro!J. ^^m^ *■ "^"^^1^ feM^rE=£: dimin. rai2. s ^ 9P=^^ One can add to the canon more than two free parts, and form the movement for five and more parts. This, however, must be done in such a manner, that the canon is not hidden altogether by the free parts. This kind of canon ;wouId be most suitable for instru- mental music. In this case one could give the imitation either to an instrument, which would be most prominent by its volume of sound, or else simultaneously to several instruments, at the same time furnishing weaker or less instruments for the free parts; allowing them also to accompany softer. To demonstrate such an example, we reproduce the first bars of the Adagietto from the Authors "Se- renade in four canons for Orchestra" op. 42 (Leipzic, Bureau de musique de C. F. Peters.) The first Violoncellos have the imitation of the melody of the first Violins. In order to make the entry of the imitation more prominent, the first Horn assists the Cantilene of the Violoncellos at first. 46 CHAPTER in. § T. 60. Oboe. Clarinets In A. ^ Horns in (?. Violin I. Violin II. Adagietto. ima Solo. i EEE^^ ^^ t=t E& p/j i=^ I">a Solo. i iS E^^E^EF^^f ?: -L— I k m r PP Viola. Violoncello I. Violoncello II and Contra- basso. ^m s) — g ^S! w I I fesE :^=^= PP -I 1- E5E ^^ P* pj) csyr. EE r jU: i»p §7. CANON ACCOMPANIED BY FREE PARTS. 47 ^m i -i 1- ^e -,* — ^ ^g=^ ^^ =&& #-^-^ -F—iS'- ^ *=* i Ld^ ^^^ * •— 4t- «^ t=itr=t 4 — l-J- 1 — r 1=t -f-^0- ^ =t==t gi «' ^ ^^ ■(*■ >• ^-M^ i«-^»- ^^ ^E^l m^EBi. m iElE^ ^m EEiEEEfe** 48 CHAPTER III. § 7. m f -^ -«-f- i pp cantaiile. ^^ ^ :^^ ^^^=2^ $ ^ ^.. rrrr _,s:z^:pz ^1 ^ ^^ :fci=t CANON ACCOMPANIED BY FREE PARTS. 49 P i rv-^^^ IT J L_ ="^-^^ \% — — ti? ...... 1 1.. 4J.EI ^- i_ \i p-«^H — ^— tp ' i=^—S> \ 1 1 1— -1 121= 1— • =i= -^ — '-J =^ -^-— ^ Ima Tolta. End. -12 ^-\-S>- H=^ J==* :S^ -^. ^==:t: -^ z=^ ^ ^^m^ Double-canon. § 9. The task of constructing a four-part canon as double-canon will be much easier. One allows a couple of parts, commencing simultaneously, or one after the other, to be imitated by another couple of parts. We reproduce here, (with but little alteration) the commence- ment of a canon for four male or female voices, from the Author's op. 68 (Nr. 3, Friedrich Kistner* Leipzig). The imitation occurs in the fourth; those, desirous of getting acquainted with some other, similar canons , will find, in the above mentioned work of Aug. Alex. Klen- gel's "Canon and Fugues" three for Vocal parts and two for Piano. The pupil may try his hand at constructing little movements, similar to the following. He is not obliged to work his canon with *) By permission of the putlisher. § 9. CANON IN THREE AND FOUR PARTS. 55 a reprise; it would suffice, if after the elapse of several bars of imi- tation, the parts be conducted to the end. 66. { I te i Ji i & 321 -f^—r ^ f espr. fel 3 4—4- ^ i^ ^=ffli '»— »i- rrr -25- *- r M 4-4- I I" End. I^E^ Crf* a ^ lai dolce M tei ^ P fe=fe ^rr One can form the Double-canon also in three parts, by allowing one -part to imitate the leader in similar, the other in contrary motion. One can also write two parts in contrary motion, imitating in dif- ferent intervals. The canon will be still more artificial, when work- ing with four parts, the second answers in contrary, the third in similar, and the fourth again, in contrary motion. The task would be most difficult, if two parts be imitated by two others in contrary 56 CHAPTER IV. § 9. motion. All these canonical tricks the student need not practise. We show an example of this most difficult species, simply to give an idea of this kind of Canon. 67. m Andante. ^t^=4^ 5^ zS=^=^ t^* -S- ir m iE^ ^ ^^ *-*3 ^ r^ -f>-^ -t=f= 'fm -r>^ Je* =3- # ^^^m ^r^ V--^ — •-*: :t=t :P?T ^ t=t I feE^ Inia volta End. Ht=t ^ 3t a^i ^^=t^ S This little movement could also be written down as canon inversus. We have now to mention the trick of the Clef-Canon. The latter consists of a canon in four parts, in which each part has to produce the same notes in the clef, appropriate to it, viz: soprano, alto, tenor or bass. This wiU show a canon, respectively in the second, fourth and fifth. Here follows a short example. »^ -r^ m jtj- X ^-^^ i^=r±?: ^3e t=f= !S"^ *^=x iiii: »KE^ =22l CANON IN THREE AND FOVR PARTS. 57 ^^ W jfeE ^^ 3t ■^^ ^ ^i-^^ r r- =t One used to write these artifices on one stave, placing all the four clefs and signatures in the following manner. ^^w^i^ik^ . ^^^^^ It was left to the acuteness of the reader to guess the begin- ning of the individual parts. A Canon marked in this manner, used to be called a Riddle-canon. If this happened to be a clef-canon, the solution was easy. But it became a more difficult matter, if one had to guess the distance and intervals of imitation. Example 70 is noted in that way. 70. ^Sg zc m -4=0- -0-F- tt m :3L It may also occur, that one can find a double solution to a Riddle-canon. Thus, the Author has found a double solution of the two first canons, contained in the Hauptmann- Album. In conclusion we have to take notice of the "Circle-Canon, (ca- none circolare or canon per tones). Such a canon has to be con- structed in the following manner: The leading part modulates into the key of the dominant, before an imitation has yet commenced ; the first imitation in the fifth, commences in the key of the dominant, and turns, naturally, into the key of the dominant of its dominant. Thus the canon is continued through all the keys of the circle of fifths. But we cannot find any attraction in these experiments and can scarcely call it musical. A composition modulating incessantly, within the compass of a few bars from dominant to dominant, does not deserve the name of a musical composition. Should another circle of modulations be chosen for instance a modulation of the theme into the subdominant, or into the third above or below, the matter be- comes still more unnatural and unmusical. 5S CHAPTER V. 10. CHAPTER V. The Poly-part Vocal-Canon in unison or in the octave and the Canon with Free-accompaniment. § 10. The form of canon most popular, is the poly-part canon for singing voices. Every child learns this kind of canon in the singing-lessons at school, and any beginner is taught part-singing by it, in the simplest manner. The melody of the whole is taught and easily retained. Other parts commence after fixed periods of time with the same melody, and the executants hear themselves as upper, — then as middle — and then again as lower-voices. Such canons are not regarded exactly as scientific canons by the contrapuntal school. They are invented easily enough. If the canon is meant to be in three parts, the piece need only be worked subject to the rules of triple counterpoint in the octave; for four or more voices, it will have to be worked in quadruple counterpoint. The method of this work is very simple. We commence a melody. 71. ie*g ^. JrtSz -f-0- * t^ ^m^ After the elapse of this period, we counterpoint a second voice to the first seven bars. 72. :.:::: ^^U^^i^^^^^^^^^ - We continue in the same manner and add further a third con- trapuntal part for these seven bars: 73. : : : ^fete J e ■^- Now let us make a note of these little movements as continued melodious sequels, and mark the entries of the parts, after every seven bars, thus §. 74-1^^^ -!»—•- S: 10. THE POLY-PAST VOCAL-rCANON IN UNISON etc. 59 s ^fe^^^^^^^ gj^SF^^ ^^^ i ^ ^ g^g ^^ -s-»-F- -!•—•- :?=l= fefe ^^^ d=3: ^ -»— ^- The effect of this canon can be seen from example 75. AHejrretto. 75. AHeoretto. ^^^ E^=E ^ ^ I ^^ r-g S 4:j=^4i^i=*= b*L_J_]_,L^_ j ps^ m -^ — 0- f^0^- f^ jt^ ^=t :^±i 1^ pi ^ ^^^ P •2r=t 6S -^— •- 60 ^=^ El ?^ CHAPTER V. § 10. W--—^^ m ^^^EaJE g^-jl J J ^ J t^-n^ TW l ^^^^^^g^ 33^ i ^ ^ ^S^= #— •- I^S t=tiiJ=s i e ^ ** I k^==^ 3 S 1^ ^=* ^ -^ J-I^ ' ^^ 3^^^^ =^^=l^^=^ J*— • — ? m >^. .^ ^^ H« #- ^==t =^: p?^^ -«^- -*—»!- |aggTiTf7 ^ l^^'i-'*!. j-j J I j-;haidzat -^— •- =t=t ^ f-f-H^^,^ l^= q3p--j: 2t |P^^ ^ 3= ^^^ One will notice that certain considerations had to be observed in the preceding example, at the beginning of the movement, in order that the bars 8 — 15 should not sound empty, when sung in two parts. In this kind of canon however, one need not subject oneself so very strictly § 10. THE POLY-PART VOCAL-CANON JN UNISON etc. 61 to all the rules of the two-part phrase, as such little movements do not pretend to have any real contrapuntal value. In a similar manner, we can construct a movement for four parts. If the voices have to follow one upon the other after every two bars, we form the melody in such a manner, that always two following bars give the counterpoint to the preceding ones; for instance: Allegro. 76. < ^ EE £ m ^m ±::t ;f^^r= ^E ^■ -•I- ^^ In this manner we get the following canon, which we place here, marking the entrance of the parts. Allegro. 77. "^ E ^ ^^ ? ^— K ^ I* ^y f—^ 5 i w- i=t: ^^ thus: The finishing-chord of the canon would then sound in four parts 1^ =^^ On this principle it is easy to construct canons for six, eight, ten and more parts. The succeeding melody of six bars will give a canon in unison for 12 voices. 78. ^ ^ ^- let ns sing a mei - ly song in ca - non, ^ f^'-t^ now high, now low, o The entrance of the parts has to occur always after two quavers. The harmony contains only the chord of the tonic and dominant. 62 79. CHAPTER Y. % 10. Allegro. i ^-- E^^^^^E U let BS sing meiry song m Ca - non , 3E S let us sing a » merry song in Ca let us sing a =? S ^ — »i- merry song in i let us sing a merry =1- i let us sing a i let us ^t s U ^— 2— i^ :l=t §10. THE POLT-PABT VOCAL-CANON IN UNISON etc. 63 5^^S — *- now high, — ■I-L-,! now low, ^i^ 3= let us sing a ^5=1^ ^^E^ -0--g- — •»- now low, now high. let us f=ij-T-=m^^i-j\r- -?— ^ ca - non, now high, now low. m ^^^=^=^ ^^ ■=^=i song in ca non, now high, now low, m i^=s^ ^E 7 N =2=^ ^ mer-xy song in ca non. now high. i :^M-4- 5^ sing a mer-iy song in ca now high, m ^ s :3=* let ns sing a mer-iy song in ca non, ^ =*=t -»^ — •- t^iri: let ns sing a mei-ry song in ca non, i SEi ^3^i SE -^^— « ^ let us sing a mer-ty song In ca non, i :f5=:fc ?= ^^^^-= g ^ ^=3= let us sing a mer-ry song in ca- i ^ let ns sing a mei - ry song in ^ ^ 6 let us sing a mer-ry 64 CHAPTER V. § 10. i E^^E^ ^=^3.^ mer-ry soiig 111 ca non, now high, ^ m ^=i'- sing a mer-ry song in ca — * now high, ^^=rs; i5=dV s^ -* ^ J : w z±=i=fz let us sing a mer-ry song in ca non, i ^ ^ ^^1^^ let us sing a mer-ry song in ca non, ^ ■— b ^^~ ' low. let us sing a mer-ry song In ca non, *< — N ^^^3 =^2 1^-1^ -» — ^ ca- now low. let us sing a mer-ry song in -N ^- ^- ^±=^ high. now low. let us sing a mer-ry song in i -N— *- -N — N- — •! id now low, now high, let sing a mer - ry :fc::fc -• — ^ iJ^ ^ — <^ ' ^— now low. now high, let us sing a :5_=:^ :¥=^ ^^=f= T now high, now low, let us ^B^^ -:& ca non. now high. now low, y 00* ^^=i- ^s=t song in ca - non, now high, — • »i— now low, 10. THE POLY-PART VOCAL CANON IN UNISON etc. r I'™ ~i End. ^ I 65, T- -I- S^ — * — low, low, to the end. i S ^ -* ^ — #^-#^ now low, to the end. now low, I ¥=i= ^ -1 — ^-H■ — : S < ^ ' high, to the high, end. i ^ =p tsz^fci: =#=Ji now high, now high, to the end. i r=i: »—- ^- '-^=^ to the end. i ^ E^ r =^ -0- to the end. I UJ-^-1^ ca non, ca - non, to the end. song in ca- song, :?=S- -J^EIZJi to the end. K N ^5=ii -^ y mer-ry song m mer-ry song to the end. ^ ^^ -J-^— ^^-4 ?: sing a mer-ry. sing a song to the end. i ^^^^^^^ let us sing n, let us sing to the I ^S :is=!t end. ^ -^ Itl :^— •- let us Jadassohn, Canon and Fugne. the end, to the end. 66 CHAPTER V. § 11. One could write this canon also in unisons and octaves for mixed voices, soprano, alto, tenor and bass, and have it executed by three Choruses. The first soprano of the first Chorus commences after two bars, the soprano of the second enters, and after two more bars, that of the third chorus would have to commence. The other parts begin in each bar, always after two, four or six quavers after the soprano. One will see that it would be easy to write canons in this way, for any number of voices. The artistic value however of such pieces, would be lessened in the same degree, the more voices take part in the canon, and the closer the imitating voices follow one another. One could write a canon like the one Nr. 79 into the Album of a friend as a joke; but it would not be of any musical signifi- cance, as the effect of all the 12 voices would consist only of these two harmonies The pupil must not occupy himself too much with these musical playthings, he might perhaps form one small movement of this species for three, four, and six parts. If the entrance of the voices does not occur too closely one upon the other, one would be able to compose very graceful canons of this species. The Canon with free-harmonic accompaniment. § 11. A canon with free-harmonic accompaniment, constitutes a piece of music, in which two, sometimes — or perhaps only at times — more parts are formed in a canon. These are not accompanied by free contrapuntal parts, but by chords ; although this does not exclude the accompaniment, sometimes taking a contrapuntal style. Just most modern time has produced so much that is beautiful, graceful, grand, humoristic, and serious in this sphere, that we possess a rich canonic literature, especially since Mendelssohn, and still much more so Robeet Schumann has cultivated this kind of canon. Nearly all important composers of the present age have created something in this sphere, but it would lead us too far, if we mentioned even a small part of such works or the names of their authors. A sui-prisingly large number of canonic works, amongst these Symphonic ones. Suites and Serenades for orchestra. Characteristic pieces for piano. Two-part songs with piano-accompaniment. Choruses for male a female voices. Duos for Violin and Piano, Four-hand piano works etc., have been published and found approbation, not only with connaisseurs on account of their artistic form, but also with musicians and amateurs, by the worth of § 11. THE POLY-PART VOCAL CANON IN UNISON etc. 67 their contents. The very, circumstance that most of these works belong to secular music, and that we find contained in them thouroughly modern musical contents, proves satisfactorily, that the canon, the most severe, constrained, and most inflexible of all contrapuntal forms, shows itself perfectly adapted for the expression of sentiment, pro- vided the author reigns over it supremely, and be able to use it freely and without coSrsion. MoRiTZ Hauptmann in his preface to the canons and fugues of Klekgel, calls the polyphonic-contrapuntal style "a language formed by itself for the characteristic expression of musical thought". We can interpret this utterance as meaning that this style is a language for itself, forming the expression of individual musical thoughts. The reciprocity of substance and form is the same here, as that of interlect and language. The canons of the present day delight us not only by their artistic form. The constrainedness of the severe form may act upon the imagination even impulsively. Let no one imagine that the inventive power of the composer be lamed by the coersion of the canon*). As these species of canon belongs into the dominion of treatise on composition, we must withdraw all further remarks on this sub- ject. We will however give a small instance of a canon with free- accompaniment; it is the commencement of the third canon from the author's Serenata in eight canons for piano op. 35. (Breitkopf and Hartel, Leipzig). One should however not progress to the compo- sition of such pieces, until one has attained sufficient knowledge by the study of Canon and Fugue. For our immediate purpose it would suffice, if the student had worked conscienciously those canonic exer- cises, allotted to him within this book; he may after that progress in good spirit to the instructions for the Fugue. 80. Scherzo. AUegro giocoso. te J5- ten. -^-9 ^ ^=^ -*-•- p grazioso. ^ ^^^ i fl ^^ -»H«- ten. lUt *) We have already demonstrated this some time ago, in a paper, pnhlished in Nr. 18, annual course XII of the "Musikalisches 'Woehenhlatt", 5* 68 CHAPTER V. 11. ^ U#^^ ^^ 1^^^ ten. =9^ 3: "^» "^ ^!=f= :M pi ten. J .^. ri I Jma -fi- ^=i=3 ^^ :j=t ■^-*- 1 I .=Uii j^l ji =i=i= r— ^ =?2^ te ■,-i^^ia- ^B f^^^^^-^i^^ ^J ^S P?^^S*¥ ^^l J2*i J s^y= * With this we conclude the instructions on the Canon. The so- called free imitations, viz: those which are not carried out with ca- nonic strictness as to equal distance and equal interval, but those, which imitate at pleasure a motive in free intervals, the student will be able to form easily, after having practised the strict imitations industriously; he would also know, where to place them suitably with ability and cleverness in suitable places. The student has been made acquainted with these in the treatise on Counterpoint § 16, and in this part of the volume, in the "free parts", examples 57 and 58; this will be still further explained in the study of the Fugue. PAET SECOND. Instructions on the Fugue. CHAPTER VI. § 12. The fugue is a musical movement formed of sometimes two, mostly three, four or more parts, in which the principal subject or theme is produced at first by one part alone. A second part bmgs the same subject a fifth higher or a fourth lower, the third again in the octave of the tonic, a fourth repeats the theme in the octave of the fifth of the fundamental note. If there be more than four parts engaged, their entrance follows in just the same order, so that the subject be brought first by one part in the tonic and then by the following in the fifth. The principal theme in the fugue is called the leader, (dux) the repetition of it in the dominant the response (comes). After the first part has presented the principal theme, it con- tinues, while the second part produces the answer in the dominant, by bringing a counterpoint to the theme, which is called contra-sub- ject, or also contra-theme. If this counterpoint be repeated regularly by one part — although with unessential alterations — the fugue is called a strict one. If the counterpoint changes with the diflferent entries of the subject, or if it be sometimes or always different, the fugue is called a free one. If one give the counterpoint of the principal subject the import- ance of a real contra-subject, and introduce both themes at the beginning, one calls such a fugue, constructed on two themes, a Double-Fugue. The second theme must however preserve its inde- pendance and be repeated with the first one, so that one theme serves the other as counterpoint. Other contrapuntal parts may be employed freely in conjunction. In a well eveloped Double -fugue only one principal theme is at first worked out; after that appears — best after a half-cadence — the second theme, which is now in its turn 70 CHAPTER VI. § 12. treated, either alone at first, and later on with the first theme in combination, or it is brought at once after its first appearance, to- gether with the first theme. Such themes are generally constructed in such a manner, that they do not begin exactly at the same time ; one hears then more easily the different beginnings. The themes should be also different in rhythmical structure. One can also write fugues with three, even with four themes. If the fugue be a larger and more elaborate movement, one finds sometimes within it, freely worked parts; also the end of the move- ment is free. The fugue has developed itself, from the strict form of the ca- non; it is based essentially on free imitation, and offers, through this medium, a much wider field, than the canon. One can perceive, that the fugue became the stepping stone from the old music to the new; out of the former all kinds of modern forms have developed. It is superfluous to state, that the study of the fugue is absolutely necessary to every composer. The fact that all prominent composers of the past and present have occupied themselves in the most thor- ough manner on this field, proves satisfactorily, that the serious study of the fugue is indispensable to every musical author. Even to those, who have not the intention, ever to compose a work in the form of a fugue, thorough study in this sphere will render an excel- lent medium for educating and developing the power of imagination. Every follower of art will learn here the sure mastery of the matter, every one will be enabled by the perfect and sovereign government over the style of the fugue to the composition of freer creations. The study of the fugue will be an excellent medium of education to every one. Every fugue contains, besides the theme, the answer and the counterpoint or contra-subject to the theme and answer, a number of interludes, the latter of which are mostly founded on a motive of the theme or the counterpoint. These interludes serve for the connection of the principal groups of thematic entries. After there have been at least two, but generally several of such principal groups of themes and answers, the (Engfuhrung) "Stretta" will follow; although there are fugues, in which the stretta takes place immediately after the first principal group of entrances has occured. Such fugues have often several strettas. (See fugue in i)|}-minor Nr. VIII, Wohltemp. CI. part I). The stretta is — as already mentioned in the instruc- tions of the canon — a compressed sequel of thematic entries, in more or less strict canonic style. But one finds also many and very complicated, and largely planned fugues, in which no real stretta is used, as sometimes the theme of the fugue is not adapted for such § 13. INSTRUCTIONS ON THE FVOVE. 71 compressed representation in canonical manner. The stretta therefore cannot be considered as an absolutely necessary part of the fugue; however one or more strettas will render an especial interest and charm to the fugue, and the stretta will, principally towards the close of the fugue, afford a climax in the development of the theme. The Organ- or Pedal-point is even less necessary than the stretta, although its use will be of very good effect, especially in four or more part-movements. It is found in most cases on the dominant or on the tonic towards the end of the fugue ; but it can also occur in the middle of it. An organ-point cannot take place in a two-part fugue and in the three-part one only, if a fourth part be added for the organ-point, as bass. Rarely occurring exceptions as for instance the sequence for two parts over the bass-note F, in the fugue for three parts, Wohltemp. Clavier part II, Fugue XI, bar 61 — 65, or the sequence over the note D'^, same work fugue XVIII, bar 93, 94, have, in spite of the lying bass, not the character of an organ-point. Let us observe then the essential parts of a fugue more closely. In the first line, we have to direct our attention to the theme, and to explain the manner in which the latter should be constructed, in order to allow the fugue to be properly developed. The Theme of the Fugue. § 13. Not every musical subject will be suitable for the form of a fugue; there exist even many and very beautiful ones, which would not bear a contrapuntal — or as it is often called — a poly- phonic treatment*). We have to make a difference between a con- trapuntal development of a whole theme, or only of a motive, taken from the theme. In most cases in modern music only a motive of the theme will be employed for contrapuntal compilation. Often one makes use only of the rhythm from a motive of the subject. The reason for this lies in the nature of our modern themes, which, moving freely and unhampered on an harmonious basis, would allow now and then of another melody along with it, but could not bear several of them continually as equally authorised. But the theme, the principal subject, being the most important and melodious sequel of the fugue, *) The expression "polyphon" (many parts) does not quite coincide with its original meaning, as a movement may he written in four, Ave or more parts, without containing any contrapuntal combinations at all. But, as many-part mo- vements are generally worked more or less in a contrapuntal manner, and one has identified the expression "polyphon" with "contrapuntal", we shall also employ this term as terminus technicus. 72 CHAPTER VI. § 13. ■will have to suffer other melodious — essential parts, with it simul- taneously; it will present itself, (although being the principal subject,) now as upper, — now as middle, — and then as lower part, and allow other pai-ts, (which are not simply harmonious accompaniment to the theme), free space for their development. By its predominating nature, the modern theme carries, within itself, the laws of periodical construction. This again conditions a certain expansion of musical thought. A really good and beautiful theme of a modern composi- tion would be mostly too long for use as the subject of a fugue. The essential conditions of a suitable theme for a fugue are then the following. A theme for a fague should be short, in order that the hearer can take it in easily, and follow it up in its entirety, even in com- plicated combinations. It has to define well, its musical contents in comparatively small space, say 2 or 3, the utmost, seven bars. In such cases, where we find with Bach longer spun-out themes, they contain sequences, which make them easily comprehensible and soon retained in ones memory. % :E^S^S-=^f^?p?^^ 81 g£g^ ■P ■P-^-«- fm^^ ^^ip: .0 — — 0. -f^-s-^- i 83. ^^ ^^^ 5^ i Eg ^^^ :^ The theme of a fugue should never be formed by periods. It will be clear that the periodical formation of a musical subject is contrary to the nature of the fugue. The symetrical links of two- § 13. INSTBUCTIOm ON THE FV6VE. 73 or four-, three- or six-bared periods, are not suitable for the for- mation of fugues, as the coercion of regularity hinders the free development of several parts. As each melody possesses its own harmony, which it brings forth almost as its own inmate, in the same way a theme of a fugue will contain such, although it is but seldom represented by a simple, har- monious accompaniment. Still also this case occurs. We find in fugues by Handel, (see fugues from Israel in Egypt, in the Fm. Suite etc.) that the principal subject is brought simply harmonically, against the end of the fugue, after the contrapuntal development, self- under- stood in such a manner that the soprano contains the theme and the other parts give nothing but a subordinated harmonious accom- paniment. How much we are in the right with our argument in contradiction to the teaching of others, can be easily proved by those themes which contain harmonious figures. In these cases the harmony is clear and easily recognizable. In the above noted theme of the Organ-fugue in A-minor by Bach, the bass in the succeeding example, is doubt- lessly to be considered as the harmony, contained within the theme. 84. i i=s- m i 9-^=#^ -•-■ C; V- k ^^^frr-ffrf m M^,^^ * This can be seen still more clearly in the themes Nr. 82 and 83. It is quite incomprehensible to us, when it is argued, that a natural harmony to examples 85 and 86 can only be imagined with diffi- culty. In our opinion this is clearly and definitely announced by the intervals of each of these themes, and we notate them, as they pre- sent themselves most naturally. 74 CHAPTER VI. § 13. i , Largo. . — ■ ■ — ■ | ' i l l' 1^^! ' ,"| ' '] 85. , Pi A #- — d— W— i M -i# — *- ^E ^ r*-- S p?^-- mEESL ^i=^=^ s -^ 86. { ^E^^=E^^ ''U Jp I bi i ^ i?ii^ i ^i >i j: ifkfe^ S^^^fe^S While a modern, periodically constructed, theme can begin with almost any note of the scale, we find, that nearly all themes of fu- gues commence only with the tonic or with the dominant of the key. As a few and very isolated exceptions, we show here the themes of the f'^ major and B^ major fugues. (Nr. XIII and XXI, Wohlt. Clav. Vol: IF. 87. i a m 1^=^ tr • ^ •- ^*~~*" ::» ^=^i^^^ § 13. mSTBVCTJONS ON THE FVQVE. 75 I iA# ^^-^ 1 — ^^ "1- *^3 88. | %'^^^-p^j j^ ^^^i^=^^ ^ These two themes are the only exceptions, in 48 fugues of the Wohlt. Clav. 18 organ fugues by Bach (year XV of the BACH-edi- tion) and in the six well-known Piano-fugues by Haudel, which do not commence on the tonic or dominant. In most cases we shall as examples make use of, those above mentioned masterworks of fu- gues, which we expect are in everybody's possession. Should the student take the trouble to look into the fugues of other celebrated masters, he would be all the more convinced of the truth of our remarks. One should therefore not begin a theme on a second, third, sixth, or seventh. The answer of a subject, commencing with one of these mentioned intervals would clearly prove the unnaturalness of such a beginning. Nearly all themes finish on the tonic or third, after the pro- ceeding cadence or half-cadence. In rare cases, an ending would be found also on the fifth ; for instance. 89. Fuga VI, Wohltemp. CI. Th.. I. tr ^' ^^^=^#i We cannot imagine this last A, as anything but fifth of the key of Z)-min'or, as the natural harmony of the end of the theme proves ; we may accompany the A by the chord of the dominant, or by the chord of the tonic. 90. ^ ^^^ ^ ^ I d: IV f3E^ES=^ ^ d: IV "? One would therefore only be able to look upon this a as tonic in -<4-minor from the second crotchet of the bar after the appearance of the note B in the answer. 76 CHAPTER VI. § 13. 91. -^^F- '^- ^?=t^ £ ^ Sometimes the end of the theme will be left doubtful to the student, because of the finishing of the theme being closely connected with the counterpoint, which the part continues, in answer to the theme. 92. i Answer. "] te =P^^g^ Theme. ^^^^^^^r^ p^-»^ Counterpoint. ^=^ ^- The beginner would feel inclined to search for the end of the theme perhaps on the second crotchet F^ or the third D of the se- cond bar. He would however find after a close investigation, that the theme does not imitate more than the above noted little phrase. Naturally the end of the theme would fall on an accentuated part of the bar. The theme of a Fugue should be characteristic. As the melody of such a theme cannot be carried out so freely and unconstrainedly, as a melody in modern music, the theme of a fugue, on the contrary, having to acknowledge other equally authorised parts, the invention of a characteristic and significant theme for a Fugue will be really a very difficult task, which the solution depends entirely, on in- ventive power and ingenuity. Directions or rules are almost impos- sible, we can only draw attention to the means, by which a Fugue- theme can be made interesting and characteristic. This can be effected either by sharply defined rhythm, by striking leaps of inter- vals, or by the conjunction of both these means. If we observe the theme in example 92, we will find, besides the striking feature of its rhythm, a pronounced leap of a sixth from below upwards ; both conjoined give to the theme impetus, fire, and dignity. The themes 85 and 86 contain also striking leaps of inter- vals, which infuse to both thoughts a character of imploring fervor. The more characteristic a theme is — be it by its rhythm or by its cantilene, — the easier it would be recognizable in all the § 14. THE ANSWER OF THE THEME IN THE FVOVE. 77 parts, (even in the middle ones) and in all complications. We give at the end of this chapter, as an illustration the theme from the Fugue in ^-minor by Handel. 93. ^r: ^:^=^4 ^^M^^^:^ CHAPTER VII*). The answer of the theme in the Fugue. § 14. Concerning the answer of the theme in the Fugue, diverse views still exist amongst theorists. As it must be of great importance for practical instruction in counterpoint, to clear up this point as much as possible, let us try to demonstrate, aided by the help of the most celebrated works on the fugue, by what principles Bach and Haudel have answered their themes. We will choose for this purpose the "Wohltemperirte Clavier" the "Kunst der Fugue" (Art of the Fugue) and the large organ -fugues by Bach, and also the piano-fugues by Handel. Scrutinising then the themes of those Fugues, we perceive, that we can divide them into two kinds. Those, that do not leave their principal key, and those, that modulate into another key, in most cases that of the dominant. The first kind is the most frequent. Thus we find amongst the 24 fugues of the first volume of the "Wohl- temperirte Clavier" only four themes, which modulate into the key of the dominant. These are the themes of the 7*1* fugue in ^l^-major, the two-part one Nr. 10*'' in J5-minor, the GJf-minor Fugue Nr. 18 and Nr. 24 in 5-minor. Although it seems to be natural that a theme of a fugue, no matter whether it be intended for voices or instruments, cannot have a very large compass, we meet in the "Wohltemperirte Cla- vier" only with two themes, which, starting from the fundamental note, do not transgress the compass of a fourth, and which, within this compass, do not touch the fifth of the scale, the dominant of *) The contents of this chapter have heen puhlished for the most part at some former time, under the Pseudonym "L. LAebnau" in the "Musikalisches Wochen- hlatt", (annual XIII, Nr. 1, 2 and 3) in a paper hy the author. We reproduce here this paper, revised, and completed for the purpose of this treatise. 78 CHAPTER VII. § 14. the key. These are the themes of the fugue in C|t-minor for 5 parts (Nr. 4 in the first volume) and the one for four parts in .E-major (Nr. 9 in the second volume) . These themes form their answer in such a manner that each note of the theme is responded to by the consequent part a fifth higher, and that the answer, if not beginning in the key of the dominant, still turns towards it. All the other themes in the "Wohltemperirte Clavier" have more extended compass and come in contact with the fifth ; even the theme of the fugue in Z)-minor Nr. 6 in the first volume gives it as final- note. Here we arrive at the disputed ground; it is the answer of the fifth in the theme. For the first answer of a normal theme, especially when finishing in the fundamental key, the following principal rules are availiable: 1) Each note of the theme is answered in the dominant a fifth higher, or a fourth lower. 2) A leading note must always correspond with a leading note. Of course this concerns only the strict fugue. In fugated move- ments, called Fugatos, such as are found in instrumental pieces and in polyphonic Choruses by Bach and Handel, we meet with exceptions to this rule often enough, be it, that this theme is not imitated quite strictly, be it, that it is answered in another interval, as that of the fifth. Also in the course of the strict fugue we find, especially in more complicated strettas, alterations of single notes of the theme, as also in the answer of it. We speak here only of the first answer of the theme in the fugue. One note however, makes a very frequent exception to the above two stipulated principal rules for the answer of the theme. This is, the fifth of the scale. If this note be the first note of the theme, it must be answered, in all cases — immaterially, whether it appears as an essential note on the thesis, or as an unessential one on the arsis, — always by the fourth (the octave of the fundamental note) and never by the fifth ; while all other notes of the theme (granted that this does not finish in the key of the dominant) are responded to regularly, in the fifth. As a proof of this, we mention all those themes of the "Wohltemperirte Clavier" which commence with the fifth. These are the fugues Nr. 3, 7, 11, 12, 13, 16, 21 and 24 of P* volume; Nr. 1, 2, 12, 14, 15, 16, 17, 20 and 24 of IP* volume. We add further the themes of the large Organ-fugues by Bach, beginning with a fifth, and their answers: § 14. THE ANSWER OF THE THEME IN THE FVOUE. is answered: „ f-f-f-f - '■ ^= etc. 79 95. 9ii--=^g=£ answered: 96. 97. I ^f -0~s)- m ^ 4=^ the first note of the theme is shortened at this answer one crotchet. 98. answered : 99. ,^ ^^ l. p^f. 1 JL.^ etc. In the "Kunst der Fuge" Bach answers the theme (contrapunctus 12) 100. fo'3 J =1 etc. by 101. 9^1=- etc. the contrapunctus inversus 102 103 ■m^^^^^ etc. by etc. the theme (contrapunctus 14) 104. iyb r, ' r -R-^— etc. by 105. ^ ^^3^ etc. In like manner Handel proceeds in his piano-fugues, which first theme : 106. 107. i W^"' ^ T J ^ ^ ®*''- ^^ answered by ^i ^-^-irj etc. In the same manner he answers the theme of the second fugue : 108. ^^^ ^ etc. by 109. eeeS^ etc. 80 CHAPTER VII. § 14. in the third fuo;ue 110. . ^^=^=M=^ etc. by 111. g!g!^-Q-^ W- etc. in the fifth fuarue 112. m=t^=^ etc. by 113. i t=* likewise in the sixth fugue. 114. ^b=t5=l=^^lE etc. by 115. ' ^^=^g^ etc. etc. We consider therefore ourselves justified in adding to the two above mentioned principal rules, a third one of this purport. 3) If the theme commences with a fifth, this fifth, (but only this first one,) has to be answered invariably in all cases with the fourth, (the octave of the fundamental note,) all other notes, on the contrary, must be answered, regularly a fifth higher in case the theme remains in the principal key, or which is the same, a fourth lower. We cannot suppress here the remark, that a great number of themes of fugues commence with a fifth. Less numerous is the number of such themes, which bring, immediately upon the tonic, the dominant as second note. We mention here from the "Wohltemperirte Clavier" the themes of the fugues Nr. 2, 8, 17 and 22 of the P'' Vol. Nr. 1, 3, 7, 11 and 21 of the II* Vol. the Contrapunctus 1, 2, 3, 4, 7, 8, 12 and 13 and the final-fugue from the "Kunst der Fuge". In all these cases the theme remains stationary in the principal key, and we see, that the first fifth is answered not only by the fifth of the fifth, but similarly by the fourth, as the octave of the fundamental note. In the face of these numerous examples, to which we could add a great many more from the works of the classical masters, we state as the only exception from the above mentioned works, the contrapunctus 1 1 from the "Kunst der Fuge". Here the first three notes : 116. 1^ j=^ are answered by 117. ^£r^— |^^^ j|~ | *' :l=P= Consequently we consider ourselves justified, in bringing forth a fourth principal rule, thus: 4) If the Dominant appears in a theme, — which remains in the tonic — as an essential note soon after the latter this first fifth § 14. THE ANSWER OF THE THEME IN THE FV6VE. 81 has to be answered by the fourth, the octave of the funda- mental note ; all other fifths however by the fifth of the fifth*) . The theme of the e'C fugue (Nr. 7, vol. II of the "Wohltemp, Clav." will demonstrate to us how strictly Bach observes this rule. Here we find in the first three notes of the theme, the fundamental note, the fifth, and closely after, the fourth: 118. ^ g^ ^ ^ :i: t *-»-f- i^mt: the answer is this 119. »0 i;: =1= t The first fifth B? is answered here, as well as the fourth A?, next to it, with -E?, the octave of the fundamental note ; all other notes B^, in the theme, are responded to by F. *) We mention, as an isolated exception to this rule the fugue in Bc-major Nr. XXI "Wohltemp. Clav." Vol. I. In this theme, although it does not modulate into the dominant, not only the first, hut also the second fifth of the answer has heen responded to by the octave of the fundamental note. This occurs also in the 24**' fugue; hut there, evidently for the purpose of leading the answer of the theme — which has modulated into the dominant — by the response in the sub-dominant, hack again into the fundamental key. The answer of the first and second fifth in the C-major fugue ("Wohltemp. Clav.'' vol. II, Nr. 1) is easily ex- plained by the character of an ornament '■k, which the beginning notes carry with ihem. Bach answers the mordent (written) figure i l^g^ by similar * tt because in the theme the second G is a principal tone. That Bach writes F, at the beginning of the theme the JP by B writers chose "nearly i ^ *-Til- and answers tzttit is also easily explained, if one considers, that old always the tonic note, instead of the chromatically altered one ; for instance answered by the tonic note B ^^ This tonic note F is afterwards to avoid bringing an entirely foreign note B^ ^^ —^ — into the preceding C-major and the succeeding -minor, the B9 in the third bar of the theme has been answered by E, the leading note F'il, in the fourth bar, by B? in the seventh bar. After having elucidated and explained these few exceptions in the answer of the first fifth in the theme of the fugue, we believe, we can formulate the rule in this way. If the theme remains in the fundamental key the dominant, occurring in the commencement of the theme as principal, melodious note, is always answered by the octave of the fundamental note. Only when the theme leaves the fundamental key an exceptional response will be justified indeed for the purpose, of leading back the answer, as soon as possible into the original key. If, however, the fifth does not appear at the beginning of the theme, as an essential, theme characterising note, but, on the contrary, enters in the course of the theme, it is . answered like all other notes, in the fifth as well. Thus we see in the "Wohltemp. Clav." and others, the themes of the fugues Nr. 1, 5, 6, 9, 10, 14, 15 and 20, vol. I, in which the fifth does not appear at the beginning of the theme, and is not of essential importance; this note answers, like all other intervals. The result is that the answer of the fifth will be in accordance to its significance, a difi'erent one. But from the above examples it will be easily learned, how the answer can be formed in individual cases. Therefore the fundamental principle is: Avoid in the answer of the theme, as much as possible, becom- ing removed unnecessarily far from the fundamental key, but § 15. THE ANSWER OF THE THEME IN THE FVOUE. 87 try, on the contrary, when the theme has left the tonic, to return back again. It has been shown already in examples 96 and 97, how the first note of the theme may appear shortened. In the same way, it will be seen from examples 94 and 95 that the answer can commence upon another part of the bar than that, on which the theme began. An answer in contrary motion has been shown in examples 102 and 103. We shall return to this subject at the explanation of the fugue in contrary motion, "fuga al rovescio", or "fuga per moto contrario" § 36. At present we may dismiss this kind of answer. The first exercises of the student will now consist in forming various themes and their answers. One may invent at present themes that do not modulate. 1) Such, which do not contain the fifth of the key; for instance; 137. 3EE 1= 3E The answer is formed entirely in the dominant. 138. d^ :t ^ ^ The leading note B in the theme has to be answered by f!^. 2) Such themes, which do not bring the fifth as an essentially characteristic interval in the first notes, but only in the course of the theme and consequently answer them, quite regularly. (See ex- ample 92, chapter VI, § 13). Here follows example 139. Theme. 139. ffei =t ^ ^ 3=^1 m Answer. # =t: ■^ 3t * =t 3) Such themes, which commence with the fifth, and answer this first fifth with the octave of the fundamental note, the other notes of the theme, however, in the dominant, as has been demonstrated in examples 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114 and 115 and also from the fugues of the Wohltemp. Clavier, at the beginning of this chapter. 88 CHAPTER VII. § 15. Here example 140. Theme. 140. I ¥ -* -0 — — — ^— ,—•,■" -w-^i^- jr Answer. IS ^ 4) Invent non-modulating themes, which commence in the tonic, but bring the dominant soon after as a note essentially characterising the theme, and answer this, as shown in examples 118, 119 and 120. Example 141. 141. Theme. Answer. k=^- * as2 EH #— #- g^EEEfEj -^- i ^-0- t=t :i^ tl- 5) Form such themes, which modulate into the key of the do- minant, and form the answer in such a manner, that it leads, in a suitable and not striking way into the key of the sub-dominant. . The finishing of the answer would then return into the fundamental key. Examples for this, see Nr. 123, 124 and 125. Here an example Theme. 142. ps * ^ :t S It :© ^* <-^ rm: — r*i^^ — M- m^ ,-#- Answer. ^^ 3^ 3^= tSzt a y^4,j5S4 .^ ^-^-v^ • ii SR i^ i But it must be expressly mentioned here, that only the end of the theme in the dominant requires, at a suitable place, a returning answer into the sub-dominant. If the theme brings only passingly before its end, a modulatory evasion into the key of the dominant, and § 16. CONTINUATION OF THE THEME AS A COUNTERPOINT etc. 89 returns, after that, into the original key to find its conclusion, the modulatory turn into the dominant, contained in the theme, is imi- tated exactly by the dominant in the key of its dominant, as the following example from the (r-minor organ-fugue by Bach distinctly manifests. Theme. 143. ^^^^S ^ -1^1 -Hi L a Answer. yTTTT T m ^HH^-^= ^^ I g3Sfe? m: -^-•\ K' itfl ^ , LU LU 1 Here the modulatoiy turn into the dominant (Z)-major) in the second bar of the theme, is imitated in the answer by the modulation into the dominant of rf-minor (^-major); just as the modulation into 57-major is responded to, by the answer in i^-major. We advise the student to avoid modulations in the theme, as much as possible, at the invention of own fugue-themes; the answer of such could possibly embarrass him. The beginner should try to construct his themes, on the conti'ary, in a short, simple, and concise manner; let him however guard against the mania of inventing at these, his first essays "interesting" themes. It would perfectly suffice, to compose useful themes and to answer these correctly. CHAPTER VIII. Continuation of the theme as a Counterpoint for the answer. § 16. Formerly one used to call the progression of the theme after or during the entry of the answering part : the Counter-harmony or Coun- ter-subject, presumably for this reason, that the contrapuntal accom- paniment should contrast rhythmically and metrically to the answer. But this should be the characteristic of every well-worked counter- point. Further than this, the contrast should not go. The accompani- ment to the answer, cannot have an essentially different character to 90 CHAPTER nil. § 16. that of the theme, standing, as it were to the theme, as its natural continuation. This continuation has to be formed in such a manner, as to be suitable for accompanying contrapuntally in the answer, the re-appearing, principal part of the theme. By so doing, an exterior difference, as to rhythm and meter, will occur, not however an oppositional contrast. Therefore we shall relinquish the expression "counter-subject or movement", the same as we have hitherto avoided the expressions: "Zearfer" (dux or Fflhrer) or ^^companim^% (comes or Gefahrte) and instead of speaking of counter-subject to the companion and leader, we shall call it : counterpoint to the answer and the theme. How little this counterpoint is intended to become oppositional to the theme, can be proved by many fugues of the great masters, in which the counterpoint imitates figures, that were contained in the theme; it has grown, as it were, out of the theme and must be con- sidered its natural continuation. Only the general contrast of the counterpoint to the cantus firmus, as in every counterpoint, will have to be regarded. If the cantus firmus — in our case the theme of the fiigue — consists of sustained notes, the counterpoint will have to be florid; is, on the contrary, the theme formed of florid passages, the counterpoint will have to be composed in a sustained character. If the theme contains long notes and rhythmical figures, the counterpoint would have to imitate, during the long notes of the theme, its rhyth- mical figuration, and bring sustained notes against the florid ones of the theme. But all this shows far more the uniform coherence of theme and counterpoint, than a contrasting contra-movement of the theme against the counterpoint. Some examples, taken from the "Wohltemp. Clavier" will clearly demonstrate this. tr 144. fo gB?=t5 = S3^^^i^ S^ =t g^ »^ l=!2I ^ I r pj— gs^r^ S^'^==W^FT=^^ s ^ § 16. CONTINUATION OF THE THEME AS A COUNTERPOINT etc. 91 Er^ O^O:^ III! I I M BS3 asz etc. s & The imitation of motives, contained in the theme, by the coun- terpoint for the answer of the theme, is easily recognizable. 145. I I ^ ^ f -i ^ r-T^ ^E ^^ ^ J"J^ .' j- ^ =9^3^ -»!—*- etc. ij^^QiL^ » i?« r Clearer still than the preceding example, the counterpoint S^' J ' * 7 i ^ r~ 3^^ — ^ — shows the imitation in contrary movement > — and similarly the from the thematic motive last quavers of the counterpoint 17' p f contain the imitation contrary motion of the beginning of the theme r/^ bi^— *? " "- Lj ff^ 146. ^ ^^31 l=^J=^=^3=^^;^ 92 CHAPTER Yin. § 16. k •n^ m i=rsz ^ • m - -:^:^rt- ^=:r=^^^^ etc. ^ Here, evidently, the essential part of the counterpoint is formed from the motive of the theme ^?Ntj t°| \ 147. <^ ^ Iz ■ P 7 -?-?^ -^ p^rp -^^^. g" V -» rr ^ I ut il-^i .i' i ^iEE^I; a=t S ^ etc. ^- w =V=?- The leaps in fourths, characterising the theme, have been con- tinued in the counterpoint. 148. I E ViFrr rt7tr £s' ^ __ ,-^ _^ ^^ ^ ^ B=a _ _ ^^ i±E ^^ fe ^^a ^__J 1 m E_ -» gw^ '» * :.d »- i2z^ =F- ^f: 3&. ^ ^-.oiggji etc. ^ The motive of the theme second bar of the counterpoint. ^ is spun out in the § 17. CONTINUATION OF THE THEME AS A COUNTERPOINT etc. 93 149. [ ^^ gfe^^ag ^S^-:^^^ ^7 etc. ^r rr-r ic: fe ^ The motive occurring in the fourth bar of the theme is continued in the counterpoint. 150. te -^^=i^ A^ ■f-^' -M- ^^^^^ :f=4 -<•-•- -?- fe^ g S^==^ etc. m^ E^^ ^ The employment of similar motives from the theme is evident. In all the foregoing examples, extracted from Bach's fugues, to which we would be able to add many more, one cannot surely speak of a counter-movement We will then, in future, in lieu of that formerly employed technical expression, use the word counterpoint. This term expresses exactly, what the continuation of the theme, for the accompaniment of the answer, is meant to express. The term counter-movement or counter-subject would mislead the beginner easily into exaggerations. In order to produce something very oppositional, he would be tempted to write a very florid counterpoint to a sustained theme or its answer, or vice versa, by which treatment the uniform character of the fugue would be lost. § 17. We have termed the counterpoint for the answer, as it were, the continuation of the theme. This designation will at once explain that we have to treat with something not less important. The counterpoint returns in the strict fugue (with immaterial alterations) 94 CHAPTER Vni. § 17. at least in one part; it remains the same, just as the theme remains the same. This is mostly the case at the principal groups of the en- tries of the theme and answer, until strettas of the theme prevent the entry of the counterpoint. If the counterpoint remains the same in one part, we may add in a Fugue for three or four parts, one or two free parts. In the strict fugue for four parts, we often find two counterpoints in two parts, returning regularly with the theme. The carrying out of this requires sometimes an interruption of the counter- point in one part; another has to continue it. Sometimes the two contrapuntal parts exchange their roles from similar motives in the middle of the phrase. One part continues the counterpoint commenced by another, whilst the other part takes up that of the former. Let us regard for this the fugue in four parts in F-minor (Nr. XII Wohltemp. Clav. Vol. I.) The theme presents itself in the tenor in these three bars. Theme. .0.^.0. 151. ^te * ~-t=t^H M^ .fe. 4= ^ -V> =p :?2: E^ As this theme offers no rhythmical figures for imitation in the counterpoint. Bach forms the latter quite independently at the entry of the alto thus: 152. Answer. i gfe^ p fi»-p- Counterpoint I. -^ i&SE ^ -t!^ p p - After that, the alto overtakes the counterpoint, so far conducted by the tenor at the entry of the theme in the bass; the tenor gives now the second counterpoint to these two parts. The fugue being written for piano and not for voices, the parts may transgress the compass of the latter. The trifling alteration in the first notes of the counterpoint is easily explained by the necessarily different inter- vals of theme and answer at the beginning of the theme. § 17. CONTINUATION OF THE THEME AS A COUNTERPOINT etc. 95, Counterpoint I. pSS^^Si 153. <^ I fel ^^ ^ iv m^=^^ ^ Efe Gounteipoint II. jb. 9t^fe^ rrr-ff-Fr= ^ ^ri;g=t^ S^^ Theme. |^^^1^^=^3=^ .b. .♦['■^ P&^^^ ^^S5 tj^j ^ ^^ ^ ^ =^ ^ >-! In the first nine bars of the fugue the tenor renders the quel, marked as follows: 154.^^^ :£ ■ft- ■•■ t=^ V fH t=t= -» » I* » > y ^ A^rtiLf^ S ^H^ ^5^ ■•H^ ^iS^^ ^ 1^ f: P3^^^^ ite ^El^fct ^y=r=¥=^^=^^^g Example 1&3 shows the contrapuntal employment of these rdne bars amongst the different parts. Exactly in this manner, we find through the whole fugue, (with little alteration) the same counterpoint to the theme and the answer. 96 155. J CHAPTER nil. Theme. § n. #-r; 1 Counterpoint III. Counterp. H. m ffiEE= ^Se^3^5=e le^E i^ Counterpoint II. ;e=f^^ EM'^=?=Fp^i*g Counterpointl i te ==^^= r=i3 ffil ^ SE Jztv Tr3fe 1^^ Counterpoint III. H^^-?- ^^ ^^-J— I- ". .' Counterpoint II. SE ^ ife-fe ^ BlEt t- if^^a^Eg=a^=fi^^ pgi i^^i»-p- ^s Alto and tenor bring alternately the counterpoint II, and a free part. The tenor begins the second group of the exposition of the theme in bar 19, and brings the theme in the dominant. The employment- of the two counteipoints with the unessential alteration at the begin- ning of the second counterpoint in the soprano, as well as the change of the two counterpoints in the upper parts, in the middle of the first bar, scarcely needs an explanation. The characteristic step of the minor ninth in the first counterpoint will be perceived by the ear as a minor second in consequence of the crossing of the parts. § 17. CONTINVATION OF THE THEME AS A COVNTEBPOINT etc. 97 156. m B^E: | a^ ^^=pp m m -» — («■ I>Lrg_^i: ?^ ^^ ^^g^^ ^^^§ f^u ^ a^f ^v I^^J^^ ^ E^ i^^a :^ i"^!^ ^ =t In bar 27 of this fugue, we perceive at tte entiy of the theme in the bass, not only the two mentioned counterpoints re-appearing in the other parts, but also the fourth part, which we marked as coun- terpoint III, in example 155. Cp. ni. 157. rr^r^gri Cp. I. gg^^ ^ T mj^sEt Theme. 'JXFt=^ 3E^^ 4^ ^m- 98 CHAPTER VIII. § 17. I ^^. ^ i te^? &. EfeSE ^^ ^ ^= S?Ei ^ ^: ^t After this analytical explanation of the beginning of the fugue, it cannot be difficult to the student, to analyse for himself the remainii^ entries of the theme, bar 34 in the alto, bar 40 in the tenor, bar 47 in the soprano, and bar 53 in the bass. One woiild find also in other fugues by Bach, Handel, Mozakt, and other great masters the same kind of employment of the counterpoint in the slriot fugue. If, on the other hand, the counterpoint alters at the different entries of the theme and answer, if it become sometimes changed or different each time, the fugue is called a free one. Older theo- rists, amongst those the highly celebrated Mokitz Hauptmann, would not recognize this kind of fugue. It is true, a counterpoint con- stantly changing, strives against the nature of the fugue, and we find few instances of this kind with the old masters. Even the ^-rninor fugue in two parts (Wohltemp. Clav. Nr. X, vol. I,) shows consequently the same counterpoint to the theme in all entries. The next task of the student will consist now, in composing a counterpoint to his own themes, which can be used in connection with the theme or its answer as double, and also in a fugue of several parts, as triple contrapuntal movement. We show this in the following very simple example. Theme. 158. ^ Counterpoint I. 1— =^ ^ s^ss ^p^ i Counterpoint II. i^ P § 17. CONTINUATION OF THE THEME AS A COVNTEBPOINT etc. 99 159. ^ ^m ^ ^d^^ ^^ ¥=i-- ^ ^ i^ ^^ ^ P ^ mm * ^ One will perceive at once, that the jnovement, worked in triple counterpoint from the entry of the bass, will be suitable for dif- ferent inversions. See treatise on counterpoint § 25 and § 10 ex- ample 75. The student will have learned from the preceding examples, that the answer of the theme can take place on the final note of it, or shortly after it. But the answer can also commence shortly be- fore the end of the theme. Let the following example explain this. I 160. i ^Li 7-] ' \> ■ Theme. - P fpTf^—t~^ ^t^ -m^^^^3- Answer. ^^jS|^ ^ III! U. etc. The beginner may write down, in his first essays, only theme and answer with the counterpoint necessary for the latter, in two 100 CHAPTER IX. § 18. parts. Later on he may try to sketch out theme, answer and return of the theme, with two counterpoints, worked in triple counterpoint, as example 159*). CHAPTEK IX. The Interludium. § 18. The term Interludium means one or more bars which are inserted between the end of a theme, or its answer, for the pur- pose of preparing the re-appearauce of the theme or the answer. Interludes should be short in small fugues, and, entering upon the preceding theme, or its counterpoint, take its material from either of them. A short characteristic theme from the theme or its coun- terpoint, treated in a free imitative manner, would be best adapted for introducing the re-entry of the theme. We give here the first interlude from the i^-minor fugue, analysed in § 17; it forms the connection between the expositions of the theme, contained in the examples 153 and 155. 161. I fel F5tF -i*-» JHJ=^ 3 * fgS-^#^ I J 'S' §SS^E3E^£^ rg'-'ia^it^ *) We haTe again expressly to remark, that the key of the dominant, need not always appear simultaneously with the entry of the answer of the latter. The key of the tonic still predominates sometimes in the first and second hars of the answer of the theme in the dominant, and only in the course of the answer, it modulates in to the dominant. This will occur in the answer of such themes which begin with the fifth. Compare with the fugues Nr. 1. Wohltemp. Clav. vol. II, and Nr. 11, part I. But also other themes give sometimes the beginning of the answer in the dominant in the key of the tonic; for instance fugue 11. Wohltemp. Clav. vol. II. ^^ § 18. THE INTERLVDIVM. 101 J— ^ y ay=^^jg=i-as%^ This interlude is formed by imitations from the first motive of the counterpoint, as all other interludes of this fugue make use, in a free, imitatory manner, of motives of the counterpoint. Only more lengthy and complicated fugues allow the employ- ment of Interludes of an independant nature, as for instance, the regularly returning sequences in the 5-minor fugue (Nr. XXIV, Wohltemp. Clav. vol. I.) These offer, as all other larger Interludes in more complicated fugues, as it might be, resting places to the ear, and serve, to make the re-entry of the theme appear all the more powerful and effective. Although such lengthy Interludes take their justified position in broadly conceived fugues for organ or orchestra, we must nevertheless adhere to the principle, of looking upon them in general, only as connecting links between theme and answer, or between the principal groups of thematic entries; and therefore we propose to make the Interludes short and simple in our succeeding exercises. Between the first entry of theme and answer, an Inter- ludium cannot take place. But if a third part reproduces the theme, and a fourth the answer, the Interludes required should also be kept as short as possible. They could be composed, in these cases, by a few chords, often even only by a single one. After having pro- duced theme, answer, and theme in the fiigue for three parts; and in the fugue for four parts, theme and answer by two parts indivi- dually, and the first principal group of the entry of parts, has thus been achieved, a more detailed Interludium may follow, to prepare and introduce the second principal group of exposition of theme and answer. We shall see, later on, (at the order of modulation of the fugue) that this first, more developed Interludium, leads mostly into the key of the dominant; in fugues in the minor-key also into the parallel-major, and finishes by a cadence, best however, by a half- cadence. Has the Interlude been derived from a motive of the theme or its counterpoint, is it well connected by an imitative turning, it will then not appear as an external means of connection, and not inter- rupt the flow of the Fugue. It would transgress the limits of this treatise, to enumerate here a number of Interludes; we refer in 102 CHAPTER IX. § 18. this case also to the "Wohltemperirte Clavier" by Bach, which we anticipate to be in everyone's possession. The task of the student is now, to form the beginning of a fugue in three parts ; this must be managed so, that after theme and answer, the theme is reproduced again, and a short Interlude takes us into the key of the dominant. Allegro. 162. I te ■-^ ^^^^^ffirEj ^^ i ^^=J^ m m tizistftt i^^S I— I I I ! , ^ ffi :OT= ^-,— ^g^-» T^r -p-»- =l=t -JCT-J:i h IS *.' — -± ^ Jirg3l -^-t-F- U=J^ -• — ^ :ti=t ^ Pii -^ ■•■ f *-!•-•- 1=^ EE - r I !* . » F »- 3::tt: # - J— J Interlude. f *• I -^ ^ Pi 1^ 'te etc. ^jgj^ § 18. THE INTEBLVDIVM. 103 Althoiigh we find frequently enough a short Interlude, in the fugues of the best masters as connection for the entry of the theme in the third part, we will observe in the first exercises of the stu- dent, that the first three entries of the parts be given without an Interlude in concise form, as in example 162. In the fugue for four parts an Interlude may be already em- ployed after the entry of the three parts, which would prepare the entry of the fourth part. After the fourth part has given the answer of the theme, the Interludium follows for the modulation, into the key of the dominant, or in minor, into the parallel major key. Both In- terludes have to gather their material from the theme or the coun- terpoint. Lento. 163. J ^ e ^^5=j^ -z5 ^— •— F- :£fc eEeShe m i gtesgEfeE ^^W ^# 44feil --t=^F^ r t^^ta — I Q I -f-f- — -'- ^ffif rtf^ ^i^^^^ m dEft ^E^^^l 104 CHAPTER IX. § 18. m Interlude I turning to ^ T-^r^^fV ^^^m^^^^^^^ M the Dominant. f • #f^ r* ip *i ^ !uJ l?S5f=3=# A S*: ^r^-^-^^:^ S 3fc ^=-^^ l=t: ?^^ tt i^rij:: ^^^^^3 I r I -^ J I i -r T ^ mm -f-ii= ^^=3^ -5?*- I r Interlude II with the modulation into key of the Dominant. ^SjgsfS^^^ fe±^ ;3=^ -:S — *—m-- -»—^- tefe m^E^^^^:^^ _^ fe^s gP?lE^:^g^ -*-• ♦ #- ? _£2- =i^Pfela-.»- etc. fc^=±=t § 19. THE 8TBETTA, (CLIMAX) (ENGFUHRVN6). 107 The student may now try to invent such a little movement; let him choose a very simple theme of a few notes for this purpose. That would give him the possibility of a concise and nevertheless true entry of theme and answer. We demonstrate this in the follow- ing, very simple example. Theme. 166. '^ t r^j- ^ ■»■ ^1 ES=B Theme in contraty motion. 112 CHAPTER X. 20. This Stretta can he continued, by trying to bring theme and the other parts in contrary motion. Later on, one may try a Stretta, on which four parts participate, for instance: i^ Theme. 174. ^ft^ W I r - 175. ^ 8E F=PVR^ =fef J a mm -^ S ■*■ — ^- ¥=f=F— -^-F ^fil ii i etc. 1^ ^F=^^ -5^: 176 o. ■ 4«i pte 33 ^ygHF i p jif^^.r^ -r 3?t — i ^- ^ * -f2- EFE^ i m fe 1765. =B: M^ I I "^r 1 I 4 J J i J 20. THE STRETTA, (CLIMAX) (MGFUHBVNO). 113 ^^^^firff^gj^M^ i » te=i i ,^ lUj^ etc. E^ ^ t=t The pupil has been made acquainted with a Stretta in three parts, in § 7, example 62 of this work, in which the imitation has been efifected by enlargement and diminution. The student, who has practised and sharpened his insight for contrapnntal-imitatory com- binations by serious study in Canon, would be able to form with ease, one or the other kind of Stretta with nearly every fugue -theme, having the choice of any kind of imitation in any interval at his pleasure. So much however as a Stretta, or several Strettas serve as an adornement for a fugue, the Stretta is nevertheless by no means an absolutely necessary requirement of it. We have mentioned this before and repeat it here, in order that the student in his succeed- ing exercises, should not be prevented, from treating a good and characteristic fugue-theme, even if this should prove by accident, not suitable for a Stretta. One should also take care, to construct the theme, before the commencement of the composition of a fugue, so as to suit the requirements of a Stretta. Generally speaking, every really good Fugue-theme will be constructed so as to allow, in one way or an- _other, the employment of it in a Stretta. But many magnificent fugues of Bach and other masters prove sufficiently, that a fugue without an elaborate Stretta, will be also justified. A Fugue needs even less an Organ- or Pedal-point, as we have previously remarked; the latter is to be employed mostly, only in fugues of four or five parts. It can enter on the dominant or on the tonic, or even on tonic and dominant simultaneously always however at a place rhythmically and metrically well defined. If the organ- point appears towards the end of the fugue, and the bass of the organ-point does not remain until the completion of the composition, one must not conclude it abruptly. (See Manual of Harmony § 58). Jadassohn, Canon and Fugue. 114 CHAPTER XI. § 21. CHAPTER XI. The Form of the Fugue. §21. After having enumerated the constituent parts of the Fugue and explained their nature, there remains only for us, to demonstrate to the student, how the different members of the Fugue should be connect- ed to an harmonious, well-balanced entireness. This can be done in mani- fold ways, as the form of the fugue is by no means so strictly limited, as, for instance, that of a Menuet, a March, or a Dance. The form or model of the fugue cannot be fixed quite definitely. We can only characterise its general outlines. The expansion of a Fugue will depend on the nature of the theme, on the number of parts, that take a share in it, on the executant factors, on the imagination and larger or smaller contrapuntal mastery of the Author. Generally speaking. Fugues should not be extended, so far, as to run the risk of fatiguing the listener, or incapacitating him from following the contrapuntal combinations of the composition with full and undivided attention. A fiigue of such length and expansion, as the marvellously beautiful first Kyrie in Bach's Mass in 5-minor, stands unique in its kind. It would be advisable as we remarked before, to insert ela- borate free interludes into more lengthy and more developed Fugues. In shorter Fugues one should observe the same order of modulation, that which sei-ves as a fundament for all musical forms of composi- tion, as all our modern forms of musical composition have been developed out of the Fugue. The theme commences in the fundamental key; the answer en- sues in the dominant, with the finishing of the theme, sometimes shortly before, sometimes shortly after the end of it. A third part reproduces the theme again in the fundamental key ; if the Fugue be in four parts, the fourth entry must be effected again in the dominant. It has been shown that short interludes can be used, between the entry of the third and fourth part. After this first group of entries of theme and answer, an inter- lude leads into the key of the dominant; and then commences the second group of entries so that that part, which had performed the theme in the fbndamental key — in the first exposition — has to bring it now in the key of the dominant, and that, in the form of the answer. Upon the answer, that part succeeds in the tonic, which had in the beginning of the Fugue , brought the answer §21. TBE FORM OF THE FVOVE. 115 in the dominant ; the third part renders the answer again in the key of the dominant, the fourth, the theme in the tonic. Has the Fugue been conceived in the minor-key, the interlude may lead into the parallel major key, and the second group of entries contains again the theme, transposed into major in that part, which had the theme at first, at the beginning; the second part brings the answer in the dominant, the third the theme again in the parallel major key, and the fourth part the answer in the do- ininant. / This however is only possible, if the theme be adapted for a transposition into the major-key. Often this would be impracticable, as the theme would lose materially in its charm. Altogether much more freedom governs the second group of entries, than was permitted in the first exposition of theme and answer. The entries of theme and answer may follow, one on the other, sooner or later, at pleasure. The answer may appear in one part, in the shape of a commencing stretta, before the first part has quite completed the performance of the greater part of the theme. But the answer may also commence later, so that an interlude is intersected between the theme and the answer. One is also less strict in the choice of the key in the se- cond group of entries of theme and answer, as was the case with entries of the first group. One gives the answer or a succeeding entry of the theme in the second group, sometimes in the key of the sub-dominant, or in another nearly related key. Sometimes theme follows upon theme, answer upon answer, inasmuch, as the modu- lation into one or another key seems to make this desirable. But it is mentioned repeatedly, that modulations into foreign keys, or entries of themes or answers in these kre not at all in accordance with the nature of the Fugue. Even the largest and most developed Fugues of our celebrated masters pass only into keys nearly related to the tonic-key. We have demonstrated this already at some length before (§ 14) but return again to the subject on account of the great importance of this matter, as the harmonious and modulatory ar- tificialness lies, so to speak, in the air, and the student tempted naturally by the desire, to make his work "interesting" may be led into carrying it into the Fugue, where it would certainly be not suitable. The third principal group, to which afeo leads an interlude, is an astringent, (stretta) contracted representation of theme and answer, in the same order, as in the first group of entries ; this is the "Stretta". Before it, a resting point, best in the form of a half-cadence, may occur, in order to make the entries of the Stretta still more marked; however this is not necessary. We would even prefer, that such a resting point should not exist, as it always interrupts the natural 116 CB AFTER XI. § 22. flow and the current development of the Fugue. After the stretta, the parts are conducted in a free manner to the end. This is the shortest and simplest form of the Fugue. Fugue in Two parts. § 22. We wish now to demonstrate the above mentioned shortest form of the Fugue in the simplest possible example, and shall, for this purpose, place before the eyes of the student a small Fugue in two parts. He may work his earliest attempts also in two parts and in a most concise form. But we regard such exercises only as pre- liminary work for the study of the Fugue, solely for the purpose, that the student may learn to construct the smallest shape of a fugue. In Fugues of more parts this smallest form will, of course not be kept up, or at least seldom. The two-part phrase stands totally in contradiction to the nature of the Fugue. Therefore a Fugue for two singing voices would render a very poor result by the scantiness and restrictions of the two-part style and would remain ineffective. If one has to compose a fugue for two parts for piano, organ, or two violins, certainly we can command more auxilaries. One would be able to indicate the harmony by melodic figures, and to represent the harmony, as one might say, in breadth. In this manner Bach goes to work, in the only fugue in two parts of the "Wohltemperirte Clavier". The harmony woven into this theme by the melodic drawing of it, cannot be misunderstood, and we do not err, if we conceive it in this manner. In like manner Aug. Alex. Klengel proceeds in his piano-fugues in two parts, from which we give here some themes. ^J Ej'J^^ i^rt § 22. THE FORM OF THE FVOVE. 117 ^m fe^ ^^ 180. ^ '^m I S^ ■1— r :-=i: ^ P ^*ff^^ ^^ 1 18i.^^^^^^^^ i-*-^^ ♦ ^^^ii^ 4^ =^ But tlie working out of such themes is a task, which we could not impute to a beginner, and still such themes are necessary, if one desires to write so effective a composition as a fugue in two- part style. After that it appears to be far a more difficult task to compose a fugue for two parts than for three or four. Nevertheless, we have to begin our work in two parts, in order that the student may get acquainted with the fugue in its most limited form. One should however not detain the beginner too long with these exercises; we consider them at present only as preliminaries the fugue in more parts; one should also not criticise these essays too severely. After he has succeeded with a few of these specimens, and was learned to invent suitable themes, good counterpoint, and to con- struct the fugue "in nuce", one may proceed to the work in three parts. The following theme : 182. g is answered quite regularly in the dominant: 183. t '-^ 118 CHAPTER XI. § 22. Our next task will be to invent a counterpoint to the theme which, if not true to every note, is so in its principal features, in order that we can employ it again with the theme, according to the nature of the strict Fugue. We could use this counterpoint as well for the theme with a few alterations, which would be necessary, on account of the mod- ulation. 185. 1^ T==T -^ s ^ ^ ^- ^^ ** m g^^Sg r J f\ tp^ ^ But we could also place the counterpoint a fifth lower, and bring it in that form with the theme. 186 a. m -*-^ ~-=^^ ^^^^^^. ^^m ^ -p-»- H=^=F S^EEB^IES ^ i § 22. THE FORM OF THE FD6VE. 186 J. In the Inversion. 119 :p:f: P^S The student will learn, how this counterpoint finds use in the Fugue itself. It will be shown in the course of the "Fughetta" (little fugue) that the theme is also well adapted in the regular way with the answer in the dominant for the stretta,. We commence now our work, which requires no further comment, having placed the neces- sary indications over the notes. 187. Piano. ' Allegro. First group of the Theme. m ^ ^m m Inteilude I leading into the key of the dominant. 120 CHAPTER XI. § 22. ^^5 ^ Second group of tlie part entries. ^ ^^ M^ ES ^ 4j=1= ^ t ?= S ^^^^^ ?P^ Leading into the funda- mental key. feE^fe ^fegS P t^ t. ^^t^^-v^ ^^ ^^^ ^ ±i 1 ^Ees fei: ;F^=t i^ t^-t- ^SpEi^Sips^i ii Interlude II returning into the fundamental key. ^ Efe '»^ ^* ^ r^j=fe3^ ^ ■^~^=s—* ■* ■* Stretta. m -^-*- P m 0- -•-^-» -i I r f «-^^-# it? =£ gn-f^ ^ > F rff H I >^ ^^S ^^ 23. STRICT FIOVE IN THREE PARTS. 121 r sg 'm^Ete =^ feg ^ } #s^ End. -^-0- » mm^ 'm, H*-T— ^ -»T CHAPTER XII. Strict Fugue in tliree parts. § 23. We have already remarked (§ 17) that we need two coun- terpoints for the theme in the strict Fugue for three parts. We can make use of these in difierent inversions in the Fugue, whereat how- ever, we need not work with rigorous strictness. We have shown in the examples 155, 156 and 157, how See. Bach always reproduces his counterpoints to the theme or the answer and the license he allows himself therein. The repetition of the same counterpoints is, selfunder- stood, only possible as far as the stretta. As the mentioned fugue in i^-minor does not possess a stretta. Bach was enabled , to use the same counterpoints throughout the whole fugue. We will now proceed exactly by the given analysis in § 17 of the i?"- minor fugue, and note down firstly, the theme of a fugue in three parts with the counterpoints belonging to it, according to ex- ample 154. We show now the counterpoint, according to example 152. _ ::::::: %J • • • s j ^ <-:^-i '^^m manner ■ ■ aa • ■••• The second counterpoint could be invented in the following |^l^[p"Tl p ^piP ^ g jjif ■* -^jz-* We could notate these 24 bars also in one line, according to example 154, as a connected melodious sequel; the student may not- ice this in example 188. This little movement allows of being presented in six inversions- 189. I rH^=r ^ ^^-^^ ^^^^m a=t ^W ^ 1^ m ^s *: I § 23. STRICT FV6UE IN THREE PARTS. 123 3^ Le££^j;5=g feE i aqJ ^T]: ^EfeS -^^-*-JV ^^^T ttcrrc^i^ 3. PVt-L Lir ^^ B*-H» 2^fe ^^?t ^^ ^^s i *-p- H»=f=f -^'^t j l=t= g ?}=F^ ^^^^ 4:A=±^ 3. g^^^ I I I — I — \—^ h- ^ 1 rltX I ^ t=* j:>^ I 1 1>^ ^ ^ ^^^^^^^^^^^ ^ 't ^^..-4^^ >"#- =t=t ^*-^• ^s 124 3. 1. { CHAPTER YII. y I J. F-i?7]-IJ5- ;^ ^ :tttt §23. ^ ^P^^ -P-#- ^^ [ gib 1 ■> I ng^^ :^ J=3EE I ^=p^ l S»-H^ ^g^ +-^. ■~:t ^ft- it::^^ ^ ^SErf as ^^^ -l«— a— •- ^^^ t^ ^^ T I Li «« J 1 iz±±Jt -•-=- 3. "^ ^ -r^ ■3=3^ w 3=:^- ^ f=!2p £=^ |6 = F^ ga^^^ps I^T^T^"^^ ^^ ^^^ = ^^^ i}1^ <-^ ^-^ hi*- 23. 2. |2 !**± STRICT FUGVE IN THREE PARTS. 125 q^ :J -^^ :ir-^- ^ 3f^- e ^ s 3^ ^■ ^S Sfe ^ ^ ^ tt^ ^^^^^^^ ^a ^^ It ■will be seen from example 190, how tMs little movement can be used at the two principal groups of entries of theme and answer, what liberties one is allowed to take, and what alterations one can submit to the counterpoints, in order to render them suitable for the theme as well as for the answer, and what little variations, ornaments and adornments they may receive in rhythmical and melodious formation partly on account of their execution, partly to gain a greater fullness of harmony, partly also, to avoid monotony. We mark also this fugue for piano, as one would scarcely make use of such a one for three vocal parts. 190. Piano. First principal group. Allegretto tckerzando. rf-^ -4 Th ft ^^ ' Cfi"^ LLnU^Lf ^^ 126 CHAPTER XII. 23. Antw. Cp. I. '^- i ^•^ 1 ^2 Afgk5 r g ^ i Leading 1>ai. --fe Cp. I. -^-^^^^'^ ^ -h=F=f =Pr ^ fc i =^r]^ ^ ^5=j= eS =t==P=t=; -^*^ m -f—0- ^ f^^- ^ ^c=tt . !;.,-'; F=#J-^t^ -rfT=H 23. STRICT FVOVE IN TBREE PARTS. 127 Interlude. " ^*^°"^ principal group. Answer. ^^?^^F^ =f -i4J ^ -U-'^ill4f ^ ^ I. Cp. ^ jWl -r\ ' ^i^- Jb; =j= ^g it-t ^ p . . ^ * ia Cp. I. fT^T-, rr-T £1 r J j g^J JlJl^/TJ j Answer. 128 CHAPTER XII. § 24. m j^\ ptj From here also the inversion example 191. ^fe ^^^ iin^: ^^^^^=9 §. 24. We have drawn attention to some alterations of the counterpoints in example 190, others the student will have detected easily without especial intimation. Instead of beginning the entry of the answer in the key of the dominant and finishing it in that key, as has been done in the last eight bars of example 190, we wish now to eman- cipate ourselves a little from the model, in order not to hear inces- santly the key of the tonic and dominant. We may draw also other closely related keys into our combinations, and give the last eight bars of example 190 so, that the finishing bar of the theme experiehcBS an unessential alteration. ^^ i_m_ j 191. ^m i^rzjr^ ~1 t^£::JZ WiTTli m^ ■*'^\-*-^ mi- FV . , a^ m rs-»fts- ^ ^"^ff=if i^^^S^^ ^m § 24. STRICT FVGVE IN THREE PARTS. 129 With the object of gaining the modulation of the dominant of D-miaor, we allow the bass to finish the answer with B and A. i w^ It does not lie in the character of the Fugue to bring often half or whole cadences. These retain their justified position only before the principal groups of theme and answer. For this reason we give — instead of the last ninth bar of example 191 — the continuation noted under 192: a detailed interlude, found- ed on the commencing motives of the theme, which leads into the subsequent stretta. 192. I m m at L&'l^ a=p= :s-^ i-j 9i rit ^= ^^m ^-^ ■•■ ■•■uJ :i^ L:^fe r3S ^^^ B\0—0 #-S#- —\ 1 1 C__ TR C r ff g^ M^F^^ ^ ^^3=i=t= P^ ^^^^ f ' ■ ' S ?ir=^ Here commences the stretta ; the entries of the parts would be more pronounced, if the part had paused before it, or, as in the last bar of example 192, the part — here the bass — effects a striking leap before its entry. In the Fugue for two parts one cannot very well effect the former, as the movement would become conducted by one part only, but in fugues of more parts one likes to cause the parts to pause before their entry. Jadassolin, Canon andFngue. 9 130 CEAPTEE XII. § 24. 193. ^=^^ ^ ^^^ - i-T " r±r''g&' "C^ ift i^^-^ gg #-l—- 195.^^^^^^^ ^SN ^^^^^ ^ Do not choose themes, for the beginning, which have a large compass. Short themes which do not transgress a sixth or seventh in their melodious compass, will be treated more easily than lengthy themes with larger compass. Let the student consider that each theme has to re-appear, either a fifth higher, or a fourth lower, in each part as answer. Although the beginner need not take regard in his present first exercises to the compass of real § 24. STRICT FVGVE IN THREE PARTS. 133 singing voices, nor to the practicable reproduction by an executant, still he should consider that his present endeavors purpose to lead him to the composition of Fugues for voices, for piano, and organ. For a Hrst exercise let him make use of the theme noted under Nr. 195, although in general, the method of furnishing themes to the pupils, is not at all sympathetic to us. He should learn to invent suitable themes by himself, independantly . If one gave him a theme and counterpoint for his work for a strict fugue, there would be scarcely anything else left to him, but the mechanical putting to- gether of the whole fiigue. 196. h^^'^T^^^^^^ ^^tim^ The student may form the counterpoint to this theme in such a way that they re-appear at the principal groups of the thematic entries, though of course with the necessary alterations. To furnish always different counterpoints to the themes, runs diametrically against the nature of the Fugue. K one scrutinizes the Fugues of our great masters carefully, one would perceive, with what wise economy the same material — if we may use the expression — has been brought into use over and over again. It must be left to the imagination and the artistic taste and refined sense, to develop out of the theme, and the counterpoint to suit it, the whole Fugue. We find only isolated exceptions, when in the course of a fugue, moving in slow time, a new counterpoint in essentially quicker time is added, as is the case in Bach's fugue in A-m&iox (Nr. XIX Wohlt. Clav. vol. I.) or in his i^-minor fugue (Nr. XIV vol. II.) But in such a case, the new counterpoints are kept for further development. For this reason we dispense with the practice of the so-called Free-fugue with changing counterpoints, especially as it would be easy enough to construct such a one , provided the strict Fugue has been studied thourougly. 134 CHAPTER XIII. § 25. CHAPTER Xni. Free Fugue in four parts. § 25. After the student has attained perfect sureness in the construction of the strict Fugue in three parts, he will be able, to commence the studies in the free Fugue in four parts. We have to overcome here the great difficulties, which the style in four parts offers. Experience in teaching of many year's standing has tought us, that it would be unpractical to commence at once with the Fugue as a strict one in four parts, with one or two, always recurring, counterpoints. We find also with the masters comparatively not a small number of Free Fugues in four parts, against few free ones in three parts. Besides, every strict fugue in four parts with re- maining equal counterpoints, takes more or less at once the character of a Double-fugue. The student has, therefore, to conduct his first attempts in a free manner ; the counterpoint, chosen at the beginning of the answer, need not return. It could possibly be brought again, entirely or partly in another part, if it should accidentally show itself adaptable ; but no regard need be taken to make it so, at the outset. On the contrary, one would do well , always to pay attention at the formation of the counterpoint, to the latter finding support in one or the other motive of the theme or the first counterpoint, and to harrow the development , from already existing material. We consider it a total failure to employ for a changing counterpoint something strikingly new, melodically or rhythmically, or something especially conspicuous and adverse to the character of the Fugue, thereby damaging the unity of the composition. It would be a different matter if — as has been remarked § 22 — a new counterpoint in accellerated movement should be added and remain. (Compare Wohlt. Clav. vol I. fugue IV. bars 36 — 94.) A perfectly strict maintenance of keys of tonic and dominant cannot be recommended at the second principal group of entries. One would remain too long in the same keys of tonic and dominant. This is better avoided, by bringing the second principal group at once as a Stretta, as Bach has done in his jB-major fugue, Wohlt. Clav. Nr. IX. vol II. 197. S ■-^ f r T ^ae §26. FBEE FV6UE IN FOVB PARTS. 135 m h m tn 1 I -^ -S- H — -3- Uff ^ j=d=^d=fa=J=j=^ ^ But definite rules cannot be given also for this. It will depend on the extention of the theme, as well as from the preceding interlude, whether it be advisable or not to keep to the keys of dominant and tonic at the thematic entries of the second principal group. The case often will occur that the theme appears with the same note, but still in a different key, as in the succeeding example of the just mentioned fugue. 198. § 26. It would be difficult to find two Fugues which are exactly alike in their conceptive structure. In regarding the Fugues of our great masters, we find in each Fugue, not to mention the difference of style individual to composers, a divergence] from ^that] form, which we have recommended to the student as a model for his work. The point of interest will be now, to show, what has to be sanct- ioned, as deviation, the rules, originally ^ven. The most in- fallible means of assertaining this will be always the careful a nalysis of as many Fugues of good [masters as possible. We give an example of a simple, but more developed Fugue in four parts, with ^an explanation of its structure. Lento. 199. i tt **EE Theme. J^ jJ^aJ 3 ^fr-r-gf ^ ^ Bass. 136 CBAPTEB XIII. % 26. m Tenor. Answer. ^ 3t ^^^U^,,J^^ -0—^ E£ffi ^f^ Counterpoint, m Alto. Theme. =F=r ^ ■k^ r ffif^ rrfi rs*- eE ^**s -Xlff- ^^^ F^^^ -n t t s ' ' n ^ rt :M i' ^^ c/ 1 r r M^ It An interlude founded on a motive of the theme prepares now the entry of the fourth part. Interlude I. with a turn to the tonic. 200. ^%^^=3=^" #rr~ I T ^^ g ^ P5: § 26. m Bte FREE FVQVE IN FOVB PARTS. j Soprano. Answer. 137 w f 5=3 If i-^JP I ^t H^H% ^ m i XJ^i J J JjJ^PfJSE^^f i|j tt ^ ^^m m E^ r » I . L- k - I— g-j T? ^-1 = ^ m ^T^ ^ ^Yf^ ; t I With this the first principal group of entry is concluded; the latter must be formed perfectly regularly. Nevertheless exceptions can be found; (compare Bach, Wohltemp. Clav. vol I. Fugue I.) Now follows the second interlude for the preparation of the entries of the second group; this period finishes with a full cadence in the key of the dominant. Simultaneously the bass intonates the theme in G'f-minor. 201. "l* Inteilnde II. formed by the same thematic motive, as inteilud 5 J TiSi ^ ft r 5^3^ ^ Tff Commencement of the entries of the second principal group. — ^^ ■ ~ , . r. r f nf U i j ^ , ^^^^^^ m ^ ^^ M ^^^^^^ .1 ^— , ^K4 f r Bass. Theme. 138 CHAPTER Xlll. 26. Instead of returning to the tonic C|f-minor, a short evasion into ^-major ensues. The soprano gives the theme in this key, the bass the answer, in a Stretta conducted with canonical strictness, in notes twice as long as the original theme. 202. { ^^ First Stretta. Soprano Theme. "SEf^ ^*fF ^ =si: m r «f^ ^^ =JjTji m ^uu^ r-Q' r -i^ t±^ ^ lE ' Bass. Answer In the Sub- dominant. n^ IFFPf ^ tzU-i:^^ ms UiS iP 4- Tfw «r ¥ te^= Wi^ -•— «. N=^ -i — ^ 3=?^*^ 1^1 m ^ g=3=h^ f V ' Tenor. Theme. -J J ^ r?«fit?T ^ «- r i# *LJ=i itJr -^ •- =r — r sr^ r § 26. 1^^^^ FREE FV6VE IN FOVB PARTS. 139 -w — •- Zt±i ^ J J J fr^ -r rr ^i| J, ^ J Jt^ I j =6J^ i J ^^^^ l#i ^ _ Alto. Theme. _j1_ ^l_J U_j ■t-r ^ .Oi^ f^f=f=ftr i-J-^L^-t,^ i^ ^ S &^ m^7-tr=^f^r7-r=^ r Pi^.=tfJ^^_=j:^z4z=j=^EJEJ^^^ Bass. Theme. Close of the second, and commencement of the third principal group, ■with the theme in the baas in Cj^-minor. 203. 3^ Tr g'' 140 CHAPTER XII J. 26. Soprano. Theme. ^^ ^ ^ ^ m ^ M: ^m. -*—i- Organ-point of the Tonio. I ft P ^ ^— *—#- w 'f*¥r f f p#^ ;U4- I r iita^sri ^^^ ^ Second Stretta. Theme. Soprano. =P?= -i5>- jS 55- ( I zMzfz ^ ^^ «J-i=^ J Bass, Answer, A m m tes -HrJ- itS*i ia^N =^ =FT ir=T=f= ^fcr4 J U a ^ :t=^ iE&-^^ SE4- H ttt± a. E^ S W^ f^^ 1 -^—0- '=p= --i- 4 ^ w^^. 26. FREE FVOVE IN FOVR PARTS. 141 Originally the Fugue would finish here ; but there follows a coda ; (postlude) which contains the theme in the bass. The accompaniment to this coda is worked intentionally only harmoniously and not con- trapuntally. Deceptive cadence on account of the lengthened close. 204. ^^ &^m f^WW^ i tii diminuendo. »» j^pp^^^ss^ #5 3 Theme. Bass. =86 ^ ^ :#£ «a -P' iOS- Mf* p ^^=rj^^=g^ ^=1= =tf^ "ly — ^"^» rail. 9# ^ ^ Pt ^ 3*^ We will now still have to make a few general remarks. It is not necessary in a Fugue for four parts to employ these four parts constantly; nay it will be better, that one part should pause before the entry of the theme or answer; the entry would be much more efifective. One cannot however break off a part abruptly at pleasure, but only, after having finished a melodious sentence, as is the case in the bass of example 202 bar 10. It is also not good, to allow that part, which has been pausing, to commence again at pleasure, and, as it were, accidentally. The entry occurs best with the theme or the answer. Although the preceding Fugue*) is a free one, the counterpoint. *) From the author's "Preludes and fugues," op. 56, Leipzig C. F. W. Siegel (Linnemann). 142 CHAPTER XIY. § 27. nevertheless preserves a uniformity, by the frequent employment of the same thematic motive. The theme has been introduced fourteen times in its -whole entirety : six times in the tonic CJj-minor, three times in the key of the dominant Gff-minor, twice in the key of the third above -E-major, and three times in the key of the third below, ^-major. The modulation moves therefore only within the nearest related keys. The Fugue also contains a Pedal-point of four bars duration; the student must observe carefully to commence the Pedal-point only on a point, rhythmically and melodically defined. The Pedal-point can however not be broken of at pleasure; this can only occur at a suitable place. (Compare § 20 and Manual of Harmony § 58.) For his first attempts the student may choose short themes with small compasses. After having obtained some practice and sureness, let him try to invent not only useful, but also characteristic themes. But we warn against employing too much artificialness, such as con- trary motion, enlargement, diminution or retrograde motion (per moto retrograde.) The theme should only be used in contrary motion , if it can be employed for that purpose in a natural and un- constrained way. The student should also not place too much value on a Stretta which is too artificial and many-parted. All these matters should only be means for the purpose of inventing within the limits of the fugue, a good, congenial, and organically-shaped composition. CHAPTER XIV. Strict Fugue in four parts; Fugue for singing voices with and without accompaniment. § 27. The Strict Fugue for four parts is formed mostly by two counterpoints, recurring at least at the principal entries ; the fourth part nearly always remains free. It has already been shown (§ 17) at the analyses of Bach's f-minor Fugue , (Nr. XII Wohltemp. Clav. vol I.) how one has to invent the theme as principal subject, the first counterpoint as continuation (postlude) to the theme, and the second counterpoint as continuation to the first , so as obtain a small movement in three parts, worked by the rules of triple counterpoint, with which inversions one acts more or less freely in the course of the Fugue. The student may analyze some of such four-part Fugues, worked in this manner; he would see, for instance, in the i^-minor and (r-minor iNr. XIV and XVI Wohlt. Clav. vol I. also in the § 28. STRICT FVOVE IN FOUR PARTSi FVGVE FOR VOICES etc. 143 ^if-major fugue Nr. XVII vol. II.) and also in others, that they are all composed in that manner. One proceeds exactly as at the composition of the strict Fugue in three parts; but one has the advantage of being able also to employ the fourth part in the course of the work. The strict Fugue is employed more for vocal than for instru- mental music. In the latter the equally repeated words of the text appear as a necessary condition for the returning and recurring counterpoints. § 28. In order not to make our treatise too lengthy, we gather together the directions for the strict Fugue in four parts, and the Fugue for voices in mixed chorus. Firstly we have to take into consideration the words, with regard to the composition of a Fugue for vocal parts. Not every text can be made use of for the purpose of serving as words. In selecting words, we have to take care, that the text be neither too long nor too short, that it expresses a meaning, condensed in a few words, for the principal movement, and that it contains one or two addi- tional sentences to which the musical codas, interludes and the counterpoints in accordance with the sense of the words may be placed. If we wish to make use of only the same recwrring counterpoint one short sentence wUl suffice, sometimes a single word. Even for the principal movement the only word "Halleluja" may be sufficient; for this word expresses, in its combination of the words "Hallelu" and "jah", (the contraction of the name of God-Jehovah) the meaning "Praise the Lord". One could therefore make use of the two words: "Hallelu, hallelujah". However to our knowledge no use of this justif- ied arrangement has been made. The words "Amen" could be given to the counterpoint to the theme. We advise the beginner to write as first Text-Fugue to these words; he will have the advantage, of the word, Halleluja allowing the accent on every one of the four syl- lables. That the word "Halleluja" in the theme, and "Amen" in the counterpoint can be repeated, is self-understood. Also the word "Amen" can be accentuated at pleasure, and bears the emphasis as well on the first, as on the second syllable. We add a few more texts for other work. "Praise ye the Lord, for He is kind and His mercy endureth for ever". The princi- pal subject would have to be composed to the words : „Praise ye the Lord", presumably with repetition of the words. One can use the words "Praise ye" and "the Lord", as well at the beginning, as also at the repetition of the single words "Praise" and "Lord", also "Praise ye" and may perhaps organise the words in this way: „Praise ye the Lord, praise the Lord"; "Praise the Lord, praise ye the Lord". The first counterpoint would be placed to the 144 CHAPTER XIV. § 29. words "for He is kind" the second to the words "and His mercy endureth for ever". Here one can also use at pleasure, either the whole sentence, or repeat single words from it; for instance: "and His mercy, His mercy endureth, endureth for ever, ever" etc. One can however also take the words ,,Praise ye the Lord, for He is kind" for the first theme, and use "and His mercy endureth for ever" for the first counterpoint. If it be desirable to add a second recurring counterpoint, one can choose one or a few words suitable to the verse used from Scripture, for instance: "Hallelujah". Another suitable text with a recurring counterpoint would be "Great is the Lord", (theme) "and His power endureth for ever" (counterpoint) . Another: "Praise ye the Lord, oh my soul" (theme) "and all that in me is. His holy name" (counterpoint). Another: "The Lord hath redeemed Jacob" (theme) "and iS powerful in Israel" (counterpoint). Or: "Eejoice ye heavens" (theme) "for the Lord hath done it" (counterpoint) . Lastly : Shout joyfully to the Lord" (theme) "who is our strength" (counterpoint) etc. One can also put a second counterpoint to the same words or a part of them, it rests with the composer, to choose those, most adaptable. Hatdn composes the final fugue in his Spring of the "Seasons" to the words "Honour, praise and glory to Thee, eternal, merciful God". He gives the theme to the beginning words "Honour, praise and glory to Thee" and the counterpoint to the words : "eternal, merciful God". The student must observe in the first place at the invention of a Fugue-theme to have a right and natural declamation of the words; he may not separate that which belongs together, in order to lay it at pleasure under the theme or counterpoint. The treatment of the text must never be an arbitrary one. § 29. How then should a theme of a Fugue for voices, and how the counterpoint be invented? At the invention of a theme as of counterpoint proper, regard must be taken, that both can be executed with ease by one and the same voice in the tonic, as well as also in the dominant, (a fifth higher, or a fourth lower) and in other nearly related keys. It will be advisable not to transgress either in a theme, or in a counterpoint^, the limits of a sixth, seventh, or at the very most an octave; otherwise the execution of it by the same voice in the dominant would be difficult, nay impossible. We show here theme and counterpoint in one and the same § 29. STRICT FVOVE IN FOUR PARTS; FV6VE FOR SINOINO etc. 145 voice; the limited compasa permits the transpoailjons which we have marked. We choose the text: "All Thy mercy and all Thy truth govern over us in eternity. In eternity thank Thee Lord". Alto. 205. Tenor. 1 ^5 ^^ j±: i J J F All Thy mer-cy and all Thy trnth m All - Thy ^m r^^^ gov vei us ^^ ^ :ee - *— f-PH«-- »- mer - cy and all Thy truth gov i^E^^ ^^ ^TWT d = ^^ ter . ty in e ter - ni - ty. Praise and ^ P S ver us, u thank Thee, o Lord. Has the tenor to render the answe/, the alto overtakes the counterpoint an octave higher. 206. F?r=r=r It * ^^ ^^ :t ^^ * Jadassohn, Canon and Fugne. 10 146 CHAPTER Xir. 29. £: m -)»- ' M » ^ ^ M ^ ^ E d&fc £ rt^^T^^^ ?EE^ If the alto has to bring the theme instead of the answer, the tenor takes the counterpoint transposed in this way: 207. ^3 ^ --^ -0—F- :tT^ ^ SE ^B :t=t ^^ S E e Here the compass of the voices has not been transgressed any- where. It is evident, that example 205 could be sung also by the bass, just as it is written. In the same manner example 206 is executable in equal pitch by soprano and alto. Both parts of example 206, placed an octave lower, can be sung by bass and tenor, the bass giving the answer, the tenor the counterpoint. Example 205 is practicable for alto and soprano, if written an octave higher, and in this way, a good many other transpositions will be possible, from the beginning of the counterpoint, between the different voices, with few alterations, and without transgressing the limits of the indi- vidual voices anywhere; for instance: Sopiano. 208. Alto. m 33E Jfe^ TT^^^ ■0- *- etc. 4=--t ^^ The student will perceive from these examples that theme, as well as counterpoint, have to be transposed a fifth; he may practise at present, composing such themes and counterpoints to words and § 30. STRICT FVGVE IN FOVR PARTS; FVOVE FOR SINOINQ etc. I47 try after that, to invent non-accompanied vocal Fugues for four parts. Although this kind of Fugue may occur now-a-daya seldom enough, even in more elaborated Motetts, Psalms, Hymns etc., still the exercise will nevertheless remain an excellent and indispensable practice. § 30. We propose now to give an example of a FuguQ with two equally recurring counterpoints. The Fugue is taken from the Author's "Trostlied" op. 65. (Breitkopf and Hartel, Leipzig). It is accompanied by Orchestra. The instruments go, as is the case in many accompanied fugues, almost always with the vocal-parts, and give, only, in the first bars, a bass and a filling part for the per- formance of the theme by the tenor. We show first the theme and the two counterpoints, of which the first brings the same words as the second. The regularly recurring employment of the two counter- points is so easily perceptible, that the Fugue does not need any further explanation. Theme. 209. ^^i-^=j ^ ^^-n rlr r ^§ For she hath re - ceiy'd two-fold re qnitalfiom the ^ for all - her ^^ ^ fhW-t^ for all, for all - M ■W=f^ hand of God. I tei ^ e^S guilt for all her guilt. ff^^F^pF her — — guilt. Now follows the Fugue ; we give its orchestral accompaniment as a Pianoforte-score. The two counterpoints enter at once in the instru- ments with the presentation of the theme by the tenor. 10* 148 210. Soprano. Alto. Tenor. Bass. Piano. CHAPTER XIV. 30. ^ Bosienuto Fuge. Allegro deciso. & tel; fes S »S 1^ ^ ^ (=p= :^ that ex - pia- ted her guilt. f peaante ==r~ z^=WZ ■^ ^. • sempre f marc. For she hath le- _J_^ |B_ iS*- ■•- ■♦• eM^ -(u — F— ^- ^ S=4^ t y pesante sempre f marc. SE m teiE B fe ^^ m =p ceiv'd two - fold re qui - tal from the hand of m^2 ^ i i J ^ ^ J- ^te iS.^ m^=^f=^=^ S^^^W^^W ■p-"^"?" §30. STRICT FVOVEJNFOVR PABTSi FVOVE FOB SINGINO etc. I49 P ^- sempre f marc. For ahe hath re - oeiv'd two-fold re - qui - tal from the r J- J?=^ ^ ^ God, from the hand of God foi all her ^ ^ ffi ^ra^4?^ tji^ H^ felE sempre f marc. n ^ ^. }^ r^ % fer ^ For she hath xe- . -\ ^W f* « — w- hand of God, — from the hand, from the> h»nd of gnllt, ^ ^ S X.^±—,^ for all - her guilt, for ^ ^ I fel s EE3 *[>■*■ . i ^g=^=5j ■^nfTT -*it»^ i=S ^g f 150 CHAPTER Xir. 30. tefc & It =^ ^ ceir'd two - fold le - qui tal from the hand of P :t if E£ -^ Ood for all hei guilt, for all - her ^ ?^ PS IS •^ ♦ * * ■•• ^ L ,J=i 2fe: =1^f I I »* m 2==^ r^ Ood ^ for aU — for all — her k^S^ If^ ^. 5^ ^^^^ =t ^^ gnllt, from the hand of God for all, — for pi ^. ±^:=* SE^ from the hand of God. sempre f marc. ^a ^-^ -¥=r=w It I M For she hath re - ceiv'd twofold re - qui -tal from the I I i s ^3 n w=t- -« * »s g^ ^ t?' g ^^J=r ^^ ^^F=^ ^—*- ^ ^ § 30. STRICT FUGDEIN FOUR PARTS; FVQVE FOR SINGING etc. 151 toLjLX ^^ g .f ■ 0: gnilt, — — for all — — het guilt, from the hand of ■ t, ;-j I |. bp-j^' J I ;■ t all, — — for all te^ hei gnilt, - for m ^^ s^ hand of God, of 6od, for hath le- fet fHfiJ j l y-f^^ ^ n' m 8 .nt-fi 4 Ei ^ m ? r^^ tet *^ ^ ■j H u. God. — — for all, — — for all — — — her fe ^^ m ^ ^ ^ M all, — — for all — — — her gnilt, — — for ^ ^ ^E^ ::^ S ffl ceiv'd two-fold le - qni - tal from the h,and of r r r II ^^^^^^ 152 CHAPTER XIV. 30. |S^ ^^lj \ fj ^jl^ > l - ^ '^^j^ ^ gailt, — for all, — — for all — her ^^ -dr- ;^'' l^fd .-#-^L L^ 1* her all, — — for all — — for all — I fe ^ • fe^-g=^^l^^-^ ^ guilt, for she hath re - ceiv'd twofold re qul-tal from the ^ fe^fc* guilt, frota the hand of God' -X . J^ P for all, — — for TO^-^r^ kff *: ^ f.' P V ^ ^ God, fee for all, for all her guilt, for 3^$ 5 ^ ^ ^J-f-g f * * ^ 4-c^=t: =^ [ -^^^^^^ F — • § 30, STRICT FVQUE IN FOVB PARTS; FV6VE FOR S1NQIN6 etc. 153 I k^F==?^ :^2=^^ ^ «iL-p_:z| M--jr-^^^ T i^f^ hand of God, ^- from the hand of fe s s ^ ^-f^ s « l * all — bei guilt, for all hei I tel= w. -Tg =f=^fc ^^ ii^^^f^ ^^^^ :§ E^ all, for all hei guilt from the hand of ^^=^ ^-l/ ITt ^ r^ ^^i E ^F^ ^ f^ ^ I s^ I fe ^ -lZ«-4- aoi for all her 1^ ^ 3^P ^ :^ ^ guilt, for she hath le - celv'd two-fold re - qui - tal from the j=i-^H7g-^ ^J^: for all. for all — — her if^ m '-sg-^r- God, J?*- ^^^^ ^^- ^ S3:: -^^ 154 CHAPTER XIV. 30. ^3^^^^ ^ r— ?-a m :i=t 'B ¥:^ t=t ^ gnilt, for all her gnilt, — — for all, for all her I fe ^- & ^ -.*^ :^=q all her hand of God for all, — — ^m 3=^ -^ It :t==t^ ^ P=^ ^^ ai guilt, for all her guilt, — — for all, for all her ^ m ^ !i> i-i i=*h^ i ^ ^ ' ■<»■ iS ^ ^ ^f-r-r^ :i=x m ^^ - — * — ^^ — t ^ ^^^ guilt. i te S ^ ^a^^ all guilt, for for all — — her &^f=t - ^^^ ^^ guilt, g^zz^^^rtt^T^ for all — — her ■ » ' I for she hath re - celv'd two-fold re - qui-tal from the i ^^ r ^ f- "?■ ^ ^s 4 "S I;j j il^ p^, i;i i jii-ft^ §30. STSICTFUGVE JNFOUB PARTS; FUOVE FOR 8IN6IN0 etc. 155 ^ ^^==fF^ ^^ * V — V- J^rom the hand of God for ^i^^ jjM-f r r ra ^ guilt, — her guilt from the Lord, P^ iJ f i T^iL^ J I r j:ii^ guilt, — her guilt from the Lord, for she hath le- Ss :j^^^-r-^rfr=t r^ hand of God, from the hand of God ^^ rrrr-f =3^=^ ^ di ^ di=^ ^^ ^ ^^ H ^ » I ^ =t ^&^ ^^ ^ 1=t: aU, for all — — — her guilt for aU her P9 - i-i- ^ :t i^ ^ P i^& for all — — her guilt, for all her ^ y=(^ 1 — ri *^^ r'd two - fold re - qui - tal from the hand of ^ Wz ^^^^^ ^i^3F# ^^^5i =^ 156 CHAPTER XIV. 30. pr^ f T - r 'r i^ m^m guilt, — for all her feE fe^E^^g m ^ it=t: guilt, — — for all hei guilt, for I i^b J- T"^ :fe=t E^ ?^?E i^i: ^ =t God — for all — her guilt, for ^ ^5^ :t=t for all her guilt. for all — — her I ' W f M i P • — r^ — h^M — 1« s 1=: 1 ■ ?- ^^m p f=i^== f^ =rr=^ I I m^z^^^^= =E^ -^— 5» I ^^^^ Ef^lE fe^ guilt from God, ^^c» PP for ^ ' * < i S ±' aU — her guilt, for she hath re - ceiv'd two-fold re- te^ tt-k- m ^'= — I — -I— I — = all — — her |uilt, ^ guilt from God, .§: for all. =^ for I 6^te » ^^ i * EEEEgEE -»—:*- =F^ §30. STRICT FVOVE IN FOVR PABT8; FVOVE FOR SINGING etc. 157 I ^ ^ m -!■ 0- *=* ^EfeS all, — for all, for all her guilt, — for ^ ^^^^g_^ i:^ qni-tal from the hand of God for fer m for ^^ + 1^^ b.> :£=^ ♦ t^^ ^. ^ ^^ all, — for all — — her guiU, — — for fe 5^ zkJz :^-i m ^^ MlM-M h—t-^^fLM—^ gfcjf ^^ H I Kf ^ PT^-Fg ^^ -^ — •- -^ — > — J It -4- all — — her guilt, — for all — — — her fefel I B? ^ S ^' - s - «l w aU — her guilt, — — for all — — her P?^ s ^ ^ ^ :3= her guilt, for all her r¥^F=^f=^ ^ -# — ^ 1^ ^s all — — her guilt, — for all — — her I ^^ ^ I . I- ^ I t ^ i g= ^^P^ --^ — r S W=r£ ^ ^ P^3^ 158 CHAPTER XIV. 30. g te^ piii f e eresc. « ^^ ^' =i^=* gailt, from the hand of God, I ^ m. guilt, from the hand of God, of God, fiom the hand of I te^ BU-^-i^ -^ — i ^ guilt, from the hand of ^ *=^ ^^E ^l=i=^ g^EE^ -B i— ^ guilt, from the hand of God, of e?j^ ^^^ ^e f «!-- f .. ^ - g f ^ =p: ■I I I e^E£ ^ //, *r- & ^E^ ^^ ^ ^ * — »i- J=i S^ S ^i=^^^^^ | fezfap^ ^^^ ^^3:::g^fe £g y -» =!?==!?: hand of God for all — her guilt, all — — her I ^^»=^ m ^^^^^^m m^^^^ . -e^-fe#--- fe »-a — • ■ F - | "— r^" ^Lj^-i^-u I ^ g— i ^g - 8-g - ^p^gi^^^ & -^ — 5^ ^^P k=i^^^ 160 CHAPTER XIV. 30 m ff ^ 333=5 ?S= 4=^j^ *-i? w^^ — #" yrij t^ri^^^ , i;^ ,i^ .,..G^^ guilt, all — her guilt, for all her guilt from the ff ^^^^^=^^^^^^^3^t^E^ Ss ■fL-b^-^gi^- f- f , r 3Etzw fr^?=f= vCniC w -UJ-W-^ yy Trumpets |tes^g ^^S^^3^^ ^ ^^ ig^^lEl !« PTn-i^ cresc. •m.oV.Q. ^ -J _J_;i^^J^ ^-P^ E^^ ^=^=F-^=3?TO=3=rJ^^^4J =g!EgE^ -* — #- hand of God, from the hand of God, from the hand, from the hand of ^^^^^ 3^^^^^ ^?^-f !•■ ^^ // l^^^^^S^S ^ ^ iv-t!r: -v^P- from the hand. from the hand. I fe^ c«sc. mollo. ^^- ^-T i-i^ iS^^a^ S^ ^f^-^ E^e ^.?i § 31 STIilCT FUOUE IN FOUR PARTS; FVGVE FOR SINGINO etc 161 largammte. ff » ?-i--i-ca S ^^^ God, fiom the hand of Ood. fte±±-.ta- T) . 1 -- f^^^ //■•-. ■»■ ■»■ t=T=t ^^^ 5r^=t 9^i ^^— ^-U: ^ S E^EE=E {ar^amente. ^^^^^=^^^JpiEE^EjEp= f.f gyrf ' j: tft=^ ^ One frequently finds especially in Handel's Fugues that the theme appears after manifold expositions, towards the end of the Fugue in the soprano, accompanied only harmonically by the other parts. The student will perceive, from the orchestral score that the instruments accompany the voices, not only in unisons, but also in double octaves higher or lower; how they fill occasionally the harmony, and how they assist and mark the vocal parts after the rests. § 31. But the accompaniment of the orchestra can also appear in a more independent manner; it can follow the voices by suitable figures, invigorate the rhythm, give an harmonious or contrapuntal accompaniment, nay, even take a share in the polyphonic weaving of the Fugue, by introducing independently conducted contrapuntal parts. Lastly, the theme of a Fugue may make its appearance in the orchestra, while the vocal parts only give a motive. This is parti- cularly effective, when the theme appears in weighty brass-instruments, or in the enlargement. Here follows! an example from the eight- part Fugue for double choruses, taken from the Author's 100th Psalm (op. 60 Leipzig, Breitkopf & Hartel). The theme runs as follows: Jadassohn, Canon and Fngne. 11 162 CHAPTER XIV. § 31. 211. I fe E i-^-- ^ 2^ ^^E^^^^eS ■Wor-ship the Lord with gladness, come be - fore his sa - credness Towards the end of the Fugue the commencing bass of the theme resounds, simultaneously played by Trombones and Trumpets in the enlargement. The two choruses accompany this by a motive of the counterpoint. 212. 2 TiTimpets. 3 TTomhones. Sopiano. Alto. Tenor. 2 5- Bass. m Sopiano. Alto. Tenor. Bass. » i tA m m i ii ■B lS>- 5 «!3. .=^ t- ■^^jEi r=^^^ =^£^E^^ with joy-ful, O with joy-fal, an gtZ O EBEiEg^g^ =p=^= fef=fcE^^^^^ 42=^15 — t — 5C -— r^^s— r— 5 ^ i r B — F—r-i- ^ -i 1 q^nz^^z '-^-^ — i- ^^ with joy-ful, ^=^Z=-^ :i=^=^ with ^ ^ I r ro ^ =^=^=^ »R= r=i=^ ^^=a-F-^'^^ =^= -v=5L. §31. STRICT FVQVE IN FOUR PABTS ; FVGVE FOR Simim etc. 16S m e£e m- ^ I L-j-^,k=5B: = ^= 1= with joy - - ful — songs, with j^np^g^ 1=4=^=^^ -^-m-s-0-^ ^ %=4=C^-£J-=P # — r^ — •- ^i^g^^ PfelE ^^^a=^^ 1-^ — t^.^^ =i=t ^^ — * = ^ h ^- To ns Xhy good -ness flows, we give Thee ^ ag:g=OS -^ ^^=Mf^ ■0- +- I ■ ffU - -TO^- tefEs n^^^ W l> ^ ££ m ^ ^=^ =b=tc To UB Thy good -ness flows, we give Thee I ^j^-n ^=^ m piaise andthanks, piaiseand thanks to ns Thy ^^^^m j^ =f m ^ -»!-*- ' '&' l^^frr^^ I ^ *=t!= piaise and thanks, etc. S? — ;P: I good - ness flows -fitfft-- *- fi^p ■<— I- -# — E 166 CHAPTER XV. % 32. The orchestral part may also produce short, independent move- ments, in the middle of the Fugue. But these "intermezzi" would always have to be based on motives of the theme or counterpoint in a manner suitable to the style, in order that the uniform character of the composition be not injured. This would aflford to the vocal parts a suitable resting point, especially in more developed Fugues. We draw attention to the five-part Fugue of the Kyrie, in the .B- minor Mass of Bach. We find in this Fugue an instrumental prelude, before the entry of the vocal parts, and an instrumental interlude in the middle of it. An instrumental postlude of a few bars may also occur occa- sionally, to allow the close of a movement to sing out well at the end. The great variety of form in the more developed kinds of Fugue and the manifold treatment of the Orchestra in the accompaniment of them, does not allow us to give individual examples for all cases. We can only refer the student to the works of Bach, Handix, Haydn, Mozabt, Cheeubini, Beethoven, Mendelssohn, Schumann and many other excellent masters of the present day. We desire also finally to mention, that a Fugue can be accompanied harmo- niously by chords only, as for instance the Fugue from Handel's Israel in Egypt: "He slew all the first-born in Egypt" is accom- panied at the beginning only by chords, later on the instruments go with the parts. The chorus, from the 95th Psalm by Mendelssohn. "For Thine are the Seas" is also accompanied only by chords, although it is worked for the greater part as Fugue. CHAPTER XV. Double-Fugue, Fugue with three or four themes. § 32. We call a Fugue a Double-Fugue in which two themes are introduced and developed. We distinguish three kinds of Double- Fugues. 1) Double Fugues, in which both themes appear at once and are developed with each other. 2) Double Fugues in which at first only one theme is brought to an issue. Later on the second theme appears, best after a half- cadence. Simultaneously the first theme associates itself with the second as it were, forming a counterpoint to the second, and is developed together with it. § 32. DOVBLE-FDOVE, FVQVE WITB THREE OB FOVB THEMES. 167 3) The most extended form of Double-Fugue is that, in which at first one theme is brought by all parts. After a half-cadence a second theme is introduced, which is worked out in its turn. Finally both themes are treated together for the last develop- ment. But we wish to remark, that in none of the before-mentioned kinds of Double-Fugues , both themes should ever commence quite simulta- neously. One allows, on the contrary, the second theme to begin a little sooner, sometimes also a little later; in this manner both themes contrast better with each other. Both themes are required to contrast rhythmically, as much as possible. For the first mentioned form Double-Fugue, in which both themes are introduced at once and worked out together, we cite the Kyrie from the "Requiem" by Mozaet. The first theme is sung to the words "Kyrie eleison", the second to the words "Christe eleison". The bass intonates the first, the alto the second theme. Allegro. 214. J ^ -? K N - ^ 1^=P V>-# Chil-ste e - le — — f=v^ » — » . ^ ^=fi= Ky - li - e e - le Entry of the Sopiano d^ ^ with the fiist theme in the dominant. Ma ^ Entry of the tenor with the second theme. ^ -^»4i Se m-0- son, e lei - son. Chii-ste 168 CHAPTER XV. § 32. The alto begins again the first theme in D-minor towards the end of the entry of the themes in the Dominant by soprano and tenor, the bass overtaking the counter-theme. To this joins immediately (bar 11 of the Fugue) the entry of the tenor, with the principal theme in the dominant, the soprano overtaking the counter-theme. Then follows a short interlude, as connection to the parallel major- key. Now the soprano intonates the first theme in i^-major (bar 1 6) , the bass sounds the counter-theme ; the end of both themes mo- dulates to, the dominant of G-minor. On this harmony the tenor commences with the second theme. In bar 22 the bass takes up the first theme in C-minor, the alto renders the counter-theme. Bar 26 brings an entry of the soprano with the principal theme in B\>-majoT, the tenor performs the counter-theme. Now follow various highly interesting Strettas until the conclusion of the Fugue, in which mostly both themes take a part. The last entry of the principal theme in the alto ensues, in connection with the second theme in the bass, used in Double counterpoint in the twelfth. Ky -il-e e-le - i 215. ) I f^^ =P ^ ^ -f—^ -J-J-^ - Chri-ste e son, S N N m v^ le J 1 son etc. ^=r=Ff=v¥f-rr- m^ le The counterpoints to both themes are free parts, but they con- tain, rhythmically and melodically similarities of various sorts. They have grown out of the theme, and we see here again the principle, of employing material in the Fugue, taken as much as possible from the theme, and to bring again similarities in the counterpoints. The §§ 33, 34. DOVBLE-FUOUE, FVOVE WITBTHREE OB FOVR THEMES. 169 orchestral accompaniment is reduced to a mere assistance of the vocal parts. The instruments go generally in unison with the voices ; now and then the trumpets and drums give a few notes for fillin g in the harmony. Only once, in bars 5 and 6, the 'celli and basses assist the soprano and alto with three quavers — f- :, by which the bass-voices gain breathing-time. The careful study of this magni- ficent Double-Fugue is indispensable to the student. § 33. As a perfect, and as we may anticipate, universally known sample of a Double-Fugue of the second kind, we mention the Fugue from the .B-minor Suite for orchestra op 115 by Fbanz Lachneb. At the beginning the following theme only appears. 216. m^ =^S^^p This theme is developed through 41 bars to a half-cadence on the dominant. After that the second theme appears and both are treated together. 217 J t :t ^ W^ g p rtt s — - ±i SE^ ff^r-l- ^^ ^ EP ^^ § 34. As a sample of the third, the most developed form, of the Double-Fugue, we point out the first choral movement in the 170 CBAPTEB Xr. § 34. Author's "Trostlied" op. 65, (Leipzig, Breitkopf & Hartel). The first theme is composed to the words: "An den Wassern zu Babel sassen wir und weinten, wenn wir an Zion gedaohten" (By the waters of Babylon we sat and wept when we thought of Zion). It first appears in the tenor, accompanied by 'celli, basses, violas, bassoons and horns; we add the accompaniment in piano-score. Lento. p espr. — 218. iW E :^ ^^^^ By the wa-ters of Ba - by- E ^^m -•p- ^^- r espr. Ugato ^ ^ ^fcf==t - « l « — s . ». — I — ■ — » — •»! — » - 3 I STal 3l m t ^ if ^^^ ^^ X Ion we eat and wept, — and wept, — ^^^^^^^^^ *^* ^ :l=^= Alto: By the rrt lE^ -^ — •- ^^^:?^ when we le-mem-ber - ed Zi ^^^^^^ i^^^ ^=3^ ^ -ar ^ r' ^ f 34. DOVBLE-FVaVE, FVOUE WITH THUEE OB FOUR THEMES. 17] This theme is brought to an issue by all voices. After three bars of an instrumental modulating interlude, from ^-minor to C-major at the end of the first exposition, the second theme appears also first in the tenor. 219. p espress. f;s^ ^^^^z^^^^35£^m And we hang ed OUT haips i—m ^. jx, upon the wil- -f-\^ ^^^^^^^^^ t-- 1^.^ ? (" ^ * ^ J ^ —^ - M ^ r. =^-1^ =tik r 'xm \^rTff=^=t -^3^ X — lows, in the midst there - of ■Jlil J J k X etc. ^ FgTfe^ ie p ~ • 1-* T ^ p — I— « — ^3 S=3=22 tLir f — ^ r trr The development of the second theme by all parts, leads to a half-cadence on the dominant. Now the two themes join the com- binations, marked below. The accompaniment has been simplified essentially, without the figurations of the Violins. 172 220. Sopiano. Alto. Tenor. Ba83. Piano. i ^ CHAPTER XV. dolce § 34. ^^ By the wa - ters of Ba - by Part. I. / dolce '=¥ p^B=f f dolce Part II. -f f^ =t=C And we / dolce 9^1- rr-i-^ ^^ ^ 1— ia 10 m^M^^^ m We ^^ hang * By the wa — — — ters of ^ I I I ¥ ^^ ^ 4: Ion we sat and wept, — — and wept — sat — — and wept, — — and wept, — — when id onr harps ^^ upon the wil . - - lows. E^e f — ^ ■^-mX-"^g^ =t Ba - hy - Ion we sat. there we sat, wept hit -J kti^ti j- i==^ l^LZ^ JHj J, -trT m zfi^ J JJl ^ ^ ^^ ■0-*- § 34. DOVBLE-FVOVE, FDOVE WITH THREE OB FOVB THEMES 173 / i i ^^ -^ — ^ :t=t r — TxT I ■when we le-mem - ber- ed thee — Zi cesc- Part. H.f we cresc. 3E^^ on, thee mem - her'd. And we hang — ^ t^ — rf^ ^ in cresc. the midst there of, -•— #^ ^=:f: P *E ^ in the midst. Part. I / ^ tzat =9=tc ter By the wa - ters of Ba - by- i ^Efefe --^ ^^^^^m T i -J-J=r-.uwO H*-^ F*=^ 12^ i^ 174 CHAPTER XV. 34. - we re-mem -ter-ed Zi - oi Part. II. ^ -0 1* I And we f hang • — n- \ J -J ^ T H=^J=3=^ m cresc. the midst there of, and we hang / ed our 1pf--rirf^ ^^ ^Aj^(^ ^ ±^ E& we remem her-ed crcsc, ^ Zi - on, by the ri Part. I. -f— =-T— •- vers of Ba - hy- ^^^g^M=^^^gEa^-^ r-=^=^ when we remem - ber - ed Zi - on. By the j n I ^ ■ ters of Ba - by- j-ti Tj J rr^i-^^-{i J — j^ iJ ^S^J^ ^^*a^J-^«j^ m t—h^- ^ 9 ^ ?E^EE* SeeEe |^3eg s - h — N ^3 ^^^=g^=^ ed our harps — n-pon the wU — — — lows l=?3^ ^^ harps up - on the ■ml - - lows the wil lows, i ^^m -("_ ^ j I ^ - lon we sat, wept ^ bit - ter - ly and ^^E wept ^ It Ion we sat and wept, — and wept, — — ^^^^^^^ f \,-S^ tr-V ^t^^ fe^- -^ — ^- eS r I I I § 34. D0VBLE-FU6VE, FVQUE WITH THREE OR FOUR THEMES. 175 / i the frrrn midst there-of and wept, by the Part. I. ^ hit i ^ m =p=f -b ter - ly, and wept, by the 13= gy-r-rnrtiriE ^^ I when we remem - be - red Zi on, wept bit - ter - ly, when ~~~^ • ■ . 1 ^ -*-^i* P -* — f- ^wrmi :=^ I Part. II. lempre f molto espress. m U^J'r" -(■ — ^ -F-»- SS :tir And we hang - ed our harps — up-on thewil- 1^^^^^^^^^^^^ wa-ters of Ba - by Ion we sat and wept, — i p=i-- ^ =p=i= m =t ^ i: li-veis of Ba by Ion we sat and wept, — and ^^^^^^^ thee Zi - on le-mem ber'd, wept 176 CHAPTER XV. § 34. & piiJ f cresc. r^^ It « • F — h- ^_j 1^ i lows, wept bit - ter - ly wept tit - ter - ly, and pStt f cresc. wept, — — wept ti I - ter piii f cresc. fe f! 0- ^i^ ES 1?=^?- wept, — — — when we re-mem -be - red Zi piii f cresc. 9i=^-=F= *- — &- bit -ter - ly, wept bit ter i 5^ Lj_ S^J I J- .^ )^ f i J nir^ iij2 :^ Ji ^ r r f r i EEE^ dim. wept and wept wept dim. >-~T- and wept, and wept, wept on. wept bit - ter - ly, and wept, wept P__ ^ ~~^ m ^^ ^ T i ^ by — 0- and wept, wept § 35. DOVBLE-FVOVE, FVGVE WITH THREE OB FOVR THEMES. 177 etc. --^- 3 I § 35. After the student has practised the strict Fugue with equally recurring counterpoint sufficiently, it will afford him no trouble, to compose a Fugue with two, even with three themes. The differ- ence is not so very great , and consists in fact only in this , that the themes are simultaneously entered, and are developed as strictly as possible one with another in the Double-Fugue, while in the simple, strict Fugue the counterpoint only appears after- the conclusion of the principal theme, as we called it significantly "Post-lude, coda, of the theme", and returns later on, connected with it, in a more or less strict form. One would be quite justified in calling the Fugue in F-minor from the Wohlt. Clav., scrutinised in § 17, a Tripel-Fugue, for it possesses two secondary themes, as well as the principal one, which are consequently carried through one with another, as examples 151 — 157 demonstrate. That we called these secondary themes, coun- terpoint and that they did not enter simultaneously with the prin- cipal theme, does not alter much the character of the matter. As has been remarked before, the "Wohltemperirte Clavier" offers a great many Fugues, which are, according to their nature, in reality, Double- Fugues. One could call the Fugue, notated under 210, also a Triple- Fugue, for it contains two secondary themes, besides the principal one, which are worked out consequently together with the latter. Jadassohn, Canon and Fugue. 12 178 CHAPTER. XVI. § 36. For the composition of a Triple-Fugue it would be necessary, of course, to work the three themes in triple counterpoint. If one intends to compose a Fugue with four themes, one would have to work them in quadruple counterpoint. We do not however en- courage this task. The restrictions which it imposes, and the difficulties arising from it, are so great, that the imagination is lamed altogether. Besides, one would rarely succeed in inventing four the- mes, written in quadruple counterpoint, which would have the characte- ristic features as such, and which would distinguish themselves, one from another, rhythmically and metrically. However, supposing this experiment to have succeeded, nothing else would have to be done, than to bring into connection some of the possible 23 inversions by sui- table interludes in an adaptable manner. But we do not propose to make the composition of the Fugue a dry, contrapuntal study. With the composition of the Fugue, we glide over to the commencement of Free-composition. All contrapuntal art should serve only as the means, by which the creative individual imagination should rule and govern with ease and sureness, as might be deemed adapted for its higher purpose. CHAPTER XVI. Fugue in Five parts, Fugue for Double-Chorus in eight parts; the Choral-Fugue and the Contra-Fugue. § 36. As the movement in five parts offers greater fullness and richness of harmony, than the one in four parts, a much more im- posing effect can be obtained in a Fugue for five parts, by the asso- ciation of all parts, than would be possible in four part-writing. But one should not suppose that the movement must be always, or mostly, in five parts. The effect would be heightened, if it were now in three, four, and sometimes five parts. This is offered often enough in Piano-Fugues by the consideration taken for the practibility of exe- cution. Thus the Fugue in .B|7-minor for five parts contain only 20 bars, (out of its 75,) in five parts, the C-minor Fugue (Wohltemp. Clav. vol. I. Nr. 4. only about 26 to 28 at an extention of 115 bars. But it would also be unpracticable in five part Fugues for Organ, Vocal parts, or Orchestra, to employ the five parts continuously for any length of time. The listener would soon be fatigued, if he had to § 36. FVOVE IN FIVE PARTS, FVOVE FOR DOVBLE CHORUS etc. J 79 follow attentively and continuously such a large number of real parts. As a rare, perhaps only exception, we mention the often named mar- vellous Kyrie-Fugue from the 5-minor Mass in five parts by Bach. In that Fugue, which is sublime beyond description, the movement is not only generally, but always in five parts. In a vocal Fugue in five parts, one would do best to have the chorus composed of two sopranos, alto, tenor, and bass. For a Fugue in five parts for Piano, Organ, or Orchestra it would not signify, which parts to double. The above-mentioned Piano-Fugue in ^jj-minor is evidently written for a soprano- alto- tenor- and bass-part. At a vocal Fugue for five voices the limit of the theme will have to be carefully considered as to its height and depth. One should keep it within as small a compass as possible, so that each voice may bring it in the tonic, and also in the dominant, a fourth lower or fifth higher. In a Fugue for Piano, Organ, or Orchestra these constraints need not be imposed. Bach's theme, in his ^l^-minor Fugue, Nr. XXII. Wohlt. Clav. vol. I. contains the compass of a ninth, the answer, that of a tenth. 221. ^^^^P LLUri ! 1 J , J^ J-J-9 j etc. The i^-minor Fugue for Organ in five parts possesses the following theme, comprising a tenth. Sto: tjr? , T h 222. 2Ep The theme of the Organ-Fugue in C'-minor goes to the compass of a ninth. 223. ^^^ ^^E^^ E ^£fe^|Ep|i The theme of Fugue in C-major has only the compass of a se- venth. 224. ^^^^^^ We recommend all these Fugues of Bach for especial study. The last mentioned Fugue only becomes five parts after the entry of the theme in double enlargement in the pedal ; the answer follows at once, 12* 180 CHAPTER XVI. § 37. in the pedal, as well as also in the enlargement. With this exception the theme appears also in contrary motion in the enlargement towards the close of the Fugue, and twice again in the pedal. If one write for orchestra, the compass of the theme may- be extended at pleasure. In the third symphony of the Author's, (Z>-minor, op. 50, Leipzig, Fr. Kistner) contains a developed Fugue for five parts, on the following theme; it forms the Menuetto of the Symphony. Allegro non troppo. f marc. 225. ^i^ -•-!■- -P-»- 9^ E^ s^^ In the author's Preludes and Fugues op. 56 Leipzig C. F. W. Siegel (Linnemann) will also be found as Nr. IX a small Fugue in five parts for piano. The practice in five-part Fugues is indispensable for the Student. We recommend especially the writing of such Fugues for organ, as one has the help of the pedal for the leading of the parts, and on that account, need take less regard for the capability of execution, than in the Piano- or Vocal-Fugue. The architectural exposition remains so far the same, in as much as at first theme and answer appear, after that again theme and answer, and with the entry of the fifth part the theme is brought once more. After that, one would be at liberty, to use the entries of the parts in a freer way; it would be advisable to form longer or shorter interludes, according to the length, nature, greater or minor importance of the themes, in order to prepare the beginning of the groups of entries or the entry of the individual parts themselves. We should not advise the student to try his hand at the invention of Vocal- Fugues in five parts, before he has composed Fugues in five parts for Organ, Piano, and — should he have already acquired sufficient knowledge in instrumentation — also for Orchestra. § 37. A Fugue for eight parts in double-choruses would re- present itself most advantageously as a Double-Fugue. One of the choruses intonates the principal subject in one part; the counter-theme is brought simultaneously in one part of the second chorus. After that, one allows the two choruses to alternate with their entries of themes and answers. In most cases, both choruses join towards the end of the Fugue into one four-part chorus ; Handel does this nearly always in his movements for double chorused Fugues. II will seldom occur in a Fugue for eight parts, that all light parts act indepen- § 37. FlIGVE IN FIVE PARTS, FVGVE FOB DOUBLE CSOBUS etc. 181 dently as real parts, even for a few bars. But by the contracted entries of five, six or seven parts, a great gradation may be produced in a Stretta. Here follows an example of a Fugue for eight parts from the author's 100th Psalm (op. 60. Leipzig, Breitkopf & Hartel.) The orchestral accompaniment has been marked as a Piano-score. 226. Soprano. Alto. > i Tenor. Bass. Soprano. »E^^^^^ Alto. m Tenor. Piano. Allegro moderate. -iR=JJ M^^ f* Wor-sMpthe fe-r-1-^ H/-M- -^- Wor-sMp the Lord with '^-^F=^=^=^- theme. -^ --^ Wor -ship the Lord with glad ness, ^^^- Come ^-B»- be - fore his ^B^=^ eoun-te-nance, m Come be -fore his coun-te-nance. songs, come ^^^^ zsz i fc songs, J- beM. ^^ come, come, r^^ ^ ^* ^ '--a m^^E E^ ^m^^^ kA 182 Lord with songs, come, — be ^ t -^ -4- glad ness, come be fore his coun te- ag =5 =y ^E Worship the Lord o f—f- -p — 0- ^=i z^. come be -fore his coun-te - nance, come be - fore his i ?^:fc: i r==^— i^ =j= hS- sii "Wor-ship the Lord with glad ^ ness, tt ^1^ It Wor-ship the Lord -with glad ness, come be- / f=^ Wor-ship the Lord with glad-ness, ^=i,t=^y S -0^^0- =t=t= come be - fore his coun-te - nance, to his i J- i J I s^t^^W^l^^^f^^^^ ^j^^= m- 5—8= § 37. FUGVE IN FIVE PARTS, FV6VE FOR DOVBLE CHORUS etc. 183 ^m ^^ ^s fore his coun-tenance come, come with Joy-ful % ! * -!*-^=^ ^ ^ fe ■d — i/- it3=2gi: nance, come with songs, worship the Lord with glad - - ness, ^ F=f=g-g-r=m ^ come to his coun-te-nance. ^^ !E^^ te-nance. tez*! i^^ come to his coun-te-nance. f^^^ ^^^=^S fore to his coun-te-nance. Wor-ship the Lord with ^f^pfe ^^ g^ — p-4-^i^^ ^ come to his coun-te-nance. Wor- ship the Lord with glad- m=f^ ^^ -^m te - nance Wor-ship the W: ^^ -J r; # i=i=^^ ^^ ^^ lii I 5 ir-^- Si^^ T feE^ 184 CHAPTER XVJ. §37. i / JS— -V; t^±^^ songs, Worship the Lord with ■f- / . =b= to his ored ness. 1^=-^ Wor-shipthe :^=^ Wor-ship the Lord with glad - ness ^ m Wor-ship the Lord — 3=^: -*— ^v t: -•-— »i- Woiship the Lord with glad ^^P ?^ P^ glad ness, — the Lord, the Lord. ^^i W=?^- m $ p* ness, Lord -s>^ with with glad ness theJLord. m ^s^ -^z ^^.J=^-- % -m W- ^ -\ — f^-i- ^s § 37. FVOVE JN FIVE PARTS, FVGVE FOB DOVBLE CHOBVS etc. 1 85 m * fe^ztrzJt glad gfe Q T^??3 ness, come be - fore his coun-te-nance, come, -with ^ -S) • — • r-m a — » +H^ Lord with glad - - ness, come be - fore his coun te- "Worship the Lord with gladness, serve i m 1^^ i^^ ^^^ ^^ Wor-ship the Lord with glad - ness, with glad '^ fe^ ^ 3=rj=3^=± 1 P t^=^ =E g =^S Itzt 186 CHAPTER XYl. § 37. f S^teg f-0-^- joy - - ful songs -t^-^ nance. — WorsMp the Lord with 9f^E^ t^ £==^ ^ :t him. Wot-ship the Lord with glad /#■ .£=;=§ ^ti=i= fi--i^ — •- -iA-w- Wor-ship the Lord with glad ness,the Loid, i E^^= Worship the Lord with 3=3=tf iig -P=i? Wor-ship the Lord with glad ness, Wor-ship the m^. ^^S * Wor-ship the Lord with I ti^ J=& ^^^ §37. FV6VE IN FIVE PARTS, FVOVE FOB DOUBLE CBORVS etc. 187 9^^ 1= // -!•■ f- ^^^E =t ^ Wor-ship the Lord with glad-ness :t: glad ness, with glad-ness =t Wor-ship God with glad - ness, ff £ joy s ful glad - ness ff k^^ =1=. glad te ;a^Ez: ness, with glad-ness -IS— -P--^^-^ * rt etc. te Lord with glad-ness fj -t :te T: * i4 Wor-ship the Lord with glad - ness _, // , ._ ^ i ness, with glad - ness •g-S«5- ^ * ^- i J25— ^ a JE=5^ i: 4: Sometimes one allows the theme to be sung by the same part in both choruses, or even gives the first four entries in such a manner, that are united both choruses, into one. This is done for the purpose of bringing into hearing the theme or answers, contra-themes and counter- 188 CHAPTER XVJ. § 38. points fully and strikingly; only afterwards the choruses separate, alternate, or go together, as may appear suitable to the composer for the representation of the whole. Handel even brings his prin- cipal theme in the magnificent Fugue "I will sing unto the Lord" (Israel in Egypt, part 11 No. 44.) at first, by all the altos and tenors of both choruses in unison ; only with the coda of the theme (bar 4) the parts divide in this way, that the altos and tenors remain united. In the ninth bar, the Fugue becomes double chorused, and only in the twelfth bar more than four parts are developed. Towards the end of the Fugue, both choruses are again united into a four part chorus. The student will remember from our treatise on counterpoint § 30, that in the face of the extraordinary difficulties , which one encounters in the progression of eight real parts, one either unites occasionally the sopranos or basses of both choruses, or allows the basses to go in parallel octaves, or leads sometimes the alto of one chorus with the soprano or alto of the other, or combines both choruses to one in four parts. § 38. There are left now for explanation some rarely occurring species of Fugues. These are the Chorale-Fugue and the rarely found Counter-Fugue (fuga al rovescio.) One forms a Choral-Fugue, by taking for a theme the beginning of a Chorale-melody. But there will not be found many Choral-melodies that would be suitable for this purpose. The effect will be a more striking one, when in the middle of a Fugue the Chorale-melody enters, accompanied by the other parts, by thematic entries or contrapuntal motives. One allows the Choral-melody to enter at a suitable place, and allows it to rest after each pause. The accompanying parts however continue with their fugated movement and form, as it were, an interlude, until the Choral-melody recommences. We cite as an instance, the first chorus from Bach's Passion-music St. Mathew, which we anticipate to be known by everybody. If the latter cannot be called a Fugue it is still written predominantly in the most splendid Fugal-style. The choral "0 Lamb of God innocent" enters as "ripian-part" to both choruses. Is one desirous of adding a Choral in the course of a Fugue, one would do well to form the theme and the counterpoint accor- dingly, in order that one or the other, or perhaps both, be adapted for accompanying the latter. One should not manage in an arbitrary manner, by accompanying the chorale with material that is new or not thematic, and which has not occurred in the Fugue. It would be best to spin out a characteristic-rhythmical motive of theme or counterpoint during the entry of the Chorale-melody. §39. FU6VE IN FIVE PARTS, FUGVE FOB DOUBLE CHORVS etc. 189 § 39. Counter-Fugue is, that kind of rarely occurring Fugue, in which already the first answers of the theme are already given in con- trary motion. But Counter-Fugues can also be found, in which theme and answer are given in two parts in the first instance in similar motion; in that case, the third part brings the theme in contrary motion and the fourth answers it, also in contrary motion. One might then commence a Counter-Fugue in this manner. 227. ^fe^ ^^ i JiJ P »ii= g^^fe^^ ^ nsz J. i^ii. if3=t: :^: Ffcr ±3 =F — F-f-c T=f=W ^ J J=^ '-^r ^ ^ ^ t=t= rT"f — ^^ I J J— J h m t-r r=^t etc. m^ One might also begin the Fugue in this way; 190 CHAPTER XVI. § 39. 228. i ;E= »E^fe& Uj^lA -0—0- -(^- TZy- -¥- P* -^ 'iM-L^J^ i^S3^^^ :pEteEfe #-»- •XsaisJ- i i J J ^ =F=r=c?= pf %^ — 4 *= ^^^^^^p^ I |z^^=J:^ -!■-•- Pi^ I, I u iiM etc. ^^ I r We consider the kind of Counter-Fugue, shown under Nr. 228 as the most feasable, and advise it to be practised diligently. Of course, such themes must be invented purposely, to suit the contrary motion. We conclude our instructions on the Fugue with the remark, that in the choruses of the old masters, as well as in modern music free-fugated movements occur, in which the answer of the theme, and the entries of the different parts, are not treated with that strict- ness, as would be the case in a real Fugue. Such compositions are not essential Fugues, and do not purpose to be such. Licenses, which §39. FU6VE IN FIVE PARTS, FVOVE FOR DOVBLE CHORVS etc. 191 may be permitted in such a Fugato-movement, dare be allowed in a Fugue. Often, the freely fugated movement stands in the middle of a not strictly contrapuntal composition ; the free style alternates with the strict one. In the Fugue we have to deal only with the strict style, even if, in some cases, a free ending be added. Here the treatise ends, not so, the contrapuntal studies of the striving student , artist , or composer. Even he , who has fulfilled all the requirements of this book with the greatest ardour and con- scienciousness and who has acquired a perfect knowledge and sureness in contrapuntal forms, will, (if he does not continue his contrapuntal studies, of all kinds from time to time), soon make the experience, that also this intellectual technic, like any other, requires constant exercise, if one does not wish to forget again the greater part of it. Constantly renewed contrapuntal studies will act impulsively on the artistic intelligence and the imagination of the composer, and any one will experience this , who occupies himself constantly and seriously with such work. INDEX. Answer of the Fugue-Theme (response, comes), 69, 81, 82. regular, 87. BacJi, see Wohltemperirtes Clavier. Organ-Fugues, 78, 109. Kyrie, 114, 166, 178, 179. Passion-music St. Mathew, 188. Beethoven, 166. Cadence in the Fugue, 129. Canon in general, 1 — 6. in equal motion for two parts, 5, 21. unaccompanied in two parts, 7. in the Fifth, 8. in the Fourth 12. in the Second, 13. in the Seventh, 15. in the Sixth, 17. in the Third, 18. in the Octave, 19. in Unison, 19. in enlargement, 20. in diminution, 20. in retrograde motion, 21. in contrary motion for two parts in all intervals, 22 — 30. in two parts, accompanied by free parts, 30 — 49. in three and four parts, 50 — 57. Double, 54. Double in contrary motion, 55. clef, 57. circle, 57. Mirror, 57. Inversus, 57. al rovescio, 12, 22, 38. Eiddle, 57. for Vocal-parts, 58. accompanied by free parts, 58. chromatico ed enharmonico, 4. with free harmonious accompaniments, 66. adapter I, 1—21. II, 22—30. in, 30—50. IV, 50—57. V, 58-68. VI, 69—77. Vn, 77—89. Vm, 68—99. IX, 100—105. X, 105—113. XI, 114—121 XII, 121—133 Xin, 134—142. XIV, 142—166. XV, 166—178 XVI, 179—191 Cheruhini, 166. Clavier, Wohltemperirtes, 70, 71, 73, 74, 77, 78, 80, 84, 86 87, 90, 91. QS 100, 101, 102, 105, 106, 108, 132, 133 , 134, 137, 142, 143, 178, 179.' "' INDEX. 19; Climax, Stretta, (Engfiihrung), 105. Comes, response of the Fugue-theme, 69. Continuation of theme in the Fugue, 89. Counterpoint Double in the Octave, 145, 146. Triple in the Canon, 58. Triple in the Fugue, 122. Quadruple in the Canon, 61. Double in the Twelfth, 168. Countersubject, counter-theme, 69 — 89. Double Canon, 1. Fugue, 166. Dux, leader, principal Theme in Fugue, 69. Ending, Free Canon, 2. Engfiihrung, Stretta, Climax in the Fugue, 70 — 105. Entry, of parts in the Fugue, 115. of first group, 115. of second group, 114. Exposition of theme in Fugue, 161. Free-parts, as counterpoint in Fugue, 91. Fugato, 78, 191. Fugue, general renlarks, 69. Theme of, 71. - — answer of the Fugue, 77. Counterpoint in, 89. in two parts, 116. in three parts, 121. . strict one, 121. strict one in four parts, 142. Free one in four parts, 134. for vocal parts, 143. with instrumental accompaniment, 143. for eight parts, 162. for five parts, 178. for Double Chorus, 179. Triple, 177. Double with three or four themes, 166. Counter-Fugue (al rovescio), 190. with Chorale, 189. - - for Organ, 178. _ _ - Orchestra, 179. Handel, 75, 77, 78, 166, 168. Piano-Fugues, 79. Harmonious Themes in Fugues, 84. Hauptmann, Moritz, 25, 57, 67, 98. Haydm, 166, 168. Imitation, see Canon. Instrumental Fugue, 178. Interludium, 90, 100. Israel in Egypt (Handel), 166. Klengel, Alex. August, 3, 51, 54, 116. Kunxt der Fuge, die, 71, 80, 82. JadasBolia, Canon and Fngne. 13 194 INDEX. Kyrie (Bach), 114, 178. (Mozart), 167. Iiachner, Franz, (Double Fugue in E-minor), 169. Leader, (dux) in Fugue, 69. Leading-note in Fugue-answer, 81. Wendehsohn, 66, 166. Mozart (Kyrie), 88, 167, 168. Orchestral accompaniment in Fugue, 147, 162, 178. Order of entries in Fugue, 69. Organ-point, (Pedal-point), 71, 113, 142. Fugues (Bach), 179. 'Paragraphs: 1 page 1. 9 page 54. 17 page 93. 25 page 134. 33 page 169. 2-7. 10 - 58. 18 100. 26 135. 34 169. 3 - 16. 11 66. 19 105. 27 142. 35 - 177. 4 22. 12 69. 20 - 109. 28 143. 36 178. 5 25. 13 71. 21 114. 29 144. 37 180. 6 30. 14 77. 22 116. 30 147. 38 188. 7 35. 15 82. 23 - 121. 31 161. 39 - 189. 8 - 50. 16 89. 24 128. 32 - 166. Meineche, Carl, 51. Response (Answer of Theme), 69. Rest, before entry of parts in Fugue, 143. Rheinberger, Joseph, 51. Ripian-fa,Tt, 188. Schumann, Eobert, 66, 166. Sequences in Fugue-theme, 72. Stretta, climax, Engfiihrung, 70, 105, 115. Text-words for Vocal-Fugues, 143, 154, 155. Theme of the Fugue, 71. Compass of, 77. ending of, 75. — — - - in the Key of Dominant, 75. abbreviation of first note, 79. in the answer, 77 — 89. enlargement, 50, 109, 162. diminution, 110. abbreviation in Stretta, 105, 129. in contrary motion, 22, 49, 108, 189. in retrograde motion, 21. ■ harmonious accompaniment, 73, 141, 161. Text for Vocal Fugues, 143, 154, 155. Vocal Fugues, 132. see Text for. Wohltemperirtes Clavier, 70, 71, 73, 74, 77, 78, 80, 84, 85, 86, 87, 90, 91, 98, 100, 101, 102, 105, 106, 108, 132, 133, 134, 137, 142, 143, 178, 179. Printed by Breitkopf and Hartel, Leipzig. APPENDIX. AN ANALYSIS or THE FUGUES AND CANONS CONTAINED IN JOE SEB. BACH'S "ART OF FUGUE" BY Dr. S. JADASSOHN. TRANSLATED FEOM THE GERMAN BY ERNEST BRENTNALL. LEIPZIG PRINTED BY BREITKOPF AND HARTEL 1899. "The Art of Fugue" by JoL Seb. Bach. Having published some years ago, the Analysis of 20 Fugues from the "Wohltemperirtes Clavier" so that I might give the same to my pupils, let me now continue in the same way, the explanations and hints for those Fugues and Canons contained in "The Art of Fugue". The following, originally French written article, appeared first, after some delay, in the "Eivista Musicale". My treatise, which I have now considerably enlarged, and com- pleted, may also possibly interest English readers. "The Art of Fugue" contains 15 Fugues and 4 Canons on the same theme. The 25"' volume of the "Bach Gesellschaft" gives still another Fugue with 3 themes, this certainly does not belong to the work. There is nothing in the same, that resembles the theme of the foregoing Fugues, and I shall therefore not include this Fugue in the group for consideration; it has remained unfinished. I will also not go further in my explanations, than Counterpoint 13, the 14*'' being, from the sixth bar an exact repetition of the 10*'', bar 27 to the end. There remain therefore only 14 Fugues, which I will classify, according to their various forms, in the follow- ing manner: 1. Counterpoint 1 and 2 with the theme "rectus". 2. Counterpoint 3 and 4; the theme is given "inversus". 3. Counterpoint 5 with the theme rectus and inversus. 4. Counterpoint 6; the theme is given rectus and inversus in notes of different value (per augmentationem et diminutionem). 5. Counterpoint 7 ; the theme is given rectus and inversus, in notes of 3 diflFerent values. 6. Counterpoint 8; a three-part Fugue with 2 themes. 7. Counterpoint 9; a four-part Fugue with 2 themes, "alia duo- decima". 8. Counterpoint 10; a four-part Fugue with 2 themes "alia decima". The second theme is taken from Cpt. 5. APPENDIX. 9. Counterpoint 11; a four-part Fugue with 2 themes. The second theme shows the first of the three-part Counterpoint 8, in- versus. 10. Counterpoint 12; a four-part Mirror Fugue. 11. Counterpoint 13; a three-part Mirror Fugue. 12. Two four-part Fugues for 2 Pianos. I will analyse the 4 Canons at the end of this treatise. COUNTERPOINT 1 shows a simple Fugue on the theme: 1-JlE^^ i^F^^^S The Alto begins; the entries of the other parts follow without delay. The Soprano gives the Answer bar 5: -4-- m :?5= -fS- * 3f ?^ The Bass gives the theme, bar 9, and the Tenor the Answer bar 13. The beginning of the 17*'' bar ends the first group of en- tries in D-minor, a short interlude (episode) of 6 bars follows. With the 23=^* bar the Alto begins onee more with the theme, and after two bars modulating towards ^-minor, the Soprano brings in the Answer in that key, bars 28 — 33. The Bass then enters with the theme before the Soprano has finished the Answer. Bars 36 — 40 contain a second interlude. The Tenor, with the Answer, ends the second group of entries ; bars 40—44. Three other entries each showing the theme in the form of the Answer are to be found at bar 49 in the Soprano, at bar 56 in the Bass and at bar 74 in the Tenor. Between these entries are two Interludes, the one of three, and the last of 14 bars. The Fugue ends at bar 78. COUNTERPOINT 2 shows the same theme with the following, rhythmically altered, ending in the last bar: 3.i5E^^ THE ART OF FVGVE BT JOB. SEB. BACH. 5 The rhythm of the so altered figure is kept up by the accom- panying counterpoint throughout the Fugue. The entries of the Theme and Answer are as follows: the Bass begins, the Tenor gives the Answer, bar 5, the Alto the Theme, bar 9, and the Soprano the Answer, bar 13. The second group begins at bar 23, with the somewhat disguised entry of the Theme in the Alto: =1= m E^ &c. The Soprano follows at bar 25, the Bass at bar 32, and the Tenor at bar 38. In this group also, the entries of the Theme and Answer change about in a regular manner throughout. With the 45* bar begins the third group; the Soprano brings in the theme, the Alto, the Answer, bar 49. In bar 53 the Bass introduces the Answer first, and in bar 61 bringd in the Theme again. The Tenor gives the Answer at bar 69, with the first bar altered by syncopation : m 3^ ^ 4= t ^^^_^^ I &o. The last entry of the Theme is in the Soprano, bar 79; the Fugue ends at bar 84. COUNTERPOINT 3 begins in the Tenor, with the Theme inverted: 6. ms=^=^- eSe ^^ the Alto enters at the fifth bar with the Answer. The counterpoint of the Tenor, which accompanies the Answer in the Alto, is repeated at every entry of the Theme or Answer, throughout the whole Fugue, although sometimes a little varied; it is what is termed a "fixed counterpoint" (Contrapunto costante). The other entries of the first group follow in the ninth bar in the Soprano with the Theme, and in the Bass with the Answer. The second group of entries begins at bar 23, in the Soprano; the Theme is thus rhythmically changed: APPENDIX. 7. *^ gz F::^^|^g^^%Frfi#^ E^e I have indicated the notes of the inverted Theme by asterisks (*), as by the added syncopation, and by the principal notes being tied on to the quavers, the Theme is a little disguised. The Answer to this entry of the Soprano, follows in the Tenor in the same manner; the original counterpoint is here slightly varied. After a somewhat longer Interlude, the Soprano once more introduces the Theme, bar 43, this time in its first form (without the inserted quavers and not syn- copated); the Bass gives the Answer at bar 51 in the same way. The Alto shows us at bar 55, the Theme in regular rhythm thus varied: 8-|5fc^E^^^ :t ^m The Soprano answers, at bar 58 in the same way. The Theme appears for the last time at bar 63 in the Tenor, as it appeared in the Alto [in the form of the Answer), at bar 5. Six bars, of which four are formed on a Pedal-point, end the Fugue at the 72°* bar. COUNTERPOINT 4 contains a Fugue of greater extent than the foregoing, and shows some interesting contrapuntal complications. The Soprano begins with the Theme inverted, not however as in Counterpoint 3. Counterpoint 3 shows first the inversion of the Answer of the Theme, Counterpoint 4 on the contrary shows the inversion of the Theme in the first original form. 9. --^ ^ 3 =t =t=t ^33fE. The Alto gives the Answer, bar 5 ; the Soprano accompanies with a Counterpoint, which again appears with the entry of the Theme in the Tenor bar 11, in the Alto, correspondingly transposed. We find this Counterpoint once again with the entry of the Answer in the Bass, bar 15, in the Tenor. The Tenor and Bass in bars 15 — 19, are the same as the So- prano and Alto in bars 5 — 9. The last named upper parts have free Counterpoint in bars 15 — 19. The closing figure of the Theme THE ABT OF FV6VE BY JOB. SEB. BACH. forms the material for the eight-bar Interlude which now follows. Imitations of this figure in similar and contrary motion, alternate between Tenor and Bass for four bars and between Tenor and Alto for other four. The Soprano and Alto give in the first four bars of the Interlude, bars 18 — 22, a new motive in imitation, which appears again later in other Interludes, partly rectus and partly inversus, as accompaniment to the imitations of the closing figure of the Theme. One observes by this, that the great master Bach uses for once in the strict Fugue, economically, so to speak, given material for the motives. The second group of entries begins in the Soprano, bar 27, the Alto gives the Answer, bar 31, the Tenor takes the Theme, bar 35, and the Bass the Answer. The following Interlude, beginning at bar 43, is formed from, and resembles the first Interlude; the parts are here however inverted in quadruple counterpoint. With bar 61 begins the third group. The Bass introduces the Theme, the Tenor, bar 65, the Answer; the Alto gives the Theme, bar 73, and the Soprano the Answer, bar 77. A very long Interlude of 26 bars now follows; this shows us in its last four bars (102 — 105) the bars 53 — 56 of the second Interlude in quadruple counterpoint, with inverted parts. The first Stretta of the Theme proceeds in a very concise manner bar 107. The Tenor takes the Theme on the first crotchet, the Bass follows with the imitation on the second crotchet of the same bar in the lower Third with syncopated notes. Bars 111 — 114 show a second Stretta: in this one the Soprano gives the Theme in syncopation, the Alto begins at the same time a sixth lower with the imitation in ordinary rhythm. The accompaniment of the Tenor and Bass is like that of the Soprano and Alto in bars 107, 108 &c. These Strettas form the fourth group of entries. After an Interlude of 14 bars (115 to 129), the Tenor once more takes the Theme, bar 129, the Alto gives the Answer, bar 133, and ends the same, bar 137, in the last bar but one, of the Fugue. COUNTEKPOINT 5 contains a "Counter Fugue", that is a Fugue, in which the Theme is given alternately in contrary motion (per moto contrario), the Answer in similar motion (per moto retto) , or vice versa, the Theme in similar and the Answer in contrary motion. In this case the Alto begins with the inversion of the Theme: APPENDIX. 11. Alto. U^^- fi P t=t £E mveraus. The Bass enters with the Answer in the fourth bar. 12. Basso. -»=-- g^^ it S S^ rectus-. At bar 10 the Tenor introduces the Theme in the same way (per moto retto) as the Bass had it at bar 4, the Soprano answers (per moto contrario) at bar 17. Once more the Tenor enters with the Theme, bar 20, this time in the key of the Dominant (^-min.) in similar motion, the Bass answers in the key of the Tonic (2)-minor), in the inversion. The Alto introduces the Theme in the key of the Tonic, bar 26. Bars 30 — 33 contain a short modulation to F-major. This is founded on imitations of the closing figure of the Theme. Bars 33 — 37 contain a most interesting Stretta between the Bass and Soprano, the inner parts accompanying in similar and contrary motion: Soprano. 13. Basso. inv. lEii^^EEF lE rect. ^^^ ^ =3=j; ^1 b f - E ■p P*- ^ Bars 41 — 45 show a second Stretta between Tenor and Alto, the Soprano and Bass accompanying the thematic parts: rect. Alto. 14. \ Tenore. l^-f^^^^ ^^ li:fcrEZ=^ EEE -»< • _» ^ THE ART OF FVOVB BY JOB. SEB. BACH. A third Stretta is to be found in bars 47 — 53. The Bass has the Theme per moto contrario; the Tenor follows a bar and a half later in canon all' Ottava: ^ EE £ ^ ^^ g^^ J- -^ ^ :f^=W f» -^y ^ r-. ^=f=f ^^ ^^ * The upper parts fill in the harmony with accompanying Counter- point. Bars 53 — 56 show a short four-part Canon, the first six notes of whichjare taken from the Theme (per moto contrario) : 53. Soprano. Alto. 16. Tenore. Basso. ^ /v r H^ s -fe 54. ]]l? | ^r I t- ^ fe=f^=l^ g^ -0-0- a $=c=i=g : ^^g The Soprano and Alto form another canonical Stretta in bars 57 — 62; the lower parts accompanying. 10 APFEymx. Soprano. 17. Alto. ZEE i=^h£: fcEE3? BE pfe* pt^^^:^f=— =^-.^^p=:, fs— ^^^^ ^n — y-E i—^ -i The imitation in bars 65 — 68 eorresponds to that in bars 53 — 57; the motive of the Theme is however this time not inverted. 63. 66. 76. Soprano. Alto. 18. — f- -fi-#. ^^^t==^ m ^ -0^ -ip — «--•"- ^A=- -•^-^ The Tenor gives the Answer, bar 7, (inversus per dim.); the Alto has the Theme at bar 8, (rectus) in notes of the original value. The Soprano answers at bar 10, (rect. per dimin.). Bars 13 and THE ART OF FVGVE BY JOE. 8EB. BACH. 13 14 contain a aho t Interlude, modulating from ^-minor to D-minor. The Bass enters at the fifteenth bar: it gives the Theme inversus et per diminutionem ; the Answer follows at bar 16 in notes of double (i. e. original) value (rectus). On the third beat of the same bar the Soprano appears again with the Theme inversus et per diminutionem. As soon as the Tenor has finished the Theme begun in bar 16, on the first crotchet of bar 20, it takes up the inversion of the Theme on the third crotchet of the same bar, and ends the same in bar 24. Modulating back into 2^-major, the Alto now takes the Theme (rect.), bar 25, the Tenor follows, bar 26, with the Answer (invers. et per dimin,). Bars 29 and 30 contain another modulation to D-minor. The Theme (rectus) then appears in the Tenor, bar 31, and the Answer (inversus et per dimin.), in the Alto, bar 32. All these Strettas make little two-part Canons; they are accompanied by counterpoint in the other parts, which more or less resemble one another, they cannot however be "fixed counterpoints", as the Canons in themselves are so different, according as the imitating part follows the other, at one or another interval, after a long on short period, or in similar or contrary, motion. Bars 35 — 39 shows a canonical Stretta in the Soprano, Bass and Tenor, so formed that the Tenor imitates the Soprano after 2Y2 bars in diminution and in similar motion at the interval of an octave, at the same time imitating the Bass, which enters one bar after the Soprano, in contrary motion at the interval of a fifth. The imitation, which commences in the Bass, is given in diminution and in contrary motion to the Soprano at the interval of a fourth. The Alto accom- panies bars 35 — 38 with a free counterpoint; the Bass here breaks off without bringing in the closing figure of the Theme, and becomes a free accompanying part. For the sake of clearness we here give bars 35—39 in fuU: 33. 36. Soprano. Alto. 23. f -s ^^ -4- ifiEEEiEE^S Th. retto per dim. Imit. 5 t 14 APPENDIX. 37. EEit= rhythm altered. 39. .=:^t2^ P'*- =M=t -#-»- ^^ ?^ te: Th. inv. per dim. Imit. per moto retto all 8Ta, per moto contr. alia SK ta; m^ r^»---==^ alia ita per molo contrario. ^ in^ ^ ?^ Tfczta r A two-part Interlude (Bass and Soprano) follows, modulating to 5-flat-major; in this key the Alto takes the Theme accompanied by the Soprano and Bass as free parts. Bars 44 — 47 take us back into i)-minor. With bar 47 another Stretta begins between the Bass and the Tenor, which part enters a bar later in contrary motion and in diminution. The two imitating parts are accompanied by the Soprano and Alto. We find the same imitation in bars 58 — 61, between Alto and Tenor; but here it commences half a bar sooner. The first begins in bars 46 and 47 as follows: 24. fl^E^ Ten. inv. mSEE 3 Th. retto per dim. per moto contr. zi^ 3= &c. ^=^ S The imitation beginning in bar 58 shows the imitating parts, which are accompanied by the Soprano and Bass, in the following position : 25. WBz THE ART OF FUOVE BY J OH. SEB. BACH. 15 E^ Imit. p. m. contr. i£^^^ ^:-^^^ Bars 63 — 68 bring in the Theme uninverted and in diminution; the Soprano follows, bar 64, with the Theme in contrary motion in notes of double value, the Alto enters likewise at bar 65 with the Theme rectus, but per diminutionem ; the Bass accompanies this Stretta, which ends at bar 68. The Fugue ends with the following Stretta (bars 74 — 79), formed on a Tonic Pedal: 74. 75. Th. 3E^ 26. ^^ -^^ m i^tE 76. 77. '"S rmmm ^^t ^M.1 m ^ Th. * .m. .-.. tt p pr p ^fe^^^^ 9^ ^ 16 APPENDIX. 78. 79. ^^ ^ 4J=t 'f-ff-p #^^ fc ^^^^ ^^^^ S:t=^55i COUNTERPOINT 7, a 4 per Augment [ationem] et Diminut [ionem] gives the Theme of Counterpoint 6 per moto retto e contrario in notes of three different values. The Tenor begins : Tenore. 27. w~cr r =^^^=^=^^==m=^ -^;==^-r-i* u i^ r The Soprano gives the Answer, bar 2 (per moto contrario e per augmentation em) : Soprano. The Alto gives the Theme, bar 3, (per moto contrario e per diminutionem) Alto. ^=^ #■ T- ^t=f=t , fftf-f ftff i g 29-l^BE The entries of the Alto, bar 7 (rect.), and the Tenor, bar 9 (inv.), are per diminutionem. THE ART OF FXJOVE BY JOB. SEB. BACH. 17 The Bass begins at bar 5 (inv.); it gives the notes of the Theme in the following way, augmented: Basso. 5. 8. 9. iO. n. 12. 13. 30. ^ £ s^ :?£=»: m^m t=:t The Bass finishes at bar 13; in the middle of this bar, the Soprano enters, with the Theme (per moto retto) in diminution: Soprano. -^-jv 31. E i^^^^^i The Alto answers this entry of the Soprano in the following bar in contrary motion (per augmentationemj : Alto. 1 4. 15. 16. 17. 18. 32. gjzJ3=:^z^=j^^g= C -^ ^^^^ The Tenor enters at bar 17: Tenore. 1 7. 18. 19. 33. ^ b(^-^— '-^^ ^^^^E^ =£t -i^*- ^sr- Bar 20 shows the entry of the Tenor with the Theme; after two crotchets the Bass gives the Answer in contrary motion: 20. 21. Tenore. 34. Basso. — *" ^ — r ■■ ^ ^^m l • — ^^ ~ -it-p ^ak( ^t ^^f^^^^^ ^ fpE 22. -f 0^ F— f- Jadassobn, Canon and En^e. 18 APPENDIX. The Alto enters at bar 23, giving the Theme per moto retto e per diminutionem. The Tenor follows after one crotchet in double augmentation [J. against J^), and in contrary motion. The Soprano entering on the third crotchet of bar 24, gives the Answer. The Tenor finishes the Stretta at bar 31. The Bass entering with the Theme (rect.) is followed, after six crotchets, by the Alto in Canon air Ottava. The Alto finishes on the third crotchet of bar 3t. Now follows a short Interlude, bars 32 — 34, to which are attached the following entries: in bar 35, the Theme appears per moto con- trario, and in augmentation («? against J), in the Alto, in bar 36 in the Tenor (rectus) in augmentation (^ against J), and in bar 38 in the Soprano (rectus), similarly augmented. In bars 42 — 44, the So- prano and Alto give the Theme in canonical imitation (all' Ottava) in contrary motion. In bar 45 the Alto commences the Theme (rectus) and is followed after five crotchets by the Tenor in contrary motion. The last entry of the Soprano with the Theme (rectus) in aug- mentation (iff against J), appears at bar 50. The Alto follows, bar 51 (per moto contrario e per diminuzione), and again takes up the Theme at bar 54 (per moto retto e per diminuzione). At bar 56, a second Soprano is added, as a free part to the Theme in the first Soprano, the latter ends at bar 58 and the Fugue itself at bar 61. COUNTERPOINT 8, a 3 is a Double Fugue for Soprano, Alto, and Bass. The first Theme is new and is worked out alone for 90 bars, the second Theme enters at bar 94 and is likewise worked alone as far as bar 135; the two Themes entering for the first time together, at bar 147. The Alto begins the Fugue: Alto. 35- -ti^Vf^-^^ T^&^^. J W 0-J—i- The Answer of the Bass is in this case given quite strictly. The A, the first note of the third bar, the fifth (Dominant) of the key, appears first in the course of the Theme; it is neither particularly striking here, nor does it characterize the Theme. For this reason the Answer of the Bass gives in bar 8, the note K The Soprano takes up the Theme at bar 11; it is accompanied in the Bass by a counterpoint, which corresponds to that of the Alto THE AST OF FVOUE BY JOB. SEB. BACH. 19 in bars 5 — 10. After an Interlude of five bars, we find a Stretta between tbe Alto beginning at bar 21 and the Bass following at bar 22, wMch is not fully worked out. The Alto ends this Stretta on the first crotchet of the 25*'' bar. Bars 28 — 30 contain the beginning of the Theme; the acoompanying counterpoint in the Alto corresponds rhythmically with the "Contra- punto eostante" (fixed, similarly recurring counterpoint) at the be- ginning of the Fugue. The G of the Theme (bar 3) is here answered by the two crotchets CJ| and C (bar 30 third and fourth crotchets). In bar 35 the Bass introduces the Theme; it is accompanied by both the upper parts with "free" counterpoint. The Soprano has the Theme at bar 39, accompanied in the Alto by a new counterpoint, which likewise recurs in the Soprano at bar 43 against the entry of the Theme in the Bass and also proves itself, at other entries of the Theme, to be a "fixed counterpoint". The entry of the Theme in the Alto, bar 49, is accompanied in the same way by the second "fixed counterpoint". The Interlude in bars 54 — 59 shows imitations of the closing figure of the second counterpoint. The Theme enters afresh in the Soprano at bar 61; the Alto accompanies with the second counterpoint. In bar 67 the Bass introduces the Theme, with the first note B-' changed into two quavers b\^ and O as foUows: Basso. 36. ^i^^ r^ :fep= &c. The second counterpoint is given in the Soprano, the Alto is a free part. Now comes an eight bar Interlude containing allusions to the Theme and the second counterpoint. The Theme then reappears in the Alto, bar 79; the second counterpoint is given in the Bass. The Alto, this time, gives only the first eight notes of the Theme taking over then the second counterpoint in order to accompany the Theme entering at bar 81 in the Soprano and ending at bar 85. Bars 88 — 90 show a part of the Theme, for the first note of which two quavers are again substituted thus: i^3 *^- 37.95^^^ 2* 20 APPENDIX. The other notes of the Theme are unchanged; the upper parts contain the second counterpoint. The second Theme now enters, bar 94, after an Interlude of three bars, in the Alto, accompanied in the Bass by the fixed counterpoint given with the first Theme. One recognizes without difficulty in the following notes, the Theme of the first Fugue : Alto. 38. p i^1^=i=F^^^=^^^^^ ^^f=^=:^- 39. Rectus. 10 m ^£=t 40. Inversus. ^£^ EE^ =t=t • I P eS^^ The Answer of the Bass follows at bar 99 and is accompanied by the second counterpoint; it ends at bar 103. The Soprano takes over the Theme at bar 105. The opening motive of the first Theme introduces the entry of the same, bars 113 — 118, in the Alto. 41. Motive. Alto. .^ t: Wz y? Theme. E^ ^=g§t§ 113. 114. 115. 116. 117. The same Theme enters at bar 125 in the Alto and Bass together, in counterpoint alia decima, accompanied by the second fixed counter- point. In bars 131 — 135, we find the first Theme again in the Bass, accompanied, in the Alto, by the second counterpoint. After a long Interlude, both Themes appear, worked together; the Soprano commences the first Theme, bar 147, and the Bass foUows at bar 148 with the second Theme. This Stretta of the two Themes is accompanied in the Alto by the second counterpoint. Bars 152 — 156 show the inversion of the foregoing bars, in triple counterpoint. The Alto takes the first Theme, the Soprano the second THE ART OF FU6VE BT JOH. 8EB. BACH. 21 and the Bass the counterpoint. We find another inversion of the parts in triple counterpoint in bars 158—162. This time the Bass has the first Theme, the first note [G], is here only a quaver (unless one reckons the previous quaver A as the first note of the Theme; the opening figure admits of this acceptation). 42. The Alto gives the second Theme and the Soprano accompanies with the second counterpoint. If we compare bars 170 — 175 with bars 182 — 187, we find in the latter an interesting inversion of the former. Both Themes and the second counterpoint are combined in the bars mentioned. Bars 182 — 187 show the inversion of the Soprano and Bass in double counterpoint, with the Alto transposed an octave higher. See the following excerpts: 170. 43. Soprano. Alto. Basso. 171. Theme 2. 172. m Ete rrw^^=rz Counterpoint 2. Theme 1. IT ^%~tr^ [^— l-3 = nzj 3 _^. 173. 174. 175. End of Theme ^: ^^E 11^ End of the Inversion. S^ fF^^=^= ^^ i^ ;iL— ^-4^-^ W^ ^^5^ m End of Theme 1 . ? ^^ 22 44. Soprano. Alto. \ Basso. 182. Theme i. APPENDIX. 182. 184. ^^te|^^^ Counterpoint 2. m T^=^£fe^ajg^^^g-^^^ Theme 2. fc^^^^ =3=^= ^- 185. 186. End of Theme 1. 187. 188. End of the Fugue. ^= ?^P^ g PP^^ ^:^ End of the Inversion. a^^ ^F^^^^ £S ^^=^3E -^-:J S"^ End of Theme 2. *i= fe^^^^^^ COUNTERPOINT 9, a 4 alia Duodeeima is a four-part Double Fugue, the second Theme of which appears in bars 35 — 43; it is the original Theme of Counterpoint 1, per augmen- tationem. On account of the somewhat protracted length (eight bars) of the first Theme, Bach only gives one group of entries and Answers of this Theme. The Alto commences with the Theme, bars 1 — 8, the Soprano gives the Answer, bars 8 — 15, the Bass the Theme, bars 14 — 22, and the Tenor the Answer, bars 22 — 29. In bar 85 both Themes enter together: 35. Thema 2. 36. 37. Soprano. 45. Tenore. i EE Theme 1 ^^^^^m THE ART OF FVGVE BY JOB. 3EB. BACH. 23 38. 39. 40. #== ^^==^f^^ F^^^ S^^ m 41. 42. 43. End of Theme 2. 1=t End of Theme 1. te 1=^= m -• ^ •-# ^ The Alto alone, accompanies with a counterpoint, which seems to be founded on the counterpoint of the Soprano in bars 16, 17 and 18; from bar 36 to bar 58, the Fugue remains in three parts, the Bass testing. The Answer of the entry of the two Themes is contained in bars 45 — 53. The Alto has the first and the Tenor, the second Theme; the Soprano accompanying with a free counterpoint. 46. Soprano. Alto. Tenore. ti" ^J 4S. . Free Cpt. 46. a ^^^t^^ Theme 4. w=^=^^= ^ ^ ^^ Theme 2. ^E^ 47. 48. 49. lF^ ^==^g^f^ g= p-^^^ SlE ^E -M- -^-»-^ XU^ -^-S-0-^-T-P- &Ei 24 so. APPENDIX. 51. 52. ^ gglg^ ^^ 53. ^ End of Theme 1. ^m ^^^^^^ tea End of Theme 2. IE :t f=P=F= Another entry of the two Themes begins with bar 59. Here the Alto has the second Theme, the Bass entering after 22 bars rest on the second crotchet of bar 59, with the first Theme; the Tenor rests, the Soprano accompanies the two lower parts with a free counterpoint, similar to the former one. This Stretta ends at bar 67; to it is joined a short three-part Interlude of three bars. After 36 bars, through which the Fugue remains in three parts only, all four parts enter again simultaneously, bar 73. The Tenor gives the second Theme, the Alto, the first, in counterpoint in the Twelfth, Soprano and Bass accompany with free counterpoint. 73. 74. 75. Alto. 47. \ Tenore. ■]^> r. 1 r ' ■ -^ — ^- — '-*3tli -H 'J'^Jill Theme 1 & la 5 a. — ^ ' ' I ' ■=■ Theme 2. £^=#g#^ ^&^% THE ART OF FVGVE BY JOB. SEB. BACH. 79. 80. 81. End of Theme 1. 25 P=f -fl^^_M^ w=^^ End of Theme 2. -• ^ 1=1: ^a Bars 80 — 88 contain a three-part Interlude which modulates, by interesting imitations, from -^i-minor back to D-minor. At bar 89 the Fugue becomes four-part again. The Bass has the second Theme and the Soprano the first; the two middle parts accompany: 90. Soprano. Alto. 48. Tenore. Basso. ^ ^-^ 3E =fe=^r ^^EEz Theme 4 (alia lama.) r=t Cpt. ^ cpt. ^^ Theme 2. 91. 93. i ^^^^^ ^^m w- m ^^=i^d^=^4 S f~Y l L E ^^ r — Ir^^^ m i^ 26 rf 94. APPENDIX. 95. 96. 97. -t— I- lE^ ^^^^^ 1=^=^^ ^ ^^ :f =i—i-j- m :^^= ^ It After one modulating bar, the Tenor enters with the second Theme^ and the Alto with the first (alia duodecima) in G-minor, bars 99 — 106. A long Interlude prepares for the last Stretta of the two Themes in Alto and Tenor, bars 119 — 127; the Fugue ends with bar 130. COUNTERPOINT 10, a 4 aUa decima is a Double Fugue. The first group contains the first Theme in the Alto (rectus), the Answer in the Tenor (rectus); the Bass gives the Theme (inversus), the Soprano likewise the Answer (inversus). All these entries follow one another so closely, that the first group finishes with the first crotchet of bar 12, notwithstanding the Theme itself is only four bars long: 1. Theme (rect.) Alto. 49. Tenore. SEEEl^^^fe^^l^^^ ■•- #■' Ans. (rect.) ^E^ ^= fe^gT-|,g::Cz^ |^^ Soprano. Alto. Ten ore. Basso. ^ THE ART OF FVGVE BY JOB. SEB. BACH. 7. 8. 27 Ans. (inv.) P= =e ^- -^^gf Cr-r End of Ans. E^ Theme (inv.) fcp=^ Uit S^^^^^ ^ 9. 10. j=|i LL-_4— ^ ^ 11. 12. End of Ans. ^^^ %= d^t-r-4- p ^ ^6: ®Et ^ ^fef End of Theme. M^ ^ J I ; :^ g As early as bars 14 — 18, we find a very contracted Stretta between the Alto (rectus) and Tenor (inversus). We recognize the second Theme of this Fugne as the Theme of Counterpoint 5. In this Counterpoint (10), it enters at bar 23 in the Soprano; the Alto answers, bars 24 — 26, with the first few notes only, of the Theme, leaving the Tenor to complete the Answer, bars 26 — 30. There is another entry of the Theme in the Bass at bar 31, the Answer of the Alto following at bar 34. Both Themes enter together at bar 44, the Alto giving the sec- ond Theme (rectus) and the Tenor the first (rectus); they are accom- panied in the Soprano and Bass by counterpoint. This Period ends at bar 48. The combination of the two Themes (rectus) is continued in the Alto and Bass in bars 52 — 56, and in Soprano and Tenor (rectus) in bars 66 — 70. The Soprano and Alto, 28 APPENDIX. bar |75, now give the second Theme (alia decima) whilst the Bass has at the same time the first Theme; the Tenor accompanies with a free counterpoint. This Stretta ends at bar 79. In bars 85 — 89, we see the first Theme treated in double counterpoint in the tenth, in the Soprano and Alto, the Bass simultaneously giving the second Theme; here again the Tenor is the accompanying part. Another combination of the first (Tenor and Bass, rectus alia decima) and second (Soprano, rectus) Themes, accompanied by a free counterpoint in the Alto, extends over bars 103 — 107. All these Strettas are connected with one another by Interludes, containing highly interesting imitations. At the close of the Fugue, we find the following Stretta, bars 115 — 119: Soprano. Alto. 50. Tenore. Basso. P= 1^ Cpt. 115. 116. ^=^ ;e m ^EE §ii^ ^ ^El Theme 1 (rect.) h la 10a. 4= ^ Theme 2 (rect.i -S-P0- -f •- -:?^m ^ 117. 118. H9. f^r^ H^— -M^^ -^ g 120. m B to-^^a-u g£=;^ End of Theme 1. g^ S ^^^ * End of Theme 2. ^ =£ THE ABT OF FVOUE BY JOE. 8EB. BACH. 29 COUNTERPOINT 11 (li 4) is another Fugue with two Themes; the first of these, is the inversion of the second in Counterpoint 8, and the second, the inversion of the first in Counterpoint 8. For the sake of clearness we here give the Themes in full: 51. rect. 52. Theme 1 of Cpt. 8. m^ f— M^ ia S3^^^ Theme 2 of Cpt. 11. wit'Jl^ J i' pp j-Z]7T = g 53. rect. Theme of Cpt. 8. ^^^-^^^g^=^^Epgz^ Theme 1 of .Cpt. 11. 54. . ^ m. ^nrrfri-^F-P^P^^ E^^-l^gS^gg The first group of entries shows an exception in the answering of the Theme, a thing which very seldom occurs in Bach. The Alto answers at bar 5 and the Tenor at bar 13, in such a way that the Tonic B is imitated literally, i.e. fifth by fifth, by the Dominant A. We find in the Answer, the same leap from A to E, although the Dominant A, is here the second note of the Theme, at the same time being the highest, the most conspicuous and there- fore the actual characteristic note of the same. The parts enter as follows: the Alto gives the Theme in bars 1 — 5, the Soprano answers, bars 5 — 9, the Bass has the Theme, bars 9 — 13 and the Tenor the Answer, bars 13—17. An Interlude of four bars, formed on imitations of the last bar of the Theme, leads up to the entry of the Theme in the Soprano, bars 22 — 27, in which latter bar the Alto introduces the second Theme. A "fixed counterpoint" (Cpt. cost.) alternately changing from the Soprano to the Bass and vice versa, is given for this Theme: 30 APPENDIX. 27. 55. Soprano. Alto. Soprano. Tenore. ' Basso. -P— tV 28. Cpt. cost. 1. 29. g^:-^j^E^E^^j =H^^H="r Theme 2. ^ *=3t ^i ^=ttefe^^P^^^ e ^ Theme 2. ^-— d — N =j^^:^F^^p Cpt. cost. 4. gfF^ =-^^=f=^ ^^E^_^^ 34, 35. 36. 30. 31. 32. ^y9^F— ^^ -x-=t. m] Alto. 60. I Tenore. llEt 3j2ia ^^^^^^ ^^^^il^g^ Basso. Soprano. ZZECS ^l*=t^ &; =^S ^S Alto. Stef ^^^ ^g ^ Tenore. flUzi* f-» 13^^ :K -*-#■ =S Basso. iteS g^ ?:-^— jgjjs^3^ The Theme varied. 23. 24. * =^^-^ ^ =££^ 3^E^ :^: S^^^ ^S^F=^^ ^ 38 APPENDIX. ^^m ^ s ^^f ^ ^^ m m -Pl W gr :i— * ^ r E£ ^- ^=3E3 If anyone wishes to test the strictness of the inversion, they only need to fix in their mind's eye the note F, and they will find that the F of the one Fugue is given again as F in the corresponding pai-t of the other. With due regard to the harmony, the F is some- times changed to f!^. That these two four-part Fugues are not meant to be regarded as one eight-part and that Bach never intended both Fugues to be performed at the same time, is very evident. In the first place the harmony of the one would at times sound very harsh with that in the other. And of course altered 'notes would be sounded together with unaltered ones, and one part of one Fugue would often move in perfect fifths with another part in the other, as is the case in bar 26 between Soprano (rectus) and Alto (inversus). The other entries of the varied Theme are to found, in bars 32 — 36, in the Tenor (rectus) and Alto (inversus), in bars 42 — 46, in the Bass (rectus) and Soprano (inversus), and at the end of the Fugue (bars 50 — 54), in the Alto (rectus) and Tenor (inversus), where the Soprano in the upper Fugue, holds on A (inverted Dominant Pedal-point) which forms in the under Fugue a Tonic Pedal^point in the Bass. All the entries are accompanied by counterpoints, 'which are partly "fixed" and partly formed from one another. The Fugue contains 56 bars. COUNTERPOINT 13 k 3 (rectus et inversus) is an equally wonderful master-Tvork of the highest contrapuntal art. It deals with two three-part Fugues, in which the second part of the one is reflected, so to speak, in the first part of the other, the Bass of the original Fugue in the second part of the under one and like- wise the extreme parts of both Fugues. THE ART OF FVGVE BY JOS. SEB. BACB. 39 The excerpt whioh I gave from Coiinteupoint 12, will suffice to show the reader, who has not "The Art of Fugae" to hand, what is meant by the term "Mirror Fugue", I will therefore here confine myself to indicating the various entries of the parts, which I will call Soprano, Alto and Bass. Of course the parts are not to be looked upon as voice parts, but as imaginary, as is the case with all the numbers in "The Art of Fugue". That the whole Work is not intended for actual performance, speaks for itself. The Theme enters in the Alto (rectus) and Soprano (inversus); the Answer of the Bass (rectus) and Alto (inversus) occupies bars 4 — 7. In bars 8 — 12 the Theme is given in the Soprano (rectus) and Bass (inversus). The other entries are: bars 19 — 23, Alto (inversus). So- prano (rectus); bar 26 gives the beginning of the Theme, somewhat veiled, in the Soprano (inversus) and Bass (rectus) : Soprano. 61. Basso. ^^^^ ^-^^ ii^E ^ ■0 \ iV. ^^ML^ ^jEETf ^ rj^^ i U:^-r-^^^ ^^ The Bass of the upper Fugue and the Alto of the lower one then begin the Answer, bar 28, rectus and inversus respectively. In bars 32 — 36, the Soprano gives the Theme inversus and the Bass rectus, and in bars 4? — 51 the Alto has it inversus, and the Soprano rectus. An Interlude of ten bars follows, after wMch (bars 61 — 64) the Bass gives the Theme rectus and the Alto inversus. The Answer follows in the Soprano (inversus) and Bass (rectus), bars 65 — 69, This Fugue, which one might call a "Counter and Mirror Fugue", ends with bar 7-1. FUGA k 2 CLAV. has the same Theme as Counterpoint 12. We have here to deal with a four-part Fugue, in which one Piano gives the Theme (rectus) and 40 APPENDIX. the other the Answer (inversus). The second Piano begins, the first gives the Answer (inversus), bar 4, and the Theme (rectus), bar 8. The entries alternate between the two Pianos and it will suffice to show their order in the following table: Pianoforte II, bar 19 (inversus) X. I, » 26 (inversus) I, » 32 (inversus) n, » 86 (rectus) n, » 47 (inversus) I, » 61 (rectus) 1, » 65 (inversus). ALIO MODO. FUGA A 2 CLAV. This Fugue brings in the entries of Theme and Answer in the following order: Pianoforte I, bar 1 (inversus) » II, » 4 (rectus) » II, » 8 (inversus) » I) » 11' (rectus) » II, » 26 (rectus) n, » 32 (rectus) I, y 36 (inversus I, » 47 (inversus II, » 61 (inversus n. » 65 (rectus). THE FOUR CANONS are two-part, and are written for Piano in the G and F Clefs. One recognizes, in spite of the variation, the original Theme. The first Canon is called CANON PER AUGMENTATIONEM IN CONTRARIO MOTU. The notes marked with asterisks show the Theme of Counter- point 1. ^^^ii^ii^fPii^ii 62. m- *^ ^=3 J=3t THE ART OF FVGVE BY JOB. 8EB. BACH. 41 The imitation begins in the fifth bar, (alia Quinta) in contrary motion and in notes of double value. This imitation continues as far as bar 29; at this point the imitating part (Bass) has only reached the first note of bar 13 of the leading part (Alto), and as the imi- tation must be carried on, the Alto part in bars 29 — 52 is free. With bar 52 however the Canon begins again "al rovescio"; the Bass becomes leading part, in notes of original value, and the upper part entering at 57, imitates alia Quinta per augmentationem and in motu contrario. The Bass takes over, at bar 81, the same free part as the Alto had in bars 29 — 52 , and becomes leading part to the end of the imitation, bar 106; from here to the end of the Canon, bar 109, it accompanies the Alto free. The second Canon bears the title : 63. CANON ALLA OTTAVA It has the following Theme: i p *— 1(- 3^ m i ^ ■^=^3i j'l^' / The asterisks show the original (inversus). The leading part rests in bars 23 and 24 and takes up the Theme again at bar 25, in the form of an Answer. With due respect for the Leading Note, the G in the second bar is here changed to C^ (instead of C): 64. I gfi= g ^Jp-4 ^^ NB. ^^W=B^ i ^ m +=^=?= *=^ At bar 80 begins a reprise of the Canon from the fifth bar. Bars 99 — 103 form a free cadence. 42 APPENDIX. THE CANON ALLA DECIMA, CONTRAPUNTO ALLA TERZA shows, with slight rhythmical modifications, the Theme of Counter- point 1 (inversus). The imitation commences at bar 5, and is continued as far as bar 39. The imitating part then becomes the leading part, and the Canon is repeated "al rovescio". The lower part shows, in bars 41 — 44, some trifling licences. It looks at first sight as if the Canon was going to be continued all' Ottava; but if we compare bar 45 with bar 10, we see that the Canon is worked alia Decima as far as bar 79, where the Bass once more takes the Theme fper dim. and syncopated.) The Canon ends at bar 82. The last CANON ALLA DUODECIMA, CONTRAPUNTO ALLA QUINTA shows, in the first notes of the first four bars, the original Theme. The imitation begins at bar 9, alia Quinta; the Canon goes as far as bar 34, from which point it is continued "al rovescio". At bar 75 there is a repeat marked, which is most skilfully worked in. The last three bars have the sign "Finale". May this Analysis of the Fugues and Canons be a welcome guide to those who earnestly take up the study of the "Art of Fugue"'.