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Full text of "Analysis of J.S. Bach's forty-eight fugues (Das wohltemperirte clavier)"

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 



$ v^o 

In Canada 




SOif O SELLING AGtNTS 




(CANADA) LTD 
209.13 VICTORIA STREET. TORONTO 2 ONT 



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 hs 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 and unimportant, and call for no special 
comment (see bars 15 to 19 and 33 to 35 ; the others are quite frag- 
mentary). 

Middle Section. This commences with the first episode, in 
bar 15. In bars 19 to 22 the subject, in A sharp minor, is treated 
as a canon in the octave for alto and treble. In bars 24 to 26 it is 
employed in close stretto, the voices entering at one beat's distance, 
the alto in a rhythmically modified form and the bass incomplete. 
In bars 27 to 30 there is another canonic stretto in two parts and at 
two beats' distance, but now at the fifth below ; and to this follows 
immediately the first appearance of the subject by inverse move- 
ment, given to the treble, and in the key of the relative major. 
A pair of entries (subject and answer) by inverse movement 
occurs in bars 36 to 41, in the alto and bass respectively, the 
latter somewhat disguised by the ornamentation of its opening 
note: 




Stretto is resumed at bar 44, a canon in the octave, between 
bass and alto, providing a companion, but by inverse movement, 



Forty -Eight Fugiies. 20 

to that noticed at bar 19. Two neat little canons, strict as to 
intervals so far as they extend, but not completing the subject, 
follow in bars 52, 53 and 54, 55 ; both are in the octave, but in the 
one the subject is in its direct, in the other in its inverted form. 

Final Section. An isolated entry in the treble, in bar 57, 
marks the return to the original key. In bar 62 a new device 
makes its appearance, the subject (alto, from bar 61) being imitated 
by the bass in augmentation ; and before this is completed the treble 
(bar 64) introduces the answer by inverse movement. A somewhat 
similar series of entries (bass, alto, treble), but without inverse 
movement, occupies bars 67 to 72, and a further entry of the 
answer (alto), bars 72 to 75. Finally, an entry in the treble by 
augmentation (bars 77 to 82) is accompanied by close, but free, 
stretto of the other voices without augmentation, and a coda of 
five bars brings the fugue to a close 

It will be observed that the subject by augmentation, which is 
the characteristic of the final section, is given once to each voice, 
and that the combinations used exemplify double counterpoint 
in the twelfth ; compare, for instance, the alto and bass of bars 62 
to 64 with bars 67 (second half) to 69. The use of other than the 
principal keys (bars 67 to 75) is exceptional. 



FUGUE 9 

E MAJOR (THREE VOICES). 
Exposition. -The subject is announced in the alto 



30 Analysis of J. <S'. Bach's 

The answer, in the treble, is real, and slightly overlaps the close 
of the subject, but not so materially as to produce a " close fugue, ' 
a term used to denote those fugues in which the first exposition is 
in stretto. There is a countersubject, commencing immediately 
after the close of the subject and reaching to the fifth semiquaver 
of bar 3 ; but it does not accompany every subsequent entry (see 
bars 1 6, 19, 20), and even where present is sometimes incomplete. 
The bass introduces the subject at the end of bar 3. 

Counter-Exposition. A counter-exposition follows in bars 6 
to i o ; the order of the voices is now treble, alto, bass, and as the 
strict rule is followed, of giving the answer to a voice which before 
had the subject, and vice versa, there are here two entries of the 
answer. 

Middle Section. The middle section begins with a short 
episode (bars 1 1 to 12, first beat), based on material from the end 
of the subject and the countersubject, and contains a rhythmically 
irregular entry of the subject * in the treble at the second beat of 
bar 12, in C sharp minor, a regular one in the alto (bar 16) in the 
same key, and further episodes founded on similar material to that 
of the first. 

Final Section. The return to the original key is made at bar 
19 ; a complete group is given, namely: subject in bass, answer 
(altered) in treble (bar 20), subject in alto (bar 21). The episode 
which follows (bars 22 to 25) is interesting as containing, for its 
two upper parts, the inversion of the upper parts of bars 1 3 to 1 6, 
but with a new counterpoint in the bass. In bar 25, in the treble, 
the subject once more appears in its original form, and in, bar 28 

*Some editors have had the impudence to amend (!) Bach by making this and another 
irregular entry at bar 20 comform to the original rhythm of the subject. 



Forty-Eight Fugues. 31 

the actual cadential formula is pressed into the service for a partial 
entry of the answer. 



FUGUE 10 

E MINOR (TWO VOICES). 

The only two-part fugue in the collection, and naturally offering 
less scope for elaboration than those written in a larger number 
of parts. There is not, however, any actual feeling of thinness, 
the extensive use which is made of arpeggio serving to enrich the 
harmonic effect. 

Exposition. The subject extends to the first note of the 
third bar: 




As it modulates into the key of the dominant, the strict rule would 
have demanded a tonal answer, returning to E minor. But there 
is no third voice to be introduced, and hence no real necessity 
for a return, which, indeed, Bach has not provided; he has 
preferred a real answer, and avoided a modulation to the unre- 
lated key of F sharp minor by closing the answer on the leading- 
note of B minor. There is a regular countersubject commencing 
after the semiquaver rest, and terminating on the first note of 
bar 5. 

Middle Section. Middle entries appear in the keys of G (bar 
n), D (bar 13), A minor (bar 20), E minor (bar 22, as answer to 
the A minor entry, not as a final return to the tonic key), D minor 
an unrelated key (bar 30), and again A minor (bar 32). 



32 Analysis of J. S. Bach's 

Final Section. The final entries are somewhat irregular, that 
in bar 39 being uncompleted, while that in bar 40 is still more 
altered, having lost the characteristic arpeggio of its commence- 
ment, 

There are four episodes. The first (bars 5 to 10) is inverted to 
form the third (bars 24 to 29), and the second (bars 15 to 19), to 
form the fourth (bars 34 to 38). The occurrence of unison passages 
(bars 19 and 38) is extremely rare in a fugue. 



FUGUE 11 

F MAJOR (THREE VOICES). 

Exposition. The subject, which is announced in the alto, 
consists of a rhythmical phrase of four bars : 




As this begins on the dominant, the answer, in the treble, is tonal. 
beginning on the tonic. The countersubject commences on the 
first semiquaver of bar 5, with the second note of the answer, 
After a bar of codetta, the bass enters with the subject (bar 9, third 
beat), the countersubject being given to the treble. 

Counter-Exposition. After a short episode founded on the 
countersubject in the bass, with new counterpoint above it, there is 
a complete counter-exposition (bar 17, third beat, to bar 31, first 
beat). In this the order of entry is: subject in treble; answer in 
alto ; subject in bass, with a redundant entry of subject in alto, two 
bars after the bass, and therefore producing the first stretto. The 
countersubject is transferred from alto to bass in bars 18, 19, has 



Forty-Eight Fugues. 33 

its first three notes in inverse movement in bar 26 (treble) and is 
incomplete in bars 29 to 31 (bass). 

Middle Section. The middle section commences in bar 31, 
with a second episode, which is founded on the third bar of the 
subject in the upper parts, with a free bass. The appearances of 
the subject in this section are in stretto, and are very orderly. 
Bars 36 to 44 are in D minor, the stretto in the octave at two bars' 
distance, all the voices participating, beginning with the highest ; 
bars 46 to 54 in G minor, the stretto at the same interval of pitch 
and of time, but beginning with the lowest voice. To each stretto 
is added a codetta of two bars ending with a perfect cadence. The 
third episode (bars 56 to 64) is built on similar material to the se- 
cond, but quite differently treated. 

Final Section. The final entries are slightly irregular. At 
the last semiquaver of bar 64 the subject enters in the treble, with 
its first note shortened and the following bar ornamented. A bar 
later the subject appears in the alto, making the closest stretto 
which the fugue contains, but its form also is varied, and it is 
abandoned at bar 68. On account of the stretti, neither the middle 
nor the final section employs the countersubject. 



FUGUE 12 

F MINOR (FOUR VOICES). 

A remarkably fine fugue, rivalling No. 3 in the richness and 
variety of its episodes. It contains no stretto. 

Exposition, The subject 



34 Analysis of J. S. Bach's 

\H 







is announced in the tenor, and is given a tonal answer in the alto 
(bar 4), in order that the initial dominant may be replied to by the 
tonic; but it is noteworthy that this tonal form of answer is not 
heard again throughout the fugue. There is a regular countersubject, 
commencing on the second quaver of bar 4 and reaching to bar 7, 
first quaver; this accompanies every subsequent entry except that 
in bars 40 to 43, and even here the alto and bass give fragmentary 
suggestions of it. The bass enters with the subject in bar 7, and 
the tenor has a new counterpoint, which is so frequently used with 
the subject and countersubject (see bars 13 to 16, 19 to 22, 28 to 
30, etc.) as almost to rank as a second countersubject; the three are 
worked in a triple counterpoint. A codetta of three bars (bars i o to 
12), derived from the countersubject, precedes the entry of the 
fourth voice, the treble, to which is exceptionally assigned 'the 
subject instead of the answer. 

Counter-Exposition. As the next two entries (bar 19, tenor, 
and bar 27, bass) are still in the original keys, and with the 
answer leading, it is possible to regard them as constituting a 
partial and irregular counter-exposition, though they are separated 
by an episode. 

Middle Section. Unless the above-named two entries be in- 
cluded, this only commences at bar 30. In any case it embraces 
the subject in A flat major (bar 34) and answer in E flat major (bar 
40) and closes at the first beat of bar 47. 

Final Section. This section consists of the answer in C 
minor (bar 47) and the subject in F minor (bar 53), together with 
the intervening episode and a three-bar coda. 



Forty-Eight Fugues. 35 

The first episode (bars 16 to 19) is a free inversion of the 
codetta, treated sequentially. The second (bars 22 to 27) is similar 
to the first, with inversion of the two upper parts. In the third 
episode (bars 30 to 34) the first bar of the alto in the codetta is 
treated sequentially in the bass, imitated by the tenor, with a new 
counterpoint in the treble. In the fourth (bars 37 to 40) a part of 
the countersubject (bar 6) is worked sequentially in the treble and 
made the pattern for some free imitation in the alto, with a florid 
counterpoint in the bass. Episode 5 (bars 43 to 47) gives a new 
and more elaborate sequential treatment of the codetta with the 
addition of a fourth voice; all the other episodes are in three-part 
harmony. The sixth and last (bars 50 to 53) is a slight modifica- 
tion of the first, transposed into the dominant key. 



FUGUE 13 

F SHARP MAJOR (THREE VOICES). 

This fugue is simple in form, and similar in its construction 
to Nos. 7 and 9. 

Exposition. The subject is of exactly two bars' length : 




It is given out in the treble and, beginning on the dominant, takes 
a tonal answer (alto, bar 3 to bar 5, first quaver). The counter- 
subject commences with the second note of the answer. After the 
exposition it is always modified at its beginning and end (bars 1 5 to 
1 6, 31 to 33) or is quite fragmentary (bar 20, second and third beats) 
or absent (bars 28 to 30). There is a redundant entry of the subject 
in bar n, allowing of the inversion of subject and countersubject 



36 Analysis of J. 8. Bach's 

We find in this fugue for the first time an episode (bars 7 to 
n) formed of new material, not developed out of subject, counter- 
subject or codetta. It is, however, not only made the foundation 
of the other episodes (bars 13 to 15, 17 to 20, 22 to 28), but also 
furnishes, by inverse movement, the figure which forms a new bass 
to the subject and countersubject in bar 12, and the treble to the 
entries in bars 20 and 28. 

Middle Section. The entry of the subject in C sharp at 
bar 15 claims careful attention. A part of the countersubject (bar 
15, third beat, to bar 16, third beat) is inverted in double counter- 
point in the twelfth instead of the octave ; a new counterpoint is 
added in the treble.. The other appearances of the subject are in 
the relative minor (bar 20, bass) and the subdominant (bar 28, 
alto) and call for no special comment. 

Final Section. In the final entry (bars 31 to 33) the same 
combination is used as in bars 15 to 17, but transposed into the 
tonic key and with the two upper voices inverted. 



FUGUE 14 

F SHARP MINOR (FOUR VOICES). 
Exposition. The subject is announced in the tenor : 




The answer is real (bars 4 to 7, alto), and there is a regular 
countersubject. A codetta of one bar succeeds, developed from 
bar 2 of the subject, ana the subject enters in the bass in bar 8. 
Then follows a longer codetta, which is an elaboration of the 



- 
Forty-Eight Fugues. 37 

previous short one. The remaining voice (treble) is given the 
subject instead of the answer (compare Fugue 12). 

Middle Section. The episodes (bars 1 8 to 20, 23 to 25, 35 
to 37) are short, and comparatively unimportant. The first is 
tbuno\ed partly on the codetta and partly (from bar 19) on the 
countersubject ; the third entirely on the counter subject. 

In bar 20 the subject is introduced in the alto by inverse 
movement, commencing in B minor and modulating into F sharp 
minor. The countersubject is absent, though a free adaptation of 
its opening figure is employed as a counterpoint to the later part 
of the subject (from the end of bar 21). The next entry is in the 
direct form, in the treble (bar 25) ; it is somewhat disguised at its 
commencement by the substitution of 

JTCfJT 1 I for 

f U^ rZ^~~^ 

' f f I '~ =: kut is otherwise regular, and is accompanied 
by the countersubject in the alto. 

Final Section. At bar 28 a return is made to the original 
key, and it is possible to regard the entry in bar 29 as the 
beginning of the final section of the fugue, in which case the 
closing appearance of the subject (bars 37 to 40, mostly on a 
dominant pedal) could be described as coda. The normal 
tripartite structure is not clear in this fugue, the keys being little 
varied. At bar 32 the bass responds with the subject by inverse 
movement, with new counterpoints, the countersubject being 
absent. Against the final entry (coda) the countersubject is 
incomplete, but is partly doubled in sixths ; and its characteristic 
figure is introduced again as the tenor of the cadential chords. 



38 



Analysis of J. S. Bach's 



FUGUE 15 

G MAJOR (THREE VOICES). 

An extremely interesting and ingenious fugue, and one in 
which the musical grace and charm are in no way impaired by the 
technical elaboration. 

Exposition. The subject, announced in the treble 




remains in the tonic key throughout, and only touches the 
dominant incidentally in bar 3. The answer (alto, bars 5 to 9) 
is consequently real. The countersubject accompanies a part 
only of the sifbject (or answer), commencing at the second half 
of bar 6 : 




The codetta (bars 9, 10) before the entry of the third voice 
furnishes the germ of all the episodes. The first episode (bars 15 
to 19) is formed of a sequential treatment of the codetta with the 
addition of a third voice. 

Counter-Exposition. In the counter-exposition (bars 20 to 
31) both subject and countersubject are given by inverse move- 
ment, but with the last bar of the latter omitted. The order of 
entry is as follows : subject in alto (from bar 20) witji counter- 
subject in bass (bar 21); answer in treble (bar 24) with counter- 
subject in alto (bar 25); subject in bass (bar 28) with counter- 
subject in treble (bar 29). 



Forty-Eight Fugues. 39 

Middle Section. The last of the entries in the counter- 
exposition is not completed, the second episode commencing 
at the beginning of bar 31. Of this episode the first three 
bars are an inversion of bars 17 to 19; at bar 34 a scale 
passage is added above the figure of bar 10: the parts are then 
inverted with one another, and the two bars repeated in inverse 
movement. 

In bars 38 to 45 the subject and countersubject in their direct 
forms, and in the key of the relative minor, are answered by 
inverse movement ; the bass takes no part in these entries. After 
a third episode (bars 46 to 51; another variation of the first 
episode) the subject is treated as a two-part stretto in the octave, 
in the key of B minor, at one bar's distance, the treble leading, 
the bass responding, but breaking off at the end of bar 53. The 
fourth episode (bars 54 to 60) is a new sequential treatment of the 
codetta, with different counterpoint. The entries in bars 60 to 63 
(alto and treble) are analogous to the preceding ones, but in D 
major, with the lower voice leading, and with an added counter- 
point. The fifth episode (bars 64 to 69) is yet another variation 
of the first, with different distribution of the parts. 

Final Section. At bar 69 a return is made to the key of G, 

the subject (inverted) being assigned to the bass, and the counter- 
subject (likewise inverted) to the alto. The last episode (bars 73 
to 76) consists of free inversion of bars 34 to 37. To this follows 
the last stretto, with all the entries more or less incomplete ; the 
alto leads by inverse movement, the bass responding at one bar's 
distance ; then the treble and alto in thirds (the lather fragmentary) 
resume the direct movement. A coda of five bars brings the 
fugue to a close. Additional voices are introduced on the tonic 
pedal (bars 84 to 86). 



40 Analysis of J. S. Bach's 

FUGUE 16 

G MINOR (FOUR VOICES). 

Exposition. A very regular fugue in construction, and not 
difficult to follow. The subject in the alto, begins on the dominant 




and therefore takes a tonal answer. There- is a regular counter- 
subject (bar 3 to 4, first beat) which accompanies every entry 
of the subject except the last, but is curtailed in the stretti. A 
codetta separates the answer (treble) from the return of the subject 
(bass, bar 5), to which the answer (tenor, bar 6) follows immediately. 

Middle Section. There are only two episodes (bars 8 to 12 
and 24 to 28), separating the middle entries from the exposition 
and from the final section. Both are founded on the second bar 
of the subject, direct or inverted. 

After three entries in the relative major keys (bars 12 to 16), 
the alto with subject, tenor with answer, and bass with subject, the 
first stretto commences in bar 1 2 ; this is at the interval of a fifth, 
two voices participating, namely, the bass and the alto. Two 
entries of the subject in C minor (bars 20 and 21), and one of the 
answer in G minor with a passing-note D inserted between the 
first two notes, complete the middle group. 

Final Section. The final section, starting at bar 28, is again 
in stretto, the treble, tenor and bass commencing the subject at 
successive intervals of half a bar, but only the tenor absolutely 
completing it; the alto gives a fragment of the countersubject. 
The two last en ries (alto and tenor) call for no special comment 



Forty-Eight Fugues. 

FUGUE 17 

A FLAT MAJOR (FOUR VOICES). 
Exposition. The subject of this fugue, 




like that of No. 6, closes on the dominant without modulating ; 
hence the answer, of necessity, terminates with the supertonic ; 
but the earlier E flat, being approached by leap from the tonic, is 
capable of being answered by the tonic, and Bach has consequently 
chosen a tonal answer, the second note being changed. 

After the entry of subject in the tenor and answer in the bass 
there is a relatively long codetta of two bars, and then the other 
two voices enter regularly subject in treble, answer in alto. 
There is no regular countersubject, but the counterpoint in bar 2 
furnishes much of the material for later development. The 
codetta is founded partly upon this, and partly upon the subject. 

There are five episodes. The first (bars 7 to 10) is founded 
on the counterpoint of bar 2. The second (bars n to 13) is made 
from bar 3, with the addition of a third voice in triple counterpoint. 
The third (bars 14 to 17) is an inversion of the second, the outer 
parts of bars n and 12 being here inverted in the twelfth. 
Episode 4 (bars 19 to 21) is a new inversion of the triple counter- 
point of episode 2. The last episode (bars 25 to 27) is a sequential 
treatment in the tenor of the semiquaver figure of bars 2 and 3, 
with sequential counterpoints added in treble and alto. 

The entries of the subject and answer present no very striking 
icatures. In bar 10 there is a redundant entry of subject in tenor 



42 Analysis of J. S. Bach's 

in the original key of A flat, and consequently to be regarded as 
the close of the exposition. 

Middle Section. After the first episode the subject appears 
(bar 1 3) in the alto in- F minor ; at bar 1 7 in the tenor in B flat minor, 
answered by the alto. In bar 21 there is the only approach to 
stretto which the fugue contains, two incomplete entries of the 
answer being introduced at half a bar's distance. In bars 23 and 
24 an altered form of the subject appears in alto and treble, the 
leap of a minor 7th being substituted for a 6th. 

Final Section. The final group (bars 27 to 31) is irregular 
in key, only the bass and alto being in the tonic key, and the alto 
(answer) in one of the modified forms, ending on the tonic ; the 
tenor modulates into C minor, and the treble into D flat. The 
coda begins in bar 31, and contains one isolated entry of the 
subject, in bars 33 to 34. 



FUGUE 18 

G SHARP MINOR (FOUR VOICES). 
Exposition. The subject is announced in the tenor : 




It will be observed that it makes a modulation into the dominant 
key, and a tonal answer will be required in order to return to the 
tonic. But as the new key is entered by the striking interval of 
he augmented fourth, which must be preserved in the answer, 
there is no alternative but to make the tonal change after the initial 



Forty-Eight Fugues. 43 

dominant, thus touching transitionally on the key of the sub- 
dominant. As in many tonal fugues, a real answer is used later 
(see bar 37). 

There is no codetta in the exposition, the voices following at 
regular distances of time tenor, alto, treble, bass. There is a 
regular countersubject accompanying the entire subject 

Counter-Exposition. There is comparatively little variety of 
key in the entries in this fugue. Those in bars n, 15, 17 and 19 
though not fulfilling all the conditions of a regular counter-exposi- 
tion, are all in G sharp minor or D sharp minor, and on this 
account may be regarded as constituting an irregular one. 

Middle Section. The middle section properly begins with 
the episode in bar 21, for in bar 24 we get the subject modulating 
into the unrelated key of A sharp minor, and in bar 26 the answer 
in the key of B. 

Final Section. The final section begins*at bar 32, with the 
subject in the tenor in the original keys, accompanied by the 
countersubject in the alto, and answered, after three bars of episode, 
by the treble, commencing in C sharp minor and returning to G 
sharp minor, the alto giving a few notes only of the countersubject. 
At the entries in bars 17, 24 and 26 the countersubject is absent. 

There are five episodes (bars 9 to 11, 13 to 15, 21 to 24, 28 to 
32, 34 to 37), of which the third is constructed of new material, 
used again, however, in a modified form for the commencement of 
the fourth episode (bars 28, 29). The rest, together with the end 
of episode 4, are founded on the last six notes of the subject. 
The employment of homophony, that is, of chords proceeding note 
against note in place of combined melodies, is remarkable in the 
first episode, being extremely rare in fugal writing. 



44 Analysis of J. S. Bach's 

FUQUE 19 

A MAJOR (THREE VOICES). 

A fugue of such irregular construction that it might almost be 
termed a Caprice or Fantasia in fugal style. The limit of the 
subject is not clearly defined, but its later treatment suggests that 
it consists of the following: 




Exposition. The subject is announced in the treble, and 
answered by the alto in stretto at one bar's distance. Although 
the subject does not modulate, and contains no conspicuous 
dominant, Bach has elected to give a tonal answer, according to 
an idiom whereby he always prefers to regard the leading-note as 
the third of the dom^iant, and answer it by the third of the tonic, 
unless it be an obvious auxiliary note; compare No. 23, also, to 
some extent, Nos. 18 (second note) and 24 (seventh note). After 
a few notes of codetta, the bass enters with the subject at the 
beginning of bar 4. The next two entries, namely in the bass 
again (but with the answer) at bar 6 and in the treble (with the 
subject) at bar 9 might be regarded as an irregular, partial counter- 
exposition, as they are still in the original keys. 

Middle and Final Sections. From this point onwards, it is 
only necessary to indicate the various entries of the subject. 
These are: Bar 13, in F sharp minor, in the bass; bar 16 
(irregular and incomplete) in the bass, modulating into E; bars 23 
to 28 a group of entries in the original keys, the subject in the 
bass being given a tonal answer in the treble (varied at the end) 



Forty-Eight Fugues. 45 

and a real answer* in the alto (its first note an octave higher than 
would have been regular) ; bars 3 1 to 34, two entries of the 
subject in the key of D, alto and bass, both irregular, the latter 
modulating into B minor ; bar 39, in F sharp minor in bass, the 
initial note and rests wanting; bar 42 (presumably the "final 
section") in A major in the alto, the first note altered, answered at 
bar 44 by the bass. From this point onwards the subject is absent, 
the passage forming a somewhat extended coda. 

As a whole, the fugue is inferior in interest to most of the 
series. 



FUGUE 20 

A MAJOR (FOUR VOICES). 

A long and elaborate fugue, interesting in its construction, 
but perhaps, not one of the most beautiful. The inversion of the 
subject is somewhat ungainly. 

Exposition. The subject is announced in the alto: 




The answer is real, and is given to the treble; there is no regular 
countersubject. After a bar of codetta (bar 7) the bass takes the 
subject, the answer in the tenor (bars 10 to 14) completing the 

exposition. 

Middle Section. The episodes are few and unimportant. A 
series of entries of the subject, by inverse movement, immediately 
follows the exposition. That in the alto (bar 1 7) is fragmentary, 
being succeeded by the tenor in stretto at half-a-bar's distance ; on 



46 Analysis of J. 5. Bach's 

the other hand an additional entry in the alto at bar 24 gives the 
fuller form. In all the voices the closing notes of the subject 
undergo a slight modification. 

Canonic stretto, which is the special feature of this fugue, 
first makes its appearance in bars 27 and onwards. The treble 
and tenor give the subject, in its original key and form, in canon 
at half-a-bar's distance. The alto and bass (from bar 31) respond 
with the answer similarly treated; and in bars 36 to 40 the tenor 
and alto revert to the subject. After a short episode (bars 40 to 
43, first quaver), treble and bass give the subject in the relative 
major, again at half a bar, and its closing section is further 
imitated by tenor (from last quaver of bar 45) and alto (from last 
quaver of bar 46, modified). From bar 48, similar treatment is 
given to the inverse form of the subject, first in alto and tenor, 
then (bar 53) in alto and bass; and again with the intervention of 
single episodical bars, in the treble and alto (from bar 57) and in 
the bass and tenor (bars 62, 63, incomplete). 

Final Section. This would appear to begin at bar 64, in spite 
of some irregularity in the keys. From this point the canon is at 
the fifth instead of the octave; bass and tenor give the direct form, 
treble and alto the inverted. After the second episode (bars 71, 
72), there is another canon in the octave, bass and alto, in the 
subdominant key, followed by three incomplete entries for the 
upper voices, the tenor by inverse movement, the alto and treble 
by direct. 

The coda starts after the pause in bar 80, and contains 
incomplete stretti between alto and treble at the fifth, and for four 
voices on a tonic pedal, the bass and tenor by inverse movement, at the 
octave, the treble and alto in the direct form, at the fourth. Here 
as in several other cases, additional voices are employed for the coda. 



Forty-Eight Fugues. 4T 

FUGUE 21 

B PLAT MAJOR (THREE VOICES). 

This beautiful little fugue is one of the most perfect in 
construction and artistic finish of all the collection a veritable 
gem. 

Exposition. The subject is as follows: 




This is given out in the treble, and answered in the alto. The 
answer is tonal. The bass enters with the subject in bar 9, and 
the treble has a redundant entry, of the answer, in bar 13. There 
are two countersubjects, each with a marked individuality, and 
present with every entry from bar 9 onwards. The first (which 
we shall mark as CS i) extending from bar 6, last quaver, to bar 
9, will be readily recognized by its syncopations and iterated 
notes, the second (CS 2), bars 9 to 13, by the detached semiquaver 
figures and rests. 

Middle Section. There are two interesting episodes. The 
first (bars 17 to 22) begins with a sequential continuation of bars 
15 to 17, with the lower voices reversed, after which the bass is 
formed from a bar of the subject by inverse movement The 
second episode (bars 30 to 35) is a free inversion of the first, and 
will repay close study. 

The first group of middle entries (bars 22 to 30) begins in G 
minor, with the subject in the alto, CS i in the treble and CS 2 in 
the bass. The answer follows in the bass, modulating into C 



48 Analysis of J. S. Bach's 

minor, with CS i in alto and CS 2 in treble. The second group 
commences at bar 35, in C minor, modulating to E flat. It com- 
prises (i) an entry of answer in alto, with GS i in treble and CS 2 
in bass ; and (2) subject in treble, wholly in E flat, with CS i in 
alto and CS 2 in bass. 

Final Section. The response to the last-named entry is the 
sole entry in the original key, and therefore the only one which 
can strictly be said to belong to the final section ; it begins in bar 
41, and has the answer in alto, CS i in treble, CS 2 in bass. A 
coda of four bars is added, founded on the same material as the 
episodes. 

Of the six inversions of position possible in triple counter- 
pfefot, four are made use of in this fugue. 



FUGUE 22 

B FLAT MINOR (FIVE VOICES.) 

Exposition. The subject, announced in the first treble 




vacillates between the employment of the major and of the minor 
third of the tonic for its last note, even in the exposition (see bars 
14 and 17). The answer is tonal. There is no regular counter- 
subject. A long codetta precedes the entry of the third voice, 
which is the alto ; and three notes of codetta separate the entiles 
of the last two voices, tenor and bass. Subject and answer 
alternate in the normal way. 



Forty-Eight Fugue*. 49 

Middle Section. The middle section commences with an 
episode of eight bars (bars 1 7 to 24), founded mainly on the last 
four notes of the subject, direct and by inverse movement, and 
modulating into the key of the relative major. A group of entries, 
somewhat irregular as regards the intervals of entry, succeeds 
(bars 25 to 39), each voice taking subject or answer once, 
namely, subject in first treble, answer in second treble, subject in 
tenor, subject in bass, answer in alto ; the last two are separated 
by a few bars of codetta. The second episode (bars 39 to 45) en- 
gages only the three lowest voices. It is developed from nearly 
the same material as the first episode. The next entries are two 
appearances of the answer in the original key (tenor and bass), 
followed immediately by a fine stretto, in which the first treble 
leads, the second treble and alto follow at a minim's distance, the 
bass (varied) and the tenor at a bar's distance, and then (bars 55 
to 57) the second treble and alto give answer and subject 
simultaneously. The third episode (bars 57 to 67) is in four-part 
harmony, and is derived, even more exclusively than the other two, 
from the last four notes of the subject. 

Final Section. The final section commences at bar 67, with 
a re-entry of the first treble, and a very regular, close stretto 
ensues, the voices following one another in descending order, 
always at one minim's distance, and alternately with subject 
and answer. Both appearances of the answer are altered in 
their last note, otherwise we should have a stretto maestrale. 
The coda contains two abortive entries of the answer, in bars 
73 and 74. 

The fugue is a masterly specimen of five-part writing, though 
less elaborate in structure than No. 4. 



50 Analysis of J. S. BacJit 

FUGUE 23 

B MAJOR (FOUR VOICES). 
Exposition. The subject of this fugue, which is in the tenor 




could have been given a real answer, but Bach has elected to 
regard the second, third, fourth and fifth notes in their relation to 
the dominant, and answer them by the corresponding intervals of 
the tonic, thus giving a tonal answer, somewhat as in No. 19. 
The answer is in the alto, accompanied by a countersubject in the 
tenor. A peculiarity of this fugue, however, is that the counter- 
subject is regular throughout the exposition only, being subse- 
quently used only once in a complete form (bars 31, 32), all other 
later entries being accompanied either by mere fragments of thfc 
countersubject, or by counterpoint principally derived, in rhythm, 
from its first seven notes. The treble enters with the subject in 
bar 5, and the bass with the answer in bar 7. A codetta (to bar 
1 1) is followed by a redundant entry in the tenor in the original key. 

Middle Section. The episodes (bars 13 to 16, first quaver, 
and 26 to 29, first quaver) are founded in part on the semiquaver 
figure of the countersubject, and are not very important. The 
subject appears in the alto in bar 16, in the key of F sharp. In 
bar 1 8 it is given in the treble, by inverse movement, in the key of 
B, answered in the alto in F sharp, also by inverse movement. 
The bass then gives it in its original form, and the tenor (from bar 
24) in C sharp minor, commencing on the mediant, and slightly 
ornamented at the end. 



Forty-Eight Fitgues. 51 

Final Section. The final entries subject in alto (bar 29) and 
answer in treble (bar 31) are perfectly straightforward. 



FUGUE 24 

B MINOR (FOUR VOICES). 

A worthy close to the first part of the work. The striking 
chromatic subject 




commencing in the tonic key closes in the dominant, and in order 
to return to the tonic in the answer, and at the same time to pre- 
serve the characteristic intervals and the sequence, it was 
necessary to make the tonal change very early. TEe fifth note, 
therefore, as well as the first, is answered by the tonic, and the 
whole answer from this point is a fifth below the subject. The 
case is analogous to that of No. j 8. 

Exposition. The subject is announced by the alto. The 
answer is in the tenor, and is accompanied by a countersubject 
from the fourth beat of bar 4. A codetta of two bars, in almost 
strict canon, derived from the countersubject, is followed by the 
subject in the bass (bar 9), and this, after another bar of codetta, 
by the answer in the treble (bar 13). The entry of the subject in 
bar 21 in the alto can best be described as a redundant entry, 
being still in the original key, and giving the treble its first oppor- 
tunity of taking the countersubject. The first episode (bars 16 to 
21) also clearly belongs to the first section of the fugue, as it does 
not quit the original keys. 



52 Analysis of J. S. Bach's 

Middle Section. The middle section therefore commences 
at bar 24, with the second episode. There are, in all, four 
episodes, largely founded on the same material as the codetta, the 
closing semiquaver figure of the countersubject. The first con- 
tains further a canon in the twelfth below (from middle of bar 17),. 
and contains in bar 19 a curious abortive entry of the first three 
notes of the subject. The second (bars 24 to 30) is a modification 
of the first. The third (bar 50, third beat, to bar 53) maintains 
the semiquaver figure throughout, and the fourth (bars 63 to 69, 
first quaver) is again similar to the first. 

In bar 28 the subject is given to the tenor, in the new key of 
C minor, and at bar 34 the first stretto commences, only two 
voices participating. In bar 38 the subject, with its first note 
modified, appears in the bass, leading to a second and more com- 
plete stretto, which commences at bar 41, continues to the 
beginning of bar 47, and is followed by the answer in the key of 
D in the bass. During the stretto the countersubject is absent, 
excepting a fragment in the alto of bar 45 ; and, as frequently 
happens in stretti, only the last entry of the subject (here the 
tenor) is completed. The next series of entries (bars 53 to 63) 
is not in stretto, and needs little comment. 

Final Section. The final section commences during the 
course of this series of entries, namely, with the return to the 
original key in bar 60. New counterpoints are here substituted 
for the countersubject (bars 60 to 63). The final entries (except- 
ing the coda), are again in two-part stretto, the subject in the 
tenor in B minor (bar 69), being followed by the subject in the 
bass, beginning in E minor (bar 70) and modulating back. The 
coda (bars 73 to 76) includes a partial entry of the subject in the 
alto. 



Forty-Eight Fugues. 53 

FUGUE 25 (Book II. 1) 
C MAJOR (THREE VOICES). 

Exposition. The subject is announced in the alto : 









The answer is tonal, and is given to the treble. It will be 
noticed that as Bach treated the first note of the subject as the 
dominant of C, not the tonic of G, the auxiliary note, F, lay a. 
whole tone below it, while in the answer the corresponding 
interval is a semitone. There is no regular countersubject, and 
no codetta. The exposition ends on the first semiquaver of bar 
13, at the completion of the subject in the bass. 

Middle Section. In the first episode (bars 13 to 2 1) the second 
section of the subject is worked as a bass to a free canon founded 
on its first section. In bar 21 the subject enters in the alto, 
modulating into D minor, and followed by the answer in the 
treble, modulating to A minor. The second episode (bars 29 to 
39) is for treble and alto alone, beginning with a new treatment 
of the material of episode i, and developing (from bar 33) into a 
canon in the fifth. 

Final Section. The entries, which are technically the " final 
group," appear rather early in this fugue. The answer in the 
bass (bars 39 to 43) is separated from the two succeeding entries 
by a third episode, reaching to the beginning of bar 47, and 
furnishing new counterpoints to the semiquaver figure. The 
subject in the alto (bars 47 to 51) and answer in the treble (bars. 



54 Analysis of J. S. Bach't 

51 to 55) complete this group. The fourth and longest episode 
(bars 55 to 68) separates this from the coda ; it begins with a free 
transposition of episode i to the fifth below, with a new continua- 
tion from bar 62, still built on the semiquaver bass. The coda 
contains four partial entries of the subject, in bars 68, 72, 76 and 
79 ; a fourth voice is added from bar 80. 

Great unity of character is given to this fugue by the deriva 
.tion of nearly the entire material from the subject itself. 



FUGUE 26 (Book II, 2) 
C MINOR (FOUR VOICES). 

An exceptionally fine fugue. An unusual feature is that, 
though it is in four parts, the fourth voice does not enter until bar 
19. But it is most noteworthy for its two splendid stretti. 



Exposition. The subject 

:,; ;.; 



commencing on the dominant, takes a tonal answer. The alto 
leads, the treble follows ; and the tenor, giving the subject in bars 
4, 5, completes the exposition. 

Counter-Exposition. To this succeeds, after two bars of 
episode, a regular counter-exposition, though again only in three 
parts, and with a redundant entry in the tenor at bar n, 
transiently in F minor. The answer in the tenor (bar 7) and the 
alto (bar 10) substitutes the major third of the dominant for the 
oninor, and the subject in the treble (bar 8) slightly varies the 



Forty-Eight Fugues. 55 

rhythm. A codetta leads to a cadence in G minor, closing the 
first section of the fugue. 

Middle and Final Sections. These are not clearly differ- 
entiated, as there is scarcely any modulation away from the two 
principal keys. It would be possible to regard either the first 
entry of the bass (bar 19) or the beginning of the second stretto 
(bar 23) as marking the commencement of a "final section" ; but 
the latter is more in the character of a coda. 

The first stretto commences at bar 14, the subject in the 
treble being immediately imitated in the aUo by augmentation, 
and in the next bar answered by inverse movement in the tenor. 
From the i6th bar the subject and answer appear at distances of 
half a bar in the three upper parts, and at bar 1 9 the fourth voice 
(the bass) makes its appearance with fine effect, giving the subject 
by augmentation. The inverted and the original forms of the 
answer follow immediately in the same voice, bars 21 to 23. In 
bar 23 begins the second, and closer stretto. Here the alto and 
treble take the subject and answer at one crotchet's distance, and 
again reversing their order of entry successive appearances of 
the subject, commencing respectively on tonic and dominant ; two 
beats later the tenor introduces the subject, and two beats later 
again the bass brings it in, inverted and somewhat modified. 

The entire fugue is one of the most perfect in the series. 



FUGUE 27 (Book II, 3) 
C SHARP MAJOR (THREE VOICES). 

A very troublesome fugue to analyse, owing to the difficulty 
in determining where the subject terminates. An examination of 



f>6 Analysis of J. S. Bach's 

the latter part of the fugue shows that it should be regarded as 
consisting of only the first four notes. This is consequently the 
shortest subject to be found in the forty-eight. 

Exposition. The subject is given out in the bass: 




The answer, in the treble, is tonal ; there is no regular counter 
subject, or at least not beyond the exposition. In the third voice, 
the alto, the subject is given by inverse movement, a somewhat 
unusal treatment for the exposition. 

Counter-Exposition. A counter-exposition occupies bar 4 
and the first half of bar 5, and to this succeeds immediately the 
middle section. 

Middle Section. First the answer is given in the treble and 
alto by diminution (bar 5), and in the bass by diminution and 
inversion ; then the answer in all three voices in notes of the orig- 
inal length, the bass leading, and with continuation in canonic 
imitation; next follow two stretti (bars 9 to 10 and 10 to 12), the 
former entirely in inverse movement, the latter first inverted (bass, 
treble) and then direct (alto, bass). 

There are two episodes. The first (bars 12 to 14) is founded 
on a variation of the subject treated sequentially in the bass. The 
second (bars 20 to 24) is somewhat similar in character, the bass 
of bar 12, in a modified form, being treated by diminution in the 
treble of bar 20. 

A second stretto appears in bars 14 to 16, the answer direct 
being alternated with the subject inverted. An isolated entry in 



Forty-Eight Fugue*. 57 

the bass of bar 17 is succeded by three in diminution, the alto and 
the bass inverted, then the bass direct. After Episode 2, another 
isolated entry in the bass (bar 24, answer) leads to the final section. 

Final Section. This introduces the last stretto (bars 25, 26) 
in which the subject in the treble, inverse movement, is answered 
in the alto by augmentation and in the bass in the original form, 
though beginning on the submediant. The remaining entries, in 
bars 27, 28 to 29, 30 to 31, 31 to 32, present no specially new 
features, and need not be discussed in detail. The coda, from 
bar 32 to the end, contains one or two reminiscences of the subject 
by diminution ; as is often the case with Bach, it introduces 
additional voices. 



FUGUE 28 (Book II, 4) 
C SHARP MINOR (THREE VOICES) 
Exposition. The subject is announced in th? bass: 




The answer, in the treble, is real, and reaches to the first semi- 
quaver of bar 4 ; the rest of that bar forms a codetta, sequentially 
copying the close of the subject, and modulating back preparatory 
to the entry of the subject in the alto in bar 5. 

Counter-Exposition. There is a partial or irregular counter- 
exposition from bar 16, only two voices (treble and alto) conforming 
to the rule of tonality, while the remaining voice enters (at bar 20) 
in the key of the relative major.* 



*Riemann (Katechismus der Fugt ir-Komposition, ii., p. 32, treats this group 
as part of the middle (modulatory) section. [ED.] 



58 Analysis of J. S. Backs 

Middle Section. After a short episode (bar 21 to 23) there is 
a group of entries by inverse movement (bars 24, 26, 28), followed 
by a return to the subject in its original form and key (bar 30). 
Then comes an exceptionally long episode (bars 31 to 47), leading 
back, after various modulations, to the tonic key, in which the 
subject re-enters in bar 48. 

Final Section. Besides regular entries of the subject in the 
treble (bar 48), bass (bar 55) and alto (bar 66), there is a further 
example of inverse movement, (bar 53), the form-somewhat varied, 
and the tonality, that of A, and a final appearance in bar 67 (second 
half), in the direct form but also somewhat varied. 

The episodes in this fugue (bars 6 to 15, 21. to 23, 31 to 47, 
49 to 52, 56 to 60, 62 to 65) are extensive and of great importance, 
occupying no less than 40 bars out of 71. Almost all their 
thematic material is founded on the subject, except the theme 
given in the treble of bars 35, 36, which is subsequently combined 
with the subject in double counterpoint in the twelfth (see bars 48, 
49, and 55, 56). Thus, in spite of the large proportion of episode, 
there is great unity of character throughout, the figure of triplet 
semiquavers being maintained from the first note of the fugue to 
the end. Bars 69 to 7 1 form a short coda. 



FUGUE 29 (Book II, 5) 
D MAJOR (FOUR VOICES). 



A fugue remarkable for compactness, the whole of the episodes 
being formed from the last four notes of the subject. 



Forty-Eight Fugues. 59 

Exposition. The subject is given out by the tenor: 

* 




The answer is real, and is in the alto. A codetta of one bar the 
closing four notes of the subject treated imitatively leads to the 
subject in the treble (bar 5) answered by the bass in stretto, (bar 
6). There is no regular countersubject; the counterpoints are 
framed on the four notes already twice alluded to, and exemplify 
double counterpoint in the tenth (compare bar 3 with bar 6, etc.). 
The first episode (bars 7 to 10) is in imitation, mostly at one 
crotchet's distance, and does riot effect a modulation, but rather 
serves as an appendix to the exposition. 

Middle Section. In bars ib to 13 are two entries (alto and 
treble), in E minor and B minor respectively, and in bars 14 to 16 
the same two voices constitute a two-part stretto in the original 
key. The second episode (bars 1 6 to 2 1 ) leads to a second stretto 
(bars 21 to 24), in B minor and F sharp minor, for tenor, treble 
and alto, at one bar's distance; the answer in the bass (bar 25), 
which completes this group, is not in stretto. Another three-part 
stretto. follows (bars 27 to 29), the bass, treble and alto (the latter 
incomplete) giving the subject at distances of one beat, and in the 
interval of the octave. The third episode (bars 29 to 33) is similar 
to the first, but somewhat extended. This leads to another three- 
part stretto, again at one beat's distance, but in ascending sixths, 
and with the subject complete in each voice. Episode 4 (bars 35 
to 40) has much in common with the others, and in modulating 
back to the key of D, leads to the final section. 

Final Section. An isolated entry of the subject (bars 40, 41) 
is succeeded by the last and fullest stretto. First the answer in 



60 Analysis of J. S. Bach's 

the bass, slightly modified, is imitated at one bar's distance by a 
partial entry in the tenor, a second higher; then half a bar later 
the treble introduces a stretto maestrale, for all the voices, 
descending by thirds, and always at one crotchet's distance. The 
coda (bars 47 to 50) is similarly constructed to the episodes. 
* Altogether a marvellous little fugue. 



FUGUE 30 (Book II, 6) 
D MINOR (THREE VOICES). 

Exposition. The subject 




is in the alto ; as it reaches the dominant by step progressions 
and does not modulate, the answer, in the treble, is real. A 
countersubject, mostly in even semiquavers, accompanies it with 
the exception of its first half bar. The codetta (bar 5) is made 
from the inversion of the first half bar of the subject, treated 
imitatively. In bars 6 to 8 the bass takes the subject, the treble 
the countersubject. 

There are few changes of key in this fugue, and it would be 
possible to regard the first stretti (bars 10 to 12, 14 to 16) as 
belonging to the opening section, and the middle section as 
characterised by inverse movement (from bar 17). But the posi- 
tion of the first episode, and the dissimilarity of these stretti to 
redundant entries or counter-exposition, render it unnatural to in- 
clude them here. In any case, the division into three sections is 
not very clear. 

*I cannot refrain from quoting the rest of the Author's characteristic comment in his 
MS., though it was not intended for publication:" IVondtrJul old fellow. Bach J " [ED.] 



Forty-Eight Fugues. 61 

Middle Seotion. The first episode (bars 8, 9) is formed from 
the fragment of incidental counterpoint in the alto of bar 7. In 
bars 10 to 12 the impression of a stretto in the octave, at three 
crotchets' distance, is produced, but the bass really breaks away 
from the subject before the treble enters. After a second episode 
(bars 12, 13), consisting of a different treatment of the material of 
the first, a closer stretto is given to the two upper voices, the 
answer succeeding the subject at the distance of one crotchet ; the 
bass supplies the countersubject (bars 15, 16). In bar 17 answer 
and subject are given by inverse movement, again at one crotchet's 
distance ; and in bar 1 8 the subject in G minor, in its direct form, 
by bass and alto at the same distance of time. A third episode 
(bars 19 to 24) separates these from the final entries ; the first part 
of this episode is derived from the codetta, the rest from the 
matter of the previous episodes. 

Final Section. The final section consists of only three bars 
and contains a stretto in the octave at half a bar's distance, for 
the two upper voices, with the countersubject in the bass from 
bar 26. 

After the exposition, nearly all the entries of the subject and 
countersubject are more or less incomplete. 



FUGUE 31 (Book II, 7) 
E FLAT MAJOR (FOUR VOICES). 

A noteworthy feature of this fugue is the very small amount 
of modulation which it contains. Excepting at bar 53, where the 
key is A flat, the subject and answer are never introduced in any 
other keys than the tonic or dominant. It is, however, not 



62 Analysis of J. S. Bach 1 8 

difficult to divide into sections, the only peculiarity being in their 
relative proportions. 

Exposition. The subject is announced in the bass : 



The answer (tenor, bars 7 to 13) is tonal, both the dominant and 
the subdominant in bar 2 demanding the tonic to answer them. 
There is no regular countersubject, though a partial one, first 
heard from bar 9, second half, to bar 12, -recurs in the exposition 
(bars 16 to 19, 23 to 26). After a few notes of codetta (bar 13) the 
alto and treble enter with subject and answer quite regularly, 
except that there is here another brief codetta (bar 20) which was 
not found in the first entries. 

Counter-Exposition. A counter-exposition commences at 
bar 30, the answer leading in the tenor; the bass follows with the 
subject, in stretto at one bar's distance, and in bars 37 to 43 the 
alto and treble give the same stretto inverted, with added counter- 
points below. 

Middle Section. The first, and only episode is a rather long 
one (bars 44 to 53), mostly a canon at the fifth for treble and alto, 
with a counterpoint of free sequential pattern for the bass. It 
leads to the sole "middle entry" in bar 53 the subject in the sub- 
dominant key, with its first note altered and shortened. 

Final Section. The return to the key of E flat follows im- 
mediately (bar 59), and the final entries again employ the stretto 
at a bar's distance, now given to the treble and bass. The added 
parts are similar to those in bars 37 to 44, but not actually in 



Forty-Eight. Fugues. 63 

quadruple counterpoint. The coda (bars 66 to 70) contains no 
feature of special note. 



FUGUE 32 (Book II, 8) 
D SHARP MINOR (FOUR VOICES). 

Exposition. The subject commences on the tonic and only 
touches the dominant quite incidentally: 




The answer, therefore, is real. The countersubject, begining at 
the middle of bar 3, is only used for the first half of the fugue, 
and is not found after 23. The order of entry of the voices is : 
alto (subject), tenor (answer), bass (subject), tenor (answer). 
There is a codetta of two bars (bars 5 to 7, first quaver) between 
the tenor and bass entries ; it is constructed of new material, and 
serves as the foundation for the two episodes. As in Fugue 29, 
the first of these (bars n to 15) does not modulate away from the 
original keys. 

Middle Section. The middle section proper, as a con- 
sequence, does not begin until bar 15, where the subject in the 
bass, by a slight alteration, is made to modulate into the sub- 
dominant key, G sharp minor ; the countersubject is given to the 
treble. This entry is answered (bar 17) by the alto, similarly 
varied, but with countersubject absent, and passing into F sharp 
major, then (bar 19) by the tenor, with the countersubject (varied) 
in the bass, and passing into B, and finally (bar 21) by the 
treble in the original form and key, with the countersubject in the 



64 Analysis of J. S. Bach's 

tenor. This leads on to a stretto, in which three voices partici- 
pate, the tenor (bar 28) imitating the alto at half a bar, while the 
bass does not enter until a whole bar after the tenor, which breaks 
off after six notes only of the subject. The treble enters with the 
subject in the related key of C sharp minor in bar 27, but not in 
stretto. An alto entry in B (bar 30), and a varied one for the 
tenor (bar 32), beginning in G sharp minor but modulating to D 
sharp minor, with the addition of a codetta of a bar and a half, 
close this group of entries. The second episode begins in the 
middle of bar 35, and reaches to the middle of bar 40. 

Final Section. The subject is now heard in the bass (bars 40 
to 42) and in the treble (bars 43 to 45), the latter being accom- 
panied by the answer in the tenor in inverse movement. It will be 
seen that the treatment of bars 40 to 43 is mainly homophonic ; 
compare Fugue 18, bars 9 to n. 



FUGUE 33 (Book II, 9) 
E MAJOR (FOUR VOICES). 

One of the most perfect art works in the series. The subject 
is short and simple, but lends itself, in the hands of genius, to 
wonderful variety of resource. 

Exposition. The subject is announced in the bass 



The answer in the tenor is real, and enters against the last 
note of the subject. The other voices enter at corresponding 



Forty-Eight Fugues. 65 

intervals of time, and in regularly ascending order. There is a 
rather important countersubject 



though it does not invariably accompany the subject, and under- 
goes some slight modifications; see bars n (tenor), 37 (alto), 
38 (tenor), etc. 

Counter-Exposition. After a short codetta (bars 7 to 9) 
there follows a complete and very perfect counter-exposition in 
stretto (bars 9 to 12), each pair of entries being in canon at half a 
bar (though the first note of the alto is shortened), while the 
distance of a whole bar separates the second pair from the first. 
The answer of course leads in each pair, but as this is a higher 
voice in the first pair (alto and tenor) and a lower in the other 
(bass and treble) they are shown in double counterpoint. 

Middle Section. The first episode (bars 12 to 16) is formed 
from the countersubject, treated by imitation in all the voices. 
The next entries (bars 16 to 18, 19 to 21) are again in pairs of 
stretti (here at a distance of one bar), and although they are 
principally in the original key, they terminate in F sharp minor, 
thus meeting, in a measure, the requirement of key-contrast for 
the middle section. As noted in our analysis of Fugue i, there is 
often comparatively little variety of key in fugues containing much 
stretto. The second episode (bars 23 to 26) is founded on the 
subject metamorphosed, the leap of a third being filled in with a 
passing note, and the rhythm varied. In bars 26 to 29 is a series of 
entries of subject and answer by diminution, again as two two-voice 
stretti ; and in bars 30 to 32 the answer by diminution in the bass 
is replied to, at one beat's distance, by the subject in its original 



66 



Analysis of J. S. Bach'* 



form in the alto. The third episode (bars 32 to 35) is made from 
the subject inverted and diminished; 

Final Section. The final stretto (from bar 35) is also the 
closest. The alto leads with the answer, its first note shortened ; 
on the next half beat, the treble follows, employing both the devices 
of inversion and diminution ; again half a beat later the tenor 
introduces the subject in its original form ; and appearances of the 
answer in bass (bar 36) and subject in treble (bar 37), at distances 
of one bar, complete the group. There is an isolated entry of the 
answer in bars 40 to 41, and a short coda is added. The counter- 
subject makes its re-appearance in this final section (bars 36, 37, 
38, 40) after being absent from the stretti of the middle groups. 



FUGUE 34 (Book II, 10) 
E MINOR (THREE VOICES). 

Exposition. The subject the longest of the forty-eight 
is given out by the treble : 




The answer, in the alto, is real, and is accompanied through 
a part of its length (bars 9 to n) by a regular countersubject, 
mostly in minims. The entry of the subject in the bass (bars 12 
to 1 8), with the countersubject in the alto (bars 15 to 17), concludes 
the exposition. 



Forty-Eight Fugues. 67 

Middle Section. All the episodes are formed from bars 5, 6 
of the subject. In the first (bars 18 to 23) the last bar of the 
subject is treated sequentially in the bass (bars 18 to 20) accom- 
panied by passages of free imitation ; and from bar 20 the scale 
passage of bar 18 is inverted in the treble, accompanied by new 
counterpoint which was partly suggested by that of bar 7. In the 
second episode (bars 35 to 41) the scale passage in imitation is 
used in all the voices. In the third (bars 55 to 59) the last part 
of the subject is treated sequentially, first in the treble, then in the 
alto (bar 58), with new counterpoint for the other parts. The 
fourth episode (bars 65 to 71) presents a free treatment of the same 
material. The fugue contains no stretto. The middle entries are 
the following: subject in G, in the treble (bars 23 to 29), with 
countersubject in the alto ; answer in D, in the alto (bars 29 to 
35) with countersubject in the treble; and three more or less 
isolated entries in the three principal minor keys (by ascending 
fourths) bar 41, bass, B minor (the dominant), bar 49, alto, 
E minor (tonic), bar 59, treble, A minor (subdominant). That 
the return to the original keys does not here mark the commence- 
ment of the final section, is shown by the succeeding entry in a 
different key, A minor. 

Final Section. The final section, therefore, begins at 
bar 71, with the entry of the subject in the bass in E minor. 
This is here the only appearance of the subject, bars 78 to 86 
forming a coda, which is based largely on an ornamented dominant 
pedal. 

The countersubject accompanies 'every entry of the subject in 
this fugue. The student will readily discover it where its position 
has not been indicated in the present analysis. 



68 Analysis of J. S. Bach's 

FUGUE 35 (Book II, 11) 

F MAJOR (THREE VOICES). 

A fugue of unusual construction, in the few entries of the 
subject, and the very large proportion of episode. An important 
feature of the fugue is its two pedal points (bars 61 to 65, and 76 
to 82) : the latter is the longest yet met with in the collection. 

Exposition. The subject leaps from tonic to dominant 




and therefore takes a tonal answer. The treble leads, answered 
by the alto. A long codetta (bars 9 to 14) separates this from 
the entry of the bass with the subject. After another codetta 
(bars 1 8 to 21) the same Yoice gives a redundant entry of the 
answer; this is unusual, though occasional analogies are to be met 
with (e.g., Fugue 19). There is no regular countersubject. 

Middle Section. The first and longest episode (bars 25 to 
52) commences with a sequential treatment of bar 25, followed, at 
bars 29 to 33, with imitations founded on bars 4 and 5 of the 
subject. Bars 33 to 34 are developed from the codetta (bars 9 to 
14). From bar 45 to 52 is a sequence in the bass, made from 
the subject. In bar 52 the subject reappears in the alto, partly in 
the original key, but so harmonized as to close in D minor. If we 
accept Riemann's view that this entry denotes the commencement 
of the final section, we shall have a middle section consisting solely 
of episodical matter. But the next entry is in the subdominant 
(bar 66, bass), so that it is best to regard the final section as not 
commencing until bar 85. 



Forty-Eight Fugues 69 

The second episode (bars 56 to 66) is founded on bar 10 of 
the codetta. In the third (bars 70 to 85) we have mostly the 
rhythms of the codetta, with new thematic material e.g. y the canon 
at the seventh for treble and alto, bars 72 to 76. 

Final Section. The final entries are irregular, the first (bars 
85 to 89) in substituting a minor submediant for a major, the other 
(bars 89 to 95) in leaping a fourth (like the answer) and containing 
sequential extensions which prolong it by two bars. The coda 
(bars 95 to 99) is founded on the beginning of the first episode. 



FUGUE 36 (Book II, 12) 
F MINOR (THREE VOICES). 

A beautiful little fugue of very straightforward and simple 
construction. 

Exposition. The subject is in the treble : 




A few notes of codetta separate it from the entry of the answer, 
which is tonal. There is no countersubject. A codetta of nearly 
four bars, founded chiefly on bar 7, separates the answer (alto> 
from the return to the subject (bass). 

Middle Section. There are two middle entries (bars 25 and 
29), namely the subject and answer in the relative major and its 
dominant, given respectively to the treble and alto. 

Final Section. This is very long, commencing at bar 40, and 
consequently occupying jusi over one-naif of the fugue, in spite 



70 Analysis of J. S. Back's 

of one entry in the subdominant key (bars 71 to 75), it is not 
possible here to treat the appearance of that key as indicative of 
the middle (modulating) section; for it is answered in stretto by 
the final appearance of the subject in the tonic key (bar 74). The 
other two entries in the section (bar 40, bass; bar 50, alto) are 
both in the tonic key. 

The episodes are four in number. The first (bars 15 to 24) 
begins with a sequential prolongation of bar 3 of the subject, after 
which, at bar 17, a new sequence appears, formed from the 
beginning of the subject, with a new counterpoint. The second 
episode (bars 32 to 40) is mostly an inversion of part of the first 
(bars 18 to 21). In Episode 3 (bars 44 to 50) a sequence made 
from the last part of the subject appears in the bass, with upper 
parts suggested by the codetta. In the last and longest episode 
(bars 54 to 71) a new treatment of the first part of the subject is 
seen in the bass (bars 56 to 65), after which a modification of 
Episode 2 is introduced. The coda (bars 78 to 85) is mostly a 
new variation of Episode 2. 



FUGUE 37 (Book II, 13) 
F SHARP MAJOR (THREE VOICES). 

Exposition. The subject is announced in the alto: 




The answer, given to the treble in bars 4 to 8, is real, the dominant 
being treated as supertonic of B. into which key a passing 
modulation is made, and therefore answered by G sharp, tne snper- 
tonic of F sharp. There is a countersubject, commencing one 



Forty-Eight Fugue*. 71 

crotchet later than me subject, and terminating with the last 
accented note of the subject, not having a feminine ending. 
There is no codetta, and the bass entry at bar 8 is regular. 



Counter-Exposition. After an eight-bar episode, founded on 
a variation of the quaver figure of bars 2, 3, with new counter- 
point, a counter-exposition commences in bar 20, with subject in 
treole and countersubject in bass. A second episode (bars 24 to 
32) separates this entry from the rest of the counter-exposition, 
and consists of free canonic imitation, between treble and alto, of 
a sequence made from the first notes of the countersubject, 
accompanied by quavers in the bass. In bar 32 the answer 
appears in the bass, with countersubject in the alto, transferred to 
the treble in bar 34, last beat, and varied ; in bar 36 the subject is 
in the alto, and the countersubject in treble. 

Middle Section. This starts abruptly in bar 40, with an entry 
in the relative minor (subject in treble, countersubject in alto), 
without any connecting episode. Episode 3 (bars 43 to 52) is a 
transposition of Episode i, with the two upper parts inverted. 
The only other middle entry (from bar 52) is in the key of B, with 
the subject in the alto and countersubject in the treble. The fourth 
episode (bars 56 to 64) is a transposition and inversion of the second, 
on the same plan as the third is of the first. All the episodes in 
this fugue are of exactly the same length eight bars. 

Final Section. The entries are quite regular (bass, alto, treble, 
bars 64, 70 and 76 respectively), but the countersubject is more or 
less incomplete or varied, and is wanting in bars 70 to 74. There 
is a short coda from bar 80, founded on the second episode. 



72 Analysis of J. S. Bach's 

FUGUE 38 (Book II, 14) 
F SHARP MINOR (THREE VOICES). 

A very fine fugue, of unusual construction. It is sometimes 
described as a " triple fugue," but this is not strictly accurate. 
Two counterpoints introduced later (bars 20 and 36) are subse- 
quently combined with the subject, somewhat as in No. 4 ; but with 
this difference, that they do not first appear together with the 
subject. Thus they do not fulfil the conditions of true counter- 
subjects ; and although they have treatment somewhat analagous 
to separate expositions, the intervals of entry are too irregular to 
justify their being called new subjects. We therefore treat them, 
on their first appearance, as episodes, designed to be employed 
subsequently as countersubjects. 

Exposition. The subject is in the alto : 




The answer in the treble is tonal, the dominant being 
answered by the tonic. A codetta (bars 7 to 8) is introduced before 
the entry of the bass with the subject. There is no countersubject 
in the exposition. 

Counter-Exposition. After the first episode (bars n to 14), 
which is formed from the first note of the subject and answer, 
treated by imitation, direct and inverted, there is a partial counter- 
exposition, in which only two voices participate. The bass leads 
with the answer, which is here real instead of tonal, is somewhat 
varied in bar in bar 15, and breaks off at the second beat of bar 16, 
where the treble enters with the subject in stretto. A codetta, or 



Forty-Eight Fugues. 73 

link, leads to a perfect cadence in the key of the relative major in 
bar 20. 

Middle Section. The second episode (bars 20 to 28) 
announces the first new theme. This is given out by the bass 




imitated successively by the alto and treble at distances of half a 
bar, and then further developed with fragments of the subject (e.g., 
bar 24, alto, bar 28, treble and bass). It commences in F sharp 
minor and modulates through A major to B minor. In this key 
appears an isolated entry of the subject in the alto (bars 28 to 31), 
combined with the counterpoint (from Episode 2) in the treble in 
bar 29 and bass in bar 30. The next entry is in the bass, in C 
sharp minor, at bar 34, with the new counterpoint in the upper 
voices. The third episode (bars 3 7 to 5 1 ) introduces the second new 
theme, slightly overlapping the preceding appearance of the subject. 




This is imitated successively by the treble and bass, and developed 
at some length. A re-entry of the subject in B minor in the alto 
(bars 51 to 54), accompanied in the bass by material derived from 
the new (third) episode, could possibly be regarded as the com- 
mencement of the final section in an irregular key ; but it is more 
logical, not only on account of the key, but also because the triple 
counterpoint does not commence until the next entry, to refer this 
one to the middle group. 

Final Section. The three themes which have been quoted 
are now combined in triple counterpoint. In bars 54 to 57 the 



74 Analysis of J. S. Bach's 

subject is in the treble, in the tonic key, slightly modified at its 
commencement, the triple counterpoint being found in bar 56. 
Bars 57 to 60 and 63 to 66 contain the fourth and fifth episodes, 
with new treatment of the semiquaver figure. In bars 60 to 63 
the answer in the bass, and in. bars 66 to 69 the subject again in 
the treble. Three of the six possible positions of triple counter- 
point are employed, each theme appearing once in the bags ; bar 
56 should be carefully compared with bars 61 to 62 and bar 68. 



FUGUE 39 (Book II, 15) 

G MAJOR (THREE VOICES). 

A fugue of simple construction, requiring little comment 

Exposition. The subject is announced in the treble 




and is separated from the answer by a codetta of two bars, likewise 
in semiquavers, though with the arpeggios replaced by scale- 
passages. The answer is in the alto, and is tonal ; it would also 
have been possible here to give a real answer, starting on super- 
tonic, as the initial dominant is a note of small value, and part of 
an arpeggio. There is no regular counters ubject. After a second 
codetta, similarly constructed to the first, the bass introduces the 
subject in bar 15. Bars 20 to 23 form a codetta to the exposition, 
making a cadence in the dominant key. 

Middle Section. There are two episodes (bars 23 to 33 and 
45 to 64). They are both derived from the first notes of the subject. 
In the first, the treatment is by imitation at the interval of the 



Forty-Eight Fugues. 75 

fourth ; the second episode is largely sequential. The latter closes 
with a long dominant pedal (bars 56 to 64). There is only one 
middle entry of the subject, namely, in the bass from bar 33. 

Final Section. This likewise contains only a single entry of 
the subject, which is given to the alto. A couple of bars are added 
to lead to the final perfect cadence. 

A peculiarity of this fugue is the extensive compass of the 
upper voice, which from bar 60 to 63 goes down nearly to the 
lowest note of the bass. The flow of the parts shows clearly that 
it is the upper voice which descends here. 



FUGUE 40 (Book II, 16) 
G MINOR (FOUR VOICES). 

One of the finest fugues in the whole collection, the counter- 
subject being inverted in the tenth and twelfth as well as in the 
octave. 

Exposition. The subject, which is in the tenor, reaches to the 
second beat of bar 5 : 




The answer, in the alto, commences with the final note of the 
subject, and is tonal. The countersubject follows the subject 
immediately, and terminates either at the first or second beat of 
bar 9, but its ending is usually altered after the exposition. There 
are no codettas, and the entries of the remaining voices are quite 
regular. The reappearance of the subject in the tenor at bar 20 
in the original key, is best regarded as a redundant entry, although 



76 Analysts of J. S. Bach's 

separated from the others by a short episode. It gives the bass 
the opportunity of taking the counters ubject, in the normal double 
counterpoint at the octave, before the introduction of the new 
methods of inversion. 

Middle Section. The second episode (bars 24 to 28) modu- 
lates more freely, and clearly belongs to the middle section, as does 
also the entry of the subject in D minor in the alto (bar 28), 
introducing the new feature of double counterpoint in the twelfth. 
In bars 32 to 40 there is a pair of entries in the relative major 
keys, the subject in the treble being answered in the bass. The 
countersubject is now inverted at the tenth. In bar 45 the sub- 
ject is introduced in thirds, in the two middle voices, the double 
counterpoint being therefore simultaneously at the 'octave and the 
tenth ; and similarly at bar 51 it is in sixths (treble and alto), the 
countersubject in the tenor. The former of these entries (bar 45) 
is harmonised mostly in B flat, modulating into F, the latter (bar 
51) mostly in C minor. At bar 59 there is a still further elabora- 
tion, both the subject and the countersubject being given in thirds, 
in the key of E flat ; the resulting double counterpoint is there- 
fore simultaneously in the octave (alto and tenor) in the tenth 
(treble and tenor, and alto and bass) and in the twelfth (treble 
and bass). 

Final Section. In bars 67 to 69 portions of the subject and 
countersubject are heard in the tenor and alto (inverted at the 
twelfth) in the tonic key, broken into at bar 69, after the manner 
of stretto, by an entry of treble and bass with subject and counter- 
subject at the original interval, but accompanied by tenor and alto 
in compound thirds ; this produces again the combinations 
discussed in connection with the entry at bar 59, only with a 
different distribution of the parts. After a perfect cadence at bar 



Forty-Eight Fugues. 77 

75, a coda is added, founded chiefly on the countersubject, but with 
an altered entry of the subject in the bass from bar 79. 

The episodes of this fugue are all founded on material 
suggested by the countersubject. They are five in number : bars 
17 to 20, 24 to 28, 40 to 45, 55 to 59 and 63 to 67. 



FUGUE 41 (Book II, 17) 
A FLAT MAJOR (FOUR VOICES). 

Exposition. The subject is in the alto : 




The answer is tonal, but (as with so many others) it is only the 
first note which needs alteration. The countersubject commences 
on the second beat of bar 3 and closes with the subject, at the 
beginning of bar 5. There is a bar of codetta, founded on the 
subject. The remaining entries in the exposition are at bars 6 and 
8. The order of the voices is not quite one of the most usual, 
alto, treble, tenor, bass. An episode (bars 10 to 13), separates the 
exposition from the counter-exposition. 

Counter-Exposition. The subject again leads (bar 13), but 
now in the bass, and with the countersubject inverted at the 
twelfth (in the tenor), which necessitates the change of a D flat to 
D natural in the subject. The answer follows in the alto (bar 16) 
then the subject in the tenor (bar 18) and finally, after a codetta, 
the subject again in the treble. The countersubject is always 
present, though incomplete. 



78 Analysis of J. S. Bach's 

Middle Section. This follows immediately, the subject being 
presented in the alto in the key of F minor, with countersubject in 
the treble. The second and last episode (bars 26 to 32) is formed 
from the last member of the subject. The next appearance of the 
subject is at bar 32 in the tenor, in the unrelated key of E flat 
minor, and unaccompanied by the countersubject. The entry at 
bar 35 in the treble, in the key of B flat minor, may be regarded as 
the answer to the preceding, though real instead of tonal ; the 
countersubject is in the alto. Next follows an entry in the bass in 
D flat (bar 37), with a portion of the countersubject in the treble. 

Final Section. The subject returns in the key of A flat in 
the tenor in bar 41, with the countersubject, curiously varied, in 
the treble ; and is answered in stretto by the bass in bar 42. 
There is a coda from bar 46 to the end, containing an entry of the 
answer (but in the tonic key) in the tenor at bar 48, where a fifth 
voice is added, the first bass taking a part of the countersubject 
while the second supplies the harmonic bass. 

Although nominally a four-part fugue, there is a great pre- 
dominance of three-part writing, less than one-third of the whole 
being really in four parts. 



FUGUE 42 (Book II, 18) 
G SHARP MINOR (THREE VOICES). 

One of the longest and most elaborate of the forty-eight, 
although containing no stretto. It is virtually a double fugue, its 
second subject (or countersubject) having a separate exposition 
from bar 61 to 83, only slightly irregular at bars 71 to 75. Con- 
trast the very irregular entries of the new themes in No. 38. 



Forty-Eight Fugues. 79 

First Section. The subject is announced in the treble 




and takes a real answer (alto). There is a codetta from bar 9 to 
the end of bar 12, the subject entering in the bass at the beginning 
of bar 13. This completes the exposition proper, but it is note- 
worthy that all the four following entries (bars 19, 33, 45, 55) are 
in the original key. It would be possible to classify them as a re- 
dundant entry of the subject (bar 19) and a counter-exposition (bars 
33 to 59), but the latter would be irregular, and it must be borne 
in mind that the three normal divisions of a double fugue of this 
class are: (i) treatment of first subject separately; (2) treatment of 
second subject separately; (3) treatment of both subjects combined. 

Middle Section. A new theme is announced in the treble 
from bar 6 1 , in the dominant ke} T : 



This is answered in the tonic by the alto (bar 66). The bass then 
introduces it in the subdominant instead of the dominant (bar 
71) and there is a redundant entry in the treble in the tonic 
(bar 79). 

Final Section. After a longish episode, the two subjects 
are combined at bar 97, the first being in the bass, the second in 
the alto. In the answer to this (bar 103), the treble takes the 
first subject, the alto again taking the second. At bar in we 
have the only entry which is not in one of the original keys. 
Here the key is E, with the subjects in the two upper voices. 
The two remaining entries are in G sharp minor; in bars 125-129 



80 Analysis of J. S. Bach's 

the first subject is in the alto, and the second (not quite com- 
pleted) in the bass; in bars 135 to 139 the first is the treble, the 
second is the alto. A short coda concludes the fugue. 

The episodes, though numerous, are not of exceptional im- 
portance. They are developed, as usual, from suggestions from 
the subject (as at bars 37 and 129), the countersubject (as at bars 
115, etc.) or the codetta (as at bar 49, etc.). See bars 23 to 32, 
37 to 44, 49 to 54, 84 to 96, 107 to in, 115 to 124, 129 to 134. 



FUGUE 43 (Book II, 19) 
A MAJOR (THREE VOICES). 

A melodious little fugue, of such simple construction as to 
call for hardly any special remarks. 

Exposition. The subject is announced in the bass : 




The answer, in the alto, is real, and there is no regular counter- 
subject. The codetta (bar 4) is in sequence, made from the last 
part of the subject. The treble enters in bar 5 with the subject ; 
the bass in bar 7 with a redundant entry of the answer. 

Middle Section. The middle entries follow the exposition 
almost immediately, the subject entering in the treble at bar 9, in 
the key of F sharp minor. This is answered in the alto in bars 
12, 13, in C sharp minor. The first episode (bars 13 to 16) and 
all succeeding ones are founded on the same part of the subject as 
is the codetta. The next entry is in the key of A (bar 1 6, bass) 
and might have indicated the arrival of the final section of the 
fugue; but Bach here treats it rather as the dominant of the 



Forty-Eight Fugues. 81 

following entry (bar 20, treble) which is in the key of D, and 
therefore as still belonging to the modulating section. It will be 
noticed that it is made to close in D, not in A. The second 
episode (bars 17 to 20) separates these two entries, and contains 
incidental modulation into B minor. The third episode (bars 2 r 
to 23) modulates from D into E, and in bar 23 the subject enters 
in the alto in that key, with its sixth note chromatically lowered. 

Final Section. This may either be regarded as starting 
from the entry just noticed (as the answer leading) or, perhaps 
more naturally, as containing only the single entry, in the original 
key (bars 28 to 29), with a cadential bar added. The episode 
which separates these last two entries (bars 25 to 27) gives the 
semiquaver figures partly by inverse movement. 



FUGUE 44 (Book II, 20) 
A MINOR (THREE VOICES). 

One of the most interesting of the shorter fugues. We 
have shown elsewhere* that virtually the same subject has been 
treated in entirely different ways by various composers. 

Exposition. The subject, which is in the bass, 

> i t. f 

commences on the dominant ; the alto (bars 3 to 5) therefore gives 
a tonal answer. The countersubject commences with the demi- 
semiquaver. A codetta separates the answer from the entry 
of the treble with the subject, with a new counterpoint in demi- 
serniquavers. 

* " Fugal Analysis," pp. 107-134. 



82 Analysis of J. S. Bach's 

Middle Section. The first episode (bars 8, 9) modulates 
from the key of A minor into the relative major, in which key the 
next entry is made, in the bass, with the countersubject in the 
treble. A passing note (F, quaver) is here introduced between 
the first two notes of the subject, as is also the case in the final 
entry, at bar 25. The second episode modulates back to A minor, 
but the entry of the treble (bar 13) is in the form of the answer, 
and passes at once into E minor ; the countersubject is given to 
the alto. In bar 1 7 (subject in alto, countersubject in bass) the 
key is again A minor, but the sequel shows that we have not yet 
reached the final section ; the first note is shortened in this entry, 
and the subdominant substituted for the dominant, so that we 
have again the form of the answer. In bars 21 to 23 there is an 
entry of the subject in D minor in the treble, with the counter- 
subject in the bass. The episode which follows concludes the 
middle section, modulating back to the original key. 

Final Section. As in No. 43 and some other fugues, there 
is only one entry of the subject in the final section. This is in 
the bass (bars 25 to 27) and is unaccompanied by the counter- 
subject, with the exception of a fragment in bar 2 7. The coda 
(bars 26, 28) is short and unimportant. 

The episodes in the fugue, though short, are all very interest- 
ing. The first (bars 8, 9) commences with a transposition of the 
codetta, while the figures in bar 9 are suggested by the counter- 
subject. Episode 3 (bars 15 to 17) is again derived from the 
codetta, with new imitative treatment. In the fourth (bars 1 9 to 
2 1 ) the bass gives a sequential treatment of the last figure of the 
countersubject, which is accompanied by a canon at the fifth 
between the other two voices. The fifth episode (bars 23 to 25) 
commences with a portion of the countersubject in the bass, the 



Forty-Eight Fugues. 

rest of the material being derived from the codetta, 
are closely related to Episode 3. 



83 



Bars 24, 25 



FUGUE 45 (Book II, 21) 
B FLAT MAJOR '(FOUR VOICES). 

A highly interesting fugue, presenting seme unusual features 
The most striking is the treatment of the two new counterpoints 
which accompany the entry of the subject in bar 33. In bars 41 
to 44, the upper of the two counterpoints of bars 33 to 36 is 
inverted in the twelfth and the lower one in the tenth. In bars 56, 
57 the two counterpoints are inverted in the twelfth with one 
another; and in bars 80, 81 the second counterpoint again 
appears at the tenth against the subject. 

Exposition. The subject is in the alto : 




Here, as in No. 39, Bach has chosen a tonal answer where 
a real could also have been justified, and would have been pre- 
ferred by many composers. He answers the fifth note (the 
dominant) by the tonic, although it is in the middle of an arpeggio. 
The answer is given to the treble. The codetta (bars 9 to 13, 
first quaver) is founded on the first bar of the subject, direct and 
by inverse movement. The next three entries (bars 21, 32, 40), 
all separated by episodes, are likewise in the two principal keys, 
but do not as would at first sight appear form a regular 
counter-exposition. The first of them has the character of a 
redundant entry of the answer in the bass, now real instead of 
tonal. But the next entry (bar 32) introduces an important new 



84 Analysis of J. S. Bach's 

feature, in the counterpoints already referred to ; and we have 
learned from some other analyses that in such cases as these 
Bach sometimes prefers to maintain the original tonality. 

Middle Section. Bar 32, where the answer (again real) 
re-enters in the alto, at first absolutely without accompaniment 
and then (bar 33) with syncopated countersubject in the treble, 
and one in long notes in the bass, consequently marks the com- 
mencement of the middle section. The companion entry, from 
bar 40, shows the subject in the treble with CS i in the bass and 
CS2 in the alto. In bar 47 an entry is made in the bass in a new 
key, G minor, and the ndw counterpoints are only partially used 
(bars 49 to 51). 

The fugue contains only one small stretto, in the key of E 
flat. The subject enters in the treble in bar 53, commencing on 
the tonic instead of the supertonic, is imitated at the seventh 
below the alto at one bar's distance, and again at one bar's distance 
by the bass a sixth lower still ; but only the alto completes the 
subject. 

The last entry of the middle section is in C minor, in the 
treble, with CS i in the alto and CS 2 in the bass. 

Final Section. The return to the original key is made in 
bars 78 to 82 by the answer in the treble, in its original tonal 
form, but with E natural instead of E flat. A part of the counter- 
subject is present from bar 80. From bar 82 to the end is a long 
coda, founded on the opening bar of the subject, but without 
actual entries of it. 

The subject either its first or its second half furnishes the 
material for all the episodes. These are mostly short, and need 
not be discussed in detail. They will be found in the following 



Forty-Eight Fugues. 85 

bars ; (i.) bars 17 to 21 ; (n.) 25 to 32 ; (HI.) 36 to 40 ; (iv.) 44 to 
47 J (v.) 58 to 63 ; (VL) 67 to 78. 



FUGUE 46 (Book II, 22) 
B FLAT MINOR (FOUR VOICES). 

This fugue, quite exceptionally, is divisible into five sections 
rather than into three. These are : (disregarding the episodes) 
(i.) The Exposition, bars i to 21. (n.) The first stretti, on the 
original form of the subject, bars 27 to 37. (in.) A series of 
entries by inverse movement, bars 42 to 62 (*). (iv.) The 
second stretti, on the inverse form of the subject, bars 
67 to 77. (v.) The third stretti, combining both forms of the 
subject, bars 80 to 84, 89 to 93 and 96 to 99 ; the last group 
belongs to the coda. The exactitude of the correspondence, in 
construction, between sections i. and in. and sections n. andiv. 
can hardly escape notice. The rule that the first and last sections 
of a fugue must be in the principal keys still holds good ; but the 
middle section is extended to three sections. 

Exposition. The subject is given out in the alto : 




The answer is real, and is assigned to the treble, a rather 
chromatic countersubject accompanying it in the alto. A codetta 
(bars 9, 10) precedes the entry of the tnird voice (subject in bass), 

* The author in his MS. has spoken of this as a counter-exposition, and this seems 
a justifiable designation, as indicating its nature ; but its position atter obvious " middle 
entries' and its irregularity of intervals of entry (bars 52, 58) and even of key (bar 58) 
prevent its coming under any ordinarily accepted definition thereof. [ED.] 



86 Analysis of J. S. Bach's 

and a second codetta (bars 15, 1 6) that of the remaining voice, the 
tenor. The countersubject is employed regularly. 

Middle Section. In bars 27 to 31 and 33 to 37 there are two 
canonic stretti, each at one minim's distance ; the former is in the 
original key, between tenor and alto, the lower voice leading ; the 
latter in the relative major, between treble and bass, the higher 
voice leading ; the countersubject is absent. Bars 42 to 62 constitute 
an irregular counter-exposition, with both subject and counter- 
subject in inverse movement. The tenor leads, commencing on 
the dominant, the countersubject being given to the alto ; in bar 
46 the subject is in alto, countersubject in tenor ; in bar 52 subject 
in treble, countersubject in alto; in bar 58 subject in bass, 
countersubject in treble (a part only, bar 59). In bars 67 to 71, 
and 73 to 77, the canonic stretti on the inverted subject should 
be most carefully compared with the first stretti (bars 27 to 37). 

Final Section. In bar 80 the treble gives the inverted 
subject, the tenor (in stretto at one minim's distance) the direct 
form ; the alto, in bars 82 to 83, has a fragment of the inverted 
countersubject. The tonality is irregular (keys A flat, D flat, E 
flat minor) until the entry at bar 89, but the treatment is the same, 
so that both groups evidently belong to the final section. In bar 
89 the direct form of the subject leads, in the bass ; the inverted 
form responds, in the alto. The coda commences in bar 93, and 
contains a final stretto, in which the two upper voices give the 
direct subject in sixths, the two lower replying with the inverted 
form in thirds. 

The episodes (bars 21 to 26, 37 to 41, 62 to 66, 84 to 88) are 
also interesting, and will repay careful examination. 

This is emphatically one of the finest and grandest, as well as 
one of the most elaborate, of Bach's fugues. 



Forty-Eight Fugue*. 87 

FUGUE 47 (Book II, 23) 
B MAJOR (FOUR VOICES). 

The finest example of double counterpoint in the twelfth 
which is to be met with in the whole collection. There are two 
countersubjects, one which is used in the exposition and not 
subsequently, the other invertible in the twelfth in the counter- 
exposition and onwards. We mark them CS i and CS 2, as in 
other cases where there is more than one. 



Exposition. The subject is in the bass: 



A few notes of codetta separate this from the answer (in the tenor) 
and CS i (in the bass). The answer is real. A longer codetta, 
formed from the first and from the beginning of CS i, is found in 
bars 8, 9, and another, identical but with a 'new counterpoint 
added below, in bars 17, 18. The alto takes the subject in bars 
10 to 13, and the treble the answer in bars 14 to 17 ; in bars 19 to 
22 the bass has a redundant entry of the subject, allowing CS i to 
appear in the treble, z>., in double counterpoint. 

Counter-Exposition. After an episode of five bars, con- 
taining reminiscences of codetta and of CS i, bat largely new, a 
counter-exposition commences at bar 27 the answer leading in the 
tenor. Here CS 2 first makes its appearance: 



88 Analysis of J. S. Bach's 

A rather long codetta (bars 30-34), formed from this new counter- 
subject, precedes the entry of the subject in the alto. Against 
this entry, CS 2, now in the bass, is employed in double counter- 
point at the twelfth. In bar 42 the answer is in the treble; CS 2 
(again inverted at the twelfth) accompanies it in the alto. There 
is no entry of the bass in the counter-exposition. 

Middle Section. Bars 43 to 45 having been harmonised so as 
to modulate into the minor keys, the middle section is introduced 
without the interposition of a true episode, though there are a few 
bars of link. In bar 48 the bass enters with the subject in 
G sharp minor, the treble taking CS 2, at its original interval. In 
bars 53 to 56 the subject is in the tenor, in E major, CS 2 in 
the alto, in sixths with the subject, hence in the inversion at the 
twelfth; in bars 60 to 63 the subject is again in the tenor, but in 
G sharp minor, CS 2 in the treble, at its original interval. A long 
episode (bars 63 to 74) terminates the middle section of the fugue, 
leading back to the key of B. 

Final Section. The subject and answer alternate, separated 
by episodes; see bars 75 (bass), 85 (tenor) and 93 (treble). 
Against the first of these entries, CS 2 is not used, though a 
fragment of it appears against the first bar of the subject. 

The coda (bars 96 to 104) and most of the episodes are not 
formed directly from the material of either the subject or the 
countersubjects, but are either chiefly or entirely of new material. 
The principal episodes are in bars 22 to 27, 38 to 41, 56 to 59, 63 
to 74, 78 to 84, 88 to 92. 

The fugue contains no stretto. 



I'wty-Eight Fugues. 89 

FUGUE 48 (Book II, 24) 
B MINOR (THREE VOICES). 

This fugue is so regular in construction and so clear in outline 
as to require but few notes. There is a regular countersubject, but 
it does not appear until after the exposition proper (compare No. 4). 

Exposition. The subject, in the alto, commences on the 
dominant : 




The answer (treble, bars 6 to 12) is therefore tonal. The codetta 
(bars 12 to 15) is developed from the end of the subject and the 
counterpoint which accompanies it. The subject is given to the 
bass, and after an episode formed from the codetta, a redundant 
entry in the alto (bars 26 to 32) substitutes a real answer for a tonal. 
This entry is noteworthy for the first appearance of the counter- 
subject the semiquaver theme in the bass from bar 29. 

Middle Section. The second episode, which is built on a 
bass suggested by the countersubject, modulates, leading to a half 
cadence in D major. In this key the subject enters in the treble 
(bar 35) ; the countersubject (bar 38) is given to the alto. This 
entry is answered in bars 44 to 50 by one in the bass in the key of 
A, with countersubject in the treble. In bars 54 to 60 there is an 
isolated entry in the alto in F sharp minor, with countersubject 
again in the treble. 

Final Section, In bars 69 to 76 there is a partial stretto 
for the two lower voices ; the treble once more supplies the 



90 Aiudysis of J. S. Bach's Forty-Eight Fugues. 

countersubject. As this entry commences definitely in the tonic key, 
preceded by a formal cadence, it marks the commencement of the 
final section, notwithstanding the incidental modulation into the 
subdominant key. There is only one further complete entry, 
namely, that in bars 81 to 87 ; but the coda (bars 87 to 100) con- 
tains, in its last five bars, an incomplete stretto for all the three 
voices, the bass inserting a passing note between the F sharp and 
the D, and the treble considerably ornamented. 

The episodes, in addition to the two already noticed, are in 
bars 41 to 44, 50 to 54, 60 to 69 and 76 to 84. They are, as usual, 
made from material previously employed ; and the greater part of 
the coda is a transposition of Episodes 2 and 4. 



THE 

RULES OF HARMONY 

R. ORLANDO MORGAN 

Professor of Harmony, Composition and Pianoforte, at 
The Guildhall School of Music ; Fellow cf the G.S.M. ; 
sometime Member of the Faculty of Music and the Board 
of Studies in Music, University of London. 

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