No. 10. MADE IN ENGLANO. CORNELL UNIVERSITY LIBRARY GIFT OF Professor Robert Palmer MUSIC LIBRARY ,«|«Nfl-L UNIVERSITY U8RJRY 3 1924 051 580 003 Cornell University Library The original of tliis book is in tlie Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924051580003 NOVELLO'S MUSIC PRIMERS AND EDUCATIONAL SERIES FUGUE JAMES HIGGS, UUS. BAC, OXON. Price London: NOVELLO AND COMPANY, Limited. MADE IN ENQLAND. PREFACE. This Primer on Fugue is addressed to all who hear or play fugues, as well as to students who desire to write them. To all alike the power of analysing and resolving such compositions into their elementary parts will be found of paramount importance ; and this power, it is confidently hoped, will be secured by the careful study of the following pages. It has been assumed that the student already possesses knowledge of, and skill in the practice of, double counterpoint, and that he is familiar with the various forms of imitation ; but should any need information on these important branches of musical knowledge, they are referred to the Primer on Double Counterpoint and Canon now in course of preparation. After a preliminary chapter which gives a general idea and explanation of the construction of an ordinary four-voice vocal fugue, and includes definitions of most of the technical terms employed, a separate chapter is devoted to each of the most important divisions, as Subject, Answer, Counter-subject, S'C, The severa. chapters are illustrated by a large collection of examples from the great fugue-writers. The student is very earnestly advised to collect for himself as many other similar examples as possible, being careful, however, to select them only from the best sources, and to classify and arrange them in the manner shown in the Primer. The rules enunciated are in many cases Jiable to exceptions. This is especially so in the important matter of Anawer ; still it is believed that the examples selected are of sufficient general application to justify the rules which are given. The collection of fugues in open score at the end of the book will, it is hoped, be found valuable both as contributing to the clear apprehension of the construction of fugue and for the IV PREFACE. practice of score-reading. The charts which accompany, and are intended to illustrate and explain, the foregoing fugues offer, it is thought, quite a new system of fugal analysis. They have already proved very useful in bringing the plan of fugal structure clearly before the minds of pupils. Students are strongly recom- mended to transcribe into open score all the fugues they study, and to make charts after the method shown. In the actual practice of fugue-writing it is suggested that the early attempts should, for simplicity, be made without words, although it will be desirable that the parts should be confined within vocal compass and be made after the manner of vocai counterpomt. The limits of a Primer necessarily exclude mention of many of the higher applications of fugal writing. Double fugue has received only a few passing remarks, and space has not been found for any notice of the fugal treatment of the chorale. I cannot close these introductory observations without record- ing my thanks and sense of indebtedness to Dr. Bridge for many valuable hints and much kind advice of which I have gladly availed myself. J. H. FUGUE. — -»- — CHAPTER I. PRELIMINARY. 1. A FUGUE is a musical composition developed, according to certain rules of imitation, from a short theme or phrase called the subject. This subject is from time to time reproduced by each of the two, three, four, or more parts or voices for which the fugue is written. It will be convenient to explain briefly the nature of the several divisions and technical terms used in fugue. With this object in view we will describe the most characteristic features of an ordinary four-part vocal fugue. 2. The subject, a theme of definite character and tonality of, let us say, from four to eight bars in length, is announced in one part; for example, in the bass. At the conclusion of this subject another voice, in the supposed case probably the tenor, repeats the subject, but transposed into the key of the upper fifth. This constitutes the answer. It must be observed, that had the subject been proposed by an upper part, and responded to by a lower part, the reply would have been at the lower fourth which is, however, but an inversion of the upper fifth. 3. The broad statement that the answer is the transposition of the subject into the key of the dominant may be accepted here, notwithstanding that in certain cases a modification of the sub- ject becomes necessary when it is employed as answer. 4. When the answer is an exact transposition of the subject it is called a real answer, and the fugue in which it is employed a real fugue; when in the answer the subject is slightly modified, to restrain it within certain tonal limits, such a reply is called a tonal answer, and the fugue that results a tonal fugue. 5. While the second voice, in the present case the tenor, is singing the answer, the original voice (the bass) supplies a counterpoint against it. This counterpoint may, or may not, be designed for subsequent use in connection with the subject ; if it be, it must be written in some form of double counterpoint with the subject, or rather with the answer ; when so constructed and employed this is the counter-subject. A fugue with a regular counter-subject is generally much more artificial in its construc- tion and interesting in its performance than is a fugue without a reerular counter-subject. 3 FUGUE. 6. At the end of the answer the two voices already introduced frequently form a short codetta, thus delaying for a bar or two the entry of the third voice; this, when it enters, sings the subject but in a different octave from the voice that first announced it. In like manner the fourth voice repeats, in a different octave, the answer already sung by the second voice. 7. During the successive entries of the several voices the earlier parts generally continue, enriching the harmony with additional counterpoints ; but sometimes one or more of the previous parts may end its, or their, career before the conclusion of the second entry of the subject and answer. 8. The first section of a fugue usually closes at the point where each voice has in turn sung the subject or answer, but occasionally there is a redundant entry of the subject by the voice that first led it. When this occurs it affords the fourth or last voice an opportunity of using the counter-subject by inversion against the subject. In this case each voice will have sung both subject and counter-subject. So much of a fugue as has been described constitutes the exposition. 9. The exposition is often followed by the counter-exposition. In this the order of subject and answer is reversed. The answer now leads and the subject replies, the voice that in the exposition sang the subject now sings the answer, and vice versd. The counter-exposition is usually presented at a shortened distance oi time, foreshadowing the stretto, and often only some of the voices participate in this feature of a fugue. Subject and answer of real fugue (see par. 4) are distinguished one from the other by the interval of reply. It has been shown that the answer is the trans- position of the subject into the key of the upper fifth ; that the voice which follows the answer is in the octave of the subject, and thus a fourth above the answer. The interval of reply therefore establishes the relationship of the responding to the leading voice. In the case of tonal fugues the answer i> further distinguished from the subject by its altered form. 10. Hitherto the composition has been almost wholly drawn from the subject and counter-subject in their primary form, but the incessant use of these themes may soon become wearisome ; to avoid this the principal sections of a fugue are usually separated by the introduction of episodes. An episode, although intended as a contrast to the main features of the fugue, should yet be in consistent keeping with the rest of the composition ; this is best effected by the selection of some fragment that has been previously heard, often a member or part of subject, counter- subject, or one of the incidental counterpoints may be taken for development by sequence or free or canonic imitation. It adds to the variety of the work when such imitations are con- ducted in intervals different from those proper for the strict treatment of the initial subject. The length of an episode should PRELIMINARY. 3 be sufficient to excite desire for th^ return of the original theme, but should not become important enough to overshadow the leading idea of the fugue. 11. In the second principal group of entries (subject and answer) it is perhaps scarcely desirable to observe so much formal exactness in interval of reply, or order of subject and answer, as is essential in the exposition. In this middle group !»ften begin some of those variations in the subject, or its treat- ment, that serve to diversify the composition. The subject may be used by inverse movement and imitated in its new form. The original subject may have an inverse answer, or vice versA. Subject or answer, or both, may be augmented or diminished. 12. The section last described will probably be followed by another episode drawn, like the first, from some already employed idea, but differing in matter or treatment, or both, from the first episode. 13. The second episode is followed by the third, and probably final, section of the fugal working of the original theme, now usually combined in stretto; that is, the distance of reply is shortened, unexpected combinations of the subject with itself are made, and the whole composition is brought to a climax. In this section the employment of a " pedale " is often a prominent feature, and on this soine of the most artificial combinations are frequently built. 14. In speaking of fugue as being resolvable into sections and episodes, it must not be supposed that these parts are separated by formal cadences : perfect (or final) cadences are scarcely used at all in fugue, except at the termination of the entire composition; for although the harmonic progression "(dominant to tonic) that belongs to tne perieci cadence is often employed, yet it will be found wnen this occurs m the course of a fugue, instead of marking a point of repose, it generally becomes a new point of departure for one or other of the voices. 15. While the foregoing may serve as a general description ol a simple fugue, it must be remembered that fugues are of many kinds, as: — (a) Vocal ; instrumental ; mixed. (b) Fugues are strict or free : strict when the interval of reply, fifth above or fourth below, is constant ; free (sometimes called fugues of imitation) when the interval of reply is variable and the treatment of the subiect fragmentary. In the course of any kind of fiigue, strict or free, a reply may be at the octave or the answer may lead, in which case the reply will be at the fourth above. Most fugues are strict to the end of the exposition, but become free fugues of imitation afterwards. ^ (c) Fugues may be founded on a single subject as supposed in the preceding sketch, or there may be two or more principal 4 ruoDE. subjects. In a double fugue the two subjects on which it is built may be used on either of two plans: they may be combined at the outset of the fugue and simultaneously developed, or one subject may first be treated alone, as in simple fugue, and the second subject may be introduced by itself, in a separate exposi- tion, and afterwards the two subjects designed from the first fo( combination may be brought together. (d) Fugues in respect of subject may be diatonic or chromat .c. («) Fugues differ in the nature of the answer, which may be real (».«., exact), tonal, inverted, augmented, or diminished. (/) Fugues with regular counter-subject differ as to the nature of the counterpoint employed ; this may be at the octave (or fifteenth), tenth, twelfth, or indeed any other interval; but those enumerated are of most frequent use CHAPTER II. THE SUBJECT, i6. A FUGUE SUBJECT should be of such marked character aa readily to impress the memory : — Ex. I. Hanoel. » ^^ ^ IZ2I Ex. 2. m ^^q^ s J. S.J^ACH. HSZ ? ^ It should be moderate in length, and well defined as to key and mode, presenting a complete musical idea of sufficient interest to command attention : — Ex. 3. J. S. Bach. zan M ^ ^Ex. 4. I I r7"T1 ?' f''-r.r; | Jj^J | 'q]j^ i ;^ji Handel. 17. Most fugue subjects remain in the key of the tonic. Modu- lation between the tonic and dominant is the only ultimata modulation proper in a tugue suDjeci. 18. Ex. 5 and 6 show subjects that commence m the key of the tonic and modulate to the dominant : — i Ex.5. -9- bM*, *" J. S. Bach. TTJff iii/3IC^ ^ Ex.6. gJ;^^A r, ^ i -t- J. S. Bach. Z=iC ^ 19. Ex. 7 shows a subject that begins in the key of the domi- nant and modulates to the tonic : — Ex.7. _ ^^^^^M . -^-»---l«-# H«- J-S_Bach. (fe> rrrrrr I r f r ^iEg FUGUE 20. Sometimes a subject begins and ends in the key of the dominant : — I Ex. 8. ^ ^ m J. S. Bach. M 21. The compass of a fugue subject should not be excessive. In a vocal fugue the limit of an octave should rarely be exceeded This general restriction is desirable because the employment o{ the subject at different pitches in the manner necessary in fugal treatment would otherwise carry each voice beyond its convenient range. Subjoined are examples of subjects of vocal fugue. Ex. 9 has the compass of a fourth, Ex, lo has the compass of a sixth, and Ex. ii the compass of an octave: — Ex. 9. ^^ ac J. S. Bach. S ^ Ex. 10. Mozart. /itV ^^ ■ IPJ. / i rj iTj *t-- ( , ^j Ex. II. ^^ ± Handel. ^S \^ r.T 1 C c r J. — b<— I '^ K » ^ 22. When the number of parts is large, say above four, it will generally be found expedient to limit both the compass and length of the subject, especially in vocal fugue ; for the working of a subject of wide compass in, say, five or six parts will be less distinct, through want of room for the parts to move in, than it would be in fewer parts ; and if the subject be of great length the working of the fugue in a. large number of parts is likely to become wearisome. 23. Subjects of instrumental fugues are sometimes of con- siderable length and compass, and are then not unfrequently sequential in construction : — Ex. 12. J- S- Bach. i i ± ^ ^Fg ^ \> (\r- 1 w ^ ^ £ THE SUBJECT s J. S. Bach. HW P W^^ £3^ ^ s Ex. 4 is also an example of a subject of instrumental fugue ol wide compass. 24.. Most subjects commence on the tonic or dominant, but examples are not wanting which show the use of other degrees of the scale for the initial notes, but such examples are rare : — p. Commences on se cond of the scale. ■, d,_„ P ^^ ^ Ex. 15. Commences on third of G Minor. Mattheson. ^^ © Ex. 16. Commences on sixth of C Minor. J. S. Bach (?). •f'i.(MJn ,g ^jt^ &c. Ex. 17. Commences on seventh. J. S. Bach. ^^ ^ Ex. 18. Commences on flat seventh. C. P. E. Bach. s 4U ^ ^ "'J' ^ .45. Following the general rule of melody, fugue subjects may oegin on any part of the time, but . should generally end on an accent. In vocal fugue the subject should extend at least to the end of a clause or member of the verbal sentence, and most often will include an entire sentence : — Ex. 19. ^'"'■^ci^rrj i r/^^ Mozart. r (o Cum Sancto Spi - ri - tu, in... glo-ri-aDe-i Pa - tris. A - men. 8 FUGUE. 26. The subject should lend itself naturally to the tormation of stretto ; that is, it should be capable of combination with itself at an interval of time shorter than the original distance : — ^ Ex. 30a. £2- * :£ .^ KiRNBEKGER. Ex. 20& fT- I, J ^^ 2Z f^pt^^rr i rfrr r ^^ ■a vj. It is also advantageous when the subject can be resolved into different phrases suitable for employment by sequence, or by some of the more or less strict forms of imitation. Episodes thus formed impart great variety to the composition, and yet preserve the unity of the fugue. Bach detaches the last few notes of the following subject to serve as a theme for episode : — Ex. zi. ^^ J^ S. Bach. j^^MJm^ -- ^m jpt 28. It is very desirable for the student to exercise himself in the analysis of fugue subjects, so that he may determine the limit of the subject. In many cases the next entering voice will be found on the last note of the subject: — Ex. 22. J. S. Bach. 29. Often, however, the subject ends before the new voice enters, and a codetta is added at the end of the subject ; this is not of necessity identically imitated by the other parts : — J. S. Bach. fe^Vr, _' The completeness of the melody in Ex. 23, is alone a sufficient indication that the subject ends at the *; but additional evidence THE SDBJECT. a is furnished by the fact that the codetta is not imitated by the other voices. 30. Sometimes, however, the codetta as well as the subject K imitated in the course of the exposition. This is the case in the well-known Organ Fugue in G minor (Ex. 24). The subject ends at the *. This is felt to be the natural rhythmical and tonal close of the subject melody. The codetta grows out of the subject and is not to be confounded with the counter-subject, which, as is proper, is in contrast with the subject. That the counter-subject begins at f is further proved by the mode of its employment in a later part of the fugue : — Ex. a4-_ J. S. Bach. V ^ ;j^ Si^bject ^^^^^^m ^ Codetta. ^ Answer. ■■B,^,^ ■ Counter-subject. 31. On the other hand, the subject frequently extends beyond the point where the next voice enters. This is the case in what may be appropriately called " close fugues : " — Ex. 25. J. S. Bach. i |!^?i=: ! > /* p - ^ ^ ^ ^ m, f ^ 321 lO FUGUE. 32. Subjects founded on scale passages have always been favourites with fugue writers. Such subjects are by their nature more susceptible of fugal device and combination than those made chiefly by disjunct intervals. Bach, in his " Art of Fugue," after treating his original subject and its inversion — Ex. 263. , J- S. Bach. <£^<^ '^ ^ i d J d — in simple fugue, prepares for its more elaborate treatment by filling up all the skips except the first — Ex. 266. i ^ ^ m ^ — and thus opens the way for the wonderful possibilities of combi- nation which he subsequently displays. Dr. Stainer* has well remarked " that the ear is so ac- customed to the succession of the notes of the scale that it will tolerate such a succession even when the notes have little or no relation to the harmony with which they are heard ; . . . that a series of harmonies occurring over successive notes of the scale, or over a recurring phrase made up of scale-notes, may contain combinations which would not be borne with unless built on such a groundwork." 33. As the acceptability of a musical phrase moving toward a definite goal is a ground for the frequent use of diatonic scale progressions in fugue subjects, so it accounts for those formed wholly or in part on the chromatic scale or by chromatic intervals. The following are examples of subjects founded on diatonic and chromatic scales: — i Ex. 27. J. S. Bach. S ^ 3 ev — w ^ -9- J. S. Bach. I Ex. 28. ""4^ijJijj i ^^^j;j-: tt I Ex. 29. 4. ^ ^ ALBRECHTSBBROER, 22 ^ " A Treatise on Harmony." Fourth edition, p. 141. THE SUBJECT. Ex. 30. ^) H ^^ jfii^js ^ ^ ry'T ^^'^ II J. S. Bach. * S J. 3x. 31. 4*^ J- I 'i liiJNiiJJiJjJ J. S. Bach. Ex. 32. m. Albrechtsberger. y=^^ a ^ I IN IW l it£^ Ex. 33. ^ f-gr.i^-tfii Handel, £ ¥ SUMMARY. SUBJECT. A fugue subject should be of distinct character, moderate in length and definite as to key and mode, presenting a complete musical idea. A fugue subject generally remains in the original key, but it may modulate to the dominant, or, beginning in the dominant, it may modulate to the tonic ; but no other ultimate modulation than that between tonic and dominant or vice versa, is permissible. The subject should not be too wide in compass. A subject of vocal fugue rarely exceeds an octave in compass. Subjects of exceptionally wide compass or great l&ngth are not well suited for treatment in a great number of parts. Subjects most often begin on the key-note or the fifth of the scale, but they may begin on any other note. Subjects may begin on any part of .the bar, but generally end on an accent. Vocal subjects usually cover, if not an entire sentence of the text, at least a complete member of a sentence. Subjects should be designed for stretto and suitable for episode. A codetta of a few notes often occurs between the end of the subject and the commencement of the counter-subject. It is important to distinguish the limits of a subject. Close fugue, subject and answer used from the first as in stretto. Scale passages are frequent in subjects. CHAPTER III. THE ANSWER. 34. The answer is the simple transposition of the subject into the key of the fifth above, or fourth below, except — (a) When the subject skips, especially at its outset, to the dominant, direct, or through the third of the key. (b) When the subject begins or ends on the dominant. (■c) When modulation between the tonic and dominant, or vice versa, occurs in the subject. In all these cases some variation from mere transposition into the key of the fifth has to -be made, in order that the answer may conform to the broad rule that the tonic shall reply to the dominant and the dominant to the tonic. 35. If the answer is a strict transposition of the subject it is a real answer. Ex. 34. i ^^ B=^ zz: S wts Real answer. f'UJjjJJl-^ Ex. 35. 73-^ i E 32 fe Real answer. t r^ zz ^ 36. When, as mentioned above, par. 34 (a), (6), (c), it becomes necessary to alter one or more of the notes in the answer, in order to preserve the due relation of tonic and dominant, the answer is tonal. Ex. 36. compare 34 (a;. M g ? 3z: D t - , . ^ , . . J . . Answer therefore skips to tonic. Subject skips to dominantr '^ E 3 ^ ^ -^ THE ANSWER. 13 $ Ex. 37. compare 34 (a). w Dominant reached through the third of tonic. ^ ^^-i i ^fep p ^ Tonic reached through the third of dominant. I IE Ex. 38. comp. 34 (J). Subject begins on dominant. ^^^^^^ ^^^j^^ ^^ ^„^j^_ ^ ^ Ifiit -€S>r \$ Ex. 39. comp. 34 (i). 1 *»~ •T^r- ip Subject ends on dominant. Answer ends on tonic. ■yrr- (P Ex. 40. comp. 34 (c). ^ 22: B 71 Answer returns to tonic. Subject modulates to dominant, I Ei^i ^^^-f-iir The tonal answer, confining the melody of the reply within the limits of a acale or tone, appears to have been originally founded upon a feature of the ancient Church modes. Higg8~Fneu«.— JJoTello. B H FUGUE. The ancient modes were of two kinds, authentic and plagal. Each authentic scale had an attendant plagal scale, formed of the same notes, but conamencing a fourth below. If we regard the scale, Ex. 41a, as an authentic scale, its plagal form will be as in Ex. 4ii; — Ex. 41a, IE 32: ^ - * ^ Ex. 41b. i The authentic form lies between the Jinal and its octave, and the dominant is central. The plagal form lies between the dominant and its octave, and the filial (of the authentic form) is central. Although these intermediate notes may be termed central, it will be seen they really divide each scale into two ««equal parts : in the authentic form the lower part, C to G, is of wide compass and the upper part of narrow compass; while in the plagal form the reverse is the case, the lower part is of narrow compass, G to C, and the upper part of wide compass. A subject made upon the lower half of the authentic scale is answered in the lower half of the plagal scale, that is, it is compressed ; on the other hand, a subject formed on the upper half of the authentic scale is answered in the upper half of the plagal scale; that is, it is expanded. It will be found that exactly in proportion as these prominent notes (tonic and dominant) are brought into proximity, especially at the beginning of a subject, so the tonal answer is formed in accordance with the foregoing explanation ; but when these notes are separated by notes belonging to other harmonies of the key the tonal change becomes unnecessary. 37. The interchange of tonic fdr dominant, or vice versd, is not generally necessary when those notes occur in the middle of the subject, unless such notes are made especially prominent by length, position, or mode of approach. The following examples of particular cases will, it is hoped, make plain the practice of the great masters of fugal art : — Real Answers. 38. When the subject commencing on the tonic moves by conjunct degrees even towards the dominant the answer will be real, i.e., exact: — Ex. 42 S^ J. S. Bach. ^ ¥=* ^^^i^^ End of subject. THE ANSWER. 3 ^ IS Handel. ^ ^ End of subject. ^^ =^=^ An apparent exception to the above rule occurs when the sub- ject, descending from tonic to dominant, ends thus : — Ex. 44a. * i 732 -fTJ- -t- but this really implies a modulation. (The A (*) is the fifth of the dominant harmony of G.) The answer is therefore tonal, thus: — Ex. 446. i E "C7" 39. When the subject commencing on the tonic and remaining in the key of the tonic progresses by skip towards any other note than the dominant the answer will be real : — Ex. 45. Z3e J. S. Bach. J '' ' ^"'■J- ' T ^^ fff- ^ rT i S i6 FUGUE, Ex. 46. J. S. Bach. ^ aXl ^ : — - — ^ ^•%%-7. — ^ — = — r — ^ — F — — Tr r - |ti;_4_Sj41W— s — 1 p: cJ — 1 LJ ji ^ ^ fe: ^ ffj-w ?: ? ^^ 40. When the subject commencing on the tonic reaches the dominant through the second or sixth of the scale the answer will generally be real (but compare par. 37) : — Ex. 47. I J. S. Bach. r irf ^Jg g ^ ty Dominant reached through jj. second of the scale, fr'"^iM^^ i .fflg Ex. 48. J. S. Bach. ^ajJ^F\im:i:^^^^^Py^!^^\ Dominant reached through second of the scale. ^ ^ 2S^S s «^ ^s p ^ ^ M a ^ Ex. 49. Handel. ^^^^^gis Dominant reached through sixth of the scale. i ^ THE ANSWER. «7 S m |k"(^ r'f i f I'^Cj'i^ierjTj'g &c. 41. Subjects commencing on the second, third, sixth, or seventh of the scale usually have real answers. Subjects beginning on the fourth of the scale are very unusual. Tonal Answers. 41a. Tonal subjects are authentic when tonic and dominant stand at the interval of a fifth. (See Ex. 50, 51, 57, &c.) They are plagal when tonic and dominant are at the interval of a fourth. (See Ex. 6g.) An authentic subject has a plagal answer and vice versd. 42. If the subject commence on the tonic and at once skip to the dominant the answer will almost invariably be tonal : — Ex. 50. J. S. Bach. I ^ 5 ^ F x ^m mm. ^~T^ S! s ISL t S P^^ ^^ zz TT ^2= Ex. 51. Kaydn. m -.m e s s m- N P I w ■'Ki CJ m ^ ■i \ . s ^czpz w The second note of the subject (the dominant) is alone altered in each of the above answers, although of course this involves i8 FUGUE. the alteration of two intervals — the step of a fifth to the dominant- becoming a step of a fourth to the tonic, and the step of a third from the dominant becoming the step of a second from the tonic. There are, however, exceptions to this rule. Handel employs a real answer to ihe subject " Lowly the matron bowed " : — Ex. 52. Handel. i ;it ^ ^^ ^^ zz ^ 7zr^ i i 32 The subject consists entirely of notes of tonic and dominant harmony, and the answer of notes of dominant and second dominant harmony. (See obser- vation on Ex. 54,) When the dominant skipped to is a note of little value and slight rhythmical importance the rule is not observed, especially if the dominant return at once to the tonic through conjunct degrees of the scale : — Ex. 53. J. S. Bach. dJujJ, s Bach in answering his fugue subjects seems to have been very solicitous to retain the conjunct or disjunct form of his subject as far as possible. ThiQ consideration may explain his treatment of the answer in the Organ Fugue in G minor : — ii Ex. 54. m J. S. Bach. H ^ m &c. m WfeJj l ^ If Bach, instead of writing a real answer, as at a, had treated the subject tonally, as at 6, the free springing figure of the subject would have been destroyed, and the imitation much disguised. THE ANSWER. J9 43. If the subject commence on the tonic inflected or varied and after the inflection skip to the dominant, the reply will be tonal: — Ex. 55. ^ J. S. Bach. ^ w^ &c. fc;^ V ^;^ ^ ^ ^ Ex. 56. ^^ &c. J. S. Bach. n - ^ tJ i^'i-) in its two relations. In the first bar Eb is evidently the third of the chord of C minor, and it is answered in the fourth bar by Bi? the third of G minor. In the second bar the Eb is felt to be the sixth of G the dominant, and it is accordingly answered in the fifth bar by At? the sixth of the tonic C. 50. The sixth of the scale employed in the subject will always be responded to by the sixth of the dominant in the answer. (See Ex. 59, 61, &c.) 51. A right appreciation of the nature and harmonic value of the seventh of the scale is also very helpful to the formation of a correct answer. In many cases this note is used only as an embellishment of the note above: — In such cases it will be reproduced in the answei ;- ix. 676.,, & 1 ^ s 52. But the seventh often makes itself felt as third of the do- minant, when it must be answered by the third of the tonic : — , r. Ex m Pergolesi. i ^^ ^ i -fS (S^ ^ ::g=i [p,^^r^rH ?g rrrr r ^BE THE ANSWER. (i Ex. 69. ^ ^ nr^^ jrf^ 23 J. S. Bach. JEZ ^m ^ m In Ex. 68 the Fj( in the subject is part of the chord of D (the dominant) ; it is therefore answered by B as part of the tonic chord G. In Ex. 6g the B in the subject is the third of the dominant chord ; therefore it is reproduced by E, the third of the tonic chord. Ex. 70 shows the major third of the dominant (Fx) answered by the major third of the tonic (B#), and^the third of the tonic (B), really the sixth of the dominant, answered by the sixth of the tonic (E). This note rules the whole answer : — Ex. 70. J. S. Bach ^ m i e^VV'rf r^ *m- Hij- ff Ex. 71 illustrates the same point. The second note of the subject is rather felt as third of the dominant than as seventh of the scale, and is accordingly answered by the third of the tonic: — E^-7i. ^ h J. S. Bach. .rSj^ i ^J ^••111 . ^ ^ ' s — »■ 51a. Perfect intervals in the subject will be answered by perfect intervals, and imperfect intervals by imperfect. *«* This is a very important general rule, but see note, page 33. 24 FUGUE. 53. When the interval of a diminished seventh occurs in fugue subject it is always reproduced in the answer: — Ex. 72. . ^i -J ^ Handel. m 123. Here dominant is answered by tonic; third of tonic by third of dominant ; sixth of tonic by sixth of dominant ; leading note of tonic by leading note of dominant ; and the interval of the diminished seventh is reproduced. 54. The rule that the diminished seventh shall be reproduced is but part of a wider rule, viz., that whatever belongs to character- istic harmony in the key of the subject must be reproduced by corresponding characteristic harmony in the key of the answer. With this agrees Cherubini's comprehensive rule: — " AH phrases of the melody of a subject which belong to the key or chord b( the tonic should be repeated in similar phrases belonging to the key or chord of the dominant, and all phrases which bear analogy to the key of the dominant should be repeated in the response in similar phrases bearing analogy to the key of the tonic." It should be observed that the expression, " chord of 'the dominant," as used here, means the tonic chord of the key of the upper fifth, and has no reference whatever to dominant harmony as technically understood. 55. It has been shown that the answer to a subject that does not modulate will, speaking generally, be a fifth above or a fourth below the subject, with such possible modification as results from the substitution of the tonic for the second of the scale, when answering the dominant employed in the subject. 56. The answerto a subject that modulates will, while the subject remains in the original key, be made in conformity with the preced- ing rules, but at the point where the subject modulates (to the domi- nant) the answer, returning to the original key from the dominant, its natural seat, will be a fourth above instead of a fifth above : — X. 73a J. S. Bach. Key of tonic. Key of dominant. | JJ^jJrji ii J-j lLj- f r ' THE ANSWER. 25 Ex. 730. Fifth above subjectj fe I Fourth above subject. £ ^ In Ex. 73ii the subject remains in the original key for the first three crotchets of the time. In the answer, 736, all this portion, except the first note, is a fifth higher than the corresponding notes of the subject ; but the last part of the subject modulates to the dominant, and the last part of the answer is therefore a fourth above the corresponding notes of the subject. 57. In the case of a subject commencing in the key or region of the dominant, and modulating to the tonic, the answer will, while the subject is in the dominant, be in the tonic a fourth above, but at the point where the subject passes into the tonic the answer will be in the dominant a fifth above : — Ex. 74. ^^ J. S. Bach. ^ Key of dominant. (■vif.rfrrTg M Wff l ^Q: l-d^'-d-Key of tonic.**^^ ' s ^ i Key of tonic. | 26 FUGUE. 58. If the subject commence and remain throughout in tht key of the dominant the answer will be in the key of the tonic, a fourth above or fifth below : — Ex. 75. l?iiN j JI^J^»J ia , i- ^r . m J. S. Bach. :M ^^ 59. The answer to a chromatic subject will be found by first reducing it to a diatonic form by the omission of those sharps, flats, or naturals which produce the chromatic intervals ; this outline may then be answered in the usual mann«r, and the accidentals inserted to complete the chromatic answer. Chromatic subjects, if conjunctly chromatic from the begin- ning, generally have real answers: — i Ex. 76. J. S. Bach. ^^ r 11 f r hWJiiJJiJjJJ «^fe ^^^^^^ 60. If a chromatic subject modulate (to the key of the domi nant) the chromatic notes will as soon as possible be regarded in their connection with the new key : — J. S. Bach. Ex. 77. Mnjr]jTgi rp^rpj l£ S i* M S "n Ji il l ^ E W =feti« ^ ^ THE ANSWER. 27 The first hve notes are answered according to the rules • I St, that tonic shall reply to dominant ; and, 2nd, that the sixth of the scale shall be answered by the sixth of the dominant. From this point, where the modulation begins, the answer is throughout at the fifth below the corresponding notes of the subject. 61. In making the answer to a fugue subject its melodic form should be preserved as much as may be possible, consistently with the foregoing rules ; scale passages being answered by scale passages and skip by skip. No unnecessary change should be made. Necessary alteration should be made as soon as possible ; and should " be always made in quitting or ap- proaching tonic or dominant."* 62. It is allowed to shorten the first note of the answer when doing so secures a better entry. It is also permitted to vary the last note by lengthening or shortening it. 63. Sometimes an upward instead of a downward, or a down- ward instead of an upward, interval may be taken to suit the convenience of the voices, or for similar reasons. Thus Handel writes :- — I Ex. 79. Handel. ^ Wf^ w * ^^ '^SL p ;£Q^ \m w m m ^ rS» ^ «FP= Vf i hr ^r i i^ J ^ m 64. The answer to a fugue subject may be made by inverse movement, such inversion being usually according to the following scheme, for the major : — » Ex. 80. ^=2 S^ ■JSH -!zr -^cr. 32r ~^ ' Music." H. C. Banister. London, 1873. 28 FUGUE. Although, as can be seen, the inversion is not strict, the semitones not falling opposite to one another, yet the tonic and dominant mutually respond the one to the other, and thus preserve a broad characteristic of fugal reply : — Ex. 8t. J. S. Bach. HI ^^ r^^ . . .r Instrumental Bass. W^ tP m =?= ^ ■yrs- i m mf^ *= E^X -p- f~ fee ^ naff J** ^ jg p- r ^ fff^r irr r^' ir^ ^ i^-fn^ IJ^-^t^ '^^Hj JiiJ-LiL ^^ -c*- THE ANSWER. tr 29 Handel. $ x. 8a. tr p^ tr Han i ^ e - f1 f l — p^ f"^ tefei rFF=H ?^ 3S^ -m- 0^ f^ • \ m \ 0^ rvr w^ ^m b U I -g ^ ^ P i ^a ^ 5 H r|-+H ^ 3E i>,brjr£g]Y Lf ♦-#- ^^ f ^ ^ s * * * 'fe'. ii f r r r g^ e ^±^=a- ^^^^ i =fcti?c ^ 3ti; i ?=i^- y=^ ^»vFrr=:&^ HiRgs— Fugne. — Novello. C 30 FUQUE. 65. The corresponding scheme for the minor ia Ex. 83. i ^ F r-' i g; 122: ,-iy- Ex. 84. -=^^-* ■3?" -g^fer r r r r l^ Handel? (Casper Kbrl), m > rs ftaii I Ex. 85. J. S. Bach. ^ ^ 22 ^ ;5f^=2 ^ rE ^^^ 66. The answer may be by diminution. The example below, from Bach's "Art of Fugue," shows diminution in combination with inverse movement : — Ex.86. - - - J-.S.BACH. i 5 ■^ r-^^fsrT"|f- r:r- ^ ^:^ ^ *: ^ 67. Sometimes the answer is by augmentation. Ex. 87, also from Bach's "Art of Fugue," shows augmentation, and twofold augmentation in combination with inverse movement : — i Ex. 87. ^ ^ J. S. Bach. ■^ f F S ^ m ^^ > i Vm to^ffi^^ ^^fi ,^ •^=- THE ANSWER. 31 £ ^ f m ?#p= ffl-^? ^ f f tt ^ r rJ^_<^S^^^ ^^ W m f^ %r~cca^W^-H^ ^ "m-^-^^- ^ fcat #^ 3tit 1^ 1 I j ^ iP^ IJ r »^ ^ ^ si S gT cte ^j* ^ ^£g ^ f«i!^ ?:=»^ ^pgr~gg;Qg ^a ^' jr-zr-^ g.^^ ^# 1 -p- m I zr -ry 32 FUGUE. 68. These devices — -inverse movement, diminution, and aug- mentation — are chiefly used as variations of the subject in the course of the fugue, especially in forming the stretto. They are but seldom used as the characteristic feature at the beginning of the composition. SUMMARY. ANSWER. Real answer. Exact transposition in the fifth above or fourth below. Tonal answer. Founded on the idea of confining both subject and answer within a scale or tone. The modern application of this hardly extends beyond answering dominant by tonic, instead of by the second of the scale. With this restriction, and other incidental alterations that follow from it, a tonal answer is identical with a real answer. A real answer is proper when the subject, commencing on and remaining in the key of the tonic, moves by conjunct degrees, except downward from tonic to dominant as closing note of the subject. The answer should be real when the subject beginning on the tonic skips to any note other than the dominant and does not modulate or end on the dominant. The answer is also real when the subject under similar condi- tions skips from tonic to dominant through the second or sixth of the scale. The answer is generally real when the subject begins on any other note than tonic or dominant. The answer is tonal when the subject beginning on the tonic skips direct to the dominant or reaches that note through the third of the scale. The answer is tonal when the subject begins or ends on the dominant. The answer is tonal when the subject modulates. Distinguish third of tonic from sixth of dominant ; answer the former by third of dominant, and the latter by sixth of tonic. Distinguish the seventh used as a note of melodic embellish- ment from the seventh as third of dominant; answer the last by third of tonic. Answer the sixth of the tonic in the subject with the sixth of the dominant. Reproduce all characteristic notes and intervals of the subject. In answering a chromatic subject first reduce it to diatonic form; find answer to this outline and then fill in with necessary accidentals. THE ANSWER. 33 Preserve melodic form of subject as much as possible in the response, answering scale by scale and skip by skip. When any modification of the subject is necessary in the answer make it at once either in quitting or approaching tonic or dominant. The first note of a subject may be shortened in the reply. Answers by contrary movement, by diminution, or by augmen- tation are not much used, such devices being generally reserved for the more advanced sections of the fugue. Note to si«. Page 23. Sir G. A. Macfarren, to whom I am indebted foi the important rule that perfect and imperfect intervals in the subject are each answered by intervals of corresponding character, remarks that the rule is untenable without reservation. ' I. If dominant and subdominant occur in succession in the subject at the point demanding tonal change, they will each be answered bytonic of primary key ; so substituting unison (perfect interval) for second (imperfect interval). (See Ex. 50.) II. If subject leap from primary dominant to supertonic and return to mediant, the answer will leap from primary tonic to secondary supertonic and return to mediant in answer, substitut- ing 3rd (imperfect interval) for 4th (perfect interval). " Nun Komrn, der Heiden Heiland." T S T? h Sub ject. r^— 1-^ ^ __ Answ er. ■>• ''• " "^" * Sapertonic of G. t Supertonic of O. CHAPTER IV. COUNTER-SUBJECT. 69. CouNTER-SLBjECT is a term employed in two senses. First, and most properly, it describes the second of two subjects em- ployed in a double fugue when these subjects are announced almost together at the outset of the composition ; here the second subject is literally a counter-subject (Ex. 88, 89) : — Ex. 88. Subject. J. S. Bach. & T22 _Q_ gl Counter-subject. 1^ rTf T ^ ? f" ^ Ex. 89. Subject. i Handel, E ^ Counter-subject. h-- MJ"^r ^ ^rr i cmia i s 22= i^^ ^ 70. The second, and more common, use of the term counter- subject describes the counterpoint sung against the first answer by the part that originally announced the principal subject, when such counterpoint, being invertible, is designed for subsequent use as an escort available either above or below the chief subject {Ex. go, 91, 92):— COUNTBR-SUBJBCT I Counter-subject. ir.n jiTii I Subject. r-t i-T^r'rr t -r ' rr i i rY i ifrii "^ S Ex. goo. Subject. Ex. gr. ^m J. S. Bach a g^sa - Ea-e^^m^ i rLTr -ii ^ ^ ^^^{?f{Kn^ ^ 1 wa-'WasX^^ ^- ' $ I Counter-subject. 36 FUGUE, ^^ Ex. gz. J. S. Bach. ^=^^ — 1 — • 1 — 1 1- 1 1 Subject. -p p— — >i — T-- Subject. —m n»- 1 1 — r-m Nr-=- Counter- subject. Ife^^fM ^pii r VII r ^*irrrrjL^ir£fr,rE^^ k^a • 1 ■ 1 • i --4- • 1 Subject. Counter- subject. .-. subject. COUNTER-SUBJECT 37 Counter-subject In the several before-given examples (Ex. go, 91, 92), the counter-subjects are regular : they enter by the voice that has just passed through the subject,* They are all in double counter- point with their respective principal subjects ; and are exhibited both above and below such subjects. This is the immediate result, in Ex. 91 and 92, of the subject being announced in a middle part. 71. When the subject, in fugues of more than two voices, is first led by an extreme part, and, as is most often the case, the other voices enter in regular ascending or descending order, the counter-subject will necessarily remain in one uniform position and relation towards the principal subject, unless an extra entry of the part that first announced the subject occurs ; if this happens, the last original voice will be able to employ the counter-subject by inversion. The following extract, from Haydn, will afford an illustration. After the subject led by the bass has successively appeared as answer or subject in tenor, alto, and treble, attended by the counter-subject in bass, tenor, and alto, the subject appears * In the more advanced parts of a fugue the counter-subject is often used as may be convenient, without growing out of the immediately precedmg pnncipal subject Occasionally this is the case even in the exposition. ;j8 FUGUH. Once more in the bass, and the counter-subject is now in the treble in inverted relation to the subject : — Ex. 93. Haydn. .^^^j ..sJia.^ ^im^ iTyr^ ^ I Counter-subject. 72. A regular counter-subject must be written in double counterpoint — it may be at the octave, tenth, twelfth, or fifteenth, or, indeed, at any other interval ; but double counter- join t at the o ctave or fifteenth is mos^ used' airdlmost valuable."!]. 737 The counter- subject should be in good contrast with the principal subject and yet be consistent with it in character. It should be interesting in itself and adapted for the purpose of episode, either by sequential treatment or by free or canonic imitation. It will often oppose long notes in the subject with tOUNTER-SUBJECT. 39 florid figures of melody, or, on the other hand, employ sustained tones against more rapid notes in the leading subject. If rests occur in the subject they will but rarely happen at coincident points in the counter-subject (Ex. 94) : — Ex. 94 Mendelssohn. Counter-subject. U''r^'^^^^^^mf^^[:\ ^^ P Counter-subject. 74. Sometimes, as has been already indicated (par. 30), the counter- subject is not immediately contiguous to the principal subject, but is separated from it by the insertion of a few notes of coda between the end of the subject and the beginning of the counter-subject (Ex. 95 ; see also Ex. 24) :— 4° FUGUE. Ex.95, ■ Ma " \ jA^wJ i Usth ^^P Mendelssohn ^^Si W "* ^m ^m Counter-subject. Coda. Counter-subject. ^^^^ ^S ^ r 1 r 75. In the case of a tonal answer a slight modification of the counter-subject is sometimes necessary to adapt it to the original form of the subject. (See Ex. 92, 93.) 76. The exigences of fugal writing often cause the counter- subject to commence or terminate with considerable freedom. Bach's well-known fugue in E major (No. 9, vol. ii., of the Forty- eight) may serve as an example. The counter-subject com- mences on the last crotchet of the second bar. That this is the initial note of the counter-subject may be seen by reference to other parts of the fugue — as the alto in bar five : here the crotchet rest would be very unmeaning if we regarded the counter-subject as beginning with the full bar (Ex. 96a). (See page 91). Ex. g6a. ^ M gS ^ H^ ^a 22: m ■ P - Q ^ Counter-subject. ~mt » f P i COUNTER-SUBJECT. 4 S An altered commencement of the counter-subject may be noticed on its second appearance, in the tenor of bar four of the previous example, and another occurs at bar eleven (Ex. 966), where the middle portion of the counter-subject is plainly present, although its beginning and ending are both obscure. It should not escape observation that the fragment of the melody of the counter-subject employed is combined with the principal subject at a different point from that originally used : — Ex. 966. I s 32 m ^m m m ^ ^ Altered entry of counter-subject. * *i aqS3t m ^ ^ ^ Another illustration of a varied entry of the counter-subject is shown in Ex. 96c (bar thirty-eight of the same fugue). The first two notes of the tenor part of the extract would seem out of place and unnecessary, especially after the rests that have preceded them, unless regarded as belonging lo the Counter- subject : — 42 FUGUE Ex. 96c. I«l m ■^ 38 Z2= ^ Rtft t jrj r ■»— 1» -f-r^ SS ^^ Altered entry of counter-subject. ^ f P^ ^Hl^ -f 77. It occasionally happens in a fugue with regular counter- subject that it is not employed against every entry of the principal subject even in the exposition. The great six-part fugue from "Musikalische Opfer " (too long to quote here) is an example. The second, third, and fourth entries of the principal subjects are faithfully attended by the counter-subject, the order of parts being such as requires its use both above and below the leading theme; but the fifth and sixth appearances of the subject are without the counter-subject. This deviation from strict rule was doubtless made by Bach in the interest of variety. Some fugues have but a single subject, the counterpoint that stands in the place of the counter-subject being varied at each appearance of the subject during the exposition (Ex. 97) : — Ex. 97. J. S. Bach. S ^ ^ m tM^^^-^cT i ff^rfrfffl- l d' ^ l *'dU i K? E w COUNTER-SUBJECT. 43 ^^i^^^iS m 1^ *i ^/ m qpsp= ^ ¥^F=- ^ m K5J^^T-5rrrra?^->r tr rf -^CF w= /^ir' SI This counterpoint (Ex. 97) is exceedingly ingenious, but it is not a counter- subject. At bar four the treble is a repetition of the alto at bar two by contrary movement, but it will be seen that it falls against the subject at a different part of its course ; the treble again makes use of a similar figure of counterpoint, but differently combined against the subject in the bass (bars five and six), but we should look for a counter-subject to this entry in the tenor — the voice that last Bung the subject. Sometimes an incidental imitation of the first counterpoint may occur with- out establishing a regular counter- subject. In Ex. 98 compare the tenor of bars fifteen and sixteen with the bass of bais seven and eight. It will be seen there is not sufficient identity to constitute a counter-subject ; and, moreover, a real counter-subject would ordinarily, at this point, have been in the alto — the voice that has last passed through the subject : — Ex. 98. W. A. Mozart. f^ -m^ ^^ ^ i^rJ|Jf'ir|-r | i rtrl'^J^JJ l -i ^ ^ i ^^ ^ ^ ^ ^-J4JJj^iJ ^^;i- g^gg s^ Nj J ^lrfiMr Mrrrrrr! 44 FUBUB. The fugue in D major (No. 5, vol. ii., Bach's Forty-eight) is another im- portant example of fugue without counter-subject. Ex. 99. J. S. Bach. i ^^ ifcte ' ^ p f p ^ ^ fefr.i^JrT-TT3j J hJ^f4 ^ i ^ ^^ i^ s :£: ^^ ^^ ftfr^^=^ ^^ 78. Occasionally a new counter-subject is introduced towards the middle or close of a fugue ; but such a theme is usualljj employed with considerable freedom. COUNTER-SUBJECT. 45 79. Sometimes counter-subjects are introduced after the ex- position, even where no regular counter-subject has been used in that important section of the fugue. An example is furnished by the great Cf minor (No. 4, vol. i., Bach's Forty-eight) : the first thirty-four bars are made on the single subject (Ex. looa) :-^ Ex. looa. (Sl^k *'- In bar 35 the first counter-subject appears in combination with the original subject (Ex. 1006) : — Ex. 100b. Counter-subject. P^ ^ i«qtft! ^ 35 ^g ^ ^ ifl ^ i -r^ te: & and in bar 48 another counter-subject is introduced in combi- nation with the subject and the previojs counter-subject (Ex. looc): — Ex. looc i 48 j_ r r rT ^tfT I r_f_r r r r r New gs counter-subject^ Jt j*. ji ^J|J ^ 80. If the counter-subject is introduced against the subject, instead of against the answer (see pars. 15c and 69), the fugue is called a double fugue, or fugue on two subjects. In this case it is essential to preserve the identity of both subjects, as they are equally important. It is, however, quite allowable in the middle of the fugue to employ either subject alone, and frequently a separate stretto is made on each subject. Subjoined is a beautiful example of the beginning of a double fugue. The subjects are first combined in counterpoint at the octave (Ex. loia, 1016), and afterwards in counterpoint at the twelfth CEx. loic) : — Higgs— Fugue.— NoTsUo. D 46 FUGUE. Ex. loia W. A. Mozart. Ex. ic IC. — |— Inversion J 1 at the twelfth. Bf Tn 1 , M L J > 1 ^ ^•ife ■«! WW J^ •^ «W*5tW: -£J^^ [-« — ^ SUMMARY. COUNTER-SUBJECT. Twofold use of the term counter-subject : — > (a) Second subject of a double fugue, in the case where both subjects are announced at the beginning of the fugue ; ib) Counterpoint accompanying answer, in an ordinary fugue, n the last case the counter-subject is usually employed against the second, third, and subsequent appearance of the theme (whether as answer or subject) throughout the exposition. The counter-subject is usually supplied by the voice that has last passed through the subject. A regular counter-subject must be in some form of double counterpoint to be available for use above and below the principal subject. A result of the principal subject being led by a middle voice, in fugues of more than two parts, is that the counter-subject is used in a varied aspect, i.e., both above and below the principal subject COUNTER-SUBJECT. 47 in the course of the exposition. Occasionally a redundant entry of the principal subject secures the same advantage in the course of the exposition when the subject is announced in an extreme part (see par. 71). The counter-subject should be in good contrast with the prin- cipal subject and yet consistent with it. It should be interesting in itself and suitable for episode. The counter-subject is frequently separated from the subject by a codetta. ""The counter-subject in tonal fugue often receives a slight mod^f fication according as it may be employed against the subject or answer. The counter-subject is often approached and quitted .with free variation oi its initial and concluding notes. ^ __. Fugues are sometimes written without any regular and recur- ring counter-subject. In the course of a long fugue a new counter-subject is frequently introduced, but this is generally treated with more freedom than the original counter-subject. The counter-subject, or second subject, of a double fugue ia in all respects as important as its companion subject. CHAPTER V. EPISODE. 8i . The office of the episode, digression, or intermediate harmony (as this supplemental portion of a fugue is variously termed), is to afford some relief from the monotony that would result from a too incessant use of subject and counter-subject 82. The place of an episode is between the several sections into which the subject and answer naturally group themselves by reason of affinity of key, interval, and order of reply. It is by means of episodes that the modulations of a fugue are chiefly conducted. 83. Something akin to an episode is often found at the end of the answer and before the re-entry of the subject, that is to say, before the entry of the third voice. This codetta (which often proves the germ from which subsequently a real episode is developed) is usually a prolongation of the immediately pre« ceding melody. The codetta is seldom more than one or two bars in length, but by delaying for a few moments the re-appear- ance of the subject it adds zest to its entry. 84. The place of the first real episode is after the exposition (or sometimes after the counter-exposition, if that feature finds a place in the fugue) — that is, after the subject has passed at least once through each of the parts or voices. 85. In the formation of episodes care must be taken that they do not show themselves as parts disconnected from the rest of the fugue with which they should "be Taound. if not by identity of matter, by unity of style. They should connect themselves naturally both with that which has gone before and with that which follows ; and they should grow out of that which has pre- ceded, without abruptness or patchy effect, and lead naturally to that which succeeds. 86. In general, those episodes are best which owe their origin to some previous motive selected from the subject, counter-subject, or from a mere fiUing-up part. A thought thus suggested may be treated in many ways. It may be freely imitated in any interval ; it may be employed, if suitable, in canonic imitation at one of the strict intervals — octave, fifth, or fourth ; it may be prolonged by repetition in sequence ; it may be augmented or diminished ; it may be inverted, and after inversion subjected to any of the foregoing modes of treatment. 87. The fugue in C minor (No. 2, vol. i. of Bach's Forty-eight) EPISODE. 49 furnishes an excellent example of episode made on the essential matter of the fugue. The subject and answer are shown at Ex. 102a ; — i Ex. 102a. J. S. Bach. 'mrTrJrr^F r r rj ^ g ij,L^' ^B^f^^ ^^= U^f^.I^^ fiJ . .^ ir-^ "' 6av3g£^;Qf i^gf^'^gg A codetta — a fragment of the subject treated in sequence at Ex. 1026. This occurs at the end of the second and before the third entry of the theme : — Ex. I02&. The fragment above is next used as an episode ; it is employed in imitation, and enriched with a moving bass (See Ex. 102c.) Ex. loac. $ i!=3= & -p^ j J , ;; n J '=S ^ ^ ^m v-'h""'w L^-x^^Y ^ WjrfflTBw'^ffiggf^^^j I After another appearance of the subject the bass of 102c is employed by contrary movement and furnishes the treble of the next extract (Ex. i07.d) : — so FUGUE. Example io2« consists of three bars. The lirst bar and a half is the inversion at the twelfth of the original codetta (Ex. 102b), to which is added an upper part in interrupted thirds with the fragment of the original subject. The second half of this extract is a further inversion, now at the octave, of the immedi- ately preceding part : — ^ir rii/rrctf^^ ^ Ex. 102/ exhibits a modification of Ex. 102c, the bass of which is now differently combined with the imitating parts, and sequentially extended. The two last bars of this extract display a further variation in the form of the motivo : — "^^^w^^n Et>ISOD&. 51 In all the preceding examples it will be seen that unity has re- sulted from the employment of one idea, but great diversity has been secured by the varied methods of treatment; for while some portion of the leading idea has generally been present, yet the accessory accompaniments of that idea have become im- portant elements. Compare counterpoint of Ex. 1026 with loae and bass of 102c with 102^ and 102/. 88. Sometimes a single figure furnishes almost the entiie subject-matter of all the episodes in a fugue. Thus, in the fugue in D minor (No. 5, vol. i. of Bach's Forty-eight) the portion of the counter-subject inclosed in the bracket (part of bars four and five) does duty in almost every episode (Ex. 103a) : — Ex. i03«. J. S. Bach. The episode at Ex. 103& is made by sequence upon portion of the counter-subject indicated above : — Ex. 1036. ^ i ^ \IJ ^ \ i ^ M' '^gr r ' ^g^r ^ ^-rnr^ At Ex, 103c, see it employed by contrary movement against fragments of the first part of the subject also used in contrary motion : — Ex. 103c At Ex. lo^d another episode is presented. This is an inversion of Ex. 1036, but diversified by some remarkable contrary movement of the lower parts : — puauE. Ex. loid. I f r I ' "7 I V 1^ r T ^ Ex. 1036 shows an episodic incident drawn from the codetta of the subject. (See 103a at #.) This idea is employed in what may be termed unsymmetrical sequence : — Ex. i03«. i'drm^!^ 89. Bach's great organ fugue in D minor (No. 3, vol. iii., German edition) shows episodes of a highly artificial character. A short theme that first appears in the codetta at the end of the first answer, and is there imitated at the sixth above, is in the course of the fugue employed by imitation in all kinds of intervals and at different distances of time. This variety of place and moment of attack imparts uncommon and ever fresh interest to this masterly and beautiful composition. The subject and answer are sho^n at Ex. 104^ ; — Ex. 104a. J. S. Bach. P m ^ w=^ f r^^^f fT i r r r-r i ^u ■^i=A rlr G-ICJIiciIl'Icrd'c' l -^^-P^ The codetta that follows consists of a theme tor imitation led EPISODE. 53 by the aito in bar 15 and answered by the treble in the sixth above, at the distance of half a bar: — Ex. 1046 15 ^ ^^^-rJJ2 J* lie'- ^ ■ U'' rl^i W^ This is inverted in bar 26, where the imitation appeals a third below. (See 104c.) Ex. 104c ^m ^^ ^ ^s 26 m m=^ It should be observed that only the imitating parts are here shown ; but gene- rally these are accompanied by a part or parts necessary to justify the harmony. An imitation a fifth aoove. at the distance of a whole bar: — Ex. 104^. m 36 r^ I * ^ti ijat f^^ r-irrJir rjir j-^u^^jj An imitation a second above, at the distance of a minim : — Ex. 104^ 78 e> • j^H-1- %.i° '■ ^ s 54 FlIGUB. An imitation a fourth below, at the distance of a minim :- Ex. 104/. m T ^^ ^^ ^ 88 iS !-#• i=5 f^W ^=5=^ m 3^ An imitation a seventh below, at the distance of a minim : — Ex. 104^. |~M' rrlr Ji'lr^-'J^ 95 :^ ^m s fc ^ ^ An imitation a fifth below, at the distance of a minim ; and an eighth below, at the distance of a whole bar : — Ex. i04/>. i 32e: S ^ ^ 67 1^ S S J^ i J i.r i ^^=F =3 An imitation a fifth above, at the distance of a minim ; and an eighth above, at the distance of a whole bar : — Ex. 104/. i g^ £===: 125 feMf r^ ry i r J 'Y^^r^'^j i^J- » ^nrriyru i ^f-- "^i ^ j <^ ^ > tg J EPISODE. 55 An imitation an eleventh below, at the distance of a minim ; and a fourth below, at the distance of a whole bar :— An imitation a fourth below, at the distance of a minim ; and a third and a fifth above, at the distance of a whole bar: — Ex. 104Z. i £rr J ^ IfeM^ r'rlr J'r -n^TJ-'-^- ^^- [p[M '^■UM^ ^ All the foregoing imitations are introduced episodically in reliei to the fugal working of the principal subject and its counter- subject. 90. Occasionally an idea entirely foreign to the principal theme is chosen for an episode. Bach's organ fugue in E minor is an example of this : — Ex. 105a J. S. Bach. r'lj i fjijgi'J' i J'iU Tu'^^j n .1 ^ 56 FUGUE. J. S. Bach ^^riUr^!5Wr^^;w^ r. v@*p% ^-g^ ' P^" ^ Q^ ' n ry Here Bach does not treat the new idea on which the episode is founded (Ex. 1056) with any kind of contrapuntal device, though he maintains the consistency of the whole work by interweaving the leading theme (without fugal imitation) with the new episodical idea. 91. Haydn, in the fugue at the end of his " Stabat Mater," introduces as an episode solo passages of almost bravura cha- racter; and the final chorus of the "Creation," "Sing the Lord," may be referred to as a more familiar example of similar treat- ment. 92. In choral music a fugue is frequently preceded by intro- ductory matter, and the subject of such introduction may furnish episodical ideas of great interest. In Handel's well-known chorus, " But as for his people," the characteristic pastoral phrase that occurs in the beginning of the chorus is introduced as an episode in the midst of the working of the fugal portion of " He brought them out." 93. Yet another mode of forming an episode may be illustrated by reference to No. 2 of the " Six Fugues on Bach's Name," by Schumann. The subject is : — Ex. 106a. Schumann, EPISODE. 57 This he employs as an episode (to borrow an expression of recent musical application) by metamorphose of the initial notes of the subject : — Ex. 106&. Schumann. I > HhH I-" f f J^K _-• ** 1^" J nJ I ^ |J 1^^ I ^ i ^ y ^ ^'' ^1'' I '^' \i h m r i ^r r ^ 94. It is perhaps not too much to say that it is in the episode of the fugue more than any other part that its composer shows his individuality. Just as in the free fantasia, or development, of the " sonata form," the composer, released from prescribed method and rule, is able to give unbnaiea rein to his genius, so in episode an opportunity is afforded for the exhibition of what- ever is characteristic of its author. Here the habits of his mind, and the idiosyncrasy of his taste and genius, can assert themselves without offending against precepts and laws of binding authority. 95. School fugues of pedantic strictness (ricercata) may be written without episode of any kind. They may show the learning of their author and his mastery of-the art of combination, but they will rarely touch the affection or kindle the emotion of their hearers. SUMMARY, EPISODE. Episode : Intermediate matter introduced as a contrast and relief to the more essential parts of the fugue. Frequently the means of modulation. 58 FUGUE. Often the development of a germ found in the codetta. Place of the first episode after the exposition or counter-expo- sition. The best episodes are those formed on some motive previously employed in the fugue. Variety of matter or treatment, or both, essential in the several episodes of a fugue. Free Episodes : Introduction of foreign themes. Individuality of composer often shown in his episode. CHAPTER VI. STRETTO. g6. Stretto, from stringere, to draw close, is the name applied to the approximation of the subject and answer at a shortened interval of time. The entry of the reply earlier than the ante- cedent usage of the particular fugue leads the mind to expect it, quickens the attention of the hearer, and greatly adds to the inte- rest of the composition. 97. In an elaborate fugue there will generally be at least two of these approximations (of subject and answer), the latest of which should be the most ingenious and probably the closest. Stretto should be prepared for in the selection or composition of a fugue subject. The suitability of a subject for combination at various intervals, and at several distances of time, should be regarded from the outset. A good stretto does not come by chance, but will reward patient study and diligent search. 98. Stretto, by direct motion, is most satisfactory when it replies in the regular interval of the fugue — upper fifth or lower fourth — but it is quite allowable to lead with the answer and respond with the subject ; the response is then on the fourth above or the fifth below. Response by the octave is also frequently employed in obtaining varied approximations of subject and answer, and, indeed, replies by any interval aie allowed, but order and method should characterise the relation- ship of the several replies within the same section or group of attacks. If a reply has been made at the seventh, another reply in the second below, that is, in the inversion of the seventh, will be unobjectionable ; but to follow a reply at the seventh with another at the sixth, or third, would be somewhat incongruous. An enumeration of some of the devices by which stretto may be obtained will be useful. 99. The reply may be at the upper fifth or under fourth ; the upper fourth or under fifth (this is the case when the answer leads) ; or at the octave above or below. The imitation may be at any other interval, but the above are the best. 100. In a tonal fugue, either form, subject or answer, may be taken for canonic imitation. loi. Any of the above devices may be employed by augmen- tation or diminution, or the reply maybe by contrary rnovements, either in notes of the same value as the subject or in notes of augmented or diminished value. 102. Accents may be reversed if needful. 6o FUGUE, 103. If the subject fail to yield good strettos by some of the foregoing methods, it may, as a last resource, be slightly altered. This is frequently done with considerable freedom at any point beyond the second entry of the theme. 104. All the voices should at one time or another engage in the stretto. It frequently happens in a stretto employing all the voices together that the bass voice maintains the dominant pedal on which the closest stretto is built ; more rarely the tonic pedal is used in a similar manner. The following collection of strettos will, it is hoped, furnish the student with ample models for imitation. 105. Ex. 107 is from Richter :* (a) shows a subject designed for stretto ; (6) the same subject with the entry of the answer at full distance ; (c) with reply at fourth above at the distance of two bars ; (d) reply at fifth above at the distance of a bar and a half, the accents being reversed ; (e) at the fifth above at the distance of one bar ; (/) shows the answer of b leading, the reply being at the original distance but a fifth below instead of a fifth above ; {g) is an inversion of c; and [h) of e; {j) shows the use of the subject at two bars distance in the octave ; and (k) another variation in the employment of the octave at the distance of a bar and a half with reversed accents : — Ex. 107. (a) Richter. ^3 ^ ^ "Cr i ib) \^ beJ 1=^ (c) i i feei r ^rW ru r f-f i^ f^ f^ I (i) ^ ^M ZZ±i r^rVf^'i^^rr rf :^ 2se: (*) M^juj s T7~ 3s:= ~g3~ rr 'f" ^-j>r^f : L^r r rr ' From " Lehrbuch det Fugue." E. F Ricbter. 1874. Leipzig : Breitkopf and Hartel. "^ STRETTO. 6l (/) Compare with b tf ' 1 Hi 1-— f^ ' P ?(S> '-p . - |rv i p , ^ (g) Compare with c ^b ^> [fclJg 4^P^ ^ SE ^ r^ (A) Compare with e J bJ I J ^J icTT. (ft) ^i^ J | ci- J 3e: =^ io6. The next e^iample is from the fugue in Bb minor (No 22, vol. i., of Bach's " Forty-eight Preludes and Fugues "). It is at equal distance of time throughout, and at the ordinary interval ol reply, dominant responding to tonic in each case. The first, third, and fifth voices have the subject in exact form ; the second and fourth are slightly varied after the point where the succeeding voice enters : — Ex. 108. J. S. Bach. i St m m ^ ^^^ - IJ , i rr^tiJl^iiJ^rl^ ^ ^ ^m ^^ - r J ^^ ^ ^ 107. The following example is from Haydn. It is formed on a dominant pedal ; the stretto is led by the answer, the subject Higga— Fugue— Novello. B 62 FUGUE. responding. The consecutive fifths are not intended for the stu- dent's imitation, but may possibly show that Haydn regarded the integrity of his imitation as in some cases more important than a pedantic observance of the rule that forbids such progressions : — Ex 109. (a) Subject. Haydn. i t ^ ^ w ~r?~ i (6) First stretto at two bars. rz: J I J. J , . -zy- r f ' r' r (c) Second stretto at one bar on dominant pedal. J J , A -. J. rr"tf^ -ry- 108. In the formation of a stretto the subject is often taken by inverse movement. Ex. no: (a) shows the subject of the A minor fugue, No 20, vol. i., of Bach's "Forty-eight Preludes and Fugues ;" (b) shows the same subject by inverse movement with imitation at the fifth below at the distance of half a bar ; (c) shows the subject in direct movement with imitation in the octave at the distance of half a bar ; (d) shows these imitations combined on a pedale ; the inverse form of the subject being now imitated at the octave, while the direct form is imitated at the fourth below. Although a four- voice fugue, the imitation of the stretto (built on a pedale) is in itself in four parts. The pedale may be re- garded as an added part, and is an example of the employment of a ionic pedale, on which the subject is combined in the harmonies of a plagal (subdominant) cadence : — Ex. iioa. _ Bach. ^ ^ 1 . r i I r i I I '-Pf Ex. 110&. ^^^^^^m STRETTO. 63 Ex. HOC. i-ii£!^[liJ \ ^ - wf^nf Ex. nod. $ h^^^i^P£, ^ ^n^rjm jD CJ im &iz P^ ^ fifirrr'^.^.^:^^ 4 -^ M zz: ^ 109. The extract (Ex. iii) from Mozart's fugue in G minor (original form a piano duet) also shows the employment ol inverse movement. At a the imitation is At the distance of one bar, while at b the imitation is at the distance of a bar and a half, but the imitation is more exact at b than at a, and thus the interest of the composition is maintained : — ijx. III*. W. A. Mozart. 64 FUGUE. m 'yr V I' r ^ J. » ' ' s I f" ^ ^'^- ■■•^'^ Ex. I lib. m fc =d= ^- /3i^/^-i .j.Ji , ^^- ,.rr:^^J -^:3- ^5^ i^ ^^^^^ ^^r^^p^^ .c^ no. The next example, also by Mozart, shows the employmeni of augmentation in stretto : — Ex. uza. Subject. W. A. MosART. ^^^Hr i rT W rn ^ Ex. 1 1 26. rr^ STRETTO. 65 III. Example iiac, from J. S. Bach, displays augmentation in combination with inverse movement : — J. S. Bach. rvTioj-^ , /^.^g^ iTr^ ^m mi a Ex. ii2d and ii2e are other extracts from the same fugue, displaying close approximations : — Ex. iizd. ^^^ ro , ^ \ J f. Ex. ixze. iL., 1 ;h.fTJ1 .^j^ i j-j^j?m '^ ^ ^ a -•- '> 1 m r r - m^ r J^.P ^jl^-r:' S^ i i T-,^ is I I "^ - ^ ^1;=^ t 112. Ex. 113 is from another of J. S. Bach's fugues; Ex. 113a shows the original subject: — J. S. Bach. Ex. 113a. ' rti 7n~J- ^ J j I ri J I J I Jj I ! 66 FUGUE. Ex. 113& shows a stretto by augmentation. It will be ob served that the first half of the augmented form of the subject is combined with the original form, while the inverse form of the subject is used upon the latter half of the augmented subject. This is inverted by counterpoint at the twelfth. The commence ment of the inversion is shown : — Ex. 113b. j i >a ^nm-^- M ^''"V^rii^jry? r r iTr'r Counterpoint at twelfth ^m ^ fe^^ fcp m -E3- J.. 1 l b/:: I ^ j-j-: b J ^m ^^ r^rr ffi ^ J^Jr^-S2^;3^_-^_ ;sj />J^^— ^ ^ Inversion at twelfth A 4O ^m It eS^^^^^ ^^ ^^ : gg-.;^iL ^ &c. g^i' i W '^^ m 113. Ex. 114 is from Mozart's " Davidde Penitenle;" it shows the employment of the subject in stretto at 1 146 and 114c, at the distance of one bar at the fourth below and at the fifth above; Ex, 114^/ and 114* show the imitation at the distance of two STRETTO. 67 tars at the octave in direct movement; at 114/ the subject iji used in inverse movement; Jti4^is a fragment of close stretto: — Ex. ii4«. W. A. Mozart s ^^ ~p~ T7~ i Ex. 114&. 321 =gz= =^ ro: - T7~ ~g7~ T5~ Ex. 114c. s^ ~7J~ •yj- ^ icz: ~nr m Ex. 114/^. ini ~n~ i Ex. 1 14/. •TJ~ CO; - Q Ex. 114/. o I " •T3- ^ 68 FUGUE. Ex. Il4g i ::j3: -^^ -rr- W^f> 1 1^; T ¥ n ^ r 114. Ex. 115, from Bach, shows the employment of imitation at the less regular intervals. 115a displays the subject; 115^ and 115c show the imitation at the seventh above and second below ; at ii^d and 1156 the subject by inverse movement is imitated by the second above and by the seventh below; at 115/ the subject by inverse movement is imitated by contrary movement, resulting in the original form of the subject ; at 115^" the original form is imitated. by contrary movement; at 115/fthe form of 115^, but altered as regards position and interval of reply, is enriched by the addition of thirds (or their inversions, sixths), and formed into a quadruple counterpoint : — Ex. 115a. J. S. Bach. ^m y j i J^j-^j- i jjD^jjj^ H o n ^ ^^ Ex. 1 156. ^^^^^^^^^^^^^^ ^m ^ £i- ^ i f rr rfrffEfff i m Ex. 115c. ;f^^r I' r Ff i rfrrC:[rtiirr . - -J J J Ir J g ^ #' * < ^ Ex. 115/ cEi rrrri ^ f^ I r r HlfffM Ex. iisff. /I i? ue 1? ^ =-1 h 1 HT TT- re*):, |> to F~^~F fg-j- -^-H, p , * I* , I* 1* - V ^-'b'>1, -^j ^^':^ "^ t-iii-^ ^ ^ z^^^^^^zz Ex. 115A. irnifmfWr\ 115. In paragraph 103 attention was called to the- frequent alteration of the subject in stretto at a point beyond the second 70 FUGUE. entry of the theme ; Ex. 1 16 will illustrate this. The original treatment of the subject is shown in Ex, 93. (See also Ex. 117-) Haydn. Ex.116. , J ; g J I J. > ^ ^ P^ r r Ln ^^7^^ ^ ^ ^ig ^g ^ SUMMARY. STRETTO, Stretto, from stringere, to draw close. The narrowing of the interval (of time) between subject and answer. Two or more such approximations, of increasing interest, are common in im- portant fugues. Preparation for stretto to be made in designing the subject. Stretto most satisfactory when in the regular interval of the fugue {i.e., fifth above). Answer may lead and subject reply (i.e., fifth belowr). Answer in the octave always allowed. Answer may be made in any of the less common intervals of reply. The subject, answer, or both, may be used by augmentation, diminution, or contrary movement. Accents may be reversed. The subject may, if unavoidable, be slightly altered to fit it for stretto. All the parts should engage in the stretto. Stretto often made on " pedal." CHAPTER VII. ORDER OF REPLY — MODULATION — PEDAL. ii6. As the order of reply is a point of some importance, it k necessary to devote a little space to the consideration of the entries of the several voices or parts ; first in the exposition and afterwards in the remaining portion of the fugue. Order of entry in the Exposition. 1 17. In general the order of subject and answer in the exposition is alternate, the odd voices of the fugue (first, third, and fifth) singing the subject, and the even voices (second, fourth, and sixth] singing the answer. 118. The voices of the ordinary quartett — bass, tenor, alto, and scprano — may be conveniently regarded as two couples or pairs of voices, bass and alto forming one pair, and tenor and soprano forming the other pair; each member of a pair being of corresponding range with its companion, but differing from it by an octave in actual pitch. The subject being announced by any voice will usually be answered by one of the voices of the other pair. The close order of the parts is almost invariably observed, and each new entry is in general made by a part outside {i.e., above or below) those already engaged. This arrange- ment insures a certain prominence for the newly entering part. iig. When the subject is assigned to an extreme part (bass or soprano), the other voices may commonly be expected to appear in regular ascending or descending order as — I. S. 3- 4- B. T. A. S. OR S. A. T. B. "120. When the subject is first led by one pf the middle parts the other voices are added above and below, the close order being observed; of course, the final entry will be made by an outside part. I. 2. 3- A- T. A. s. B. T. A. B, S. A. T. S. B. A. T. B. S. 121. It should be noticed that when the subject is led by one of the middle parts an opportunity is afforded for the use of the counter-subject in its twofold relation, i.e., both above and below 72 FUGUE. the subject. When the subject is assigned to an extreme part, and the other voices enter in regular ascending or descending order, the counter-subject of necessity retains one fixed relation to the subject throughout the expositioa 122. Subjoined is a table of the first entries of the several voices in the whole -of the forty-eight fugues in " Das wohltemperirte Clavier," by J. S. Bach. The three-voice fugues are for conve- nience described as for soprano, alto, and bass, quite irrespective of the compass of the several voices. Table showing the order of entry of the several voices in the whole of the Fugues contained in " Das wohltemperirte Clavier" J. S. Bach. (Note. — In this table B. stands for bass, T. for tenor, A. for alto, and S. fov soprano. Thick letters indicate the subject and italics the answer. VOL I. VOL. II. No. I. C major ... A. 5. T. B, (i)... A. S. B. „ 2. C minor ... A. S. B. ... A. S. T. B. „ 3. C# major ... S. A. B. ... B. S. A. (3) (4) „ 4. CJ minor ... B. T. A. S\ S'. ... B. S. A. (3) „ 5. D major ... B. T. A. S. ... T. A. S. B. „ 6. D minor ... S. A. B, ... A. S. B. „ 7. Eb major ... S. A. B. ... B. T. A. S „ 8. E!7 minor ... A. S. B. S. A. B. „ 9. E major - A. S. B. B. T. A. S. „ 10. E minor ... S. B. ... S. A. B. „ II. F major ... A. S. B. ... S. A. B. „ 12. F minor ... T. A. B. 8.(2)... S. A. B. „ 13. Fjf major ... S. A. B. ... A. S. B. „ 14. fJ minor ... T. A. B. 8.(2)... A. S. B. „ 15. G major ... S. A. B. ... S. A. B, „ 16. G minor ... A. S. B. T. (3)... T. A. S. B. „ 17. A'? major ... T. B. S. ^.(3) .. A. S. T. B. „ 18. GiJ minor ... T. A. S. B. ... S. A. B. „ 19. A major ... S. A. B. ... B. A. S. „ 20. A minor ... A. S. B. T. (3)... B. A. S. „ 21. Bb major ... S. A. B. ... A. S. B. „ 22. Bb minor ... S'. S». A. T. B. ... A. S. B. T. (3) „ 23. B major ... T. A. S. B. ... B. T. A. S. ,, 24. B minor ... ^ A. T. B. S. ... A. S. B. (i) Notice the order — subject, answer, answer, subject. ^2) The order is — subject, answer, subject, subject. (3) These fugues do not employ subject and answer in close order, but end with a middle part. (4) In this fugue the third voice (alto) employs the subject by reversed motion. ORDER OF REPLY — MODULATION PEDAL. 73 Summary of Table of Entries '• S. B. (i) 10, vol, I. li. B. S. A. (2) ... ... 3, 4, vol. ii. 111. A. S. B. (lo) 2, 8, 9, II, vol. I. 1,6,13,14,21,24, vol. ii. iv. S. A. B. (14) 3, 6. 7, 13, 15, 19, 8, 10, II, 12, 15, 18, 21, 24, vol, i. vol. ii. V. B. A. S. (2) ... ... 19, 20, vol. ii. B. T. A. S. (4) 5, vol. i. 7, g, 23, vol. ii, T. A. S. B, ^4) 18, 23, vol. i. 5, 16, vol. ii. VI vii. viii. A. S. T. B. (3) i, vol. i. 2, 17, vol. ii. ix. T. A. B. S. (2^ 12, 14, vol. i. A. S. B. T, (3) 16, 20, vol. i. 22, vol. ii. xi. T. B. S. A. (i) 17, vol. i. xu. B. T. A. S». S'. (i) 4, vol. i. xiii. S^ S^ A. T. B. (i) 22, vol. 1. 123. By an inspection of the above it will be seen that Bach makes the closing entry of his exposition by an outer part forty- two times out of forty-eight ; closing the exposition by the bass in thirty-two fugues and by the soprano in ten fuguesl He announces the subject by a middle part in twenty-four cases, by the soprano in fifteen, and by the bass in nine. Other useful deductions may be drawn from the table by the student. Order of entries after the Exposition. 124. Definite order of reply, and the relation generally of sub- ject and answer, are not as stringently observed in the subsequent parts of a fugue as in the exposition. Often subject is followed by subject, and answer by answer; not unfrequently the answer leads and the subject responds, and even disconnected appear- ances of the theme occur. There are, however, some rules or maxims of a general character which it is desirable to observe. 125. The same exact order of entry should not occur in two immediately successive groups of entries. It is, however, possible to find examples of authority where this rule is not observed, but in such rare cases some new aspect of counter-subject or other incident producing variety of effect may usually be discovered that vill more than justify the deviation from general rule. See B major fugue, vol. ii., Bach s " Forty-eight." 126. The voice that has just concluded a group of entries with subject or answer should not begin the next group of attacks, and the theme should not appear twice in succession in the same part. This rule is necessarily relaxed however, at least in two-part fugue, as otherwise the subject and answer would each be confined to the voice in which it first appeared. 127. ICach new entry of subject or answer should be made prominent ; to this end the reappearance of the theme is rnosi 74 FUGUE. often preceded by a rest, or, if the subject is approached by skip, the same end, prominence, is to some extent attained. 128. Modulation in fugal music is generally confined within the somewhat narrow limits of relative keys. It is, as has been already said (par. 82), effected chiefly by means of episode, but sometimes it is accomplished by the employment of the answer in some unusual interval, or by a new harmonisation of subject or answer. 129. Cherubini and, after him, other authorities have given the following as the best course of modulation for a fugue in a major key: — 1st. To the dominant [major] ; 2nd. ,, sixth [relative minor of principal key]; 3rd. ,, sub-dominant [major]; 4th. ,, second [minor of sub-dominant] ; 5th. ,, mediant [minor of dominant] ; 6th. ,, dominant [major]; 7th. ,, principal key. The change to the minor mode of the tonic is also good if em- ployed briefly, and if it leads to a suspension on the dominant as preparatory to the final attack of the principal key. The order prescribed as best for a fugue in a minor key is: — ist. To the mediant [major]; 2nd. ,, dominant [minor] ; 3rd. ., sixth [major]; 4th. ,, sub-dominant [minor] ; 5th. ,, seventh [major] ; 6th. ,, principal key [minor or major]. 130. Sir F. A. Gore Ouseley remarks on the above order ol keys: "These modulations are not strictly obligatory ; nor need they be always followed exactly in the order just laid down ; but as a general rule this order will be found convenient and effective." 131. It may be well to draw attention to the fact that in addition to the more definite modulations made from time to time in the course of a fugue, there is, wherever subject and answer are used in adjacent keys, a continual subsidiary oscillation as it were between two nearly related keys ; for example, in the exposition of a fugue we pass in and out of the keys of the tonic and dominant. 132. This natural changefulness of key is a consideration not without weight, especially in that section of a fugue in which the dominant becomes for the time the principal key; for if we were to reply to the subject, when led by the dominant, by its fifth, according to usual fugal habit, we should be led into the dominant of the dominant, a key too remote for a satisfactory modulation. The difficulty however is avoided by making the dominant section the inversion or counter-txposition of the fugue ORDER OF REPLY— MODULATION — PEDAL. 75 The answer led as subject in the dominant is replied to by the subject usad as answer in the key of the tonic. 133. The naturally related keys for a composition in C majoi may be shown thus : — C, F, G major a, d, e minor Of these the following admit of employment for fugal purposes when the answer is in the upper fifth : — Subject. Answer. C — G C — G 1 F — C } "'^J°'' a — e , d - a ^'"'"°' But the dominant G major (in the supposed key of C major) and its relative e minor cannot be responded to in keys of their uppei fifths without transgressing the limits of naturally related keys. 134. This inter-relation of keys is especially noticeable in the expositions of fugues in minor keys. The writer of the article "Fugue" in the "Dictionary of Musical Terms"* calls attention to the difficulty of connecting two minor scales a fifth apart, and says: " It takes some little time to accustom the ear to the sound of the minor third of the new key, but the leading note of the old key must of necessity be discarded before the re-entry of the subject." This frequently involves more formal modulation than is common at the corresponding point in a fugue in a major key, and the modulation to the minor key of the dominant obtains a prominence not usual in music, other than fugue, where the first modulation in accordance with the plan prescribed above (even for fugue) is into the key of the relative major. 135. The nature of the subject, and the number of the parts in which the fugue is written, are considerations thaft have a direct bearing on the modulations just alluded to ; for if a subject begin and end in the key of the tonic, and be treated in three parts, it is evident the exposition will close in the key of the tonic ; but a subject that closes in the dominant, being treated in three parts, the exposition will close in the dominant. Conversely, .if a subject that ends on the tonic be treated in four or any even number of parts, the exposition will tend to close in the dominant 136. The pedal is a device often introduced near the end ol a fugue ; it consists of a holding note (dominant or tonic), often sustained through several bars ; on this the closest stretto of the fugue is frequently built. The dominant pedal is most often used. When both tonic and dominant pedals are employed the dominant pedal precedes the tonic pedal. 137. The ordinary rules for the use of a pedal hold good in • "Dictionary of Musical Terms," by J. Stainer, M.A., Mus. Doc, and W A. Barrett, Mus. Bac. Novello and Co., Ltd. London. 76 FUGUE. fugue. The pedal generally commences and always closes on au essential note of the harmony. The part next above the pedal must be as carefully written as if it were the real bass, especially in those cases where the pedal does not form an essential note of the harmony. Inverted pedals are occasionally used in fugues as in other compositions. For an example of dominant pedal on which a stretto is made, see Ex. 109. For an example of tonic pedal, see Ex. nod; and examples of both dominant and tonic pedals may be seen in the C( minor fugue by Bach, printed at the end of this book. The example below is a most masterly stretto on a dominant pedal : — Ex. 117. Subject. Gounod. Et ip -se re- di-met Is - ra - el, . Stretto OH the pedal point. \F^=F ij—^ -4= 1 , M= ^ ^ -'--r- =^=*T -U' 1— -i — -1 — -f=? =Tf =^ ^ =* ^ Jj ^ M- -^-. 44^ 'i^ ^Me L- =^ ->r^ CHAPTER VIII. THE CONSTRUCTION OF FUGUE AS A WHOLE. 138. The several parts of a fugue — subject, answer, counter- subject, episode, and stretto — having been considered in detail, and the order of reply, modulation, and the pedal having received attention, it only remains to offer a few hints on the construction of a fugue as a whole. The analytical charts of several important fugues found at the end of this chapter will, it is hoped, supply much valuable information by exhibiting in a succinct form the order, relation, and proportion of subject, answer, counter-subject, and episode, displaying as they do at the same time the course of the modulations and the variety and closeness of the strettos employed. The earnest student will find great advantage in making similar charts of as many fugal masterpieces as possible. 139. In the actual practice of fugue-writing it will be desirable to .begin with two-part fugue, and to pass gradually through three, four, and five-part composition ; this practice will lead to a methodical manipulation of the parts. 140. It will be well for the student before attempting more, to obtain some readiness in quickly seizing the right answer to a subject of fugue, and to try by mere inspection (without writing) to discover the stretto-like combinations of which a subject may be possible. The necessary mental effort for this will be profitable. Of course, the result should be recorded and pre- served. The next step should be to invent counter-subjects to suitable, invented or selected, principal subjects, trying to invent several counter-subjects to each principal subject. These counter- subjects should be thought out as completely as possible before being committed to paper. They should be in double counter- point. 141. With some of the material already invented the student may begin to write expositions of fugues in two, three, and four voices (see pars. 8 and 155). He will gain much mastery of contra- puntal resource if he is content to use one subject and counter- subject foj a considerable number of expositions first in two parts. (a) B. S. (b) S. B. Next in three parts — Higgn— Fugue.— NoTello. V (C) B. A. S. (d) A. B. S. (e) A. S. B. (/) S. .4. B. 78 FUOUB. And afterwards in four parts — (g) B. r. A. s. (A) S. A. T. B. (/) A. T. S. B. (k) T. A. B. S. 142. This exhaustive method of study will teach the vast im- portance of securing a thoroughly satisfactory and workable suiyect and counter-subject. Care must be taken that the free part or parts shall be consistent with the more essential subjects, and yet that they shall possess individuality of melody and motion. These free parts may and should differ in each of the several examples. 143. Practical acquaintance will necessarily be made with the different closes the exposition will induce, according as the sub- ject is worked in three or in four parts. 144. The next study will be episode. Each of the expositions will furnish several ideas which should be developed in turn in various ways. It is probable they will not all prove of equal value for actual incorporation into a fugue, but the young com- poser will gain aptitude in selecting and facility in treating such accessory themes, and he will to some extent realise how vast are the resources at his disposal. 145. The next separate study should be stretto. It is assumed that the suitability of the theme for stretto has already engaged attention in the study of the subject. It will now only remain to carry out those combinations which have already been foreseen as possible. It will prove a valuable plan to examine the subjects of good fugues and to discover and anticipate the use they are capable of in stretto, and afterwards compare such anticipations with the actual work of the composer. 146. After the several essential parts of a fugue have been thus studied in detail, the construction of an entire fugue may be taken in hand. Perhaps it may be well to take one of the subjects that has alread}' engaged attention, and, selecting from existing matter, it will be an easy task to combine the several parts on some well- considered and natural plan of modulation. The middle group or groups of subject and answer will, it may be assumed, cost but Httle fresh trouble. The plan of this first complete fugue may stand thus : exposition, episode, middle group, episode, stretto. Probably the fugue thus made will prove but a mechanical compo- sition ; still, whoever patiently works in the manner prescribed will gain great insight into fugal structure and considerable mastery over the art of restricted combination ; but the student must not mistake the means for the end, or think that, being able to ana- lyse a composition or to reproduce resemblances of its several parts or even an imitation of the whole, he is necessarily pos- sessed of the power to produce a true and worthy work of art- THE CONSTRUCTION OF FUGUE AS A WHOLE. 79 The few remaining hints are chiefly recapitulations of points aheady noticed. 147. It may be useful to give a word of caution against select- ing a theme of doubtful tonality as a fugue-subject. A good subject will at once suggest (to the initiated) the proper answer, and whenever it requires elaborate reasoning to justify an answer it may generally be concluded the subject is not a good one for fugal purposes. 148. In every fresh group of subject and answer some new aspect of order or combination should obtain. No two sections of a fugue should be identical. 149. The composer should have a definite idea of the length to which his composition will extend, so that the several parts shall bear a just proportion to each other and to the whole. 150. In the plan of modulation it will be better to err on the side of restriction than to indulge in a freedom that is to a great extent alien to the essential character of fugue. 151. After a part has rested for a bar or longer it should re- enter either by proposing or answering a point of imitation. 152. The subject or answer will enter with most point and prominence in the course of a fugue if it is immediately preceded by a rest in the voice to which the entry is assigned. If this is not practicable, it is desirable to approach the leading or imitating melody by skip. 153. The episodes of a fugue should be founded on different ideas, but if the same idea is employed for two episodes it must be diversely treated. 154. The interest of a fugue, both from a harmonic and constructional point of view, should grow as the composition advances ; skill in treating the stretto and the "pedal" (dominant or dominant and tonic) is very important as contributing to this end. 155. The maintenance of continuity is an important element in any fugal composition. Frequent cadences are to be avoided ; indeed, it may almost be laid down as a rule that perfect cadences should only occur at the close of the entire composition, or at the end of the most important modulations ; and in the latter case they generally serve as the basis from which a new attack of the subject springs (see par. 14.) In many fugues the chief stretto is preceded by a half-cadence leading to a pause on the dominant. Albrechtsberger notices the frequent use of a deceptive cadence — really a cadence avoided (he calls it the inganno cadence) — at a particular point in the exposition, viz., as preceding the intro- duction of the third voice, i.e., the second entry of the subject Illustrations of this remark may be seen at Ex. 93, bar 8 and Ex. 96, bar 3. 8o FUGUE. The following fugues, printed in open score, and accompanied by analytical charts, will repay careful study : — No. I. Fugue (two-voice), E minor, No. lo, vol. i., " Das wohl- temperirte Clavier," J. S. Bach. „ 2. Fugue (three-voice), F major, No. ii, vol. i., " Das wohl- temperirte Clavier," J. S. Bach. „ 3. Choral Fugue (four-voice), B? major, from Marpurg's " Fugen Sammlung," J. P. Kirnberger. „ 4. Fugue (four-voice), G minor. No. 16, vol. ii., " Das wohl- temperirte Clavier," J. S. Bach. „ 5. Fugue (four-voice), Bb minor, No. 22, vol. ii., " Das wohl- temperirte Clavier," J. S. Bach. „ 6. Fugue (five-voice), C}f minor. No. 4, vol. i., " Das wphl- temperirte Clavier," J. S. Bach. The bars are numbered throughout, but the pages of the musical examples have been kept clear from all other indications of reference except in the last fugue, where the several subjects are shown in the usual manner. Fi^GUE, E Minor, No. 10, Vol. 1., " Das wohltemperirtb Clavier." No. I. ^ J. S. Bach. THE CONSTRUCTION OF FUGUE AS A WHOLE. 8l m^^ ^ ■_ \^--u.m^ -W-5 fmm. . 1 - Prf |W» Tvr-'i'* •J pep ■. r^.... c^ = t* J — « — ^ Lj.l r r^ ^ — PS-, _| T»*-^ — RgJ Ja&s- — ^ — ri ^ 1 16 ^Q»JJ •^"'^ i-ab 18 N^L!a^ff)^rr£gpJtF:. O "^ •' Lf^ [jr^^^irrrf^ ^*"^ * '-^'^ asa as:u F^ * r r »*j -r^rf F=^ffi ffi ifrfTto ^v^ ^ 81 ■Ui^ ^=S=^ J 1 1 1 ^p^:^ ?=^ #4^ - . > ^r 83 n»-^ — zzT pi= i II- ' ^rrn ri-iii. i i " , i , i |. , , , , , ^^ fc^'^ 8a FUGUE. Fugue, in F Major, No. ii. Vol. i., "Das wohltemperirte Clavier," No. 2. J. S, Bach. (if)bii 1 = = = i ■' J^ i^'^j"^ 1 :^^=.^==^=^^.^i=^.^^J^_^JJi^: 12 3 4 6 Mb/hi - 1 - 1 • - 1 — H--— ^ THE CONSTRUCTION OF FUGUE AS A WHOLE. 83 ^M. ij-j—u-f \ ^ ^ ~f-~\f i prr^ |£^E^i^^.=^^=^^: l^ JJ772^it^=-^P7^i;t. -?^^^: *^ 30 "~.31 32 34 34 35 ^ -, m — * — 1 1 m 1 — 1 ^ 1 "T" nT" f r Pbf i=r^ 'r ' 1^ ^-^ 1'^^ 1^- 1- 84 FUGUE. :> ^ — ^ 1 9 = fw- "T"' =1 ,^ V :fe^ W \d*'J L^^ ^ = = = -F 1 virri =F 1- 54 65 66 57 58 59 Hffi-. — - .. -. — kAH I -r-rd*^ pff ^^^^ T ^^ =1** * ^^ =3 lb r2 •^ d Lt^U X>^^ ^ M 67 68 69 ^ 78 71 72 THK CONSTRUCTION OF FUGUE AS A WHOLE. 85 The following charts will require but little explanation. The position of each voice is indicated on the left-hand side of the diagram. The perpendicular lines show the division into bars ; the alternate bars (i, 3, 5, &c.) are numbered. The thick line (^~"} shows the principal subject ; the dots ( ) represent the counter-subject. In No. 5, the subject being used by inverse movement, is represented by a curved line ^ «, and the counter- subject by curved dots . ; the inversion of these subjects is afterwards shown by ' and '. In No. 6 (being a fugue with two counter-subjects), the second counter-subject is shown by a wavy line~.-~~.. Against the commencement of each principal subject thus indicated a letter as E, B|7, &c., is placed: in some cases such letters are associated with figures, as G', D*, &c., the figures indicating that the special entry to which they refer commences respectively on the fifth note of G (i.e., D), or on the fourth note of D (i.e., G). In general these figures may be regarded as showing that the theme begins on a certain degree of the scale named. In the case of a fugue commencing on the key-note and having a real answer (as No. i), the initial note of subject or answer is gfiven ; but in the case of a fugue whose subject begins on any other than the key-note, or in the case of a tonal fugue (see No. 2 or 3), it has been thought best to indicate thefirot note of the entry by the compound method, as F", C*(see Chart No. 2). The diagrams will, on inspection, make the following points plain, viz. : — The length of the subject and the frequency of its employ- ment ; The relation of the counter- subject to the principal subject and frequency of its employment ; The place of the episodes ; The order of keys ; The frequency, closeness, and nature of the strettos used. No. I. Two-voice Real Fugue in E minor. No. 10, vol. i., " Das wohltemperirte Clavier." This fugue has a subject two bars in length, announced in the treble and answered (a real answer) in the bass. It has a regular counter-subject. An inspection of the chart shows the methodical construction of the fugue. The subject and counter-subject occur as follows: bars-1-5, 11-15, 20-24, 3034, 39-41. , , ^. . It will be seen at a glance that the subject is everywhere attended by the counter-subject ; that the answer is always at the proper fifth above or its equivalent, the fourth below; that the subject is used only in the original key and its nearest relatives ; and that the fugue is without any kind of stretto. Episodes are employed intermediately between the several attacks of the subject, viz. : bars 5-1 1, 15-20, 24-30, 34-39. 86 FUGUE. The four episodes divide themselves into two of six bars duration and two of five bars value. The six-bar episode, 24-30, is an inversion of the episode of corresponding length, 5-1 1; both are founded on the counter-subject. The five-bar episode, 34-39, is an inversion of that occurring at 15-20, which is itself made by sequential inversion, bar by bar, of an expanded fragment of the counter-subject. The fugue, although short, and written but for two parts, is an admirable example of method and order in the treatment of subject, counter-subject, and episode. No. 2. Three-voice Tonal Fugue in F major, No. 11, vol. i., " Das wohltemperirte Clavier." A fugue of considerable interest, but simple in its structure. The subject, four bars, is announced in the alto and answered in the treble. The entry of the bass in the ninth bar completes the exposition in the thirteenth bar. Bars 17-29 exhibit the subject and answer as a kind of counter- exposition ; at least, the part that previously gave the answer (the treble) now leads with the subject ; and the part that originally led the subject (the alto) now supplies the answer (generally in the counter-exposition the answer leads and the subject replies — see the distinction, par. g, note). At bar 27 commences the first stretto- like incident, the alto answering the bass at the distance of two bars instead of four. At this point only the two voices named engage in the stretto, but at bar 36 the same device is again em- ployed, all three voices now taking part. At bar 46 commences a repetition of the stretto by the voices in reversed order. The subject will be found again in bars 65 (treble) and 66 (alto), but under somewhat varied and disguised aspects. Again, it may be noticed that the modulations and the keys in which the subject is used stand in the most simple and natural relation to the principal key. Episodes. Bars 14-17 contain the counter-subject used with- out the subject, and on this a very short harmonic phrase of sequential character is built. Bars 30-36 show an episode made on the last bar but one of the subject. In bars 56-65 occurs another episode. The germ of the bass figure ( ^ j, C iJ l ) '"^y tie seen at bar 31 ; it is now expanded thus — An incidental, alteration of the subject in bar 51 (alto) suggests the figure which accompanies the bass given above. Bars 60-65 are a free inversion of the earlier part of the episode The bass. 57- 59, suggests that employed at bar 68, &c. n en o I— H g -r ; • -^1 O ; ; i L -^ * 1-). [^ . L- •g si PQ CO 0^ o (M kC fe IS ll. * o Ph 1 ? „ (>H * •o Ifc — \ m « ® s le (>H fc to e« ee N ^ oa ^ fc itr m "^ 09 »> w S. "», 2 c5 »», 1 J: & •* ri lO "C ec lO Si B » S^ fi - 1 « 1 5 .2 & I cq the construction of fugue as a whole. 87 Choral Fugue, B Flat Major.* No. 3 J. P.KmNBBROBR ^b" ■ r ■ 1 1 1 1 1 *T? ■ |r r 1 Iff * rTir^-fH^^ Hi .b !■ 'T" a«-i-^ m - , r— ■ »^i»n ^^Lh- — , »>>.-r ^ B» . . Ife" r ' r c^^ T r r r ^r-' cT 1 1 r p I' 1 1 r 1 n=,i''"^rVr If =FI^ 9 10 U ir I"-* q -d-^ 1- r J — F^r -r — = — ^ iJ J J 1^ r p rr i^ i 1 , 1 ni 1 r 1 * ^^ •■J r r r- J — 1 — 1 — U- p - p :^ 1 1 17 !=-^ 18 -is = 19 j 1 1 — P- 20 -p" — f^ — '■ icrr T ggb" ' ■ 1 ■ ■■ T- — = — -F — F — L(L_L_?L — ^ • From Marpurg's " Fugen Sammlung." Berlin, I7j8. 88 PUQUB. ^>^V "' ^ JrJjT^i • w ^^ \ r r J ^ ^^i--r-r-t-f=^ m -fs- THE CONSTRUCTION OF FUGUE AS A WHOLE. 89 ^V r r-ifJ— r ir^jrir- k r j'r i^^ cziTd: ^ 1^17 48 49 SO 60 51 go FUGUE. This interesting tonal fugue is probably now for the first time reprinted. While it perhaps has no special claim as displaying extraordinary fugal combinations, it may be regarded as a fair average specimen of a four-part choral fugue. The chart shows the exposition contained in bars 1-16. The counter-subject is only used in the exposition, and is not there employed by inversion. Bars 17-22 contain the counter-exposition made on a portion of the subject, which is employed stretto- wise at the distance of one bar. Bars 26-38 show the subject in the key of the dominant ; the answer leading, and subject responding. The subject is again used at approximated distance and in shortened form, bars 38-42 ; and in bar 51 com- mences a series of fragmentary attacks. At 60 the subject occurs in thirds between tenor and treble. Bars 66 to 76 may be regE.rded as a coda on dominant pedal, in which, however, the answer and subject in the order named again appear. The principal episode is made on a motive of four notes, see treble, bar 44. O Id PQ i O o CO !| ?il •-t m h S 5^ P5" •? w P ■ b 09 n at k* ^ IS S ^ s. . -a W » *^ *=! %. M 1 _A ni m ^ 1-1 ■"" «5 a. ■■■A ri t: » a & f tH FTi S- « S- u cb & rh o t-l A •^^ o" ® ~ ij F— t o c fcr «q IB H H (8 14 o pq THE CONSTRUCTION OF FUGUE AS A WHOLE. 91 The three fugues that follow are among the most admirable of those contained in Bach's great work, " Das wohltemperirte (clavier, Ihey are exquisitely beautiful as music, and are models of constructive skill. No. 4, a fugue in G minor, exhibits the counter-subject com- bined by counterpoint at the octave, tenth, and twelfth. No. 5, B flat minor, especially exemplifies the use of inverse movement. No one can fail to be impressed by the method, order, and balance that pervades the entire work. The close stretto-like combination of the subject with itself, both by direct and contrary movement, will necessarily command attention. No. 6 is the well-known five-voice fugue in C sharp minor. This fugue IS not unfrequently called a fugue on three subjects, but more properly it is termed a fugue with two counter-subjects. For simphcity, however, these subjects have been marked i, §, §, but it must be remembered that ^ points out the principal subject, while 2 and § respectively indicate the first and second counter-subject. The denomination fugue with two or three subjects can at most be applied with any propriety to those cases where the several subjects enter simultaneously or nearly so ; but Cherubini objects even to this, arguing that all that accompanies the prin- cipal subject is but accessory to it, and of the nature of counter- subject. Cherubini draws an important distinction between two classes of counter-subjects. He says : — "In case a fugue be so disposed as that several counter- subjects are introduced at the same time the principal subject is proposed for the first time, these counter-subjects should be invariable in their inversions during the whole course of the fugue. On the contrar}', when these different counter-subjects are employed only afterwards, either during the subject or with the response, and when they have not been introduced at the beginning with the subject itself, there is free leave then either to preserve their identity each time they recur or to alter them a little, by changing some few notes, according to the exigency and situation of the parts." (See par. 76.) Fugue in G Minor, No. 16, Vol. ii., " Das wohltemperirte Clavier." 'No. 4. j. S. Bach. 92 FUGUE. fbl" — ■ r r .1=^ f — T 1 — p-h M-^ ' ^ 1 T_J^ J 1 :! — P4- Ifci 1." ^ m . M m^l'JLSm^ ■-, r j-TJ ^T PC r 3.^^r *r1 1^ 1* * T-rr L r 'I "I * * L-T -*■ ^it== 6 =* - ■ — r THE CONSTRUCTION OF FUGUE AS A WHOLE, 93 Hlges- Fugue —Novello. O 94 FUGUE. f^'-r-j =^-J^wT^'^^^rv^^=^^^ ^ THE CONSTRUCTION OF FUGUE AS A WHOLE. 95 ^''t^'ET^ '^ qb^^^^ffi s ^4-S 5- r"3 j^i^^ ^^^^ =^ p^^ ^ FUGUE. THE CONSTRUCTION OF FUGUE AS A WHOLE. 97 98 FUGUB. Fugue, B Flat Minor, No. 22, Vol. ii., " Das wohltem- PERiRTE Clavier." No. 5. J. s. Bach. ^m tra= I. ^J^I^Li^^^ gg ; F^g f^T-^r= THE CONSTRUCTION OF FUGUE AS A WHOLE. g5 J/A^r , m Y f -p— f^ . ^fm •fv-f^ fr Jn- rrf W-n^^' — ^- :^J H£& ' 1 ' T 1^1 |P^ r ^^Q ^ ifcj-r =tT fc^i? -JU U — kj i-4J-J -H- 13 14 -j^ Pj» B— F- — ki-j-u- r 16 1- ^ J n 16 J 1 J Ji .r ^ v\K ^^ ^=y ^ ^1 ^ i 4^4- * J * *«)a ^ lOO FUGUE i f^Ur-r-^-^^^^WSg^i^^ ^ ^ r-^ THE CONSTRUCTION OF FUGUE AS A WHOLE. lOI fei,Ur^^- - f-r ^rir"^^ ^rica^rrM ^ %r-^" rg P=H^^ -m-t 102 FUGUE. g^ffr^f^^i ... uclDj;^^ THE CONSTRUCTION OF FUGUE AS A WHOLE. 103 ii>4 FUQUK. THE CONSTRUCTION OF FUGUE AS A WHOLE. 105 Fugue, C Sharp Minor, No. 4, Vol. i., " Das WOHLTEMPERIRTE ClAVIER." No. 6. J. S. Bach. io6 FUGUE. THE CONSTRUCTION OF FUGUE AS A WHOLE I07 F#=*iM'f ^i»gg»^li^:^_ r i"'^ ]^rf¥=^ A 1- % Tr- H-i 1 1 ri ri : i=u-!(- — r ' ' : J ' : fe » '.p *- ><■ 1 - - ' -* [■'■ »• 1^. r- »J -ty-tAf 1 - 1 - 1 - SI : f:-^^- tfr^lt 1 1 1 1 -rwf^rwmr' tea» 48 49 60 61a ILLLI LlCA 62 _ is _ ^^ft^mrrn ' i - i- r^ r i --r io8 FUGUE. tA m -jjJiJii^jj THE CONSTRUCTION OP FUGUE AS A WHOLE tOg Hlggs— Fugue.— NovoUo. H FUGUE ]&*A±ii;i^ ^ ^ J i_^ . J 1^. ■ I ■ 1 THE CONSTRUCTION OF FUGUB AS A WHOLE. Ill A 112 FUGUE. No. 4 (see Chart). Four-voice Tonal Fugue in G minor, No. i6 of vol. ii., "Das wohltemperirte Clavier." This is a very fine example of a fugue with a regular counter-subject. The expo- sition is contained in bars 1-17. In bar 20 the subject appears again in the tenor, and in bar 28 in the alto. These entries look at first sight identical with those first employed, but examination will show that they are now used under very different circum- stances. The tenor entry (bars 1-4) was unaccompanied by the counter-subject, with which it is now (bars 20-24) combined ; the alto entry, 5-g, had the counter-subject below (and the subsequent use of the counter-subject in the exposition has been direct or, as at 13-17, by inversion in the octave); it is now, 28-32, above, and by counterpoint at the twelfth. At bars 32 and 36 the subject is employed with the counter-subject derived by inversion at the tenth ; afterwards, at 45 and 51, the principal subject is duplicated in thirds ; and at 59 a still richer combination (subject in thirds and counter-subject also in thirds) occurs. At 67 the subject attended with the counter-subject (counterpoint at the twelfth) leads a stretto answered at two bars by the treble attended by its counter-subject in the bass at the original interval.. At bar 79 the subject appears once more, but both it and the counter- subject are in a slightly altered form. Episodes. An examination of the principal places of episode — 17-20, 24-28, 40-45, 63-67 — will show how largely the use of fragments of the counter-subject has served to preserve the unity of the fugue. No. 5. Four-voice Tonal Fugue in B\> minor. No. 22, vol. ii., - Das wohltemperirte Clavier." The principal subject of this fugue is represented in the chart by a curve y ^, and the counter- subject by curved dots ^- -, for facility of showing these sub- jects when used by inversion. The whole fugue may be divided thus: direct use of subject and counter-subject, bars 1-37; inverted N9 4 Treble. Alto. Tenor. Bass. FUGUE. G MINOR. J.S.Bach. ( • • • • r" 'i !^ •• '. ■ -Pn Alto with c. Jantprsubi iri Spls^ BOt ■■;^ -^ • - "" ] )* 1)^ InS^dsw T^or th < ;J ■• - (^ ... "i 1 '5 Ir 3rds Bass with (5* -1)T 1 1 _^ 1 :;;;.= "T" -J (r- -J _ 1 3 6 7 9 U 13 ir. 17 19 21 23 25 27 29 31 33 35 37 39 41 48 45 47 49 51 63 65 57 69 61 63 65 87 89 71 73 75 77 79 81 83 N9 5 Treble. Alto. Tenor. Bass. FUGUE. B flat MINOR. — . -^ — — . ^ J- S.Bach. ^ J ^ — ^ \ ])!. it^ — '^ ^^f ■■^ "" A> — Jk — k \V ■^ __^ _,_ -^ Bl 7 _ ^ ■■ic^"~- — ^ T5 ""* " -' u — :v.'\ -" ' 111? . \ 7 • . . Jl> ^ ^ — -^ 1!^ ■ — ' — 4^~- " At' ^ -- ::i. Id." ^ J ii> — 1 ' — 1 u _ L _ _ _ Dt' _ _ _ _j _ L ^ L u L in- U __ — L L Lj ;^ ^ 11 Zl — L — — :i\. — — — . n'rr^ ■^ — — J 3 5 7 9 U 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 -tS 47 49 51 53 5B 57 69 61 8.1 65 67 69 71 78 75 77 79 81 83 85 87 89 »1 93 9S »7 99 101 N9e IS* Treble. . V b U b rL t i. u shar P I VI ir '^l JJ < 5 V u IC ;ii s V V J- S.Bach. ~~ c r F » a 1)1 n •w -w ott I u tt rw cH «B^ Treble G r ~ c» A _ B n , Alto. ct 5S B Gt V ... Tenor. ( J? " Ct t ■ A c« : •• f D pm .Fed 1 1 ^nioPed. Bass. ( ? " " _^ _ 1 i; _ _ J _J _ _. ^ 1 B^ L , _J — 1 — . — — u — 1 J L — __ — ' u — L — — L ~ (f» -i- L L — — L — — L — — |c3 — L — — — , 1 5 ^ g H 13 15 17 19 21 23 86 ^^ »» 31 33 35 87 39 41 43 45 47 49 51 58 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 80 91 93 95 97 99 101 lOS 105 107 108 lu 118 115 do face page ti».) THE CONSTRUCTION OF FUGUE AS A WHOLE. II3 use of subject and counter-subject, 42-78 ; combination of the two forms direct and inverted, 80-101. The exposition is contained in bars 1-21. In bar 27 the subject and answer (in an irregular interval) appear in tenor and alto at only a minim distance, thus reversing the accent. This narrowing of the interval of time is repeated between treble and bass in bar 33. Bars 42-61 repeat the inversion of the exposition ; and bars 67-77 reproduce the inversion of the close imitation, but always with , quite a new order of parts. At bar 80 the close imitation is shown with the direct and inverted use of the subject between treble and tenor ; and at bar 89 the same device is seen between alto and bass ; and finally, at bar 96, all four parts engage in the close imitation after the manner of a quadruple counterpoint. The bass is in constant thirds below the tenor, but the alto is partly in thirds and partly in sixths below the treble. The student will not fail to notice the peculiar use of the counter- subject in the exposition, appearing as it does twice consecutively in the alto voice, first below the principal subject, bar 5, and immediately afterwards, 11-15, above the principal subject in the bass. No. 6. Five-voice Real Fugue in Cjt minor. No. 4, vol. i., " Das wohltemperirte Clavier." This is a fugue on a principal subject and two counter-subjects. The second counter-subject is indi- cated on the chart by the wavy line, — —. The chart will show the profuse use Bach makes of these subjects. Attention may be called to the altered entry of the second treble, bar 12— instead of— and to the conspicuous absence for many bars of the subject from the two upper parts, from bars 15 and 17; but this absence is abundantly compensated for by the beautiful and consistent counterpoint that fills these parts. The entry of the first counter- subiect is occasionally considerably altered (see bar 49). Ihe whole fugue will amply reward the most minute study, and may be regarded as an inexhaustible mine of harmonic and contra- puntal wealth. INDEX. «% THE NUMBERS REFER TO THE PARAGRAPHS. «*i Ancient modes . . , note 36 Answer . . . 2, 3, 34-68 Answer, alteration of . . 61-62 Answer by augmentation . 67 Answer by diminution . . 66 Answer distinguished from sub- ject. .... note g Answer essentially a transposition of subject . . . 3,34 Answer, if subject begin on domi- nant 46 Answer, if subject begin on tonic and skip to dominant . . 42 Answer, if subject modulates . 48 Answer, if subject reaches domi- nant through second or sixth of scale 40 Answer, if subject skip to any other note than dominant . 39 Answer, melody of subject to be preserved in . . . .61 Answer, real . . 4, 35, 41, 45 Answer to chromatic subject 59, 60 Answer, tonal 4, 34 (a, b, c), 36, 42-48 Authentic and Plagal . . 410 Cadences . . . .14, 15s „ see page 91. Characteristic harmonies . 54 Classification of voices in ordinary quartett . . .118 Codetta . 6, 29, 30, 83 Comes, companion, see Subject. Compass of subject . 21 Continuity important . 153 Counter-subject . 5, 15 (/), 69.80 „ „ see page gi Counter-subject, contrast vvrith principal subject . . • 73 Counter-subject in double coun terpoint .... 72 Counter-subject in double fugue 69, 80 „ „ see page gi. Counter-subject, modification of . 76 „ „ see page 91. Counter.subject, ordinary . , 70 Counter- subject to tonal answer . 75 " Das wohltemperirte Clavier," order of entry in exposition . 122 Digression . . . .81 Diminished seventh . 53-54 Double fugue .... 80 Double fugue, counter- subject in 69 „ „ see page 91. Dux, guide or leader, see Subject, Episode . 10, 14, 27, 81-95. 153 Episode formed firom subject . 27 Episode, individuality of composer shown in .... 94 Episode on essential idea . 85-89 Episode on foreign idea . go Exposition .... 8, 155 Exposition, counter- . . . g Exposition, order of entry in 117-123 Fugue, close • 3» Fugue, double • 15 w Fugue, strict, free • 15 (b) INDEX. "5 Harmonies, characteristic . . 54 Inganno cadence . . . 155 Intermediate harmony . . 81 Inverse movement, scheme for, in major . . 64 Inverse movement, scheme for, in minor 65 Modulation . . . 128-135, 150 Modulation, Cherubini's sugges- tion for 129 Modulation of subject . . 17-20 Order of entry afler exposition 124-127 Order of entry in exposition 117-123 Pedal . . .13. 104, 136, 137 Perfect intervals, how answered . 51a Perfect intervals, how answered note 33 Plagal and authentic . , . 41a Redundant entry of subject . 8, 71 Ricercata . • • • • 95 Scale in subject . • 32. 33 Sections . 14. 148 Seventh, diminished 53-54 Seventh of scale . 51-52 Sixth of dominant ■ 49 Sixth of scale . 50 Subject I, 2, 16-33 Subject and answer distinguished note g Subject, cumpass of . . .21 Subject, doubtful tonality . . 147 Subject, episode formed from . 27 Subject, fourth of scale unusual for initial note . . •41 Subject generally ends on accent 25 Subject, modulation of . 17-20 Subject, redundant entry of 8, 71 Subject, scale in . . 32, 33 Subject, sequential . . -23 Subject, varied forms of .11, 64-68 Stretto . . 13, 26, 96-115, 116 Stretto, definition of . . .96 Stretto, variety of device in 98, 103, 145 Third of dominant , . -52 Third of scale, character of . 49 Novello's Music Primers and Educational Serii s. d. 3 M- 15. Ifi. 17. 19. 23. 24. 24A, 25. 26, 27. 28. 29. iO. 31. 32. 32A 33. 34. 36. 37. 37A 38. 3Sa 39. 39A 40. 4IA, 42. 43. 43A, 44 45. 40 -17. 47A 4ti. 49. 50. 50A 52. 53. 54. 55. 56. The Pianoforte ... ... E. Pauer The RuDiMENTsoF Music W. H.Cummings The Organ J. Stainer The Haumonium King Hali, Singing ... ... ... A. Randegger Speech in Song iSingefs^ Pronouncing Primer) A. J. Ei-Lts Musical Forms E. Paoer Harmony J. Stainer Counterpoint J F. Bridge Fugue J. Higgs Scientific Basis of Music W. H. Stone i Double Counterpoint ...J. F. Bridge 3 CHUi.iCH Choir Training J. Troutbeck i Plain Song T. Helmore 3 Instrumentation E. Prout 3 Tme Elements of the Beautiful in MusTc E. Pauer i The Violin B. Tours 3 Tonic Sol-fa ... J. Curwen i Lancashire Sol-fa ... J. Greenwood i Composition J. Stainer 3 Musical Terms... Stainek and Bakkktt i The Violoncello ... Jules de Swert 3 Tvvo-PAiiT Exercises (396) J. Greenwood i Double Scales F. Tavlor i Do. (Continental Fintierinfi) i Musical Expression M. 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Dunstan 4 First Steps at the Pianoforte Berger 4 A Dictionary or Pia.niStS and Compo?^; rs for the Pianoforte ... E. Pauel 3 ■ Organ Pedal Teci ^iqje (I.) Horner 3 > Organ Ped^l Techni^-e (II.) Horner 3 1 Twelve TrI'.'- or '^-HE Organ ALBRECHTSBERr.ER 2 i Three-Part Srnni ics (both Notations) J. E. Vernham 2 Choral Society Vocalisation (or in Four Parts, 8rf. each ; Tonic Sol-fa, f)(/. each) ' ]. Stainer 3 ■ Do, The Exercises Adapted and Arranged for FemaleVoices Marchant 2 Two-Part Solfeggi J, Higgs 1 History of the Pianoforte A. J. Hipkins 4 Scales and Arpeggios F. Taylor 3 Sonata Form W. H. Hadow 4 A Dictionary of Violin Makers C. Stainer 4 Analysis of Bach's 48 Preludes and Fugues F. Iliffe 4 (To 6.3 3 L. Analysis of Form " H. A. Harding Harmonization of Melodies J.E.Vernham "Braille" Music-Notati n (for sighted teachers to instruct ths blind) E. Watson net. Five-Part Harmony ... F. E. Gladstone The Viola B.Tours Harmonics and Resultants C. E. Lowe Breathing for Voice Production h. h. hulbert Choirboy's Elements of Music G. J. Bennett First Steps for the Violin. (Part I.) (Violin only) Emil Kreuz 65A. Do. Do. (Part II.) (The Pieces with Pianoforte Accompaniment) 66. ScoRE-READi.'G KxERCiSES (Part I.) E. R. Davmond Do. Do. (Part II.) Method of Singing ... J. StockhauSEN A Treatise on Strict Counterpoint. (Parti.) F.E.Gladstone Do. Do. (Part II.) liXAMINATION QUESTIONS ,., C. HARRIS Voice Culture for Children (I.) Bates Do. Do. (II.) .. Do. D' . (in.) „ Do. Do. (III.) iSol-fa) (Nos. ;i to 73 complete : 5s. 6^.) The Choirboy's Guide to the Cathedral Psalter ... E. Newton Twelve Elementary Duets for the Pianoforte Harmony for Schools F. Key to Ditto ... ... F. Score-Reading Exercises Figured-Bass Playing Tenor Exercises Three-I'art Studies ... An Essay On MuSic ... The Military Band ,. Equal Temperament... .\ CuiHE TO Solo Singin ". Theok, ■■1" Music Self-FI"^' p FOR Singe The Or'.an Pedal Scal*'?; and A.^pit' v.. Combined and Florid Counterpoint G. J. Bennett Musical Noi ation ... H E. Button The Singer's Art A. Larkcom The Organ (A Study of its Principles and Practice) H. F. Ellingford Diatonic Modal Counterpoint R. Dunsta> Beethoven's Pianoforte Sonatas (Hint; on their Rendering) ... ...C. K. Lowf Ornamentation in the Works of F. Chopin .1. P. Dun. A Manual of Singing ... R. Mann Music.'.: Aipreciatiu.-^ W. J Foxell PlANOFCRTE ACCOMP- '"r'^N r W. HlCKIK Pronunciation for Voice Production H. H. Hulblr-. Eai' Training (inckidiiij; Music::] Apprecia tion and l^hy'.llmic Movc-nvents) Mabel CHAMBERLAI^ Do. Letterpress ,, Do. Mu^^ir Tnt, Instrument; of the Orchestra J. E. BoRLANr Pianoforte Pr.^ctising ... C E, Lowt A Handbook for Cmoralists H. Graci ■ FIye-Training in Music Mabel Chamberlau MyIMusic Book Mabel Chamderlau Handbook for ChOralists (Supplemei. to No. 104) H. Gkact A Student's Guide to Orchestration . J. P. DUNT: onh'iincd .) 57. Appendix to 3S. 59. 60. 61. 62. 63 64. 6^. 66a. 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