ANALYSIS
. BACH'S
Eight Fugues
(Das Wohltemperirte Clavier),
Ebenezer Front,
B.A. London, Hon. Mus> D. Trin. Coll. Dublin ant Edinburgh, and Professor of Music in University of Dublin,
UTED BY
B. Proutj A.R.A.A
London :
ASHDOWN, Ltd., H 8 mover Square
1910 by Edwin Ashdcwn> Ltd
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ANALYSIS OF
J. S. BACH'S
Forty- Eight Fugues
(Das IVohltemperirte Clavier), BY
EBENEZER PROUT,
B.A. London, Hon. Mus. D. Trin. Coll., Dublin and
Edinburgh, and Professorof Music in the
University of Dublin.
EDITED BY
LOUIS B. PROUT, A.R.A.M.
-41-
LONDON:
EDWIN ASHDOWN, LTD., HANOVER SQUARE
Copyright tyio by Edwin Ashdoum, Ltd.
UNIVERSITY OF TORONTO
FACULTY OF MUSIC
LIBRARY
EDITOR'S PREFACE.
THE present handbook, on which my revered father was working enthusiastically up to the very day of his death, is designed to supply a concise analysis of Bach's immortal " Forty-eight," for the use of students who are desirous of obtaining some insight into their construction. Much has already been written on the subject, and from many standpoints; but I am un- acquainted with any book that serves the purpose which has been here kept in view, of pointing out the essentials of the form of the fugues, systematically arranged, and unencumbered by technical details of harmony on the one hand, and by flights into the realms of poetic fancy or of psychological perceptions on the other hand.
The analyses which had been finally arranged for the press, by Dr. Prout, have been deemed sacred from any editorial interference. The arrangement of the rest has been on similar lines from his very copious manu- script notes, and my work has only been that of select- ing and editing. The author, himself, had been contem- plating the desirability of some slight curtailment, wherever possible, in order to keep the book within strictly moderate dimensions. I have, therefore, rigor- ously excluded whatever could be spared without detriment, from those analyses for the arrangement of which I am responsible. It was not, however, an undesirable thing that the first few should be some- what more extended than the later ones, as they give
iv Editor's Preface
the opportunity to enunciate certain generalisations which the careful reader can afterwards apply for himself.
No study of these wonderful masterpieces can be exhaustive. There is much of constructive beauty and meaning yet awaiting discovery in them, and the student should endeavour not merely to find what he is told to look for, but also to make original explorations for himself. Those who desire fuller guidance, especially on the evolution of the rhythmic figures, motives and other smaller sections, may find it in Dr. F. Stade's analyzed edition of the fugues, "J. S. Bach, Die Fugen des wohltemperirten Klaviers parti turmassig dargestellt," etc. ; Riemann's " Katechismus der Fugen- Komposition " also gives an abundance of valuable and suggestive criticism, including much that is aesthetic more than technical. Van Bruyck's older "Technische und asthetische Analysen des Wohltem- perirten Claviers" is very largely concerned with the last-named aspect of the subject. Both Riemann and Van Bruyck deal with the preludes as well as the fugues.
There remains only the pleasing duty of returning hearty thanks to my friend Mr. R. Orlando Morgan for the warm interest he has throughout manifested in the work, and for much valuable help and advice in con- nection with the arrangement of the matter.
LOUIS B. PROUT. LONDON, January, 1910.
INTRODUCTION.
The collection of preludes and fugues commonly known as " Das Wohltemperirte Clavier " consists in reality of two complete and separate works, each containing one prelude and fugue in each of the major and minor keys. The first, to which Bach himself gave the name which is now attached to both series, was completed in 1 722, and owed its genesis to the controversy of the period on the question of equal versus unequal " temperament " : an acousti- cal subject into which we need not here enter, beyond stating that the old methods of tuning sacrificed the "extreme" keys in the interests of precision of intonation in the simpler ones, whereas the present method distributes equally over the whole of the twelve semitones (or twelve " perfect " fifths) the slight deviations from absolute exactitude which are inseparable from our musical system, thereby reducing them almost to vanishing point. Bach demon- strates, what in our day seems the veriest commonplace, that by the aid of " equal temperament " it is possible to play in any key with equally good effect. The second collection, which was completed in 1744, was originally known, according to Marpurg, as "Twenty- four New Preludes and Fugues " ; but inasmuch as it illustrates, in common with the first series, the value of equal temperament, no objection can be urged against the inclusion of both under the common title.
Bach's part-writing, in the fugues, is as absolutely clear and definite as though each part were given to a separate voice or in- strument. The student who desires to obtain a thorough insight into them could not possibly devise a better exercise than to write them out in score, *>., with each part on a separate staff. In any case he should number the bars in his edition, in order to facilitate
vi Introditction.
reference. In the few fugues which are not written as beginning at the commencement of a bar (Nos. n, 34, • 36, 37, 48) we have reckoned the first complete bar as bar i. In the three-part fugues \ve have described the parts uniformly as treble, alto and bass ; in the four-part ones as treble, alto, tenor and bass ; and in the two for five voices (Nos. 4 and 22) we have regarded the additional one as another treble.
The text followed has been that of the Bach-Gesellschaft.
DEFINITIONS.
FUGUE. — A contrapuntal composition (that is, with all the voices of separate melodic importance) founded on a concise theme called the " subject/' which is given out singly, and then according to certain rules, by each voice in turn, and subsequently developed. The form is an application of the " ternary " ; that is to say, three principal divisions are recognizable, usually according to the keys employed, but occasionally according to the methods of treat- ment. The divisions are not always quite sharply defined, but the general scheme holds good in practically every case.
SUBJECT. — The theme on which the fugue is founded (but see 1 Answer"). If there are two or three subjects, the fugue is called a double or triple fugue.
ANSWER. — The transposition of the subject, usually into the key of the dominant, given to the second voice which enters, as a companion to the subject (hence the terms " dux " and " comes/ sometimes used instead of subject and answer). The first entries of the remaining voices usually alternate between the subject and answer, but there are occasional exceptions. There are two kinds of answer. Real Answer is an exact transposition of the subject. Tonal Answer is one more or less modified according to the
Introduction. vii
exigencies of tonality ; Its principle is that a conspicuous dominant in the subject (or a modulation to the dominant key) is better answered by the tonic (or tonic key) than by the supertonic, wincii is only " secondary" in relation to the key. Hence certain notes are answered a fourth higher (or fifth lower) whereas in a real answer everything is copied a fifth higher (or fourth lower). In the later parts of a fugue, the distinction between subject and answer is not always maintained.
COUNTERSUBJECT. — A counterpoint which accompanies the subject with more or less regularity. Of course, except in a double fugue, it does not accompany the first entry of the subject, but first appears with the answer. If the counterpoint which accompanies the answer is not recurrent, it is better not to describe it as a countersubject. In the "exposition" (see below) the countersubject is usually found in the voice which has just had the subject or answer.
EXPOSITION. — The first giving out of the subject and answer by the several voices, together with any countersubjects and other incidental matter. Normally one entry is given to each voice. Not infrequently there is also a redundant entry, or second entry of the voice which led originally. Much more rarely, the entry of one voice is reserved for a later section of the fugue.
COUNTER-EXPOSITION. — An optional second exposition, giving a second group of entries in the original keys (tonic and dominant) but quite differently arranged, the voices entering in changed order, or those which had the subject having the answer, and vice versa. Often the counter-exposition is only partial, i.e.t not participated in by all the voices.
MIDDLE SECTION. — The modulatory portion of the fugue, the keys, as a rule, being other than those of the exposition. Entries
viii Introduction.
of the subject, either in groups or isolated, alternate with "episodes" (see below), and the subject often undergoes im- portant changes of treatment. Sometimes these new methods of treatment (" stretto," " inverse movement," etc.) give sufficient freshness to obviate the necessity for new keys.
FINAL SECTION. — The portion which returns to, and contains one entry or more in, the original key or keys.
EPISODE. — An interlude, generally for purposes of modulation, between the entries of the subject. That is, a portion of the fugue in which the subject and answer are absent. It rarely corresponds to the episode in other musical forms (contrasted material), but rather to " development," being usually founded on matter contained in the exposition. Episodes are found chiefly, but not exclusively, in the middle section of a fugue.
CODA, CODETTA. — There is no special significance attached to the application of the word Coda to fugue. It is the close of the piece, often of similar construction to the episodes, often, on the other hand, containing some final elaboration of the subject. Codetta is a short passage appended to an entry, not to the entire composition, and is only distinguished from an episode by its function, or some- times by its length or by its degree of individuality. As a good generalisation — though subject to some reservations — a codetta separates entries that belong to the same group, or merely supplies a cadence to an entry, while an episode separates those belonging to different groups, making the modulations. Thus the term codetta is chiefly used in connection with the exposition, where a group of approximated entries is always expected ; but it is some- times needful to use it later in the fugue.
STRETTO. — An overlapping of two entries of the subject (or subject and answer) ; one voice entering before the previous one
Introduction. ix
has completed its course. Stretto maestrale is a stretto in "canon" (see below), each voice completing the subject instead of breaking away from or modifying it on the entry of a new voice.
IMITATION. — The copying of a passage or rhythmic figure, more or less strictly, and at a short interval of time, by a different voice.
CANON. — Strict, note- for- note imitation (though it may be at any interval) throughout a passage of some length. Canon (or stretto, or imitation) "at the octave," or "in the octave" is used to denote the interval separating the entries.
INVERSE MOVEMENT (INVERSION).— A metamorphosis of a subject, countersubject or other melody, by the substitution of ascending intervals for descending, and vice versa.*
COUNTERPOINT, DOUBLE, TRIPLE OR QUADRUPLE. — Two, three or four melodies capable of inversion one with another in any order, *>., making correct harmony whichever be placed at the bottom, or as a middle part, or at the top. Double counterpoint in the octave (or "at the octave") is that in which the inversion is normal, the lower part being placed an octave higher, or the higher an octave lower ; in the tenth is when the pitch of the inverted part is altered a tenth (compound third) ; in the twelfth when the alteration is a twelfth (compound fifth).
NOTE. — It is assumed that the terms belonging to simpler branches of musical theory, such as "cadence," "sequence," "pedal point," are already familiar to the student.
* In order to avoid even a possibility of confusion, the editor prefers to use only the term " inverse movement " in this sense, confining " inversion " to its harmonic signifi- cation. But the author's M.S. has not always been altered, and it may, therefore, be well to point out that when we speak of the "inversion" of two subjects, or themes, we mean their changed relation one to the other (double counte- point), and it is only when ontthtmt alone is in question that the word inversion h«s been allowed to bear its other meaning (= inverse movement).
ANALYSIS
OF
FORTY-EIGHT FUGUES.
FUGUE 1
C MAJOR (FOUR VOICES). Exposition. — The subject of this fugue—
co)
which is in the alto, extends to the first note in the third crotchet of bar 2. As it moves by step from tonic to dominant, and does not modulate, it takes a real answer, given to the treble. As the fugue contains an unusual amount of stretto, it has no regular countersubject ; but, in order to give unity to the composition, the last four semiquavers of the subject, marked above with ' (a) — ' , are very frequently used throughout the fugue, either by direct motion, as in bars 2, 7 and 10, or by inverse movement, as in bars 4, 5 and 6.
At bar 4 must be noted an irregularity. According to rule, the third voice should enter with the subject; here, however, Bach puts the answer in the tenor, and gives the subject to the last entering voice — the bass.
Counter-Exposition. — At bar 7, immediately on the close of the exposition, follows the counter-exposition, in stretto. This is
CofiyrigM, tqio, by Edwin Ashdown, Ltd.
12 Analysis of J. S. Bach's
led by the treble, (which, it will be seen, had the answer in the exposition), and answered at one crotchet's distance by the tenor. At bar 9 the answer is repeated by the alto.
Middle Section. — The second (modulating) section of the fugue begins at bar 10. At first sight it looks as if the bass entry in this bar belonged to the counter-exposition. But the immediately following entry of the alto on D (the fifth above G) proves the bass to be now the subject in the key of G, and not (like the alto in bar 9) the answer in the key of C ; if it were, the alto would have begun on C, a note lower. We have here reached the middle section of the fugue, as is further shown by the succeeding entry of the tenor (bar 1 2), On the dominant of A minor.
At bar 14 we see another stretto, closer than the preceding, and in which all the voices take part. It is not very common to find middle entries (as here) in the original keys of the tonic and dominant, though another instance will be seen in the third fugue of the first book; but there is generally less modulation in fugues that contain much stretto or close imitation than those of simpler construction. Note that the entry of the treble in bar 15 is incomplete ; the answer is interrupted, to allow the same voice to begin a new stretto. The treble now leads (bar 16), with the subject in C, followed at one beat's distance by the alto with the answer a fourth below ; at the beginning of bar 17 the tenor Begins the answer on A, while the bass has the subject in D minor. Observe that the first note of the subject in the bass is. here lengthened. It should also be noticed that we call these entries "subject" or 41 answer " when their keys bear to one another the relation of tonic and dominant; in bar 16, G being the dominant of C, the treble is subject and the alto answer ; for a similar reason in the following
Forty -Eight Fugues. 13
bar the tenor is 'regarded as answer and the bass as subject, because A is the dominant of D. But when the entries are at irregular distances it is impossible so to regard them. As the subject appears in a complete form in all the groups of entries now under notice (bars 16 to 18), we have here an example of a stretto maestrale.
At bar 19 we have another stretto in only two voices, alto and tenor. The following stretto — treble in G, beginning on the last quaver of bar 20, tenor three crotchets later, beginning on B — illustrates what has just been said. The tenor entry being a sixth below the treble the two cannot hold to each other the relation of subject and answer; to do this it would be needful for the tenor to begin on either C or D.
Final Section.— The final section of this fugue begins at bar 24. Here the tenor has the subject in C, and the alto imitates it half a bar later in F. We have here a short modulation to the sub- dominant key, and, for this time only, the entry in C is answer instead of subject. We have here in fact an extended plagal cadence ; it will be seen that the authentic full cadence precedes it (bar 23). The whole of this final section is built over a tonic pedal.
A quite exceptional feature of this fugue, not to be found in any other number of the work, is the entire absence of episodes. Except in bar 23 and the last two, there is not one bar which does not contain either subject or answer. There is consequently less variety in this fugue than in many others of the collection ; on the other hand there is none which displays more complete mastery of imitative writing, or furnishes a finer example of "the art of concealing art."
14 Analysis of J. S. Bach's
FUGUE 2
C MINOR (THREE VOICES).
Exposition.— This fugue is not only much simpler but much more regular in form than No. i. Its subject is announced in the
alto : —
(a)
The leap from tonic to dominant in the first bar requires a leap from dominant to tonic in the answer, which is therefore tonal. The answer is given to the treble, while the alto continues with a countersubject, which begins on B natural, the third semiquaver of bar 3, and ends on the first note of bar 5. This countersubject accompanies the subject or answer on every appearance throughout the fugue except the final one in the coda (bar 29).
Between the end of the answer and the next entry of the sub- ject a codetta is introduced (bars 5 to 7). The upper part is founded on a sequential treatment of the first notes of the subject, a descending sixth being substituted for a fourth. The alto, also sequential, is formed from the commencement of the countersubject taken by contrary motion. At bar 7 the bass enters with the subject, the countersubject being now taken, according to rule, by the treble — the voice that had just before given the answer. The exposition is now complete.
Middle Section.— The first episode (bars 9, 10), with which the middle section of the fugue begins, consists of an imitation between the two upper parts of the opening notes (a) of the subject, accompanied by the descending scale passage with which the
Forty-Eight Fugues. 15
countersubject opens. Bar 10 is a sequential repetition of bar 9, by means of which a modulation is effected to the relative major, E flat ; in this key we find at bar 1 1 the first middle entry. It is in the treble, and is accompanied by the countersubject in the bass. If we compare the alto of bars n, 12 with that of bars 7, 8, we shall see that the two passages, though very similar, are not identical ; we therefore do not call this middle voice of the harmony a second countersubject.
The second episode (bars 13, 14) is entirely founded on the countersubject. The treble is the bass of the first episode by contrary motion ; the two lower voices in thirds accompany with a quaver figure seen in bars 3 and 4, though the figure is not exactly imitated.
The second middle entry (bar 15), in G minor, has the subject (here taking the form of the answer) in the alto, the countersubject in the treble, and the free counterpoint in the bass.
The third episode (bars 17 to 20) is very interesting and in- genious. If bars 17, 18 are compared with bars 5, 6, it will be seen that the two lower voices at bar 1 7 are the inversion of the codetta in double counterpoint in the twelfth ; at the third crotchet of bar 1 8 the alto and bass are inverted in the octave. The treble adds an accompaniment in thirds.
Final Section. — At bar 20 we reach the final section of the fugue. The subject (treble) is given in C minor, the countersub- ject being now allotted to the alto. The fourth episode (bars 22 to 26) is formed from the first one (bars 9 to n), by inversion of the upper parts ; the sequence in the bass is continued ; and at bars 25, 26, we see a variation of the codetta (bars 5, 6), with the addition of a few notes in the alto.
ot a lev
16 Analysis of J. S. Bach's
In bar 26 is another entry of the subject in the bass. Note that the countersubject is now divided between the treble and alto voices. At bar 29 we reach the coda. Here the subject is heard for the last time over a tonic pedal. It is not accompanied by the countersubject, but additional parts are added to the harmony — a by no means unusual feature at the end of a fugue. We shall find many other examples of this procedure in the course of our analysis.
In spite of— possibly by reason of— its simplicity, this little fugue is one of the most perfect of the collection. Let the student examine it closely, and see what perfect unity of style is obtained by building up the whole piece from a few simple themes found in the opening bars.
FUGUE 3
C SHARP MAJOR (THREE VOICES).
This fugue, which is considerably longer than the two preced- ing, is especially interesting from the variety and resource shown in the construction of its episodes.
Exposition. — As the subject commences on the dominant
the answer will be tonal, and begin on the tonic. There are two countersubjects, the second of which is omitted in a few of the entries.
The subject is first heard in the treble, the answer being given to the alto while the treble continues with the first countersubject : —
Forty-Eight Fugues. 17
4
When the subject enters in the bass, while the alto gives the first countersubject, the second is heard in the treble : —
Let the student notice that the end of this second countersubjectis varied on its later appearances.
The first episode (bars 7 to 10) consists of a sequence in the bass, made from the inversion of the semiquaver figure seen in the first countersubject (bar 6), and accompanied by free imitation between the treble and alto. It is followed by an additional entry of the answer in the treble, introduced (as is often the case when the subject first appears in the upper part) to allow the counter- subject to be heard below it. It will be seen that the second countersubject is not present here. This additional entry is considered as forming part of the exposition.
Middle Section. — The middle section of the fugue commences with the second episode (bar 12). Its relationship to the first episode is obvious. The semiquaver figure in the treble of bar 12 is taken from the first countersubject (bar 6), now in direct, not in- verse, movement, and the free imitations between alto and bass are founded on the material seen in the upper voices at bars 7, 8. The first middle entry (in A sharp minor) at bar 14 is accompanied only by the first countersubject. The third episode (bars 16 to 19) is very neat, li must be noted that bar 16 is, excepting the first beat in the treble and alto, identical with bar 9 ; the whole episode is made from sequential continuations of the last bar of the first
18 Analysis of J. S. Bach's
episode. It leads to an entry in E sharp minor (the mediant minor of C sharp) ; the subject is now in the alto, with the second counter- subject above and the first below it.
The fourth episode (bars 21 to 24), begins with a prolongation of the preceding phrase, leading in bar 22 to a full cadence in E sharp minor. To this succeeds a sequential figure in the treble, made from the first bar of the subject, and accompanied (not sequentially) by semiquavers in alto, and, at bar 24, in bass also.
The following group of entries, answer in treble (bar 24), subject in alto (bar 26), being in the dominant and tonic keys of the fugue, look at first as if they belonged to the final section. But they are here followed by a very long episode containing so much incidental modulation that it is better to regard them as forming part of the middle section. It will be seen that both entries are accompanied by the two countersubjects. The three voices are written in triple counterpoint ; if we compare the four passages (at bars 5, 19, 24, 26) in which they have been combined, it will be seen that on each new presentation a different position is given. Of the six possible combinations, four are employed.
The fifth episode— the longest of all — (bars 28 to 42) begins with a transposition of the semiquaver passage in the treble of episode 2 (bars 9, 10) into the bass; the accompanying figure being now above instead of below the semiquavers. In the next bars (30 to 34) the bass sequence of the first episode (bars 7 to 10) is transferred, with a very slight modification, to the treble ; the alto and bass accompany with the figure seen in bar 29. At bars 35 to 37 the first bar of the subject is again treated sequentially in the treble, and at bars 39 to 41 in the bass, with new accompanying counterpoints.
Forty-Eight Fugues. 19
Final Section.— The final section begins at bar 42 with a complete group of entries (subject, answer, subject), which, after what has been said, will not need further comment. The sixth and last episode (bar 48) is an almost exact transposition a fifth lower of the first (bars 7 to 10). At the end of bar 57 we see a final entry of the subject (treble) in the tonic key, accompanied by the first countersubject (alto) ; and the fugue concludes with a short coda, additional voices being introduced (as in Fugue 2) at the last bar.
FUGUE 4
C SHARP MINOR (FIVE VOICES).
The fugue is not only one of the finest but also one of the longest and most elaborate in the present work. It is sometimes spoken of as " a fugue on three subjects " ; this, however, is not absolutely correct. In a fugue on three subjects, either all the sub- jects will be heard together at first, or each of the three will have a separate exposition, more or less regular and complete. Neither is the case in the present instance ; the proper designation of the present movement is "a fugue with two countersubjects.'
Exposition : — The subject of the fugue, one of the shortest in the "Forty-eight," consists of only five notes: —
The bass leads, and the tenor replies with a real answer. No regular countersubject is introduced at this point ; for though the counterpoint with which the tenor at bars 7 to 10 accompanies the entry of the subject in the alto is the same with which the bass
20 Analysis of J. S. Bach's
accompanied the answer in bais 4 to 7, it will be seen that quite different counterpoints are employed at the next two entries, bars 12 and 14. At bar 10 a codetta of two bars is inserted between the third and fourth entries (compare Fugue 2, bars 5 to 7). The entry of the answer in the second treble (bar 12) is irregular, not because the first note is shortened, for it is always allowed to shorten or lengthen the first or last note of a subject but because it has the form of a tonal answer, and modulates to the key of the subdominant, F sharp minor. With the entry of the subject in the first treble (bar 1 4) the actual exposition is completed ; but, as this fugue differs greatly from those already analyzed, we do not consider that the second section begins here. Further entries of the subject and answer will be noticed at the following points: bar 19, tenor (G sharp minor); bar 22, tenor (F sharp minor) with the first note shortened , bar 25, alto (C sharp minor) ; bar 29, bass (B major); bar 32, alto (E major). Observe that, though no countersubject has yet been heard, great unity is given to the first part of this fugue by the frequent — one might say the almost continuous — use of the figure of four crotchets first seen in the bass of bar 7, and employed not only by direct motion, but also by inversion (bars 17, 18, 23, 24, etc.), and even by diminution bar 26) ; it is seen in all twenty- six times.
Middle Section.— The middle section of this fugue begins at bar 35, where the first countersubject (which we shall mark as CS i) makes its appearance in the first treble, accompanying the subject in the tenor. It will be noticed that it begins with the crotchet figure just spoken of: —
36 97
Forty-Eight Fugues. 21
The entry of the alto with the answer (bar 38), CS i being again heard in the upper part, leads to the first episode (bars 41 to 44). Here the tenor gives CS i by inversion, with free counter- points for first treble and alto. At bar 74 the subject in the second treble has CS i in the bass. At bars 47, 48, CS i appears in the treble ; its last notes also serve as the first notes of a new entry of the subject in F sharp minor. The second treble now has CS i ; at the same time a second countersubject (CS 2) makes its first appearance in the alto.
50
The next entries of the subject (tenor, bar 5 1 ; second treble, bar 54) are accompanied by both CS, which are therefore written in triple counterpoint with the subject, four of the six possible positions being used in the course of the fugue (see bars 49, 52, 67 and 74), The second episode (bars 57, 58), like all that follow it, is founded on the CS without the subject. An entry of the subject (first treble) in C sharp minor (bar 59) leads to the third episode (bar 62). Here we find at bars 64, 65, CS 2 in stretto. At bar 66 is an entry of the subject in D sharp minor in the first treble. It is irregular and unusual to have two successive entries (as here, bars 59 and 66) in the same voice. The fourth episode (bars 69 to 72) leads back to the tonic key.
Final Section. — The final section of this fugue begins with the bass entry in bar 73, accompanied by both CS. This is immediately followed by an entry, again in the tonic key, for first treble (bar 76) and yet another for tenor (bar 81). In the following episode (bars 84 to 88) CS 2 is again treated in stretto (tenor second treble, bass) at one bar's distance. At bar 89 we find the
22
Analysis of J. *S. Bach's
fourth consecutive entry of the subject in the tonic key, accom- panied by CS 2, but not by CS i. At bar 92 begins another stretto on CS 2, below which is heard CS i, which here makes its final appearance. The reason is that from this point the subject and CS 2 are almost continuously used in close stretto, for which CS i is less suited. Note the stretto on the subject between the two trebles at bar 94 • —
i&
i
i
i
i
(We write the passage on two staves, to show the crossing of the parts). At the same time there is a stretto on CS 2 for alto and tenor at one bar's distance, which at bars 98, 99, is drawn still closer— to half a bar, all the voices now taking part in it. The last episode begins at bar 102, and chiefly consists of stretto of CS 2. At bar 105 begins a dominant pedal, above which in bar 107 we see the last entry of the subject in the tonic key. It is followed by a coda (bars 1 10 to 115), the last four bars of which are over a tonic pedal. Observe the entry of the subject (second treble) in F sharp minor, with CS 2 in the alto; we have here, as in Fugue i, a plagal cadence, following the authentic cadence that preceded. In spite of the comparatively small amount of modulation, this fugue is remarkable for its great variety combined with perfect unity.
FUGUE 5
D MAJOR (FOUR VOICES).
Exposition.— This fugue needs only a short analysis. The subject only one bar in length,
Forty-EUtht Fuyues. 23
takes a real answer, and has no regular countersubject. At bar 3 is a codetta of one bar preceding the entry of the subject in the alto. Notice particularly the figure
seen here in both the voices, and later in the fugue at bars 6, 7, 8, 14 and 23. The three demisemiquavers here are not triplets, as incorrectly printed in some editions. The notation here em- ployed by Bach was common in his day, and is explained in old text-books. The dot here only adds one fourth to the length of the quaver, and the passage must be played
The exposition ends on the first beat of bar 6, and there is a partial and irregular counter-exposition in the two following bars : subject (bass) in D major; answer (treble) B minor!
Middle Section. — The second section begins with the first episode (bars 9 to n). The semiquaver figure in the treble (bar 9) is an augmentation of the last four demisemiquavers in the subject, in threefold repetition ; on the last note of the phrase the com- mencement of the subject is heard in the bass. The passage is then sequentially repeated a note lower; after which a group of middle entries in G (bars 1 1 to 14) — treble (subject), alto (answer) treble (answer), tenor (subject)— -is followed by an isolated entry (bass) in E minor in bar 1 5 leading to a full cadence in the same key (bar 1 7).
24 Analysis of J. S. Bach's
The second episode (bars 17 to 21) is a free inversion and extension of the first. The semiquavers which at bar 9 were in the treble are now in the bass ; the harmony, as before, is a series of chords of the sixth descending by thirds ; and the sequence is con- tinued for one bar longer. At bar 20, the beginning of the subject is heard, as if in stretto, in all the voices.
Final Section.— As the complete subject of the fugue is never heard after bar 15, it is difficult to decide with .certainty where the final section begins; we prefer to consider it as at bar 21, after the full close in the tonic key. Notice the reference in this bar to the commencement of the episodes, bars 9 and 1 7 ; it will be seen that bars 23, 24 are built on repetitions of the first figure of the subject, and bars 25 to 27 on repetitions of the last half of it,
both by direct and contrary motion. The final section of this fugue is quite irregular in its construction, though the whole piece is very effective musically.
FUGUE 6
D MINOR (THREE VOICES).
This is a very interesting little fugue, by reason of the treatment of the subject by inverse movement and the adaptation of a part of the countersubject (from the second beat of bar 4) to accompany a different portion of the subject (e.g., bar 17), or its inverted form (e.g., bar 24) After the exposition the subject is frequently modified by the substitution of a major third for a minor (see bars 13. l8. 2I» 34)-
Forty-Eight Fugues. 25
Exposition. — The subject is given out in the treble : —
As it does not reach the dominant until the final note, and without modulating, the answer (alto) is real. It is accompanied through- out by a regular countersubject in the treble. On the entry of the subject in the bass (bars 6 to 8), this countersubject is, somewhat exceptionally, divided between the treble and alto. An irregular redundant entry of the subject in the treble, commencing on the supertonic (bars 8 to 10), gives opportunity for the countersubject to be heard below the subject.
Middle Section. — The middle section is characterized less by new keys than by new treatment. In bars 13 to 16 the subject in the treble is answered in stretto by inverse movement in the alto, arid it is noteworthy that from this point onwards, all the entries, excepting an isolated one at bar 34, are in stretto at one bar's dis- tance. In bars 17 to 20 the bass leads and the alto follows, both with the subject in its direct form ; in bars 21 to 25 the subject in bass (direct) is answered by treble (inverted), and this again by bass (inverted) ; in bars 27 to 31 the answer in treble (inverted) by subject in alto (direct) and answer in bass (inverted).
Final Section. — The final entries (from bar 39, after a pre- paratory one in the bass at bar 34) are again at a distance of one bar, and are assigned to the bass and alto, both giving the subject, and in its direct form. At the close, a tonic pedal of two bars is accompanied by additional voices, which give a bar of the subject in its direct and inverted forms simultaneously, and in thirds.
There are four episodes, all founded on the countersubject. In the first (bars 10 to 12) the figure from bar 4 is treated
26 Analysis of J. S. Bach's
sequentially in the bass, followed by a fragment of the subject • the third episode (bars 3 1 to 33) is a free inversion of this. In the second episode (bars 25, 26) the same figure is employed by inverse move- ment, accompanied by the inversion of the first bar of the subject ; and in the last (bars 36 to 38) a figure derived from the first bar of countersubject (bar','3) is accompanied by the same part of the in- verted subject, but now in thirds.
FUGUE 7
E FLAT MAJOR (THREE VOICES).
This fugue is very simple and straightforward in construction. It contains no stretto, nor any of the rarer devices of fugal writing.
Exposition.— The subject extends to the first semiquaver of the third beat in bar 2 : —
r
It is interesting, as containing both the elements which call for a tonal answer, namely, commencement on the dominant, and mod- ulation into the dominant key; hence the change of the first interval in the answer, and of that at the quaver rest. The subject is in the treble, the answer in the alto (at bar 3), separated from it by a codetta of half a bar ; and a longer one (a bar and a half) is introduced before the entry of the bars with the subject in bar 6. There is a regular countersubject —
Forty-Eight Fugues. 27
and this always accompanies the subject excepting in bar 34. At bars n, 12 there is a redundant entry of the answer, separated from the exposition proper by the first episode (bars 7 to 10), as in Fugue 3.
Middle Section. — The middle section commences with the second episode, in the second half of bar 12, and contains entries of the answer in C minor (alto, at bar 1 7), and the subject in C minor modulating to G minor (bass, at bar 20), to which follows the third episode, leading back to the original key.
Final Section. — The final group embraces the entry of the answer in the bass in bar 26, the subject, with its first note altered, in bar 29, and — after a fourth episode — a last appearance of the answer in the alto in bar 34, with one note chromatically altered, and somewhat in the nature of a coda.
The codetta in bars 4, 5, and all the episodes are founded, more or less, on the figure of the first codetta (bar 2, second half) ; the third episode, however, contains greater diversity of material than the others.
FUGUE 8
D SHARP MINOR (THREE VOICES).
A fugue of highly artificial construction, full of the resource in higher contrapuntal devices of which its composer possessed such
a wonderful mastery.
Exposition. — The subject is announced in the alto—
28 Analysis of J. S. Bach's
and as it begins by leaping from tonic to dominant, the answer (treble, bars 3 to 6) is tonal, leaping from dominant to tonic. There is no countersubject. A codetta of nearly two bars, suggested by the syncopated rhythm of the subject, precedes the entry of the third voice, the bass, which enters with the subject in bar 8 ; and a second codetta (bar 10, fourth beat, to bar 12, first beat) separates this from a redundant entry of the answer, which is, somewhat exceptionally, assigned to the same voice which just before gave th!e subject.
Episodes are few