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.. BACH'; 











Presented to the 

LIBRARY of the 


the Library of 








Wohltemperirtes Clavier 

(48 Preludes and Fugues) 




PRELUDES & FUGUES Nos. 25 to 4&) 




Printed in England 


287 Acton Lane, London, W. 


I JUN 2 3 1992' 




Analysis of all the Preludes and Fugues of the Well-tempered 
Clavier in the chromatic succession of keys: 

No. I in C-major I 

,, 2 ,, C-minor 8 

3 Cti-major 17 

., 4 ,, C -minor 24 

5 D-major 33 

6 ,, D-minor 40 

7 ,, E!?-major 46 

8 ,, E^-minor (Djt- minor) 53 

9 ,, E- major 64 

10 ,, E-minor 76 

II F-major 85 

12 F-minor 94 

13 ,, FJj-major 103 

,, 14 ,, Fc-minor 113 

,, 15 G-major 127 

1 6 ,, G-minor 134 

17 A^-major 143 

18 G|t-minor 150 

19 A-major 160 

20 A-minor 167 

21 B^-major 173 

22 B|7 -minor 179 

,, 23 B-major 192 

M 24 B-minor 204 

n. i. 


The prelude in C- major which opens the present 
book is far nobler and more stately than the one in the 
same key of the first book. It may be that it is only an 
old piece revised and extended (Spitta II, 663); anyhow 
the earlier sketch, in developed form, appeared to Bach 
worthy of being placed at the head of the counterpart of 
the great work of his youth. The chief motive powerfully 
wends its way over the doubled pedal note (Cc]\ 

Moderate, poco maestoso e sempre espressivo. 

Riemann, Analysis of Bach's "Wohltemper'rtes Clavier". 11 I 


The whole piece, consisting of eight periods, with some 
few intercalations and close-confirmations, is entirely evolved 
from the motive of this introductory half-period in which all the 
four voices take part. The correspondence of the first and 
the second half of the piece, and the almost faithful repetition 
of the principal matter with changed key, after the manner 
of sonata-form, are worthy of note, and at the same time 
they offer contrast to all the preludes of the first book. 
This is all the more remarkable, inasmuch as the course 
taken by the modulation, with the transposition in the 
fourth (under-dominant) selected by Bach for the outset 
of the repetition, is not one which necessarily leads to 
the principal key. The first part, indeed, has such a 
decided tendency towards the under-dominant that the 
transposition leads to quite striking, deep-seated, under- 
dominant effects. The modulation is naturally so plan- 
ned towards the end, that the principal key, after all, 
is reached and maintained. I cannot help thinking that 
it is "old" Bach here speaking to us, and no longer the young 
man of 1722 storming up to, and even over the do- 
minant- but one pensive, inwardly musing, and occupied 
with the origin and end of humanity (the two chords of 
the Neapolitan 6 th [*/ 2> and Q g 2 *] forming the knotty 
points in the first and second parts should be specially 
noticed) : 

(4) (6) (6a) (8) 

C+ * f( 6 ) g 7 C+ . . f* g' C" 1 " f 6 g 7 < 

ist period: in ihf principal key. 

and peiiod; tc the dominant and parallel. 





(6) (8) 

3rd period; to the parallel of the under-dominant (D-minor.) 

e b aVU f a' 

(2) (4) 

a dvn a VII o e tt a vii 



4th period: to the under-dominant (F-major). 

^ (2) (4) ffi) 

a din* a 7 a 2> e 7 e f'bT+M*" a 7 d 7 

f 7 1>7^ (1 d'^ a 7 d 7 g 7 c 7 | 

5th period: through the second under-dominant (fib -major) to the 
under-dominant (F-major). 

(NB repetition of the 2 nd to 4 th period. 

tfifi r_ 1 & TsmL-g=t.\ \ H1-- T1 

(4) " (6) 

ft 6 g 7 c-r f6 g 7 c + 7-* (,) C 6 d 7 g -t- 6 
6th period: from the under-dominant to its parallel. 

) (8 2) 

= iiz | | ; ==1=1=1 

(4) (5) (6) (8) 

a? a (g nl< ) dVUfei d 7 . . d VII g 2> I d 7 d d 7 

7th period: to the parallel of the second under-dominant (G-minor). 


free leading hack 

d gVil (2) d Y. 11 a 7 a C VII g? c + d 7 g 7 (4a)c + J. f+ 
8th period: through the under-dominant back to the principal key. 


g' C H g 7 (8) c- 1 ' f- bt? 6 c 7 f 1 " g 7 c+ 

Certainly a very marvellous piece! 

By the side of this prelude the fugue a 3 which, though 
not short, is nevertheless only a very small one, appears 
like a harmless toy: it really consists of two developments, 
and (with exception, of course, of the dominant modulation 
of the Comes) does not really leave the principal key. 
The theme belongs to those of quiet character, inasmuch 
as it keeps within triad limits (cf. I u), and revolves 
round the third, first with an attempt to soar aloft, but 
afterwards dropping into musical commonplace: 

Con mo to. 


poco f 


The Comes fulfils its task of modulating to the 
dominant, and in the usual manner, for it opens with the 
harmony of the tonic (with ornamented c instead of d, 
i. e. g c answered by c g), and then passes to strict 


answer in the fifth. The countersubject is evolved in a 
natural manner from the flowing second half of the 

^ -kfc. 

5 a uuli frrtrrrrr * 7 


The first two theme-entries fill up exactly a period of 
eight measures; but as the third (lowest) voice joins on 
immediately, we have a period of three members (after- 
section repeated) which forms at the same time the first 
section of the fugue. The very short middle (modulating^) 
section first toys with the opening motive of the theme in 
the two upper voices, while the countersubject pursues its 
course in the lowest voice; from this episode of eight mea- 
sures (extended, however, by repetition of the sixth measure) 
grows a second development, for on the concluding note 
(eighth measure changing its meaning to that of first), the 
alto enters with the theme (Dux) in D (Doric}, and is 
followed by the soprano with the Comes likewise in D 
(Doric). Without doubt there floated before Bach's mind 
a vision of the once so highly important first ecclesiastical 
mode (Dux) and its plagal (Comes)-, for our (and also for 
Bach's) ear, however, with its modern harmonic training, 
the real result of this manner of modulation is only a 
holding fast to, and emphatic accentuation of under- 
dominant harmony. I quote the passage: 







: r tf M r-r j 


The two flat 's at * certainly stamp the key of 
the Dux as a real D- minor (the harmony of the pure 
Doric opening motive is d 1 - """), and the Comes is 
evidently in pure A-minor (a}. Now, however one 
may reason, it cannot be denied that the modulation 
section introduces the theme in the parallel of the under- 
dominant. For the rest, this second development is in- 
complete. In place of a third entry of the theme, there 
follows, indeed, another episode of eight measures in which 
only the upper voices are concerned with the principal 
motive; this episode closes in the key of the under- 



dominant (F- major), and by a deceptive cadence f*~ be- 
comes a, i. e. / 6 (under-dominant); this gives rise to an 
appendage of two measures which closes in the principal 
key (7 a 8 a). The third development which now follows 
is again in the principal key, /. e. opens the concluding 
section, which, owing to an unusually long coda, is speci- 
ally spun out. This third development has the Comes in 
the bass, and after four bars episode which close the 
period, the Dux in the alto, to which joins on immediately, 
completing a second period of eight measures, the Comes 
in the soprano; thus at the end of the third development 
the key of the dominant is again reached. The coda at 
once inclines towards the principal key, and consists of 
an 8-measure period after the manner of the first episode, 
touching lightly the key of the under-dominant towards 
the close (c 1 ), repeating the after-section, and ending on the 
third in the bass with an improved close of one measure, 
but by a prepared deceptive cadence (e 1 Q e) once again 
deferring the end. There follow, therefore, first of all 
still three close-confirmations of four measures (the third 
over an organ -point c), one of one measure, and one 
of two measures; the three of four measures, on close 
examination, turn out to be another development of the 
theme (Dux) through all the voices, but in simplified 
form, without the semiquaver movement of the second 
half, for which ample compensation is afforded by the 
other voices. 

t9 f ~~ 


*f f" 

^ x* 1 x^^^ """^^^ ~* 

V ^ ' . 

--**-*.* = r ^ a- 



^ b- 

d of: 

_J ! 1 

1 t^j i^-^ i i =| 

M i 



.. ; 


II. 2. 


The C- minor prelude of the first book appeared 
to us vibrating with passion, full of restrained power, but 
that of the second book is of a milder character; a veil 
of quiet melancholy is spread over the whole piece, which 
with its almost joyful, dance-like motives (even the sharp 
articulation by means of a repeat in the middle and of 
a number of marked close-formulas, recalls dance music) 
on the one hand, and two harsh, writhing, chromatic bass 
progressions on the other hand, appears altogether a 
peculiar mixture of various moods. The opening motive 
strongly recalls that of the F^-minor prelude of the first 
book, but it is not so well rounded off (masculine endings), 
and is more antagonistic (the wavy figure, as there, is a des- 
cending one, yet in its smallest particle its subdivision 
motive of upward tendency): 

Allegro non tanto. 


This first and principal thought returns in the parallel 
key (E\>- major), at the close of the first section, with the 
outspoken character of close-confirmation- and it must be 
understood in the same sense at the commencement. There 
the c in the under voice, by which it is anticipated (/cs), 
really marks an eighth measure, which first of all is con- 
firmed by the above thought (the second half of which 
is formed, by exchange of voices, from the first half), 
and further by four measures firmly knit together in 
unity, in which the upward striving nature of the smallest 
motive makes itself powerfully felt (progression of fourths 
in the bass); also the chromatics of the lower voice, and 
the conduct of the upper voices, recalling the F- minor 
prelude of the first book, express deep-seated grief: 

pf f > 


g?" - - f ? f -- 

F- -t 

^^1=?=^ Eg=a= 





The Doric a, which occurs twice, is here (MB.) of 
quite peculiar effect. 



With eighth measure = first follows the real principal 
theme of the piece - - and it may be recognized as 
such, in that the second section also adheres to it 

a complete period of eight measures modulating to the 
key of the parallel, with half-close on the dominant (^t? 7 ), 
changed into a full-close by means of two appended 

The first section concludes with the already mentioned 
repetition of the introductory measures as close-confirmation, 
and a highly expressive close formula: 

The second section is arranged in similar manner, 
but is somewhat more extended. It begins also with 
close-confirmations as ground work, yet in conformity with 
the character of a development continues to displace the 
effect of close from key to key (eb+ b*V* e\> + , a\? + (^ vn ) 
7 V, (= eb 7 ) a (?: d\T (=/ vn ) c 1 <0 until that of 
the under-dominant (F-minor) is reached. Here a half- 
close is effected by means of three appended measures 
of passionate character, in which the bass works its way 
chromatically downwards (evidently as counterpart to the 



chromatic passage of the first section). In this middle 
part the melodic element is stronger, but it is interrupted 
by playful episodical motives, which remind one of the 
Pralltriller of the second half of the principal theme 

=- P - ==L r==SC- 
(8c) ^ 


The introductory motive is employed in the upper- 
voice of the appended triplet of measures 



Now the principal theme appears slightly modified, 
without change of meaning of the closing measure, but 
prepared by the feminine ending of the same 

again a complete period of eight measures, with full close 
in F - minor , followed by a second one as coda (still ad- 
hering clearly to the principal motive) with two extensions 
(3 a 4 a turning towards the principal key; 5 a 6 a once 
again introducing a chromatic progression in the bass), but 
without further appendage, and concluding with imitation 
of the cadence of the first section. 

The fugue (a 4 in the last two periods, up to there 
only a 3; it might be taken for an organ piece, with a 
pedal part introduced at the close) is one of the quiet, 
simple ones, inasmuch as the theme is confined to the 
fifth-compass of the tonic triad, and proceeds in quavers 
of moderate movement: 



As the theme does not modulate, the answer has to 
complete the modulation to the dominant starting from the 
harmony of the tonic (c instead of d at the commencement) 

The fugue has no real countersubject, as the theme 
is constructed with a view to strettos and combinations 
with itself in augmentation and in inversion. The first section 
runs its course in simple fashion; it consists of two develop- 
ments in the principal key, the first of which gives the 
three voice entries, alto (Dux), soprano (Comes), followed by 
an episode of two measures returning to the principal key, 
and tenor (Dux) in a period of eight measures; after an epi- 
sode of four measures begins a second period, closing in the 
parallel key; it consists first of all of two theme entries: 
Comes in the bass (ending with G -major instead of G- 
minor), and Dux in the soprano (the first two motives 

dotted: R J] Jj, whereupon two repetitions of the 

fourth measure, with gradual sinking of all the three 
voices, transplant the close from C-minor to Aty- major 
and to F- minor. The after -section now begins with the 
Comes in the alto (yet avoiding the modulation to the 
minor upper -dominant, and concluding in the principal 
key); the repeated 6 th measure changes once more the 
whole-close into a half-close, so that the bass is again 
able to take the theme (Comes), and indeed, from the 
harmony of the tonic, closing in the under-dominant. As 
the under-dominant occurs at the 8 th measure, the latter 
assumes the meaning of 6 th , i. e. two further measures 
become necessary, which by sequential formation (one degree 
higher, but without the theme) transplant the close to 
G -minor (minor upper-dominant); but as a formation by 
sequence can never form a satisfactory close, Bach adds 
a confirmation of one measure with a cadence in G-minor. 
The last bass entry, as well as the sequential formation, 
display in a most striking manner the Neapolitan sixth 
(minor [Phrygian] second of the minor scale): 





F-minor F-minor 


In both cases we have a suspension over the chord 
of the Neapolitan sixth (IV V likewise IV V), and there 
is danger of mistaking the first for an E\? -minor chord 
(^J? vu ) and the second for a rapid transition to A^ -major, 
(</t> 6 !>*), which would make the understanding of 
the progression a difficult matter. 

The close in G-minor is followed directly by the 
second section, of which the already mentioned com- 
binations form the characteristic feature. This second 
section is also in C-minor and the fugue has therefore 
no real modulating section; but here it must be noticed 
that for this loss we are compensated not only by 
contrapuntal combinations, but also by rapid transitions 
and striking harmonic effects such as those already in- 
dicated. Some are to be found, in the period immediately 
following, which consists, at the same time, of a wonder- 
ful chain of strettos (the free voices are omitted): 

Dux nJ^ K n^ fc 

TT ^r +- W~z: 


Dux in augmentation (2) f |^" "f" ^ Lj 


Comes inverted (* free note) 




Comes (parallel of the dominant) 

b .^_ L ^*w l^^^ 

rr . ^r 

U JtS (<>*) P UX (parallel) (Cc) 

.43 u h -^^ N - I^V^ K 

Dux augmented 

This period also contains several striking notes (the 
Doric sixth a in 6 a, and 6b, also the d in 6). It should 
be carefully noticed that in the first book of the Well- 
tempered Clavier such notes are extremely rare, and are 
always employed in a less striking manner. 

The remainder must probably be looked upon as coda; 
the new period entering at the close (8=1) adheres firmly 
in organ-point fashion to the fundamental note, and in the 
bass the theme appears in triple form, while the other 
voices (from this point to the end they are four in 
number), have no theme entries: 



h I h h ~~ 
J ^ " ' . 

Dux augmented (2) 


-Jwg^ 1 

(G) theme 

(but phrased differently.) 

Some strettos in 3-measure rhythm in the form 2 nd , 
3 4; 6 th , 7 8 bring the piece to a conclusion: 


tenor: c a{? b{? c f bj?al?g 
bass: c d[? c 



We are already familiar with the fact that in such 
strettos at an exceedingly short interval, only the leading 
voice can preserve the sense of the theme; the others, 
with different phrasing, become counterpoint. 

II. 3. 

In mood and structure this prelude resembles the 
C-major prelude of the first book, and, according to Spitta 
(Bach II p. 664, Engl. ed. Ill p. 184) was also originally 
written in the key of C-major. An unchanged form 
of chord movement prevails throughout the greater part 
of the piece, viz: 



Riemann, Analysis of Bach'i "Wohltcmperirtts Clavier". II. 2 



The harmonic contents of the first section are as 
follows : 

" (6) 





b (2) cj- fjft gtt' aft' (4) 

lj=rt=^ : f-^| "ZZf , , 
dET^ xr; I --.flsgEEj! ^ ^ ^= 

( 3a ) 

.. (4) 


VII- {( o d jf .. 

/. f. it keeps within the keys nearest related to the tonic 
(dominant, parallel, under- dominant), and finally settles 
firmly in the key of the dominant; this dwelling on the 
dominant must be looked upon as a half-close, after which 
the prelude concludes with a short fugato. 

The theme of this fugato (a 3) has no firmly defined 
shape*, it appears in its most complete form in the first 
entry (soprano : Dux in stretto with the Comes in the alto) 

It appears in the bass in abbreviated form with bass 
cadential progression: 

The whole fugato includes two developments in three 
periods of eight measures with a few extensions, and at 
the close of the second period (which in the fore -section 
is an episode, and in th.e after-section has the theme in 


the bass) makes a modulation to the dominant. The idea 
of combining two such heterogeneous elements in a pre- 
lude is a remarkable one: it can, however, be explained 
by the fact that the piece was originally conceived as an 
independent one; the fugato could have been further 
developed but for the great fugue which was to follow. 

The fugue (a 3) has a short theme, yet not so 
short as Debrois van Bruyck imagines; in mistaken fashion 
he only reckons up to the entry of the second voice. It 
runs thus: 

Allegretto, sempre espressivo. 




/'. e. it starts with an ingenious stretto (alto = Dux in 
inversion). The remainder of the first period consists of 
an episode containing the inversion of the counter- 
subject in the alto, and the inversion of the first theme- 
member (4 notes) in the bass. The second period, which 


joins on, begins with another ingenious stretto of the theme 
(without inversion), and immediately afterwards, a second 
one with use of diminution, 




Comes in diminution 

_1_1^J___!_ / 7 J7 


Comes in diminution 

3 F ' 

Dux (6) Dux in diminution and 


concluding freely in the key of the dominant. In both 
periods the elision of the unaccented opening measure 
of each half-section (i, 5) is strictly carried out. A third 
period, in which the Comes occurs in threefold stretto, 
with free ending, leads back to the principal key. 

It should be noted how the task, which elsewhere 
(with long themes) is assigned to the separate theme 
entries, here falls to whole developments. The first develop- 
ment remains entirely in the principal key (according to 
school rule, however, when the Dux remains in the prin- 
cipal key, the Comes should modulate to the dominant); 
the second modulates to the dominant; while the third, 



passing through the under-dominant (#ff = ./$ 6 ) regains 
the principal key. The exposition only comes to a close 
with this third development. 

The second (modulating) section of the fugue opens 
with a free merry-making between the first motive of the 
theme and its inversion, filling up the fore -section (with 
repeated second measure [2 a] and repeated second group 
[3 a 4 a]), and ending with a half-close in the parallel 
key (A- minor, <?$"*); this is followed by another clever 
stretto (Comes in AT^- minor, D-minor t G-major t [in- 



? (8) 


The second part of the middle section consists of 
an episode in which the countersubject is principally worked, 
but it concludes, returning to the principal key, with a 
stretto of the theme in diminution (not however carried 
out to the end): 

One might be in doubt as to whether such for- 
mations ought to be regarded as real developments; but 
as in the second half of the fugue, the theme never 
appears in complete form, one has only the choice be- 
tween the supposition that from the close of the modulation 
section onwards there is no further theme entry, or that 
the theme suffers a loss of a few end notes. I prefer 
the latter supposition, without however acknowledging that 
the theme only consists of the four notes which it shows 
up to the end. 


The third period of the middle section confirms the 
principal key by touching on that of the under-dominant, 
and, at the eighth measure, makes a half-close with a 
fairly intact theme entry in the bass: 


The concluding section is a long drawn-out coda: 
it remains firmly in the principal key, which by colour 
shading is changed now and then to minor (C- minor, 
with organ-point on "$), and introduces as a fresh sur- 
prise the augmentation of the theme in combination with 
its original form in direct and in contrary motion: 

It consists of two periods, of which the first has the 
I st and 5 th measures elided, while the last is complete, 
and then a close - correction of three measures (6 8, 
changing the half- into a full -close); and finally over a 

stationary bass f .jt ) still a confirmation of four 


The piece is of quiet character (the theme lies 
within the fifth compass of the triad position), but by a 
plentiful introduction of demi - semiquaver figuration it 
becomes more lively towards the end, calming down again 
in the last measures into even semiquaver movement 


II. 4 . 

The prelude is a deeply earnest piece, full of religious 
ardour, in mood most akin to the B?- minor prelude of 
the first book, yet of quite different, and more complicated 
structure; the contrapuntal writing is strictly in three voices 
with imitations. The piece can fairly well be divided 
into two halves, the second of which is a free reproduc- 
tion of the first*, it has, however, no reprise but ad- 
vances without ceasing; and nearly all the period endings 
(5 out of 8) can easily be recognized by the rising ar- 
peggio with which the piece opens (preliminary point of 
stress of highest order, 8 th measure): 

rit. . . . 

Bruyck has shown the thematic structure in a clever, 
but not exhaustive manner. Already in the first period 
imitation takes place, not only between two, but between 
all three voices; the four measures as they occur succes- 
sively in soprano (1) bass and alto, are here placed directly 
one under the other, so that they may be easily compared 

Andante con moto ma molto cspressivo. 





dj (6) 


f- r-frrf h~~E"^rrpTF 

L i p-rt ^ b iF; F-f- 


W g^ 





gft .Y n (8) d|' 

Evidently when the movement was first sketched the 
bass also had the exact theme (two octaves lower than 
the soprano), perhaps only beginning with it after the 
fourth measure, whereas now it follows one measure 
earlier (at a distance of only three measures); its first 
notes fell a prey to the bass progression of the half-close. 
For the rest, it is considerably ornamented, and the har- 
mony of the theme is much changed (and so indeed is it also 
in the enunciation of the theme by the alto voice). At 
the half -close of the alto on d%* (8=4) there is, first, a 
confirmation of two measures (when the soprano, starting 
from c J, gives once again, the last measure of the theme), 
and then a completely new after-section, which closes on 
the dominant. Herewith ends the principal theme section, 
and there follows a new, independent theme-group, in 
which the three voices imitate one another at a short 
distance (each time after 2 measures); or, -to be more 
precise, whereas in the first theme-section the upper voice 
throughout took the lead (hence the free imitation in the 
bass which is scarcely recognizable), here the lead passes 
from one voice to another, and the imitation therefore 
determines the rhythmical structure: 




*(=) t 







The first motive of this intermediate theme springs 
from the continuation of the soprano during the enunciation 
of the theme by the bass: 

and, indeed, from the counterpoint of bass and alto to 
the first enunciation of the theme by the soprano: 


But also during the close of the period and its confir- 
mation, further, though not quite strict, use is made of the 
same motive: 


(8) b' 


(8 a) 

As when the dominant is reached at the end of the 
first division, so here when the parallel key is reached at 
the end of the second, the rising arpeggio makes a 
prominent appearance; but in the latter case it directly 
introduces a new thought in the soprano, which again is 
imitated by the other voices, and thus forms a concluding 
third member of the first section: 







TEfTT r r V~ 


With this the first section of the piece is at an end, 
and the second, as already mentioned, consists of a free 
repetition (and in part transposition) of the first It begins 
in the key of the under-dominant in which the alto gives 
out the first theme; and the inversion of the voices clearly 
reveals the derivation of the motive from the second theme- 
group. When a return is made to the principal key the 
soprano again takes up the theme (as at the commencement, 
only with a richer bass); also the bass gives it out again, 
as at first, but freely diverges. It would lead us too far 
away, were we to attempt to show how Bach, by different 
grouping of the separate voices of the first section, by 
inversion of voices, lends a fresh charm to the recapitu- 
lation of what has already been set forth; but of one thing 
we must make special mention, viz. that the close of the 
prelude is a transposition of the after-section of the second 
period in the lower fifth, and that the displacement of the 
parts is brought about by the preliminary enunciation of 
the theme by the alto. 

The fugue (a 3) has no spiritual relationship with 
the prelude, and, at best, suits it owing to the sharp con- 
trast. It has, as Spitta rightly remarks, the character of 
a Gigue, and it is quite a wonderful Perpetuum mobile. The 
theme runs along in unbroken semiquavers; as it moves 
in plagal form around the toni<~, having as limit above 
and below the fifth of the key, but returning to the tonic, 
it does not actually press forwards, neither does it sink 


downwards, but runs busily, within a narrow circle, hither 
and thither. 

Con moto. 

The answer is a faithful transposition into the key of 
the dominant, which is by no means intelligible, as the 

(6) (8) 

(without the sharps indicated above) would have been 
correct and intelligible (or, at any rate, the first /x need 
not have been written). But it corresponds thoroughly 
with the hurried nature of the whole piece to fall head- 
long into the dominant. Again that Bach does not 
let the bass first come to an end, but brings in the Comes 
in the soprano two measures before its time, and, likewise, 
before the end of the close - confirmation (8 a = i) the 
Dux in the alto, is quite in keeping with the character of 
the theme, and with that of the whole piece. 

Besides the theme in its original form, rich use is 
made of it in inversion and in that it also resembles 
Bach's Gigues: 

Of the counterpoints the most important is the one 
proceeding by dotted quavers and with a syncopation at 
the commencement; its actual form is really not the one 
which it has as first countersubject to the Comes (where 


the leap to the leading-note is only made on account of 
the writing a 2 ; Bach could not well have gone to 
the /x below, because, in so doing, he would have altered 
the melodic outline): 

( Lj V 

Sometimes he has a chromatic step in place of 
the tie: 

in this form it is counterpoint to the Dux, but it occurs once 
quite at the end beginning a ^ too late, as counter- 
point to the Comes (but with dominant form [Mixolydian]) ; 

and once (in the last development but one), a fourth 
lower (/. e. inverted in double counterpoint in the 12 th ), 
as counterpoint to the Dux: 


A second and important counterpoint (to the Dux) is 
the following: 

In this elaborate form it occurs indeed only once (at the 
beginning of the second development), but it must pro- 
bably be looked upon as inwardly related to the following 
more sedate one, which occurs frequently, and is also 
often to be met with in the episodes: 

(second half) 

A descending passage, more or less chromatic, appears 
counterpoint to the inversion of the theme: 


The episodes consist, for the most part, of workings 
of the same motives (especially of the second half of the 
theme, and the fourth-fifth progression of the counter- 
subject; also of the passage rising by four degrees: g\ 
a$ b c in quaver notes). A fresh, pulsating counter- 
point to the latter introduces new life: it first appears at 
the end of the first episode: 


and afterwards forms the chief material of several episodes. 

The fugue has no less than five complete developments, 
one of which, however, is redundant, unless one prefers 
(and probably more correctly), to consider that there is a 
sixth, incomplete one. The first, foundation -laying section 
in the principal key probably includes only the first 
development and the extended episode which follows it 
(after-section of the second period with confirmation of 
two measures, another complete period, and a transitional 

The modulating section introduces first of all a second 
development (Dux in soprano, Comes in alto, and a close- 
confirmation leading to the theme in the parallel key 
\E-maj or\ in the bass), and at the end of the second 
period extended by repetition of measures 3 4, a com- 
plete development of the inverted theme soprano: 
theme in B-major (dominant of the parallel key), alto: 
theme in F^- minor [under-dominant], bass: theme in the 
principal key whereupon follows immediately a delivery 
of the Dux intact in the principal key in the alto, com- 
pleting the second period, and marking out a fourth dev- 
elopment. Here a return is made to the principal key; 
the en 1 of the modulating section, however, is not reached, 
but only the middle of the same. For after an appendage 
in cadential form of three measures, changing a whole- into 
a half -close Qrft 7 ), a specially long episode commences, 
which in three periods with several extensions, passes 
through the keys of F- minor, B-major, G$-minor (minor 
upper-dominant, in which key a long halt is made), 
C^-minor, F^- minor, B-major, E-major and A-major, 
finally leading to F- minor , in which key the fifth dev- 
elopment, forming the opening of the concluding section, 
enters with the Dux (soprano); quickly re-establishing the 
principal key. An episode, opening with the change of 
meaning of the 4 th measure to that of I st , soon turns 
towards the under -dominant side, and concludes at the 



8 th measure in A- major (parallel of the under-dominant), 
in which the alto introduces the inverted theme starting 
from c$\ the bass joins on with the Dux in direct form, 
definitely restoring the principal key. Two triplets of measures 
of bold formation lead on even to a 6 th development, in 
which are introduced, in a specially well-sounding middle 
position, still three theme entries: Comes in the alto 
(tenor), after two triplets of measures rising from the 
under-dominant the Dux in the alto; and finally, once 

confirmations of 

more, the Comes 
two measures. 

in the bass 


n. s- 


This prelude is not of fugal character, but in fact a 
splendid, real gigue; it is a correct dance movement, with 
regular groups of periods, and in two sections with repeats 
A powerful foundation-laying period, which appears at 
the beginning of the second section in inversion, 

Allegro risoluto (4 I). 


*-r * r 


Riemann, Analysis of Bach's "Wohltemperirtes Clavier". II. 3 



is followed by a sportive toying with the opening crisp 
arpeggio motive commencing with a slide ("Schleifer") 


and this lasts through two periods which modulate to the 
dominant, and which close with a formal cadence; where- 
upon, after a further complete period, follows the confir- 
mation, which as after-section only receives a triplet of 
measures (to be played with breadth). The second section 
is worked out with the same material, i. e. no new motives 
are introduced. But it opens with a somewhat lengthy deve- 
lopment (five periods, the fifth with a powerful extension), 
which preserves, however, the fresh dance-like character, 
never making a display of learning or of artifices; and 
after the inversion of the introductory period it is worked 
in a manner similar to that of the first section, but avoids 
the principal key (it is in A-major and JB-minor, dominant 
and parallel keys). The rest is a return of the first 
section, avoiding the modulation to the dominant. The 
strict writing in three voices which is carried nearly through 
the whole of the piece, but which is never felt as a fetter, 
deserves notice. 

The fugue a 4 is likewise pithy, and full of quiet 
determination, so that it forms an excellent counterweight 
to the onset of the prelude. One might almost say that 
the movement of the fugue is altogether too uniform 
(only quavers), were it not that the prelude renders such 
smoothness desirable. The theme opens with the motive 
of the C-minor Symphony (but broadened outl) and sinks 
downward from the octave to the third: 


Sostenuto, con forza (4 J ). 


Not only in its rhythmical nature (- u -), but also 
in its whole character and suitability for forming counter- 
point to itself (strettos), this theme resembles that of the 
G-minor fugue of the first book, and, despite all difference 
of keys, it must be acknowledged, that the two fugues 
stand altogether in close relationship to each other. Only 
here the graceful element of the semiquaver runs is wanting; 
and it will be wise to look upon their absence as part of 
the composer's intention, and to interpret the fugue with 
considerable weight and emphasis. 

Of the three sections of the fugue the first (exposition 
in the principal key) is the shortest, for it embraces only 
the first development with a short appendage confirming 
the close in the dominant. The four voices follow one 
another in the order: tenor (Dux), after which, imme- 
diately (without change of meaning, and with passing over 
of the fifth measure) alto (Comes, a faithful transposition 
of the Dux ia the fifth); then after two leading -back 
measures, which introduce the concluding motive of the theme 

for the first time in its rdle of principal material foi 
the episodes, the soprano follows with the Dux, and 
before it ends (4=6),the bass with the Comes. As the theme 
ends on the third degree, the close is unsatisfactory, and 
needs confirmation ; this it obtains in a new after-section 
(without elision, and with a triplet measure in place of 
6 8). The countersubject if it may be so termed 



(this also with its accented rest, recalls the G-minor fugue) 
does not only everywhere accompany the theme, but plays 
also a chief role in the divertissements-^ it never however 
comes forward in a marked manner, in that it has no 
moment of rhythmical importance (the above mentioned 
rest, certainly is of such a kind, yet no safe use can be 
made of it). 

The modulating middle section comprehends three 
periods with some extensions. The first, shortened like 
the first of the exposition, by elision of the i st and 5 th 
measures, at once begins the modulation by presenting 
the Dux in E- minor (a z> = ^ vn ) and concludes with the 
Comes in E- minor (likewise Dux in B- minor) in the 
soprano. And as though this modulation had entered 
before its time, a powerful close of 2 measures, by way 
of correction, turns the tonality back to A-major (dominant), 
and a new after-section introduces Comes (alto) and Dux 
(soprano it should be noticed, that the premature 
modulation was made with the same voices) in stretto, 
re-establishing the principal key: 

The episode of eight measures (with a triplet for 14; 
or 2 4, in which case i 2 would be wanting) which follows 
is enchanting; the four voices enter one after the other 
(alto, soprano, tenor, bass) with the concluding motive of 
the theme, but each twice the soprano indeed four 
times, but pushed on in the measure and hanging on the 
one to the other, 


-- ? +. ^ 

so that a prolonged upsoaring together with slow down- 
ward sinking, leads again to the dominant, for the purpose 
of starting modulation. The close is therefore at once 
bridged over by the alto which continues its course: 


and a complete development follows on with tenor (see 
NB.), soprano, and alto in stretto, while the bass, but 
only at the close of the period, follows alone with a 
repetition of the after -section: 




Thus tenor: Dux in B-minor; soprano: Comes in 
B-minor (Dux in F^- minor); alto: Dux in B-minor; 
bass: Comes in B-minor (but with decided entry and close 
in F\- minor). 

With this the modulation section comes to an end, 
and there follows the concluding section establishing once 
again the principal key, which after the close in F\-minor 
starts at once in D-major and, indeed, with a stretto at 
very short interval (two quavers!) between bass and so- 
prano, and even the first four notes in the alto: 




__ji 1 * t 

7*3 ? 
. . . \ 

H=6 c-&-f 

The remainder of the period (free) turns towards the under- 
dominant (G -major}, announcing that the end is nigh at 
hand, and closes in it. Now follows a stretto scarcely 
carried out to the end (tenor, alto and soprano with free 
accompanying bass), again at the distance of a crotchet, 

in , j~ j 


beginning in G- major but concluding in D-major and 
with measures 3 and 4 repeated (through B-minor); and 


an extended after- section (triplet measure for 5 a 6 a) 
settling in broad manner in the key of D-major. 

A kind of coda brings next, a highly effective pre- 
sentation of the Dux by the tenor (the voice with which 
the fugue commenced and which must be looked upon 
as the chief voice "tenor-fugue"), first accompanied in 
third parallels by soprano and alto, then strengthened 
by the bass with thirds; and finally, at the end of the 
period (8=2) a presentation by the bass of the Comes 
distorted by two chromatic notes bringing everything into 

a VII e ' (4) a I 

Then all four (1) voices enter still once again for a stretto 
at the smallest possible interval: 

and now (first of all by means of a fine triplet extension 
for 5 6) they sink down with one accord;, the after- 
section is repeated, the soprano ending on once-accented 
d t the bass on great D. 


II. 6. 

These two pieces would be equally well placed in 
the first book of the Well-tempered Clavier, for they have 
the same youthful, fresh imagination, the same bewitching 
delight which we have noted in many a number of the 
first book. In this second book we repeatedly find a 
preponderance of reflexion, work more finely thought out, 
and more intense harmonic ventures, which perhaps may 
be explained by Bach's later absorption in the old church 
modes. The prelude under notice is throughout a 2, 
and arranged on similar lines, though somewhat more 
developed, to those in F-major and G-major of the 
first book. The thematic material may be reduced to 
three elements, namely, first of all, a quiet chord figure 
in one voice in semiquavers, in the other in quavers: 




secondly, a scale motive carried out by both voices in 
contrary motion: 


and thirdly, one, more pointed, likewise more wavy, in 
both voices: 



These appear successively in the first two periods, without 
any serious departure from the principal key (only one 
sequence touches lightly on the keys of C- major, 
F-major, B^- major]. A third period brings a) as it were 
to a stand-still, to a slow oscillation at the passage: 


d) W 

and it turns to the minor upper-dominant, in which the 
first period (a) is repeated, while $) and c), quite trans- 
formed or rather changed almost beyond recognition by 
inter-workings with (a), are developed in the second half 
of the piece. The modulation only touches lightly the 
keys of G-minor t (e l = g vu ) and F-major (d^ = 0'^), in 
order definitely to settle in D-minor\ and this is rendered 
more spicy by a two-fold introduction of the Neapolitan 
sixth (e^ = V 2> ). 

The fugue (a 3), which recalls the fugue (a 2) in 
E-minor of the first book, is dashed off in a terse, simple 
manner, but is rendered interesting by the chromatics of 
the second half of the theme, and the introduction of 
the theme in inversion. The number of real theme 
entries is only seven, and only one development (the 
first) is complete. 

The theme starts upward in semiquaver triplets from 
the fundamental note to the fifth, and sinks, in the second 
half, with quaver movement, from the octave down to the 
fundamental note. 

Non Allegro. 



The answer is a strict transposition in the fifth; but 
here, as in the C\-minor fugue, the rule is so far followed 
in that the Comes enters with the harmony of the tonic, 
which changes in meaning to that of under-dominant. 

poco f 


The countersubject here shows special character, for 
it introduces new movement (smooth semiquavers in oppo- 
sition to the triplets and quavers of the theme). Before 
the entry of the third voice a return modulation of 4 mea- 
sures is inserted, commencing with 8 = 1, and ending with 
4=1, in which the inversion of the opening theme-motive 



is worked out. The motive of the second episode which follows 
the first development is taken from the countersubject: 

and this may be easily overlooked seeing that it is not 
articulated as in the countersubject (see above). 

At the close of the period the bass first enters with 
the beginning of the Dux; after two quavers, the soprano 
makes an attempt to take the lead with the inversion 
of the same, but leaps to the real Dux, while bass and 
alto continue in rivalry with each other; and from the 
moment in which the soprano takes possession of the 
octave, bass and alto (tenor?) retire ill-humored, and 
grumbling, into the depths. And now the soprano does not 
carry the theme to an end, but insolently springs up to 
the octave of the fifth, repeating once more, as if in 
scorn, the chromatic progression. The whole passage is 
characteristic and clever: 


dim. (2b) 


piu /" etc. 

v f pZ *.I S-- ~~ 

After this threefold 2, a plain 4 is naturally not 
possible; after this rivalry, peace can only be gradually 
restored. First of all a triplet of crotchets leads to the 
fourth measure, then this is repeated with voices reversed. 
But at the close (4 = 5) the Alto enters with the Dux, 
and after an interval of a crotchet, the soprano follows 
with the Comes in a successful stretto, and finally the 
bass joins in with the countersubject; thereby, also, an 
extension of the after-section becomes necessary (5 a 6 a). 
We are still in the principal key; even the new stretto 
of the inversion of the theme which follows (8 = 1) 
begins in D- minor (alto: beginning with a] but, owing 
to the entry of the theme in the bass, starting from </ 

Sat the interval of two quavers), turns to the under-dominant 
G-minor) a modulation which however announces that the 
end is approaching and, in point of fact, we find oursel- 
ves already in the last, and quite unusually extended period 
of the whole piece I The extension is effected by means 
of a tossing to and fro of the theme appendage, likewise 
of its inversion among all three voices, so that the effect 
of a close is always postponed (4 a, 40, 4C [== 5], 6, 6 a, 
6b) until finally all three voices descend in common, 
bringing about the end. The eighth measure is then, 
first of all, twice confirmed (8 a, 8b) and the fugue finally 
comes to a close with another after-section in which the 
already described rivalry of the first stretto is once again 
repeated somewhat faithfully (runs in the alto and bass 
[inversion]- complete Dux with prolonged close in the 
soprano, and countersubject in the bass). 


Here the threefold division is by no means clear; 
probably the first section must be regarded as extending 
to the close of the second period (before the first rivalry); 
the middle section then, to the end of the inversion (only 
one period); so that the section thus variegated in the 
matter of tonality (D-minor, G-minor, B^- major, G-minor, 
C- major, F- major, JB^- major, D- minor, all intermediate 
keys only indeed lightly touched upon) is the closing 
one. Otherwise there remains as closing section only a 
Coda which has no independent existence. 

II. 7- 

The prelude is a Gigue in sprightly 9 / 8 time, but 
without fugal writing, and without inversion of the 
principal motive. After a preliminary short period of 
4 measures of powerful restraint, the real structure begins 
with lines of considerable extent, 

concluding, after a period of 8 measures, in the dominant 
(Bb -major}\ in a second, there is a half-close in C-minor 
(parallel), which the repeated after-section changes into a 
full-close. In a third period the key of Bb -minor is 
touched (g = b / 7 - A also A'? -major 
(/ = d^* eb 1 afr) and F-minor, and a half-close 
is made in the principal key (^b 7 ); a period with elision 
of the i st and 5 th measures follows on, the seventh- 
progression of which in the bass, if badly phrased, ivas 
an unpleasant sound: 




_l I L. 9 




b[?' eb H ' ab f b[? 7 (4) el?- 1 - 

The after-section, formed in a similar manner, con- 
cludes in Ab-major (e\? 1 a^ dfo* eV 1 ab*\ and a new 
period becomes still more intense, in that it changes the 
leaps of a seventh, by inversion, into leaps of a ninth: 

l? 8 

Measures 3 4 also close in C-minor (# 7 = 

[ in< ] ^ 7 ^)> an d tne after-section makes a half-close in 

G-minor (parallel of the dominant)/ 


o d 




g .T 1 d 7 


The repeated after-section turns the half- close in 
G-minor into a whole one. Now follows the return, with 

imitation of the fore -section 

C 9* 0^. |-_ 0J76J fyl _ 


of the 3 rd period (d 
e\?+Y the after -section is 

' 5^1 \ J^~ 

bb f 

The half -close has a double confirmation of two 
measures, and then the opening period is repeated with 
a coda (a repeated after-section, but of three measures 
passing to the 6 th [triplet for 5 6]), and with close- 
confirmation of two measures (7 a 8 a). 

The fugue (a 4), which according to Bruyck's judgment 
is a "pattern fugue" ("Musterfuge"), and has a "scholastic 
flavour" ("nach der Schule schmeckt"), and, already in the 
theme, "spreads an odour of double counterpoint" ("den 
Geruch des doppelten Kontrapunktes verbreitet"), sounds 
exactly as if it had originally been a vocal fugue, some 
song of thanksgiving and praise. The theme seems to 
suggest such words as: "Songs, praise and thanks be to 
the Lord, who hath delivered us from death" (Lob, Preis 
und Dank sei dem Herrn, der uns erlost von dem Tod). 
It is given out with full power by the bass: 

Allegro deciso. ( I J 

(4) (6) (8) 


while tenor, alto (with a leading-back of 2 measures, 
but with 8 = 2) and soprano (after an episode of 
2 measures, likewise with 8 = 2) tower one above the 
other with ever-increasing might. 

There are two changes of interval at the beginning 
of the answer; for, in customary manner, prime fifth 
(^ __[>) i s answered by fifth prime (b\? <?>); but again 
here, the rule applies, that the Comes must modulate from 
the harmony of the tonic (!) to the key of the dominant, 
when the Dux begins with the prime and remains in the 
principal key. 

The countersubject, which often recurs, only shows 
special character (a legato slow turn) from its second 


countersubject (2) 

i : i J-ifiiiii ii 


E~f '^"f 1 

^-- ^ f r 1 1 

J "s^, ^ 

(6) (8) 

The elision of the i st and 5 th measures in the theme 
(2, 3 4; 6 : 7 8) gives to the whole fugue a somewhat 
sharply articulated and altogether definite character. The 
two insertions of 2 measures, or rather since the second 
measure changes meaning (8 a =2) the insertion of 
one measure in the early developments strengthens rather 
than weakens this impression, since the unaccented 
measure which comes between the 8 th and 2 nd cannot 
possibly be taken in the sense of i st . Between the first 
and the second development now appears an episode of 
4 measures, in which is employed the opening motive of 
the after-section of the theme (likewise the opening motive 

Riemann, Analysis of Bach's "Wohltemperirtes Clavier". U. 4 


of the countersubject); it remains in the key of the 
dominant so that the second development can commence 
with the Comes (and, indeed, with dominant harmony). 

The second development, in comparison with the 
first, is more concentrated, inasmuch as each pair of 
voices is in stretto, first tenor and bass, 





\l I 1 


then (following on immediately with elision of the first 
measure) alto and soprano: 

~~* '^ (8) 


This development also belongs to the first section 
(in the principal key). A real middle section with theme 
entries in other keys is altogether lacking to this fugue 
(which, therefore, is not a pattern school-fugue); its place 
is taken by a long drawn-out episode ending with a theme 
entry (Dux, but beginning with the Comes step of a fourth) 
in the key of Ay- major (under -dominant), whereupon 
follows immediately the closing section. This middle 
section includes 15 measures, of which only the first two 
make use of the opening motive of the countersubject; 
the others, on the other hand, especially from the 4 th 
measure, have a marked feature of their own, owing to a 
quaver figure (connected neither with the theme nor with 
the countersubject), which is opposed to the syncopation 
motive of the theme: 

(4 a) 




The sequence: cvu g ' g g a>( N B.)=bb e 



(4 a) 
' (NB.) 



leads to the key of Afy- major, in which the tenor enters 
(see above) with the theme and makes a full close. On 
reaching an a\? in the middle of this theme entry (a 
prepared deceptive cadence C Q " c in place of <?l? 7 afr) 
the soprano is silent; hence its re-entry with the correct Comes 
(similar to the preceding delivery of the theme in A\?- major t 
beginning with bfy ety t but now, already, harmonised in the 
principal key) is specially marked, and clearly calls attention 
to the opening of the final section. Here we have only 
a stretto between soprano and bass (Comes Dux) at 
the same interval as in the second development, and an 
appendage of 5 measures (repeated after -section with 
extension of the 7 th measure) in which the soprano sinks 
by degrees from <?t? 2 to eV l . This fugue certainly is not 
a show piece of double counterpoint; since, with exception 
of certain forms of stretto, it contains no complications. 



+ * 

II. 8. 

(Djf- MINOR). 

The pedagogic aim of the Well-tempered Clavier is 
a sufficient reason why Bach should have written these two 
pieces in D^- minor instead of Ep- minor. In my edition 
of the work I have transposed them into E^ - minor, because 
they are really much easier to read in that key, and do not 
appear to contain any special characteristic of keys with 
sharps (cf., on the other hand, the C^-major number of 
the first book). 

The prelude is a finely developed, specially rich, two- 
part Invention. Both hands are throughout equally em- 
ployed, and continually exchange motives. The principal 
thought (measures i 4): 



is faithfully carried out, partly in shortened form, in the 
after- section which follows 

(with the bewitching little appended motive), and, for 
the most part, forming counterpoint to itself (canonic 



treatment); yet the second section adds to it a new 
counterpoint, an arpeggio motive of somewhat hasty 

which Bruyck calls, though scarcely with justice, a "curled, 
stiff arabesque figure"; it is my opinion that the descend- 
ing arpeggio forms quite a natural set-off to the close 
of the first part: 

The interesting breaking-off of the voice in the quiet 
intermediate passage (second period), which plays an im- 
portant r61e in the first, as in the second section, 

6. PREL UDE AND FUG UE IN E 9 -MINOR (t> g - MINOR). 5 5 

and in which the passing notes e b and g b marked * attract 
notice (but still more in the imitations of the same which 
result from sequence), deserves special notice. 

The first part modulates, first of all (already at the 
close of the first period), to the parallel (Gb -major), in 
which key the second period remains; but then, to the 
under-dominant B^ -minor, in which, with repeated close- 
confirmation, it ends. 

The second part starts again from the principal 
key (b 7 ) passing through Db- major and G? -major, to 
A^-minor (under- dominant), and in it the voice -breaking 
above mentioned occasions a fresh complication: 


On closer examination, only the major 7 th (bV) appears 
strange. The rest of the piece keeps firmly to the prin- 
cipal key which has been easily won back from that of 
the under-dominant (*b = cty* </b 7 ^b; 0b 7 
</b; .. g'P~ b + [=*bni] b 7 ^b) and certainly with 
the freest use of chromatic harmonies (*b 7 [^ T V* =] 

The fugue (a 4) is one of the most interesting and 
most pensive of the whole work. The theme has the con- 
cise compass from the sub-semitone to the fifth of the 
key, belongs therefore to those of quiet character, neither 
rising, nor sinking; and yet what deep, intense expression 
is to be found in this melody-movement. Not only does 
the alto voice begin the piece, but during its further 
progress appears twice with ruling power (delivery of the 
theme, the soprano being silent): 

Sosteuuto con aflfetto. 

While the tenor is giving out the Comes (which is a 
faithful transposition of the Dux in the fifth), the alto, 
like a swan, glides quietly upwards to the dominant. 

This countersubject may well be characterized as 
one of perfect ideality: it is sharply differentiated from 
the theme, leads its own life, and is nevertheless thoroughly 
homogeneous in mood with the theme. Among one of the 
numerous errors made by Bruyck and which arise from 
lack of thorough knowledge of rhythmic formation, is the 
derivation of the motive of the countersubject, from the 
"second member" of the theme, by diminution. Quite 
apart from the fact that in the theme, d e\? f do not 
belong to one motive, only formations "by diminution" such 
as the following, could, at best, be derived from the same: 

On the other hand, no one could raise any objection, if 
the countersubject were derived from the concluding 
motive of the theme, 

inversion : 

in diminution: 


if only such derivation served any good purpose. Not 
likeness, but unlikeness, is the best thing to be recognized 
in the countersubject. 

A second countersubject, retained throughout the 
whole fugue, is mentioned by Bruyck, but I cannot dis- 
cover it - , much rather may we say that Bach develops 
third and fourth counterpoints to the theme and counter- 
subject, which here and there show signs of similarity to 
one another in that they progress principally in semiquavers, 
or principally in quavers. I here give only those which 
appear as filling -up voices to the theme and counter- 
subject, and therefore pass by those which only accom- 
pany the theme when the countersubject is absent: 

Development, bass entry (Bruyck's "second countersubject"). 
a) ^- ' 

I st Development, soprano entry, 


2nd Development, bass entry (cf. a). 

) rj- 

2 nd Development, tenor entry. 

2 nd Development: soprano entry (Dux): 


NB. Teuor and bass introduce the countersubject ia strettol 



Only c agrees with a for the space of three 
crotchets (but is otherwise articulated). In addition to this 
counterpoint there is a whole series of other counter- 
points from the 3 rd development (also indeed at the 
alto entry of the second, where the countersubject is 
absent), which, for the most part, are filling -up voices in 
the 07/0-strettos, some indeed apart from these, yet none 
occurs a second time; and in a fugue so rich in entries 
this means much. 

The sections of the fugue are: 

I. in the principal key: the four voice entries, alto 
(Dux), tenor (Comes), and after 4 leading back measures 
(5 a 8 a) bass (Dux), soprano (Comes), and still a free 
episode of 8 measures, ending with a half -close (b 7 ), and 
reestablishing the principal key. It is worthy of note 
that all the three episodes of the fugue (it has no more) 
are evolved from the same motives, and, indeed, from such 
as are derived neither from the theme nor from the 
countersubject-, they thus stand out prominently as inde- 
pendent, and appear to form a kind of intermediate 
theme. Compare for instance: 

a. within the I st development. 

b. between the I st and the 2 nd section. 



-& r [Tf r ~T ^ STf 

c. between the 2 nd and the 3 rd section : 


**^ i 

h J 

-V -^ 

II. The middle (modulating) section includes the se- 
cond and third developments, and extends even to the 
middle of the fourth (unless one prefer to divide the 
fourth into two incomplete ones*, in that case then, 


extending to the fourth, and, with the episode, stretching 
over to the last section). The second development 
has a marked change of the theme in the first three 
theme entries (bass, alto, tenor), namely the trans- 
formation of the first step of the minor second into a 
minor third; and indeed this transformation takes place 
in the bass and alto entries at the cost of the meaning 
of the threefold repeated opening note, while the second 
preserves its meaning as third of the upper-dominant. 

bass : 

b?VH Of 

(to A^ -minor [under- dominant]) 


(to Gfy- major [parallel]), 

(to A\? -minor [under-dominant]) 

But in the tenor entry, the second note (*) becomes 
fifth-, the theme indeed appears as if it were a displacement 
of the bass entry a minor third higher (in the same key 
of 'Ab -minor). The soprano introduces again the Dux in 
Ev- minor, so that the principal key is restored in the 
middle of the modulating section (a close-confirmation of 
two measures, however, gives instead of the chord of 
v -minor, that of v -major, naturally with upper-dominant 
meaning). The third development commences with 8a= i, 
and opens with a quasi-stretto between alto, tenor, and 


bass (the alto having the complete theme in A*? -minor 
the tenor imitating [from />] only for six quavers; the 
bass giving the Dux in full, but with major close [eV 1 as 
upper-dominant of Av- minor, [under- dominant]); the 
soprano, after a close confirmation of one measure (8=4 a), 
terminates with the theme in D\>- minor 

(so that the changing note /b [ 2> ] at the moment of the 
transformation of eV 1 into ^i? vn , and, likewise further on, tV*e 
Neapolitan sixth bV? [2* into 0W make it somewhat 
difficult to grasp the meaning), but also brings, at the end, 
d^ n (prepared by -|? vir ) instead of the chord of D^V -minor, 
so that a new close appendage of two measures alters 
the close to Gv -major. At this point (8a = i) the alto 
opens the fourth development with the theme in CV~major\ 
but as it enters on the dominant of Gb- major, the first 
note of the theme, which is really a fundamental note, 
actually becomes seventh: 

(2) c\>+ 

The close proceeds per inganno to A^- minor (<rt> 8 ) 
to which key the tenor entry of the theme, starting from 
cfy (really Dux in the principal key, but with dty instead 
of ^/), adheres, but exchanges it at the end for the prin- 
cipal key: 




With this concludes the second section. 

III. The final section in the above mentioned 
episode springs once more to the key of the dominant, 
and by long sustained dominant harmony (/ 7 ) prepares 
a real last entry of the theme. The same appears first 
of all (as Dux in the bass) accompanied in homophonic 
fashion with chords given out by the three upper voices' 

f eb 


and after a 2 -measure confirmation of the fourth measure 
still once again with display of contrapuntal means in 
the soprano (Dux) and tenor (in contrary motion from ^b), 
while alto and bass have free counterpoint: 

The close-confirmation of two measures, formed by 
the addition of a filling up voice, increases the number 
of voices to 5. 

6 4 


II. 9. 

This prelude j strictly a 3, with exception of the two 
sectional closes a 4 6, is a wonderful piece of the most 
jjowing polyphony; its principal thought, evidently related 
lp~the i theme of the fugue (q. v.) stands thus: 

Allegro non tanto. 

To this fore-section succeeds an after->gction_jn the 

dominant, which is only a transposition of the fore-section 
by inversion of the two upper- voices. Here we have an 
instance of that direct seizing hold of the dominant key 
so common at the period when the fugue-style nourished, 
and it must not in any way be confounded with a modu- 
lation to the key of the dominant; this indeed is only effected 


detailed manner in the 


+ " 

in an emphatic and 

period, which again starts from the principal key: e+ 
(= ,$T) _ o, ( 2 nd measure); X 11 - g^ - V# (2 a)-, 
. (= ,6) _ y-Jj? __ fr+ ( 4 th measure); b 1 e + . . \ 
(= ,J9) _/fl7 ( 6 th measure); J+ * 6 /# 7 *+, 
and works^ on after the manner of the opening measure, 
with semiquaver, movement divided between the voices 
The close of the first section forms a kind of coda 
(6^Z~80. 7 _8/;; 8<r), holding fast to the key of the 
dominant, first with an organ-point bass, which, however, 
as a new feature introduces an^jip^and down floating 
quaver motive, 



taken up afterwards by the soprano, but with freer tone 


and in the second section this also plays an important 
^/._~~This second section commences with the opening 
'Sought in B-major (but without inversion of the voices); 
at the fourth measure it makes a half-close in C- minor 
(parallel), and brings the Cjf- minor period to a close with 
an after-section, the pensive character of which is deter- 
mined by the waving quaver motive in the tenor: 


Already at the beginning of the following period the 
principal key is re-established. This must be looked upon 
as a transformation of the second period of the first 
section- there is, however, no strict adherence to the 

Riemann, Analysis of Bach's "Wohltcmperirtes Clavier". LI. - 



motives, but, as a whole, they are clearly recognizable^ 
(diatonic semiquaver movement, alternate quaver mo- 
vement etc.). The coda likewise returns, but naturally in 
"e principal key, and considerably extended, with the 
rincipal thoughts in reversed order (the waving quaver 
gure comes first in the soprano and free, as in the 
first section and then only in organ-point fashion, in 
the bass); the final close of three measures over the 
stationary bass is a genuine accession. 

The fugue (a 4), like the C\- minor fugue of the 
first book advances with measured, stately gait, but it 
is much shorter, and has also more unity of mood (for 
here we have not, as there, a contrasting motive exciting 
one's desire for further development). I cannot under- 
stand why Bruyck feels compelled to deny that the theme 
is earnest and expressive; very possibly a mistaken reading 
is again the cause of the diminution of interest. Bach 
himself wrote this fugue in 2 /j measure; but now let the 
theme be compared with that of the Cjf- minor fugue, 
both with like notation: 

cresc. (4) 

(2) cresc. (4) 

The theme of the E- major fugue certainly appears 
much gentler, and at the same time clearer, more con- 
vincing (notice the simpler lines, the rising, and then the 
falling; whereas the C\-minor theme, more absorbed in 
itself, moving round itself, appears, in contradistinction to 
the former, decidedly turned away from the world 
brooding Beethovenish); still the relationship between 
the two is evident. 



Both, certainly, could be read as a simple 3-measure 
group, according to the scheme 2., 3, 4. (._ ^ _), in 
which case the voices following one another would e'ach 
time quietly wait until the theme had come to a termination 
but then not only the E-major, but also the Cjf- minor 
fugue would have a decidedly home-baked flavour: 

(4) (6) (4) (v 5=6) 


(4) (J>=6) 

In the C\- minor fugue the annexed fifth measure (J*) 
would have to change its meaning to that of sixth, and in the 
E-major fugue the same explanation could be given; 
this, however, would cause a detailed complication in 
comparison with which the change of meaning of mea- 
sure 4 to that of 5 th appears simple and easy. Besides, 
in both cases, the harmonic meaning of the theme, as 
shown by the counterpoint, would of itself forbid that 
other interpretation: the choice between the two meanings 
is not a very difficult one: 

b'] (4) 

68 $CONt> PART. 

At and f, both motives of the theme would remain 
stationary on the tonic (at a all the dominant chords 
would fall on -unaccented beats, and therefore appear 
only to be passing ones [cf, my catechism "Kompositions- 
lehre, I. p. 46"]); and at <r,the same would appear at the 
fourth measure as suspensions, /. e. as accented changes of 
harmony on the tonic; at b and d % on the other hand, the 
first motive moves towards a dominant, and the second 
turns back and closes in the tonic. But away with proof: 
the meaning which best displays the contents of a theme, 
musty of course, in the case of a master like Bach, be the 
most correct one I 

The answer of the theme, which does not modulate, 
gives a faithful transposition in the fifth; there was no 
reason for any deviation, for by an answer in the fifth 
the task of the Comes, viz. to modulate from the harmony 
of the tonic to the key of the dominant, is fully achieved. 

The last two notes of the countersubject, for the rest, 
are changed at their first appearance (so that the Dux 


may again be able to enter on the concluding note), and 
indeed in a manner characteristic of Bach; for the leading 
note of the key of the dominant is lowered (Mixolydian) 
to that of dominant 7 th (0J) instead of a%): 

The third voice entry, on the other hand (Dux in 
alto) gives the countersubject in the tenor with its own 
, natural and expected close (the Mixolydian change would 
have turned it towards the key of the under-dominant). 
The second period would have ended peacefully in the 
key of the dominant, had not Bach once again, in the 
giving out of the Comes by the soprano, substituted a\ 
for #$ in the countersubject (alto); by that means the 
close effect is turned aside, and opportunity given for a 
close-appendage, which transforms the full close on b* into 
a half-close on b 1 . At the moment in which the bass arrives 

on b (i | J I , the tenor once more lays hold of 

the countersubject, and again gives to it its natural 



r T 




The annexed period, which in the repeated after- 
section closes in the parallel key (C$-mmor), still really 
belongs to the first section of the fugue; we have in it, 
first of all a stretto of the theme by all the voices: 









It should be noticed here how the concluding motive 
of the countersubject (the syncopation) itself appears in 
connection with the theme. The close-effect of the 8 th 
measure is broken off by the <?jf and the c$ (c^ 1 instead 
of e + )', the after-section, which thereby becomes necessary, 
takes up tjie_c^imjrsubjejct_giyen out by the tenor .in the ~^> 
8 th measure and, with augmentation of the value of the " f 
syncopation motive carries it througli all the voices (two I 
triplets of measures): c 

I I ' 



An appendage of one measure (8 'a) changes this 
half-close on gfy 1 into a whole close on ^|, at which 
moment the alto starts with the Dux in the principal key^] 
beginning a new (third) development in which ^ach pair r 
of voices (alto soprano, bass tenor) appears pressed 
closer together, though not so closely as in the firsr 
rtrettoj this development belongs to the modulation 


section, as it leads from the principal key to the parallel 
of the under-dominant (F% minor) : 

Soprano: Comes . . . 
Alto Dux 

Tenor: theme in 1?^- minor. 
Bass: theme (Comes) in B-major. 

The tenor entry of the theme introduces the same 
in somewhat prolonged form (one measure of 8 / lf relatively 
a triplet): 


which (with fresh freedom) is employed in the next 
following theme entries: 

Soprano : 


(from jFJ} minor to Cj- minor]: 

(in C^- minor). 

Hence one might be tempted to count these three 
voice entries as a development, but for the fact that the 
tenor entry is connected in too direct a manner with the 
preceding bass entry; it forms, besides, the close of a 
period and is formally separated from what follows by a 
close -appendage (cadence /# vn , c%\" + *#). It will 
therefore be more correct to look upon this soprano and 



bass entry as forming an incomplete fifth development. 
The middle section is here at an end; at least the prin- 
cipal key now reappears (already on the close in C^-minor, 
disturbing the same) and indeed directly withjhe_theme^\ 
in diminution, which now runs through all four voices ' 
(not confining itself to fixed degrees of the scale); for 
the moment the time measure will be better indicated by 
2 / a instead of 4 / 2 : 

The period is brought to an end by a close-cadence 
7 <? H ~), but on the last note (by means of a deceptive 
progression of the bass: b <r$) a new (seventh) development 
sets in, a stretto of the original Dux with the theme in 
cTTminution, and the latter in inversion (free): 



-psf.^ rf-v, . 32, 

Also the rest of this period, which closes in G-minor 
(parallel of the dominant) and has an appendage (cadence) 
of two measures, consists of a working of the theme in 
inversion and in diminution: 

But the coda forms the principal display, an 8 th 
development, a two-fold, likewise three-fold ingenious 
stretto of thejComes, Dux, inverted diminished theme and 
counter-subject in the principal key: 

T. inv. dim. Cp. 

4Mfjnf J i ; i i f +- 


K^JS. 4 J- J 

c L f r r 



D. ^ ^\ 

~AJ* T 



T. inv. dim. 


The final delivery of the theme (with appendage) in 
the bass is of imposing effect: 

What strength and fulness of expression, what unity 
and consistency, and yet what restraint throughout the 
niece i 


II. 10. 


A flowing, long drawn-out prelude a 2 (with two 
repeats) and an equally flowing, and likewise very long 
fugue, both certainly conceived the one for the other. 
The principal thought of the prelude is: 

Poco vivace e leggiermente. 


This is spun out in an ingenious fashion, now in 
imitation, now in free contrapuntal style. The characteristic 
feminine ending of the first motive appears in lengthened 
form, when opposed to the shakes in the first and second 
parts : 


Of special interest is the following modulating im- 
itation, which appears transposed in the second part: 

(under voice 8va bassa.) 



In the coda of the first part (after the shake) the 
principal motive (inverted) is already worked in imitation: 

_ _ 

The beginning of the second part, however, intro- 
duces the complete inversion with feminine ending: 

? ntftf fi- 

and the same is worked in a new and interesting manner 
(first in groups of 3 measures / 2, 2 a; j 4 (=5) 
6\ 6 a, 7 8). Also the following formations are naturally 
evolved from the principal motive. 


The order of modulation is simple. The first period 
turns to G-major (parallel), and to B-minor (minor upper- 
dominant) in which it makes a half-close; the second 


period returns by the same road to E-minor. The third 
pushes on in sequential form through E-minor D-major, 
F$- minor (in which the c'$ should be noticed) E-major t 
G^-minor (</!)) /# 7 , first holds fast to the half-close 
in B-minor (shake on /#), then changes to E-minor (shake 
on fr), but in the coda makes an elaborate cadence in 
B-minor, (b _ /jjo> _ oy. /JlX _ c ^ _ fi _ 

o/S, * vn -/if 7 " /fe. The second part begins 
in B-minor, and in the first period passes through E-minor, 
G- major, A -minor to E- major; in the second, through 
A- minor, D -minor (= f 6 ) to C- major; while the third 
remains firmly in A-minor (cadence). The fourth is formed 
from the first of the second part, and is in G -major 
(^ V1I = // 7 ), E-minor and again G-major. Period 5 repeats 
the "pushing on" of the first part (D-major j^jj- minor 
\c |fl e vl1 E-minor}, further the shake-coda (on b and e\ 
and firmly establishes the principal key by transposition 
of the first part in the 4 th , with a further close-con- 
firmation (8 a 5 6, 5 a 6a, 7 <?). 

The fugue (a 3) is one of the most simple, in so far 
as it only shows three developments, each one of which 
forms the chief substance of one of the three self -in- 
telligible sections of the fugue: exposition, (modulating) 
middle section, concluding section. The first three entries 
give Dux Comes Dux in immediate succession (without 
episodes) so that the theme is kept within clear and 
unmistakable limits; in the later ones episodes of greatei 
or less extent are inserted. The theme consists of 6 mea- 
sures, and, indeed, it begins with a fore-section of only 
2 measures (3 4), whereas the after-section is complete: 

Giojoso vivace. 






As the theme does not modulate, the change to the 
dominant falls to the Comes, and this is accomplished 
already in the first three notes (b c% d = vn /| 
V$)i the whole Comes is therefore again a transposition 
in the fifth of the Dux. 

The mode in which the countersubject is employed 
in this fugue, presents features which are specially in- 
structive. Its original form is: 


Although the same only returns once in exactly the 
same form (alto entry of the theme in the 3 rd devel- 
opment), yet the effect is as if it faithfully accompanied 
the theme to the end. For Bach divides it in an infinite 
variety of ways between two voices, as can be seen by 
the following synopsis: 


It development, bass entry. 






2nd development, soprano entry. 

--- _^' --- ^ I I" 


J J = 


The same, alto entry: 






The same, bass entry; 







Rieinann, Analysis of Bach's "Wohltemperittes Clavier". II. 

3 Development, soprano entry. 






3 Development, bass entry. 





We see that almost the whole contrapuntal apparatus 
is concerned with the countersubject, likewise with its 
various sections. 

The structure of the fugue needs no further ex- 
planation. There are no strettos, or other canonic devices, 
and the order of keys is the simplest possible, yet especially 
rich and variegated. 

I st development: 

Soprano (Dux in E- minor), alto (Comes in B- 
minor), bass (Dux in E-minor}\ episode (with 8 = 2), 
modulates in the fore-section to the parallel G-major 
(,vii [= ,6] __</?_ g+\ and firmly establishes the 
same in the after-section (c^d^g^, c^d 1 g+). 
At the eighth measure with 8 = 3 begins the 

2 nd development: 

Soprano (Dux in G-major), alto (Comes in D- 
major\ and after a somewhat lengthy episode which 
opens with 8 i, and in its fore-section modulates, 
passing through E -minor (</ * * = *) , to B -minor 


(b v< cfy 1 /ft 7 ), and in its after-section, estab- 
lishes that key the bass with the theme in B-minor 
(with 8 = 3). If, on account of the long episode 
similar to the first, this theme entry were to be 
reckoned as belonging (as Comes) to the concluding 
section, then the secuiiu development would be 
incomplete, and the third, redundant. The now 

Episode of only four measures (after-section with 
8 = 5) returns in the simplest fashion to the principal 
key (*vn--*vn|| (Doric sixth) 7 <>). 


8 4 


j re * development'. 

Alto (Dux in E-tninor)\ and after an episode of four 
measures in sequential form (e 1 <?; a 1 d^\ 
d^ g+\ g 1 c+\ e 1 ) soprano with the theme 
in A -winor (under-dominant 1). An extended close- 
appendage of five measures (episode) returns to 
E-minor (e vu b 1 ), and makes a half -close 
with pause on the dominant (/$ 7 <? vn b 1 , 
bf /# 9> 7 ). The voices 'now vie, as it 
were, with one another as to which shall re-introduce 
the theme, for all successively attempt the diatonic 


After the delivery of the Dux in the bass (- minor), 
and a coda of free rhythmical disposition, there follows 
an unfinished cadence (7 a 8 a, with c?=<5), and then an 
organ-point of three measures over B, from which the 
bass plunges downward to JD$\ the soprano, forced up- 
wards during the organ-point, likewise falls to d l $ (with 
appoggiatura and pause); and a new cadence of three 
measures leads to the end of the piece. 

This fugue may be recommended as a model for 
study and for imitation. 


II. II. 

A stately, vigorous, fully developed prelude, a master- 
piece of legato style (for the most part in strict writing, 
a 5, and hence, an excellent practising-piece) ; and, by way 
of contrast, a fugue, with a tinge of humour finely pointed, 
yet without any parade of learning. The principal motive 
of the prelude is a rolling quaver movement, after the 
manner of a turn, which runs through the voices from 
the beginning to the end; this figure brings about con- 
tinued quaver movement, and a flowing style of melody 
in the piece, which, for the rest, is conceived in a 
thoroughly harmonic spirit. It is scarcely necessary to say 
that it is written in organ style: 

Allegro, con forza. 



The especially regular structure of this prelude is 
remarkable: 2 periods of eight measures, repeated four 
times, almost note for note, but, naturally, the second and 
third time, not in the principal key, but in the dominant 
and parallel keys, and without any disturbance of the 
symmetry (elisions, changes of meaning); yes, even without 
any close-confirmation, a thing rarely to be found in Bach, 
except in his dance pieces. After the third presentation 
of the theme (in the parallel key), a complete 8 -measure 
period is inserted, leading from the parallel of the dominant, 
through the parallel, back to the principal key; and it is 
distinguished from the other eight periods by the intro- 
duction of a new motive in crotchets (which, however, is 
combined with the rolling quaver motive): 

i r 



Further details are shown by the harmonic analysis: 
ist 2 nd period: principal key dominant. 

(2) bt? c' 

(4) c e 

d(=bt?) c 7 

(8) f * 7 . 




(4) g' c- 

.. f g 7 c* f 

yd 4th period: dominant parallel. 

iBl I I 



>a(=f) g' (8) c+ I. 


ft- 8 g 7 c -f 7 f-J- 7 b^ ?. (4) C f f* 


(8) a 


5 th 6* period: parallel parallel of the dominant. 


35! G 

a 7 a dVII a 7 (8) a a [2>] dVH(=bt?) (2) 

c' f* ..() bt? (4) c 

-) aVIl (= f) 

V i \~ 

& \ ^> 

^ \ "2 11 

JL_ U 

* I 




i ' 

i ii 

g c-*- (=e) a VII (8) e 

period: parallel of the dominant parallel. 

.*. (8) at* r. J. 


period: principal key (touching the under-dominant). 






c 7 f 1 - bi? e c' f-i- e b> c 7 (8) f* 

The theme of the fugue (k 3) shoots up from the tonic, 
first to the fifth and sixth, runs on to the octave, and 
then sinks gracefully back to the fundamental note: 

Allegretto grazioso. 

f+ (2) 


9 o 


As it does not modulate, the answer must modulate, 
and, indeed, from the tonic; hence the well-known trans- 
formation of the opening step of the fifth (/f) into one 
of a fourth (cf); the rest is then free transposition in 
the fifth: 

c 7 f* c' f f (=f e )g 7 C+ f g 7 c+ 

The theme of this fugue has no real countersubject 
(principal counterpoint), yet the absence of such is 
scarcely noticeable. This, on the one hand, may be 
accounted for by the fact that the theme itself is so 
delicately developed, so sharply articulated, that it can 
scarcely endure by its side a second important figure-, it 
must be left wholly undisturbed, and, so to speak, rule 
in homophonic fashion; on the other hand, it must not be 
ignored that the counterpoints to the various theme entries 
are, in a measure, akin. The characteristic feature of the 
counterpoint to the Comes is, namely, an almost coquettish 
resistance (and also yielding 1) to the upward-stretching 
steps of the first two theme members: 



It should be noticed that in this countersubject the 
steps of a fifth and a fourth (apart from the closing 
motive) are opposed to those of the theme, in rhythmical 
inversion (the high note unaccented, the low, accented); 
this peculiarity will be found more or less in the other 
counterpoints, for example; 

lt Development, bass entry: 

(6) (8) 

Redundant Bass entry: 


2 nd Development, tenor entry: 


And now, in all ends and corners, even in the 
episodes and final closes, further reminiscent sounds 
will be heard. At times there certainly is little art in 
adhering to a counterpoint capable of inversion (/. e. to 
that of the first Comes)! 

With regard to the structure of the fugue in its chief 
outlines, it must, first of all, be noticed, that there is no 
real middle development with the theme entries in the 
dominant or parallel; and that the two theme entries which we 
have pointed out as belonging to the second development, 
really belong already to the closing section, a specially 
long one: the first of these (tenor) is, namely, the Dux in 


its original form, but harmonised, in an extremely clever 
manner, in D-minor\ but the second (bass) stands in the key 
of the under-dominant, and enters after an organ -point 
on /, i. e. the end of the fugue is announced. The middle 
(modulating) section consists rather of a specially long 
spun out episode which runs through the keys of C-major 
(dominant), D-minor (parallel) A-minor t D-minor, G-minor t 
D-minor, F-major (principal key), C-major, F-major, C-minor t 
G-minor, D-minor, and which is based principally on the 
second half of the theme, whereby, at times, it seems as 
if the theme were being worked in stretto. The first 
section includes then not only all the three voices (soprano 
[Dux], tenor [Comes], and, after an episode of six measures 
[i 4, 3a 4a] with 4a = 5, bass [Dux]), but also, after 
three measures of episode (6 a 8d] t the second bass 
presentation of the theme (Comes), which gives to the 
fugue the appearance of being a 4, likewise the four free 
measures closing the period, and establishing in a detailed 
manner, the key of the dominant. The concluding section 
begins then with the tenor entry of the Dux: 


in which, likewise, there is a struggle around the prin- 
cipal key. Then follows a somewhat lengthy episode, 
which turns quickly to the under- dominant (bk + f\ J. 
[organ-point on /]), further the bass entry of 



the Dux in B^ -major, after which, with light touching on 
the key of F-minor, a turn towards the organ-point on c, 
8 measures ;(from the 7 th to 8 th the bass descends through D 
[g 9> ] to the lower octave). At the repetition of 7 8 the 
soprano (8 = i) introduces the Dux, but with d\> in the 
second motive, causing thereby a special effect. With 
this the development is rendered complete; but even here 
the bass is determined to have the last word, and it 
enters indeed with the Dux (beginning with F) t but, 
instead of the fifth first attacks the fourth, and now 
climbs up by degrees with the fourth -progression, so 
far, that it is at last able to introduce the second half 
of the theme not in its primitive simplicity, but ex- 
tended by means of repetitions. This is a specially genial 
idea of the master's, and thoroughly in keeping with the 
humoristic nature of this fugue. 




-T-; IT-* 



II. 12. 


These are, perhaps, two of the pieces of the Well- 
tempered Clavier most easy to understand, and, even to 
those still entirely unacquainted with Bach, most directly 
attractive; hence they are specially suitable as an intro- 
duction to the work. 

The prelude, throughout, is strictly a 3, but entirely 
refrains from all complicated polyphonic formations (im- 
itations, strettos, inversions, exchange of voices, etc.), 
and, from beginning to end, leaves to the upper voice 
the conduct of the melody; thus far, it is decidedly 
homophonic. Of special regularity, also, is the metrical 
structure, inasmuch as the strictest symmetry of the group 
of two measures is preserved, and after each set of four 
measures, a marked cesura is felt (only once do two 
measures stand alone, by which, however, the order ^ 
of the group of two measures, naturally, is not disturbed). 
The piece, however, would be only half understood, if 
each pair of groups of two measures were looked upon as 
forming a half -section, and two of these half - sections 
as forming a period. Before all, it should be noticed 
that Bach, immediately after the first half-section, pauses; 
and, by the form of structure, and certainly by the degree 
of tone (p), introduces an insertion of contrasting character 
(3a 4a, sb 

Allegretto, molto espressivo. 



^ NB. l^ 


The after -section to the first four measures really 
commences when the opening motive is taken up again, 
and it ends, indeed, in the parallel key (Ab- major). 
But as the melody advances to the third (c), and as the two 
groups of two measures (5 6, 7 8) resemble each other 
strongly, are, in fact, almost sequential in form (cf. the 
bass), an intensified repetition of the after- section, changing 
the whole close in the parallel key into a half-close (on 
eP~), appears necessary; on this Bach dwells, as he did 
with the one on c* in the fourth measure, by means of 
an insertion of four measures imitated from the first one 
(fb 8b, yc 8c\ Before the close of the first part there 
is still a complete phrase of eight measures, the motives 
of which, however, only appear in the upper voice \ and, 
even there, are only new in the fore-section: 

* " (\ + ^* 

The lower voices here move after the manner of the 
opening measures, but with syncopation instead of note 

instead of: 


The after-section is developed from the motives of 
the first insertion (ja 40). 

The second part of the piece (both are repeated) be- 
gins with the principal thought in Av~maj0r, and concludes, 
at the fourth measure, with the dominant of the parallel key 
(Efy- major). An insertion of four measures, similar to 
the one in the first period, but with the figuration motive 
in the lower voice and with legato conduct of the upper- 
voices, displaces the cadence from JEb- major to Bb- minor 
(4 a) and E\?- minor (40), while the after - section presents 
itself clearly in B^- minor (key of the under- dominant), 
with E^ -minor as under-dominant (t? VI1 ); the motives of 
this after-section will clearly be recognized as figuration 
of the principal motive: 

The key of $V -minor does not, however, stand in 
sufficiently close relationship to the principal key to 
permit of a dwelling in it; Bach does not, therefore, 
introduce here as in the first section further inser- 
tions, but a new period, which changes the meaning of 
B^9 -minor to d^ Q , and, passing through A\>- major and 
D^- major to Ev- major (db** = b 7 ) and F- minor 
(<?(?! = *'), makes a half-close in the principal key. The 
motives of the period are evolved from the principal 
thought, but presented in richer melodic form: 

The period which now follows brings back the prin- 
cipal motive, and in clearer form, in the lower voices, 



but spreads out in sequential form, and leads at the fourth 
measure to the half-close on / 7 , which, by means of two 
insertions each of two measures (as in the first period, but 
with substitution of scale- for chord -figuration), 

'ftf Hff 

is turned back to the principal key (f=/ yu )' The after- 
section, taking up again the principal motive in its original 
form, ends with a deceptive cadence (c 1 ^ 2> ), corrected 
first of all by two (7 a 8 a) measures of the intercalated 
motive (the only group of 
in the piece), 

two measures standing alone 

instead of: 

whereupon the transposition of the concluding period of 
the first part rounds off the piece in the principal key. 
Whether or not the motives of the upper voice of this 
period spring from the principal motive 

Riemann, Analysis of Bach's "Wohltemperirtes Clavier". II. 7 


may remain undecided. In any case, consistency and 
proportion evidently rule the piece throughout. 

The fugue (a 3) is of bewitching grace and heart- 
winning loveliness. The motives which are annexed to 
the theme give to it a contemplative character of quite a 
peculiar kind (cf. the G^- minor fugue of the first book): 

Andantino grazioso, con amabilita. 

The fact should not be overlooked that the compass 
of the melody keeps to the triad position with upper and 
under second,* (Part I, p. 72). 

*) Julius Klauser, son of Karl Klauser, has just forwarded a 
theoretical work: "The Septonate" (Rohlfing & O, Milwaukee), 
in which he presents, not the octave scale, but, as in Draseke's 
Heptachord, a scale of seven notes as melodic basis (hence the 
terribly barbarous word "Septonate 11 which Klauser [horribile 
dictul] derives from septem, tonus, and natura) % not extending, 


As the Dux does not modulate, the Comes has to 
modulate from the harmony of the tonic to the dominant, 
/. g. to answer c / with / c\ for the rest the Comes 
is a transposition of the Dux in the fifth. 

however, from the sub-semitone to the upper sixth, but from the 
under -fourth to the upper -fourth, so that the tonic appears as 
centre (hence the sub-title "System of centralisation"): 

Klauser's idea deserves attention, although he himself quite 
overvalues its importance. It can serve as a scheme for all melodies 
lying within plagal limits (cf. for example, the theme of the 
5-major fugue of the first book), just as Draseke's Heptachord is 
available for those lying within authentic limits. But one error of 

Klauser's I cannot leave unnoticed: both tetrachords (c d e f and 

g a b c) of the C- major scale appear to him equal in formation 
and in value, i. e, Klauser, when he rises to /, feels that f as a 
terminus, and therefore mistakes the importance of the under-dominant. 
With him the third, e plays, a quite subordinate role in comparison 
with the fourth, f. If this view , based on the stand-point of the 
old Greeks (/. e. without conception of the third), be rectified, some 
use may be made of Klauser's ideas towards the recognition of the 
essence of melodic formation. I do not hesitate to acknowledge 
that my declaration "that passing beyond the sixth of the key means 
a transition to another octave position" is, as a rule, only tenable 
for melodies within authentic limits; and I acknowledge, indeed, that 
a plain melodic formation working round the tonic, is possible in 
a plagal position, without the impression of soaring upwards, or 
sinking downwards. Indeed, there is, perhaps, still a third melodic 
fundamental position, viz. one grouped around the fifth; 

but which need not necessarily keep within the limits of the com- 
pass of a seventh , as , neither above nor below is there contact 
with a semitone (Draseke's Heptachord ends above on the sixth, 
because the seventh leads to the octave; Klauser's Heptachord 
ends below with the fifth (g), because the fourth (f) leads to the 
third). In other words: The three triad positions can each be 
taken as a basis for melody, and the neighbouring degrees 




With regard to the countersubject this fugue is again 
highly instructive, in so far as a counterpoint keeping 
faithfully to the same notes cannot be shown, although the 
general character is preserved, with manifold modifications 
and subdivision among the voices. The natural quaver- 
moving countersubject to the first half of the theme 
consists of the spinning out of the semiquaver movement 
of the first half of the theme ; and when the latter passes to 
semiquaver movement, the countersubject adopts quavers: 

in each direction be admitted, in so far as the same are not notes 
leading away from the position: 

I with prime as centre. 2 with third as centre. 


(Klauser) (Draeseke) 

3 with fifth as centre. 


For No. 3 cf. the themes of the fugues I, 2, 13, 21 (first 
half), II, 13. 


If we at once add that the semiquaver movement and 
also the one in quavers (compare theme and counterpoint) 
pass from scale to chord form without the motives be- 
coming indistinct (as their character rests far more on the 
long feminine endings, likewise appended motives), we 
have then shown the whole of the motive material of the 
fugue; for all the episodes are developed from the same 
motives,and preserve, almost without exception, the feminine 
endings and appended motives. It is astonishing that the 
fugue, nevertheless, does not appear monotonous; rather, 
on that very account, does it pursue its smooth course 

The construction is simple: 

I st section (exposition in the principal key), in- 
cluding the three voice entries; soprano (Dux), alto 
(Comes), and, after an episode of four measures with 
(4=5), bass (Dux); further a close-confirmation of 
two measures (7 a 8 a). Whether the episode of 
8 measures entering with 8a=i is to be counted as 
belonging to the first or second section is a matter 
of indifference, since it appears as a real inter- 
mediate member between two developments; it 
modulates to the parallel key (Av -major) making in 
it a half-close, whereupon the 

2 nd (modulation) section presents itself with a 
second development in the key of A}? -major-, but 
the same is incomplete, as the theme only appears 
in the soprano (Dux in A? -major) and in the 
immediately following alto (Comes from Afr- major 
to EV -major)-, the close of the Comes is frustrated 
by g 1 being substituted for <?t^" h ; and there now 
follows a new episode of 8 measures modulating 
through C- minor to E\? -major (c vll = ab Q ) and to 
C- major (a*P 6 = c vli ), and closing formally in the 
latter key. Therewith the modulating section comes 
to an end, and we approach the 

3 rd concluding section, which is as long as the 
other two together. It opens with a delivery of the 
Dux (in F-minor} by the bass voice; an appendage 
(3 a 4 a) removes first of all the close from F-minor 
to B\? -minor, whereupon the rest of the period 
(the after-section) is filled out with an episode which 
makes a half-close on c + . Now the theme is like- 



wise taken tip by the alto (tenor), with a deceptive 
cadence at the fourth measure, extending into the 
fifth ( 5), d\> + changing its meaning to /. The after- 
section which follows is most remarkable. After the 
sixth measure we have the second under -dominant 
(^K vn ), and an extension of the closing group to 
three measures (triplet of measures 6 8); also, 
passing through / 7 , a close in B9 -minor.* which, 
however, as under-dominant can create no real 
feeling of close. A return is therefore at once made 
to the upper-dominr.nt (8=3), whereupon a new after- 
section, again with triplet for 6 8, closes in F-minor. 
On both occasions at the triplet of measures the bass 
makes, as it were, fruitless endeavours to lay hold 
of the theme: 

(6) T : 

s.^ __-- *X^ ^"^^r ^-^ "^.^ 




There is still the addition of a coda, which first of 
all calms down the mood by means of an episode of 
8 measures (with half close on f+ at the end} then comes 
Dux in J3ty -minor in the soprano and, with 4=5, the same, 
immediately afterwards, in the alto; and finally (with 8=1), 
still another postlude of 8 measures over an organ- point 
on C imitated from the first episode, from which, only 
at the 8 th measure, the bass moves to J\ 

ii. 13. 


The prelude (apart from the last measures strengthened 
by chords, strictly a 2) is a richly developed piece, in 
mood and structure most akin, perhaps, to the C- minor 
prelude of this second book, but brighter, of greater 
vigour, and, in the alternate play of two thematic for- 
mations, especially charming. A quietly progressing dotted 
rhythm runs through the piece like a chain, in place of 
the usual foundation of smooth crotchets or quavers 
(cf. for instance I. 6, u, 13, 21, 23; II. 2, 15, 20 etc.). 
The opening is formed, first of all, by a pithy, somewhat 
pathetic little period, 

a) Non Allegro, sempre marcato I J \ 



but the fourth measure, changing its meaning to that 
of fifth, is followed immediately by a contrasting after- 
section of evidently tenderer meaning: a gentle creeper, 
an ornamental accessary part. Notice should be taken 
of the dotted rhythm of the under voice, which thereby 
acquires new meaning, in that the intermittent pressing for- 
ward gives place to a delicate up and down swinging 



The second period which at once follows (with 8 th - 
measure = i, and re-entry of the forte] introduces a clever 
working of the material already mentioned. First of all 
the under voice takes the lead, drawing attention to itself by 
the "slide" (Schleifer) of the first theme-member, and spreads 
out into a cadence (proceeding from the dominant back 
to the principal key, rfl 7 /JJ 1 "; but then through G% 
minor and -<4$ minor, again settling finally in the dominant 



while the upper voice spins out its opposing figuration. The 
renewed pushing upwards of the bass, after the manner of 
a sequence, gives the impression of a close - displacement 
(ja 40), but opens up into an after-section with 4a=5, 
which in both voices develops the principal motive (slide 
[Schleifer], dotted rhythm, and long notes), and which, to 
be properly understood, must be given with dynamic 
contrast (p instead of /): 




The first close is feminine (with annexed motive), and 
leads in the bass to the third: 



it therefore receives a close-confirmation of two measures. 
Therewith ends the first section. On the concluding value 
(8 a), the principal thought reappears in the key of the 
dominant (with 8a i), introducing the second (modu- 
lation) section. For this the upper voice, in place of 
the dotted rhythm, takes the arabesque motive of the 
second theme-member- the after-section enters with 4=5, 
but requires no dynamic contrast, because both voices 
make exchange of their themes (principal thought in the 
upper voice). The fore-section turns to the principal 
key, the after-section to the under-dominant. A second 
period next reproduces the second theme-member (i>] in 
B-major closing at the 4 th measure in the principal key; 
the after-section exchanges the voice roles (the upper 
voice with little shakes by way of ornament) and closes 
in the dominant key. A third period (which enters without 
change of meaning) leads, as one would expect, to the 
parallel key D-minor, and, indeed, by means of a trans- 
formation of the second period of the first part (c). 
It is, in fact, astonishing, how faithfully Bach adheres to 
his themes, and how, by wrapping the one in the drapery 
of the other, he procures new situations: 


I- *- *"*- 

t r 

instead of: 



Io y 

The parallel key (half close on a+) is already 
reached at the fourth measure, and the twice repeated 
after-section (entering without change of meaning) adheres 
firmly to the same, again (8=4) making half-closes on the 
first two 8 th measures, but finally opening out into a formal 
cadence. The motive material in these periods, also in 
those which follow, is altogether the same as that which 
has been shown up to now. The period directly joining 
on modulates through the parallel of the under -dominant 
( G % - minor) back to CJf- major the dominant ( Q a 
4' - orffo gtf - efr -ff - gft - <**); there- 
upon follows a Mixolydian episode (<r$ 7 ) of 4 measures 
and, finally, the conclusion in the principal key, which, 
in fairly faithful manner reproduces the first two periods 
of the piece, but naturally avoids the modulation to the 
upper-dominant. Bach, therefore, passes over the after- 
section of the first period (b\ which he reserves as coda, 
though extended to a complete period. Thus the whole 
is rounded off in pleasant fashion. 

The fugue (a 3) does not stand, perhaps, in imme- 
diate relationship to the prelude, but agrees well with it; 
and its various parts are closely knit together. The theme 
opens energetically with a shake on the leading- note, 
imitates this cadence twice, in the manner of a sequence, 
and closes, after a digression, on the third of the tonic 
The harmonic sense (the subsequent treatment being taken 
as standard) is as follows: 

Sosteuuto ma risoluto. 


It is therefore specially rich in modulation, and descends to the 
second under- dominant, then, over the first, rises again to the 



principal key. The Comes is the faithful transposition in 
the upper-fifth. Any attempt to shape the Comes other- 
wise, according to real or imaginary laws, leads to insur- 
mountable hindrances. If, for instance, the /$ c$ of 
the second (?) measure be answered by c\ /jj, that 
could only be done at the cost of the second motive: 

or: b) 

The arrangement at b would omit the harmonic pro- 
gression from the first to the second motive, and yet not 
effect the modulation from the harmony of the tonic to 
the dominant. In order thoroughly to grasp the correctness 
of Bach's mode of reply, one must get a clear idea of 
the original form, the ornamental transformation of which 
serves as theme: 

\\ t n 

The sequential formation cannot be ignored, and will 
allow of no disturbance. 

For the rest, the requirement which we recognise as 
binding, viz. that the Comes ought to modulate from the 
(tonic of the) principal key to the dominant, is fulfilled 
in an ideal manner, inasmuch as its first note effects this 
modulation Qf$ 7 turns f\ into under-dominant); yes, one 
can go so far as to assert that the shake may be first of 
all an ornament of , and then become an ornament 

i i 



But, above all, we again emphasize the fact, that in 
the formation of the Comes, the greatest similarity to the 
theme, and not dissimilarity, is the chief point to be 

The counter subject which is retained throughout the 
fugue, and out of which grow nearly all the episodes, 
has a striking likeness to the theme of the F- minor pre- 
lude of the second book: 




The similarity becomes specially noticeable in the 
two great episodes at the commencement, and at the end 
of the modulation section, both of which are framed in 
the homophonic style of the F-minor prelude, and like it 
alternate between parallel 3 rds and parallel 6 ths (under- 
voice with counterpoint in quavers): 




Of course this similarity cannot detract from the 
value of the piece, especially as it, probably, cannot be 
determined whether Bach wrote that prelude, or this fugue 
first. The opening section of the fugue (in the principal key) 
embraces, first of all, the entries of the three voices 
in the order alto (Dux), soprano (Comes), bass (Dux), 
which follow one another directly (without insertions or 
without change of meaning), and together form a three- 
member period (after-section repeated); and further, an 
episode of 8 measures, which consists of the following 
2 -measure group repeated four times with transposition 
and exchange of voices: 

The first voice (a) is evidently derived from the 
concluding member of the theme; the second (/') from 
the close of the countei subject, or from the commencement 
of the theme which has a similar sound; the thiid (<:) 
from the principal motive of the countersubject. They 
appear in the following positions: 

2: b) \ 3'- c) \ . 4 ( i) a) ^ . 
c t?| a) h?.. b)U.o 

a) J 2 S b) J 2 S c) J o 6 

The presentation of the Dux, which now follows in 
the soprano, does not introduce a new (second) develop- 
ment, but represents tins alone, it brings the second 
period, likewise by repetition of the after- section, to a 
close, as was the case with the bass entry in the first 
period of the first development; and it concludes, at the 
same time, the first section. 

The second (modulating) section first brings the 
episode of 8 measures, which recalls, as already mentioned, 



the F~ minor- prelude, and which, passing through D$ -minor, 
G^- minor, (G^ -major) E$ -minor, closes in A $ -minor. The 
running counterpoint of this period: 

' I 



derives its figuration form from the concluding member 
of the theme, but its chief contents: 

from the middle voice (ft) of the first episode, likewise 
from the close of the countersubject. There follows 
immediately a complete third development with the following 
order of voices: bass (theme in C^-major), alto (theme in 
Ffy-major, NB. a touching again on the principal key within 
the modulating section), soprano (theme in D^- minor 
[parallel]), all three following one another directly, and 
again forming a period of three members. Also the 
middle section contains, besides a complete development, 
a second (the fourth) one, marked only by one voice entry 
(theme in B-major [upper-dominant] in the alto) as close 
of a period of three members, the first eight measures of 
which are a reproduction of the first episode, but with 
three new transpositions of voices, viz. 

i: V) 

b) , 
a)J 5 


b) J 2 

Herewith the six possible combinations of the three 
voices are, as a matter of fact, exhausted! 



The great (second) episode which now returns shows 
an exchange between the two upper voices (commencing 
with 6 ths instead of 3 rds ), and, as it begins a fifth lower, 
passes through the keys of G^- minor, C- minor (C$-major\ 
A- minor t and D\-minor. 

The concluding section (in the principal key) springs 
directly from the parallel back to the principal key, with 
Dux in the bass- the alto follows first with the Comes, 
but only after an insertion of two measures (ja ^a), which 
with their quaver figuration freshen up the remembrance 
of the F- minor prelude; 

After the alto delivery of the theme there follow still 
four free measures, which, however, by compression appear 
as two (beginning with 8 = 5, and ending with 8 = 1), 
turning this period likewise into one of three members. 
Finally the soprano, which, since the last delivery of the 
theme in the bass, has been silent, gives out the Dux 
in a high position, whereupon the fugue concludes with 
four free measures (after-section). The entire absence of 
any disturbance of the symmetry deserves notice, and 
thus this fugue, as also the one in F-minor, is easily 
intelligible. It was perhaps for this very reason that 
Debrois van Bruyck looked upon this fugue as the normal 
type of the species. 


II 14. 


A prelude a 3 of wondrous beauty an outpouring 
of the inmost soul, fresh with youth, overflowing with 
love, more, perhaps, than any in the first part of the 
work; yet in its whole disposition surely betraying the old 
master ushers in a fugue of high, earnest purpose, and 
deep feeling. 

What freedom already in the unfolding both of 
melody and rhythm in the first half-period which forms 
the basis of the whole piece 1 Notice well the insinuating 
fourth of the opening motive, the onward pressing triplets 
of the up-beat, the smooth semiquavers of the turn-like 
feminine ending of the second motive, together with its 
longing, upward -soaring, annexed motive; and also the 
bewitching syncopation-effects from the third, to the fourth 

Adagio molto amabile. 

The second voice frequently imitates the upper one, 
but not in a single bar does it dispute the rank of the 
latter as leader; with exception of a few passages, the lower 
voice is a real bass. The motive material throughout is 
confined to that given above. The second period, which, 
together with the third, constitutes a middle section (in 
which extensive use is made both of the dominant, and 
of the parallel key), alone introduces something fresh; for 

Riemann, Analysis of Bach's " Wohltemperirtes Clavier". II. 8 


while commencing with the opening, transposed into the 
key of the dominant (C$-minor), it avoids the syncopations 
from the 3 rd to the 4 th measure reserved to intensify 
the second period of the middle section substituting 
the following: 


Quite enchanting is the gentle hint at the syncopation 
motive in the middle voice 1 

The construction of the piece is easily shown. The 
first period remains entirely in the principal key (whole 
close at the 4 th and 8 th measures), but it has an appen- 
dage (j a 8 a, a second after-section) which modulates to 
the dominant (C- minor). The second period joins on 
(with 8a=i), and modulates, first, at the fourth measure, 
to the key of the under-dominant B -minor ( ^ > )t = ^^J 1 
then (3 a 4 a) to that of the parallel (A -major, with 


the change of meaning *f$ = d*)> in which key, with an 
allusion to its dominant (^? = ^ 7 ), it remains. The se- 
cond, and immediately following period of the middle 
section (which, as already mentioned, is principally occupied 
with the syncopation motive) goes once again to B-minor 
(a + ?." [= <? vn ] 7 /^ X 11 /ft 7 /S) and to 
C^minor (/flvn _o,fl vn g^ o^ft), and opens 
out, in a passionate manner, into a half -close (with sus- 
pension and organ -point) in the principal key ($ VI 

{r^ b niyj J $> .;* L == & ft J " ^ff^ L ft J ~ 

o^jj gfyi ^JlJ*,?). After the organ-point, the bass (solo) 
leads back by means of three placid triplets to the repe- 
tition of the first period: 


The repetition of the commencement is, however, 
materially intensified by a double displacement of the syn- 
copation motive (tonic under-dominant chord of the 
Neapolitan sixth): 

cresc. (3 a) 

r ir 

piu cresc. (3b) 




The after-section is followed by the coda, itself a 
second, and complete after-section; both make rich use of 
chromatic harmonies (^jj ni< =/jJ 7 [dominant of the under- 


dominant], /jj HI < =Jf 7 [second upper-dominant]), but do 

not leave the key any more. I certainly cannot find this 
prelude "harsh" ("herbe"), still less can I discover in it 
dry formality ("trockenes Formelwesen") and here again, 
must dispute the verdict of Debrois van Bruyck. 

The fugue (a 3) is likewise a very remarkable piece. 
The theme comprehends three measures in slow 4-crotchet 
time, . /. e. six real measures and, indeed, this number is 
brought about by a repetition of the first group. The theme 
is first given out by the tenor in a sonorous middle 

Sostenuto con molt' espressione. 

dim. (4) 

The answer satisfies the demand that the dominant 
key should be led up to from the harmony of the tonic; 
to the opening c$ it opposes an /#, and thus the opening 
step of the theme is changed from a 3 rd into a 2 nd . 

The counterpoint accompanying the Comes is never 
afterwards literally reproduced, and is, in fact, little more 
than a first, and extremely simple rhythmical completion, 
and harmonic unfolding of the theme: 



On the other hand, the four inserted free measures 
before the third entry of the theme in the bass, introduce a 
characteristic formation (fourth-fifth sequence), which after- 
wards frequently recurs (also as counterpoint): 

f ' r * r r r (4=5) 

By the counterpoint to the first bass entry Bach evid- 
ently meant that the first motive of the theme, in ordin- 
ary, and in dislocated position (also in inversion), should 
repeat itself continually; but as we have remarked, in 
a similar manner, in connection with the G -minor fugue 
of the first part of the work the compelling power of 
the harmonic and rhythmical relationships really produces 
formations of an entirely new character. 

^= j^^*i --~. -i_ 




. 7J1. 

The same toying with the opening motive of the 
theme now goes on through a period in which there is 
elision of the i st and of the 5 th measure, and modulation 
to the key of the dominant; also through a second (com- 
plete) after -section leading back to the principal key. 
The conduct of the bass during these ten measures is as 
follows : 

=-(2) I i "_(4JN ^(6) (8) 

and even this is evidently evolved from the theme; the close 
(with syncopation) is the old-world cadence which already 
appeared in ornamented form in the first counterpoint, 
and in altogether unconcealed fashion in the second. 

The first section (in the principal key) here comes 
to a close with the delivery of the Dux by the soprano 
(which according to customary mode of speech presents 
a second incomplete development naturally a contradictio 
in adjecto\ the theme is not even once again developed, but 
only presented once again). Also here the counterpoint is 
occupied with the material of the theme. The bass moving 
throughout in quavers answers a purpose: it continues to 


nold fast to the opening motive in direct and in contrary 
motion; but here also, the harmonic relationships lead, of 
necessity, to different phrasing: 


The middle voice is occupied with the second motive 
of the theme (displaced by one crotchet), and this is carried 
on in the after - section. The latter enters with 4=5, 
because, in place of the expected <r $ under the final note 
of the theme (/ft), /jf 7 appears, resolving with feminine 
ending in B-minor\ and, by change of meaning to d Q , this 
leads at the 8 th measure to a close in the parallel key 
(A -major)'. 

(2 a) 


The second (modulating) section of the fugue enters, 
after this broad close, in the parallel key, in a clear 
manner, and, indeed, with development of a new motive 
which the voices, gathering together once more, announce 
in succession. The kind of imitation here is not one of 
strict fugal kind (/. e. it does not take place in the fifth 
and octave)- but it cannot be denied that here it is a 
question of a real development of a new thought, which 
claims rank next after the theme, and, later on, is combined 



with it. Thus the fugue becomes a double fugue (and, 
further on, by means of a third principal thought, a 
triple fugue). The pure form of the second subject is: 

as the bass gives it just before the close of the whole 
piece. Here, where all three voices introduce it as a 
prolonged stretto, it passes through the Mixolydian trans- 
formation of the leading note now so familiar to us 
and indeed, in a striking manner, on the last quaver of 
the measure: 




M U 


7 j> j^ i ^ 

CFfcfi r ?' 


-^ p =^= 





Besides the complete deliveries of the second 
theme, here marked as II, this fragment also contains 
some incomplete offshoots; towards the end the dotted 
fourth- (fifth-) counterpoint presents itself once again, and, 
in the after -section, it is also taken up by the bass. In 
the last group (7 th to 8 th measure) the tenor once again 
introduces the II theme in JB-minor, but leaps from the 
concluding note to the delivery of the first theme, and 
in the same key. 


I *T I ^^~ 




Already this voice entry combines the first with the 
second theme; first of all the soprano begins the latter from d, 
but breaks off in favour of the fourth- (fifth-) counterpoint; 
and the bass takes it up (likewise from d\ but at the end 
suffers the Mixolydian transformation, and passes on to 
the syncopated turn-figure of the I st theme. 

8va bassa. 



In the after-section of this period there is also an in- 
complete delivery of the I st theme (in very free form) 
likewise by the tenor: 



It enters on $ 9> , abandons the repetition of the first 
group (50 6a), and, with <rjf =c vu , modulates to the 
key of the dominant, in which the bass, in a repeated 
after-section, now gives the complete theme, while the two 
upper voices are occupied with the second theme. 

c) instead of: 

The deviation at c from the real form of the 2 nd 
theme is an intentional intensification, calling attention 
to a new, and important moment; for we are now entering 
upon a third division of the fugue (which, however, still 



belongs to the middle section). At the close of the second 
theme (while the bass, instead of the shake on d, makes 
a cadence with d\ %%)* the third theme is given 
out by the middle voice. 

This theme, likewise, is not answered in fifth and 
octave, but at once appears in stretto, and in various 
positions: soprano beginning with c and ending in 
B- minor, bass beginning with /"$, then tenor, likewise 
from /$; up to this point, all at the distance of two 
measures (of one 4 / 4 measure). But now the waves rise 
higher, and the modulation reaches the second dominant 
(G%- minor) by way of E-major (/# ^ 7 <? [= Q g 

The theme here sets aside the cadential quavers of the 
close in favour of a continued smooth rolling of the 
semiquaver figure, while the quavers appear in other 
voices. A third period the first, developing the 3 rd theme, 
occupies ten measures; a second, with 8 = 1, only six [after- 
section of only 2 measures] carries the first half of the 
new theme through the voices, and modulates through E- 
major (g$ vl = e^ and A-major back to F- minor \ a fourth 
period follows, going towards the under- dominant B-minor 
in which it makes a half-close. During all this, the long 

syncopation of the first development (Jj J J | J), 
the syncopation turn -motive of the theme, and also the 
fourth -fifth -counterpoint appear as counter subjects; and, 
finally, the first theme appears again, in the middle voice, 
after the half close in/Jj 7 , while the upper voice assists 
with the dotted fourth-fifth-counterpoint, and the bass rolls 
on with the semiquaver figuration (freely inverted) of the 
third theme. 



(2 a) 


But already the immediately following presentation 
of the theme (Dux in F\- minor in the soprano; the first 
motive slightly veiled by semiquaver movement, other- 
wise carried strictly through) combines all three themes 
(the third in its complete, smooth, onward rolling shape) 
with one another: 



With this, if not already in the preceding theme entry, 
we find ourselves in the concluding portion of the fugue, 
in which occurs: first an episode of 6 measures (2, 34; 
6, 7 8), during which the bass continues to run on, 
while the upper voices indicate, in quiet quaver movement, 
motives from the i st and 2 nd themes ; further a presentation 
of the Comes in the bass (repeated after-section with 
8=5), w ith the third theme in the soprano, and the second 
in the middle voice. 

A peculiar transformation of the last mentioned episode 
(calculated to convert an unbelieving Thomas to our 
theory of phrasing: three -measure rhythm in the order 
w is transformed into four-measure rhythm of strictly 
symmetrical character; so that in place of the motive 
chain, a a b, a a b, the simple a b a b is selected) leads 
back to F-minor t in which still a presentation of the 
Dux in F\-minor (repeated after-section), with close- con- 
firmation of two measures, brings the whole to a con- 
clusion with a new transposition of the three themes: 







J 1 

! (8a) 




We certainly do not intend to become reminis- 
cence hunters, yet cannot possibly get rid of the impression 
that here souvenirs of his young days came back to "old" 
Bach; at any rate in the prelude, which at once recalls 
the C^- major prelude and the G- major prelude and 
fugue of the first book. But here, indeed, everything is 
more sedate, broader, more detailed, more emphatic. The 
prelude consists of two parts, each of which is repeated. 
In the first there are 16 measures, which, however, in no 
wise form two regular periods, each of 8 measures; but, 
on the contrary, already in the first period, fore- and after- 
section are compressed (4=5); and, at the end of the first, 
the second even begins with 8=2. The three measures which 
thus stand over, consist first of a close- confirmation (cadence) 
of one measure, of which, however, the deceptive pro- 
gression of the bass (a b) renders two more measures 
(8a=6) necessary. The scheme of the opening measures 

Allegretto espressivo. 

? _ 








determines the quiet character of the piece, for the 
fundamental rhythm is I I etc.; the 

quavers glide diatonically up and down, and the semi- 
quavers only appear as lightly vibrating figuration, thus: 



Even where, as in the second period, two voices 
move in semiquavers, after the manner of the G-majo* 
fugue of the first book, 

the quaver movement is only slightly disguised. Only in 
the closes of both sections and in the middle of the 
second section a kind of working-out does the 
semiquaver movement become a real one; but it moves 
within the simplest forms: 

The harmonic structure deserves close consideration 





l J 

ga'(-l) d+ g c a 7 d + g .. a' (8) 

d a . 7 . (8 0) d 

(8) d+ 




.. (4) b' b 


J. (4 a) b a' d+ 7. g^ 7. (4) c+ 6 

(parallel) (leading back) 

d' g+ c 6 d' g 4 - . . (S) d 7 g 4 -^) c a 

(half-close) (free repetition 

Riemann, Analysis of Bach's "Wohltemperirtes Clavier". II. 9 

1 3 o 


d^ b' (2 a) b (^g+) c d 7 (4a) g+ (6) c< 

of the 1st section.) 

The fugue (a 3) a brilliant piece is constructed 
in a wonderfully concise manner, for it has only six theme 
entries; and it actually contains only two developments, of 
which the second comprehends both the modulating, and 
the concluding section. Now as the chief law of all 
formation A B A, i. e. establishment of a principal key, 
modulation, and return of the principal key, stands above 
special laws or "conventions of fugue", it were better to 
say that the first section of the fugue carries the theme re- 
gularly through the three voices; that the second (modulating) 
section introduces it only in the bass and soprano; and the 
third, indeed, only in the alto. The theme, certainly, is 
not suitable for frequent repetition, unless, indeed, in the 
case of strettos; for it is too long: 

Vivace brillaute. 



It springs suddenly into view, commencing with the 
fourth measure, and really nothing new is introduced in the 
after-section; but the tonic is twice confirmed by c & d 1 g^. 
It is interesting to observe how Bach prepares the entries 
of the remaining two voices by an upward rolling semiquaver 
figure (which must be reckoned as part of the counter- 
subject), so that three measures are not skipped over, but 
only one (after 8 follows at once 2): 

cresc. (2) 


The Comes shows at the opening the well known 
alteration of the fifth of the key being answered by the 
fundamental note; but for this no reason can here be 
assigned, for we do not pass from the harmony of the 
tonic to the key of the dominant, as that modulation has 
already been completed by the countersubject and, indeed, 
in the rare manner, only perfectly suitable to the period 
at which the fugue style held sway viz. by a leap from 
dominant harmony (d 7 ) to the key of the dominant (d 
as tonic). The first countersubject does not return in 
strict form, and it must be looked upon as an ingenious 
combination of the two countersubjects which are employed 
throughout the whole fugue: 

l) alto entry. 




The first section includes the three voice entries, and 
the following three appended measures (6 a 8 a), which 
carry on the sequence of the two upper voices, and make 
a formal full -close in the dominant (D-major}. A glance 
at the lower voice explains the possibility of this appendage. 
For as before the entry of the alto, the soprano, and 
before the entry of the bass, the alto rolled onwards, 
introducing, first an accented measure (2), and then, still, 
a group of two measures, on the point of stress of which 
the new entry followed, so now also, the bass, satisfying 
the requirements of symmetry, rolls onward; but as there 
is not another entry, it turns round at the right moment, 
tending towards the key of the dominant by means of a 
stately cadence. 

The modulating section plays first with phrases of 
two measures borrowed from the theme (one must, how- 
ever, be careful not to look upon their first measure as 
accented, which, with regard to the theme, seems likely. 



By the transformation of g 7 into # VI1 , and the avoid- 
ance of the expected C- major close, the 4 th measure 
acquires the meaning of 2 nd ; and the period, continued 
after the same fashion, turns by means of * = * VII _tp 
E- minor, in which key, with 9 = 4, a new bass entry of 
the theme follows; then appears a delivery of the Comes 
(in B -minor} by the soprano, and quite after the manner 
of the first development. The next period already modu- 
lates back to the principal key, and, indeed, again with 
working of the same phrase of two measures as the one 
in the first episode; towards the close of this period, the 
upper voices assume a close attitude: 

This sets up a standard for the now following third 
period, which at the second measure becomes an organ- 
point on D, but with the thirds and the shakes transferred 
to the lower voices, so that the upper voice alone has to 
spin out the thematic motive. The organ-point ends with 
a half-close on the 8 th measure, and only then comes a 
final delivery of the Dux by the alto, which, however, is 
fully prepared by the filling out of measures i 3 with the 
rolling figure well known from the earlier theme entries 
intensified into demisemiquaver movement, and continued 
through all the voices: 

end of the 


Only two measures of close-confirmation, in which 
the soprano, again in demisemiquavers, rolls downward 
from a 2 to small b, are added by way of appendage. 

Bruyck, who compares the prelude to a woodcock 
hopping lightly and merrily, finds in the fugue a "deliberate 
movement which may almost be compared to the wadd- 
ling step of a duck" (,,bedachtige, fast dem wackelnden 
Entenschritt vergleichbare Beweglichkeit"). If we trans- 
form the duck into a swan gliding over a smooth lake, 
this picture may possibly be reflected in the prelude; the 
woodcock with its rapid zig-zag flight will serve admirably 
as a simile for the fugue. 

II. 1 6. 

The prelude, which Bach himself marked Largo, is, 
however, none the less (although the allabreve-stroke be 
missing) conceived in allabreve measure, as the harmonic 
analysis easily shows. In order, while attending to minute 
details, not to lose the outline, the minims, in spite of 
the very broad tempo (something like J = 8o, therefore 
J = 40), must be taken as beats. The continued figuration 
in dotted semiquavers and in demisemiquavers may seem 
at the present day somewhat roccoco\ but the rich har- 
monic contents of the piece, strictly carried out, for the 
most part, a 4, enable one quickly to forget, the some- 



what formal shape ot the accessory work, unless, indeed, 
this be regarded as principal. The figuration of the first 

Largo. -- 





is maintained throughout; without it the piece would appear 
somewhat as follows: 





\ T i 

(half-close in the dominant key) 



w s=^te^_;*_*fe5_ilc=j_g 

tr- ^ff*^ 


i I 



r^ ^= 



-^ ^^~x- ^ I 





(8 a) (Sb) 

16. PREL UDE AND Fi'GUE IN G - MINOR. j o n 

Only two periods, the first of which makes a half- 
close in the key of the dominant (D-minor) on 7 , while 
the second, passing through the key of the under-dominant 
(C- minor), regains the principal key; and yet what 
fulness of expression within these narrow limits 1 

The fugue (a 4), with its tense, and indeed some- 
what stubborn nature (see the obstinate note-repetition of 
the last member of the theme), is well in keeping, with 
the prelude. It appears equipped with the whole apparatus 
of double counterpoint, and forms a fitting sequel to the 
mail-clad prelude. 

The theme occupies an authentic position, turning, 
within a narrow circle, around the third of the key: 

Allegro poco maestoso. 




The Comes answers d with g in order to effect the 
modulation to the dominant from the harmony of the 
tonic; the rest is a faithful transposition in the fifth. The 
theme with its four measures is favourable to simple 
structure, and of this possibility Bach makes abundant 
use, first of all, by allowing the entries in the various voices 
to follow one another regularly, without intermediate episode 
(tenor: Dux; alto: Comes; soprano: Dux; bass: Comes); 
and, further, by introducing very few changes of meaning 
in the measures of periods. 

The first countersubject is strictly mantained throughout 
the whole fugue; and it is so disposed as to be able 
to be doubled in thirds, and combined with the theme 
doubled in the same manner; such a combination a 4 occurs 
in the third development: 



A counterpoint of this character not only allows of 
all kinds of inversions in the 8 ve , but also of those 
in the io th and 12 th . In the first development Bach only 
introduces the two-voice form which results in a 3 rd , like- 
wise 6 th , between theme and counterpoint on the points 

of stress of the measures ( a also 

2. a) 



Also the first enunciation of the theme in the second 
development (Dux again in the tenor 1), introduces the 
countersubject in form 2 (in the bass); but already the 
alto entry in the same development (Dux [I] in D-minor t 
or rather in F-major) transposes the countersubject a fifth 

higher, so as to produce the combination ^ (double 
counterpoint in the 12 th ); 

d) etc. instead of: 


while in the soprano entry of the theme, which follows on 
immediately (in V -major), it is moved up only a third 

(combination a or \ double counterpoint in the io lh ): 
a) instead of: 

The bass entry of the second development (Comes in 
f -major) displays the same combination, with voices reversed: 
d) instead of: 




The displacements of key which result from the trans 
positions in double counterpoint of the io th and 12 th (see 
my "Lehrbuch des Kontrapunkts", pages 79, 129, 137, etc.) 
should be noticed; a certain wavering between the parallel 
keys (D- minor and F- major, G -minor and Eh -major t 
C-minor and E^- major] is, for better or worse, the more 
or less mechanical result of employing double counter- 
points other than the one in the octave. 

The third development brings about new combina- 
tions a 3; and, indeed, the theme is, first of all, doubled 
in thirds (tenor and alto), while the counterpoint (bass) 
retains its original position: 

a) \" 
c) 2 


Strictly speaking, however, this form must be traced 
back to an accompaniment of both voices with under-, like- 
wise upper- thirds: 

or: d) 

d b\ 

(cf. here i a, likewise 2 c I. The next delivery of the 
c a/ 




is not a simple transposition and octave displacement of 
above, but introduces the counter subject transposed a third 

b\ d 

higher, /. e. the form I a ) likewise 2 c ) of the second 

\ d \ 

1 likewise 2 c 1 

four- voice scheme; or (if the question be waived as to 
whether the upper- or under-voice of the interval of 3 rd is 

to be accepted as theme) the form a I of our first four- 


voice scheme. Now follows as a special display the four- 
voice form given above (theme and counterpoint with 
thirds). The third development, forming the principal 
feature of the concluding section, gradually renounces 
double counterpoint, for the tenor gives out the theme 
(Dux), while the countersubject transposed in the 12 th 
appears in the alto; but neither comes regularly to an 
end, for soprano and bass set in with Dux and counter- 
subject (in the original form) compelling them to proceed 
in sequential form, so that the appearance of a stretto is 
brought about. Anyhow, with regard to the soprano enun- 
ciation of the theme, there results the four- voice form: 

I. e. a transfer in the octave of the first four- voice scheme; 
this, however, does not come to an end, but assumes a 
homophonic, chord-like character, leading to a formal 



cadence in G-minor. The concluding delivery of the Dux 
in the bass is prepared with great ingenuity, in that all 
four voices repeatedly start off with the countersubject, 
waiting, apparently, in vain for the theme; 



and only, when, resigned to their fate, they return to the 
cadence, does the Dux enter in the bass; then tenor and 
alto commence the countersubject in thirds, but have a 
free ending. We see how Bach made no extravagant 
use of the various combinations, but was satisfied with 
hinting at them, just as they offered themselves. 

The episodes of the fugue make use, for the most part, 
like the one last mentioned, of the beginning of the counter- 
subject, together with a counterpoint in dotted quavers, 
which may be looked upon as a second countersubject, 
but which has no fixed form. 

The three sections of the fugue are as follows: 

I. Exposition (in the principal key): the four 
voice entries immediately following one another; the 
first episode of four measures which leads back to 
the principal key; and the second enunciation of 
the theme in the tenor. The latter does not be- 
long to the second section since it is in the principal 
key; besides, it is separated from the following alto 
delivery of the theme by an episode of four mea- 
sures, which, in any case belongs to the 

II. Modulation Section, and passes through F- 
major (V=^ 6 ), C- major (f Q g*), G-minor 
(<:3' = Vii) to D-minor (d). The delivery of the 
theme in the alto is meant for D-minor, but for a 
moment, in the middle, changes into F-major\ the 


adjoining delivery of the theme in the soprano is 
entirely in B9 -major, and the immediately following 
bass entry, in F-major. Before the third development 
there again appears an episode of four measures, 
which quickly springs to C-minor (/ + = ^ m ') and 
repeats the fourth measure, when the half-close on 
g 1 is changed into a whole- close. The third deve- 
lopment begins apparently in C-minor (because the 
upper 3 rd , efy stands above the fifth of the tonic), 
but soon changes to F-major ( G g = e? Q y?_^7-t 
J7 6 c 1 f + ). An episode of two measures (ja 
8 a) restores the key of C-minor (/ s '=*r v11 ), and 
this time there really follows a delivery of the theme 

in C-minor (beginning with * I, which only in the 


middle inclines slightly towards Ev -major, and 
hence has its close confirmed (ja)', a freely formed 
after-section brings the period to an end, and modu- 
lates to EV-major (c = ab* b\??). The E^ 
major enunciation of the theme, with which this 
section closes, appears somewhat uncertain owing 
to the upper- third being placed over bb the fifth 
of the key: it, however, soon becomes clear by the 
introduction of the #i? in the countersubject. The 
close of the period consists of the return modulation 
(el?* .. [=^ vn ] d 1 }, whereupon follows the 

III. Concluding Section which has already been 

II. 17. 


A wonderful prelude, the pleasing, harmonious sounds 
of which one takes in in full, long draughts: it forms the 
introduction to a fugue of specially fine texture. It opens 
on an accented measure with which the following unac- 
cented one is immediately connected, and the contents of 
which are similar: 








^ (4) 

The after-section introduces another, now gently rising, 
now falling, motive: 

mf *y- f r*^ 

against which the beginning of the second period stands 
in soft contrast: 


With this modest material Bach works through no 
less than 76 slow bars, and, by cleverly grouping them, 
well understands how to revive the interest of the listener. 
The re-entry of the principal thought (the opening one) 
marks the arrival at the chief points of the modulatory 
development-, thus first, after the second period of eight 
measures, in the key of the dominant -b (with 8 = 2); after 
the fourth (greatly extended), in the parallel key of F-minor 
(again with 8 = 2); and after the sixth (also extended), in 
the underdominant D^- major (likewise with 8 = 2). After 
the eighth period, when its return in the principal key is 
expected, Bach, however, suppresses it, and carries on the 
piece to the end, after the manner of the second period 
of the first three sections; the ninth period, by insertions 
and a repeated after-section, is extended to 14 measures. 

The fugue a 4 is richly equipped : it has no fewer than 
15 theme entries, carries out a countersubject in the 
strictest manner, and a second one (free) ; and also provides 
fugal episodes. The theme is extremely graceful, clearly 
divisible into two members, and highly symmetrical. As 
it begins with the fifth and does not modulate, the answer 
modulates from the fundamental note, and thus contracts 
the first step of a third to one of a second: 

Poco allegretto. 

mp XI 

Dux alto (2) 


I st countersubject. (0) 

Riemann, Analysis of Bach's c 'Wohltemperirtes Clavier". II. IO 



^ V 


This first countersubject is, for the most part, retained 
as it appeared at first (with the Dux naturally transposed 
in the under-fifth); but already at the beginning of the 
second development (which is still in the principal key), 
it is associated with the Dux, without transposition of the 

it therefore satisfies the requirements of double counter- 
point in the 12 th . Also at the beginning of the conclud- 
ing section, it appears in this form, but with ornamen- 

But much more extraordinary is an appearance, 
against the theme, of the countersubject displaced by a 
crotchet (as in the third development): 



8va bassa 

In the last development there is something inter- 
mediate between the two: 

8va bassa 

A second countersubject, though never strictly adhered 
to, but appearing, in more or less free form, throughout 
the whole fugue, is the one with the smoothly running 
semiquavers (at the tenor entry of the first development): 

It returns almost exactly in the same form at the 
following bass entry, and may be traced, besides, in the 
bass during the first episode. This episode, and the one 
imitated from it, within the third development, work out 
an independent theme of three measures (!): 




with which, in addition to the second countersubject, is 
associated a smart motive recalling the first member of 
the theme: 

The first section in the principal key comprehends 
the first development (alto: Dux; soprano: Comes; and after 
two measures of close-confirmation, likewise leading back 
[7 a 8 a], in which the alto starts off with the commence- 
ment of the theme, tenor: Dux, bass: Comes two complete 
periods) ; the first episode, which, by elision of the i st and 
5 th measures, forms a period of six measures (keys: 
E?- major, Aty- major, DV- major), with one measure of 
close-confirmation, likewise a leading-back (8 a); and the 
second development (bass: Dux; and after two measures of 
close-confirmation [3^ 40], which turn towards F- minor 
[parallel], alto: Comes again in the principal key, only 
accompanied in the bass by a scale - counterpoint in 
semiquavers which only occurs this once this slender 
period kindles interest anew; also tenor: Dux, and after a 
freely formed after-section, beginning with 4 = 5, the soprano 
enters with the Dux in a second, and intensified after- 
section; in all, again two periods, but with an insertion of 
two measures, an appendage of four measures, and an 
elision of one measure, by change of meaning, i. e. 21 

The second (modulating) section, is now, exceptionally, 
not divided from the first by an episode, but, after the 
cadence in Aty- major, in which all the voices take part, the 
theme (Dux) enters immediately in the alto in F- minor \ it is 
well in performance to lay a slight emphasis on the close 
of the section. The after - section (with 4 = 5) forms an 
episode, in which fresh counterpoint is opposed to the 
second countersubject: 


(4=5) (8) 

and which closes in C-minor. Further follows the extended, 
transposed reproduction of the first episode, with exchange of 
voices, again with elision of the i st and 5 th measures, and 
repeated after -section passing from C-minor to F-minor, 
Bv -minor and E^ - minor. The remainder of the third deve- 
lopment, and of the second section, thus runs its course 
in the remote regions of the parallel of the second under- 
dominant (tenor: Dux EV-minor)\ of the parallel of the under- 
dominant (after two free measures, which make a half 
close in BV-mtnor, soprano : Dux in Ify-minor with a triplet 
measure for the last group); and of the under- dominant 
itself (bass [8 = | J] opening [/. e. the closing beat 

changing its meaning to that of upbeat of the fifth measure] 
with Dux in Dty- major, turning, indeed, at the end towards 
Dfy- minor } whereby the obscuration has reached its high- 
est point). The master now collects his whole strength, 
and, in a repeated after-section, struggles upwards through 
Ab- minor and fib -minor to a half close on eb 1 (whereby, 
finally, an impressive triplet of beats occurs over the prema- 
turely reached E9 of the bass). The second section 
comprehends therefore only three periods, but 32 measures 1 
The third (closing) section now enters definitely with 
the Dux in the tenor, followed by the Comes in the bass, 
with slight compression (4 = 5); but it avoids the repetition 
of the modulation to the dominant, in place of which, 
indeed, a triplet of measures presses quickly ( O a^ chord 
of the Neapolitan sixth) towards B^ -major (a\?+ *t? VI1 

This deceptive cadence changes the meaning of the 8 th mea- 
sure to the 4 th , and a new impulsive triplet of measures 
advances from the broadly disposed chord of the Neapolitan 
sixth, again to the upper-dominant (organ-point on eb 1 6 th 
measure), and concludes, briefly, in the tonic. The close is 
once more confirmed by three measures (triplet), but ends 
with a deceptive cadence in F-minor (city\ in the repeated 


after-section (to be interpreted with breadth) of which the 
theme (Dux), as fifth voice, among the four real voices 
conducted regularly to the end, brings about an imposing 

II. 1 8. 

Once again, two pieces of quite special interest. In 
the prelude there is the breath of fresh spring (and with 
this the nearly related key of E-major may have something 
to do); buds are bursting forth from every nook and comer: 

Vivace quasi Andantino. 




(yd period) 


The happy man, bewitched, enjoys the balmy frag- 
rance : 


and his heart opens, and new deeds germinate 

Bach himself has prescribed the dynamic contrast of 
the former (piano), and of the latter (forte) passage. A 
detailed analysis of the piece may be left to those whose 
interest is excited; I give only the scheme of the harmonic 

I st section (with repeat). 

ist period: djf I dj}, d# dj} 7 I djj; djj 7 ; djj I 


d 7 , o dft ^ o dff d , f . 

2nd period (skipping over the first measure): dtt = b 6 , cj 7 


a j|. 

3 period: 

> - jjj}> I gj}+, 3- (= o d ^ ^o> 

^ 9> 1^ ^ft 9> rt f H^ ^c-g^ dj} 

(4) (8 

4* period: g# 7 . . | cjf 7 .. fj} I b+; [==s djjvil] a |7 

(2) (4) 

ajj, VH e |( 7 ajf + (half-close in the key of the dominant). 



Close-appendage (cf. i*t period): aft laft 7 aft aft 7 I aft aft 7 

(8a) (8b) 

5th period (skipping over the first measure): aft VII* [deceptive- 
cadence harmony with change of meaning to b 4 "] fft j^ [= dft 0> ] 

6* period 

iod: ajf. . . [= fjj] g |' I cj}+; c|' ff+ 

>, .. K|.> | ..j} 

2 nd section (with repeat): 

ill'* ti*T I A Li LL*TAli LL*T 

yth period: dj(' .. gfi 7 i .. gx C {J cjj eft 7 

(2) (2a) (4=6) 


'h period: cjj 7 .. fjj 7 , . b 7 .. e 7 (skipping over the 
(2) (4) 


fS 7 [=gr n ]| d S 7 - 1 d ' g# 7 

(6) (Ga) 

5th measure) .. I a+ e 7 , a H ' [= eft VI] c ft 7 

(4) (8=2) 

9* period: o c ft, o g {f [g jjvn] d }j7 | o d JJ. .. o a ^ [== a 


aft- T dft 7 j gft-, 7. cj? 7 | fft-. 




loth period: fj} [= ajj] ^ aft* dfl+, <>djj VII I- d j}' 

(2) (* 

.. ft* df I gf 'gjt, VII I a #7 d jff f |> 



Iith period (cf. ist period): dj( I dj}?, dj} djf 7 | 

(2) (4) 

; o dft j dfl 7 t o d j{ g j(7 | , g j| f g fl7 o g jf 

(8=6) Triplet of measures 


dtt I U I 

period: ff (deceptive cadence) g$ 7 cjj" 1 " J. fj( 7 

f2) (4 

The modulation is freer than usual: one especially 
misses the parallel key among the chief points of rest 
(but in its place the key of the dominant of the parallel 
is to be found among them); the key of the under-domi- 
nant, also, scarcely makes itself felt, but, in its place, that 
of the second under-dominant {F$-minor\ and that of its 
parallel are prominent. 

The fugue a 3 glides along in quaver triplets ( 6 / 8 ) 
with lizard-like lightness. The theme, with its inserted, 
repeated 2 nd measure (2 a), disturbing the tonality, has 
a peculiar play of colour; it turns about the third of the 
key (soprano): 



Con agilita. 





The Comes (alto) enters at the close the 4 th measure 
changing its meaning to that of 5 th and is a faithful 
fifth-transposition of the Dux. As the Dux does not 
modulate, the Comes does not modulate back, and there- 
fore an episode becomes necessary before the entry of the 
3 rd voice, in order to restore the principal key. Bach 
fashions this so that it shall, at the same time, complete 
the symmetry, /. ^.-form the fore-section to the 3 rd voice 
entry (this again Dux in the bass enters with fourth 
measure changed in meaning to that of fifth). The 
counterpoint of the soprano to the first appearance of 
the Comes and the first episode, prefigure, as it were, the 
contents of a second theme of the fugue, which is a real, 
complete, double fugue. In other words: from the 
motives of the first countersubject and of the first episode, 
is crystallized, later on (in the middle of the fugue which 
contains 143 bars), a real second subject which is devel- 
oped independently, and then combined with the principal 
theme. For the I st countersubject appears thus: 

flu K I . I 1 . I fr J-r-J I--, 

i. f. it repeats twice a syncopated motive, a species of 
cadence which, however, powerfully deflects the harmony 
of the theme the first time: 



The first episode runs thus: 

wlT'FT^trP \~ -iT'i i i- ---FBi 


The second theme first detaches from the latter the 
chromatic passage, while the syncopated motive of the first 
countersubject appears as appendage (see measures 66 70): 


!" * 






This second theme is perfectly symmetrical in con- 
struction, so that when combined with the first theme, there 
arises a slight conflict', it enters at the second measure- 



motive of the latter, and gives to the second measure the 
meaning of first, in that, by its resisting harmonic and 
rhythmic nature, it destroys (as indeed the first counter- 
subject does") the cadential power actually inherent, and 
repeatedly felt, in the second measure of the theme: 

I repeat, that this second theme is evolved, as it were by 
good chance, from elements previously employed. Besides, 
already before the appearance of the second theme, the 
motive of the first countersubject is frequently opposed 
to that theme, and it is also employed in the episodes. 
The other contrapuntal material of the piece grows also 
out of the theme, countersubject, and first episode; in the 
last named, the motive of the upper voice 

is exceedingly fertile. It appears, first of all, in every 
episode of the section before the entry of the second 
theme, as chief element; and, immediately on the second 
delivery of the second theme (by the alto), is opposed 
to its appendage, as if the source of the second theme 
were to be pointed out in unmistakable fashion: 



Towards the end of the second section of the iugue 
(development of the second theme without the first), the 
inversion of the chromatic chief motive of the second 
theme, with the assistance of the above-mentioned counter- 
motive, attains to special importance: 



- *y 


As already remarked, the three principal sections of 
this double fugue must be distinguished, according to the 
thematic material, as: 

I. Development of the first theme alone. 
II. Development of the second theme alone. 
III. Combination of both themes. 
It is extraordinary that Bach has remained in the 
principal key during the whole of the first section, although 
it is very long, and the theme more than twice com- 
pletely developed. 

I. I st Development: Dux in soprano, Comes in alto 
(with 4 = 5). Then follows immediately a close-confir- 
mation of one measure twice repeated (&a, 8<), and a 
redundant delivery of the theme by the alto voice. This 
latter is detached in too marked a manner, by the extent 
of the episode which follows (8^, 8, and by a complete 
new period with triplet of measures for 5 6), from the 
subsequent theme entries, to be reckoned amongst them. 


The episode modulates in a detailed and formal manner 
to the dominant, so that the Comes may commence a 
fresh development with intensified effect. 

2 nd Development (with 8=1): Comes in the bass, 
and after an episode of eight measures, which first of all 
twice displaces the close (30 40 to C^- minor, $b 4^ 
to B- major], and next, in the after-section, returns to the 
key of the dominant Comes in the soprano. Then after 
an episode of six measures (411. displacement of close to 
C$-minor\ 46, displacement ot close to B-major\ and 
after-section with return to the principal key), Dux in the 
bass (with 8 = 5), forming another after -section which 
concludes this development, and by means of an 
appendage of two measures to be taken in broad, full time 
(70 8 a) makes a half close on the dominant, thus 
intentionally marking the entry of the second theme: 

B 5? * 

allargando .... 

II. 3 rd Development (for clearness' sake, commencing 
with only two voices, soprano and bass): the second theme 
(beginning with //$) in the soprano, and, after a leading-back 
measure (40), the second theme beginning in the alto 
with p-jf, also, after one measure of close-displacement (8a 
to Cfymitior), 2 nd theme beginning in the bass with c\ 
whereupon a free after-section leads back to the principal 
key, in which, once again, the 2 nd theme is given out by 
the soprano, but in a higher position, starting from gfa 
in this last presentation of the theme (50 So) the har- 
mony turns towards the end from G^- minor towards 
1%-minor (d$-gfr- ( ^, aj}'-jf, *jj'-*|}). From 
this high point of departure an extended period (with 
30 40) leads back to the principal key, while the above 
mentioned inversion of the opening motive of the second 
theme descends through A- minor (j m> ""*} 5 ). D\-minor 
(^m^aftT), G\-major (&* = <$<), C\-major (g^) t 
F^jL- major (cfy 7 ), to B- major (parallel), but then soars 
again upward to C$- major, in order (at the 6 th measure) 



to change this to the meaning of the chord of the Doric 
sixth (gjj in< ), so that the 8 th measure makes a half-close 
on d\ n . Over the long sustained d\ of the bass, the two 
upper voices then return to the tonic with repeated after- 
sections in form of cadence, closing the second section 
and leading to the third. 

III. 4 th Development (with 8= i): I st theme (Dux) in 
the bass, 2 nd theme in the alto; after two measures leading 
to the dominant (30 40): I st theme (Comes) in the 
soprano, 2 nd theme in the alto; then after a free fore-section 
modulating to the under -dominant: I st theme (Dux) in 
E-major (parallel to the under-dominant) in the alto, 2 nd 
theme (beginning with e) in the soprano. A free episode 
leads back, first of all, to the key of the under- dominant, 
and then modulates through F- minor (eft 7 ), G$-major 
(</{J 7 ), A\-major (g^- = e^) > D^- minor (afr), back to 
the principal key, with a close -confirmation of two mea- 
sures, gathering together strength for the 

5 th Development. This first introduces the Dux in 
the alto, and the second theme in the bass, with three- 
fold change of meaning of the 4 th measure back to that 
of 3 rd , by repetition of the close of the first theme through 
all the voices: 




At the close of the period (8 = i) the soprano then 
enters with the first theme, while the alto takes up the 
second, and the bass, with wide stretches, effects a cadence 

i Co 


The freely formed after- section ends with the closmg 
motive of the theme in the soprano: 

II. IQ. 


The prelude has the character of the Gigue, as that 
form had developed in Bach's time, /'. e. the triplet-move- 
ment is as yet only pure figuration ( I as counts; whereas 

originally |S | | was the rhythm on which it was originally 
based); so also are the opening imitations of the fugue kind, 
Poco vivace ma grazioso. 

f i 

t (2) 

and the inversion of the motive, entering already after the 
first close in the dominant key: 



The piece is strictly written a 3; the three voices, 
however, do not by any means share equally in the deve- 
lopment of the motive, for the under-voice repeatedly has 
long stretches, for example (commencement): 


or, (end of the first period): 



The first period keeps firmly to the principal key; it 
changes, first of all, the half-close of the eighth measure 
(8 = 6) into a full-close, but by means of a one-measure 
appendage, returns to the half-close (8b); with still another 
half-section (5 8), however, it regains the full-close in the 
principal key, but in an appendage of two measures 
makes a quick modulation to the dominant (a 6 \ b 1 , e+ a* 

b 1 { <?+). Now, with 8 = 1 the second period begins to 

make use of inversion, modulates to the parallel key 
in which it makes a half -close (e* b 1 ) \ e* 7 a+ \ 

(2) (4) 

i< (= /J7) I yfl (= </) e i a i- (= ,#vi) I Ai 


strengthened by two measures (7 a 8 a: cfy 1 c% 
/# vn I ^tt 7 )* an d winds up with a new after-section (with 


triplet of measures for 5 6) in the parallel key (F\- minor): 
Thus both aims after positive modulation (dominant and 
parallel) are accomplished, and a specially concise period 
not imitating the principal motive, but only making use 
of it in light fashion in the under-voice leads, after the.- 
manner of a sequence, back to the dominant: 

R5 em an n. Analysis of Bach's "Wohltemperirtes Clavier". II. II 


f -- * f ^ * . . ~ * ^- 

Ji ^i 

P I- 


At the close (with 8 = i) now recommences the deve- 
lopment of the inverted motive; the period elides the 5 th 
measure, and closes in the under-dominant (D-major), in 
which stands the next following period imitated from the first 
(half-close at the eighth measure; in the first appendage 
[of 2 measures] it is changed into a full-close, but in the 
second, [of one measure] restored). The last period regains the 
principal key (a + \ ^ [= vn ] /# 7 | /# [= <t] e 1 I 

(4) (G) 

a + t d 6 e** a+ d Q e 1 \ a*}, which the extended (5 a 6 a) 

after-period, with stationary bass on A, now retains until 
the end. 

The fugue (a 3) belongs to the smaller, more delicate, 
more simply planned ones. The theme, which only appears 
ten times altogether, preserves the compass of the triad 
position (sixth included), rises from the fundamental note 
to the fifth, obstinately gaining, as if by force, degree 
after degree, and then sinks down again to the third 






poco f 

The Comes is a faithful transposition in the fifth. 
A real countersubject cannot be shown, at least none 
which faithfully returns; still, emphasis must be laid on the 

fact that the pointed rhythm jj plays an impor- 

tant role in all the contrapuntal writing, as well as in all 
the episodes. For the most part, the counter-voices ad- 
vance by degrees with note repetition (a), or chromatically, 
(b), or replace the note repetition by octave steps c, d)\ 



J 9 ' - 

- ^ -- 

It cannot therefore be denied that unity reigns among 
the counterpoints to the theme, but the master acts with 
sovereign freedom, and by no means keeps strictly to this 
ascending direction (cf. the second bass entry of the first, 
and the alto entry of the modulating, section). Where, 
in the episodes, the dotted rhythm is wanting, the con- 
cluding motive of the theme is imitated. Finally, the first 
countersubject (counterpoint to the Comes on its first 
appearance) seems to be the one least related: 


l6 4 



its motives, with exception of the first (which, after all, 
only appears in two episodes) never return. 

The construction of the whole is of the utmost 

I st section (in the principal key): Dux in the bass; 
then, joining immediately on, and therefore eliding the 5 th 
measure, the Comes in the alto; and, after two measures, 
with return to the principal key (7 a 8a, in which the 
wonderful d setting aside the tritone g d should be 
noticed), Dux in the soprano, not, however, as repeated after- 
section, but as a new fore-section, followed after the 
repetition of the fourth measure (from A-major to E-major 
with inversion of the concluding motive of the theme) 
by still another bass delivery of the theme (Comes), 
bringing about the appearance of 4 -voice writing, as if 
the first voice (which it really is, so far as mere position 
is concerned) had been tenor. Thus the principal section 
only ends with the close of the second period. This 
close, however, does not follow smoothly on the domi- 
nant (<?+), but rather does Bach introduce, towards 
the end, the Mixolydian bending of the leading note 
(d\ in place of rf/jj), not for the purpose of returning to 
the principal key, but to change the meaning of g$, b, d 
of ^ 7 into fjj vn , and, with only two additional measures 
(70 So), to obtain a half-close in the parallel 


a passage, the harmonic essence of which is not d Q e* 
a^ b 1 etc., but: 


in which the Phrygian /$<?</ c should be noticed. 
This leads to the 

II nd (modulating) section, and there follows directly 
(with elision of the first measure) the theme in J 7 ^- minor 
in the soprano; further, after two measures of modulation 
(30 40: a* . 6 . b 1 \ e + ) E-major being exchanged for 
C^- minor (parallel to the dominant) the theme in Cjf- 
minor in the alto. An episode of five measures (2 4, 
30 40), turns first to B- minor (parallel of the under- 


dominant: g% [= t> IU <] /jf 7 /$)> an d in the repetitioa 
of the second group, back to the principal key (yjf [== 
d\ e 1 a*\ whereupon (with elision of the fifth measure) 
the bass (an octave lower than in the exposition) gives 
out the Dux in A -major', but as in the accompanying 
voices at the end of the first section the Mixolydian 
bending of the leading-note (here g$ in place of g$) and 
two additional measures (7 a 8 a), transform this Phrygian 
bend into a half-close ony$ 7 , as there, into one on cfy 1 
(b a gf\ in the sense of f [= b\ /% 7 ). And then, 
as in the first section, the bass spins out the concluding 
motive of the theme in form of sequence. But now, in 
place of the expected theme entry in B-minor there follows 
another appendage (triplet of measures for 7^ 8) in 
which the bass inverts the concluding motive of the theme, 
likewise forces its way upward, and leads to a half-close 




The delivery of the theme by the soprano, in the 
key of the underdominant, which immediately follows, 
announces the approaching end, and could therefore 
as indeed also the preceding delivery of the Dux be 
reckoned as belonging to the closing section; but this 
acceptation would not allow of an equivalent, as regards 
feeling, for the intense restlessness. It would probably 
be much more reasonable to look upon the after-section 
which follows, and which leads back to the dominant, as 
still belonging to the middle section. This after-section is 
entirely evolved from the concluding motive of the theme, 
and its harmonic contents are d* . 6 . e' 

7 | c+ i.e. the concluding e + which appears in place of 


(which expectation is strengthened by the eft of the figu- 
ration) has therefore not tonic, but dominant meaning 
(cf. Catechism "Harmonielehre" p. in), *'. e. the close 
becomes a half -close. That is also the inner reason 
why the delivery of the Comes by the alto which now 
follows, has such a variegated appearance; 



I6 7 


The key of the dominant ought not again to prevail. 
The suspense now becomes more intense, for, first of all, 
the second group is twice repeated (the concluding motive 
of the theme is employed with cadences to a + (40), 
d* (4^) and half-close on e* (4^), at which moment the 
soprano enters triumphantly (with 4^=6) with the Dux, 
bringing the whole to a conclusion (there only follows a 
close-confirmation of one measure). 

II. 20. 


The prelude is an extremely wonderful chromatic 
piece, evolved with unexampled art from a short theme: 

Nou allegro. 

This thought is first of all repeated (with 4 = 6) with 
voices reversed, and followed by two confirmations of 
one measure (80, 8), forming a cadence, first in D-minor t 
and then in E- minor. The motive of these appendages 
is developed from the principal theme, but assumes an 
independent form: 


The first period is repeated in E-minor (beginning with 
voices reversed; and, later on, with original position), followed 
by four cadence displacements similar to the ones mentioned 
above (to A -minor, JD- minor [yjj], G-major, C- major; 
the independent character of these intermediate thoughts 
deserves note), then the principal thought in C- major, 
and immediately afterwards (4=6), with voices reversed, 
in G-major. The following period now takes up the 
motive of the intermediate thought, with symmetrical struc- 
ture; in measures i 2 the second motive is introduced, 
passing to the keys of G-major and D- minor [/"$); in 
3 4 the principal thought, in J) -minor; in 5 6 the 
second motive passing to the keys of G-major und A-minor\ 
and in 7 8 the principal thought, in A -minor. Here, 
as a return has been made to the principal key, the first 
section really ends; but, in order to make the repeat effec- 
tive, a kind of coda is appended, in which the second 
motive is introduced four times (in A-minor t D-minor [/"{(], 
G-major, and closing in C- major), and then, with free 
transformation of the same, there is a half-close on e" 1 : 



At the opening of the second part, the inversion of the 
principal thought is presented, 


it is repeated in the after -section (4 = 6), with voices 
reversed, in D -minor. An intermediate half-period intro- 
duces, four times, the inversion (free) of the second thought, 
in A-minor and G-major\ a new period (4 = 2) introduces 
the principal thought, inverted in E- minor and A- minor \ 
then follows an intermediate half -period with the keys of 
C-major t D-minor, G-major, C-major (in last three, half- 
cadences), a period, with the principal thought in its 
original form (not inverted), in A-minor (starting with 
4 = 2) making a half -close, whereupon (with 4 = 6) the 
inverted principal thought (in A-minor} brings the period 
to a close. The rest is coda, which, during two compound 
periods, holds fast to the key of A-minor \ measures i 4, 
the intermediate thought based on the harmonies e a vl1 
b 1 I <? 7 , and the after-section (4=6), on the principal thought 


(free) in A-minor; the second period (with 8 = 2) contains 
the principal thought inverted on the harmonies a 1 a, 
and not inverted, on the harmonies e 1 Q e. The appen- 
dage of one measure at the close of the first section of 
the piece reappears here as a whole-close confirmation. 

The fugue a 3 is of special weight and power: it is 
similar in character to the D-major fugue of the first book, 
with which it has the sharply marked demisemiquaver 
run in common (here, not in the theme, but in the 
counterpoint), also to the G-minor fugue of the second 
bo ok, though superior to the latter in piercing sharpness. 
For the rest, it is worked out without any special display 
of contrapuntal devices. The theme advances, during its 
first half, with powerful step (Andante maestoso), and its 
second half follows in a similar strain (it should be noti- 
ced that the second half is almost an exact reproduction 
of the first, in diminution). It begins with the fifth of the 
tonic, and, as it does not modulate, demands for the first 
note the answer in the 4 th : 




Besides the countersubject here noted, which faith- 
fully accompanies the theme, the concluding motive of 
the theme is specially employed in the counterpoints to 
the theme, and in the episodes; the demisemiquaver runs 
appear sometimes broken off more sharply even than in 
the countersubject; for example (i st episode): 



or else, inverted, in unbroken runs (last entry of the 


r^- p^ i i -^^^n ^^fcL 

No really new material is further employed. 

The structure is as follows: 

I st Section (in the principal key), including only the 
first development: Dux in the bass, Comes in the alto, 
and, after two modulating confirmations, each of one 
measure (D -minor , C- major), Dux in the soprano. The 
episode (2 confirmations of one measure, and a modu- 
lating one of two measures, to G-major, JF-major t closing 
in C-major), which follows, leads already to the 

II nd (modulating) Section. The theme, beginning with 
f e (therefore Comes) is, at first, introduced in the key 
of C-major (parallel); the close (measure 4), as in the 
first and second episodes (only four times), is imitated with 
modulation through the Keys G-major, D-major t A-minor 
and E-minor. At the fourth confirmation (with 4a= 5) the 
Comes enters in the soprano, in the key of E-minor ; so that 
we again approach near to the principal key. Also here, 
three close - displacements of one measure to D -minor, 
C- major, A-minor (half-close) appear again as episodes; 
and, holding fast to the principal key, there follows one 
of two measures. All these close-displacemnts are formed 
quite in a similar manner, viz.with the concluding member 
of the theme as chief material, and the semiquaver run, 
or concluding motive of the couniersubject, as counterpoint. 

III. The concluding section first introduces the theme 
(beginning with d c, therefore Comes 1) in A-minor, then again, 
as Intermezzo, the close-displacements of one measure, but 
this time with the concluding member of the countersubject 


as principal material, while the concluding member of the 
theme appears with figuration: 

The keys passed through are: D-minor (4 a), G-major (40), 
C-major (4c), F-major (4d) and D-minor (46). The last 
close is frustrated by the deceptive progression of the 
bass (a bV} t while (with jef) the soprano gives out 
the theme (Dux), but in I) -minor (under-dominant); the 
close in the key of the under-dominant, not harmonically 
satisfying, is followed by a new after-section (close-for- 
mations of two measures similar to the former ones of 
one measure, but by the form of cadence at once recog- 
nized as related to each other) passing through C-major 
back to A-minor (a [=/]_ ^ | c + : / [=a] <? 7 I *A 

(6) (8) 

in which key a freely formed cadence is still appended 
(7 a 8 a), at the conclusion of which (with 8a=5), the 
theme (in A-minor, but beginning with d c) is given out 
once again in the bass. The piece ends with a single 
close-confirmation of two measures. 

We again see from this fugue that the transformations 
of the theme brought about by position and mode of 
answering, do not affect its real essence. Here the form 
of the Comes appears to be the real theme (it is employed 
in 5 out of the 8 theme entries), while the third at the 
commencement only occurs occasionally, as at the opening, 
to emphasize more sharply the beginning of the tonic 



fl. 21. 


A prelude, sonata -like in form, and of extended 
development (87 bars of the original notation, not coun- 
ting the repeats of both sections). The opening, and 
principal thought is written strictly a 3, and is set out in 
polyphonic character (with imitations in the two under- 

ufr 1-2- /-^ T ^in- 

_^ fi ^ _ 


> IP () S g^j | 

j; t ^ S-^~ q 



J =: w 



rj-r^-tr-1! rPrr- -MS-r^-r- T^-T-nr-i 


-P E^_ x y v * ^-^? r; ^ ^f s^~i 




' (8) 

rb fl rfVtf-pT-* 

* f f ^ t * ^~ 


E -h^g '&&-** i> ^ 


f ? (2) 

(half-close in the principal key) 



(8) cj 

(half-close in the dominant) 



There follows a contrasting thought (a 2), which 
balances first of all on the chord of six-four (c\\ passes 
on towards B^- major (/J), and makes an unsatisfactory 
close in that key (third in the bass); this key of B^- major 
produces, however, quite the effect of under-dominant of 
F-major> so that a further period has to be added, which 
makes, anew, the modulation to the dominant key. The 
latter is then maintained until the close of the section 
which, indeed, makes a wide digression (up to the chord 
of the Neapolitan sixth o/ 2 " [gb+]). The subordinate 
thought (in stretto with the under- voice) is as follows: 

(after-section likewise, in J& -major, with reversed voices). 
The period completing the second modulation, which 
joins on, really introduces a kind of second theme: 


(8) f - 

The remainder of the first section, especially after 
the repeated confirmation of this close in the dominant 
key, again resembles the first theme in structure, and 
forms a genuine cadential period. It contains an extra- 
ordinary annexed motive to the fourth measure, and it is 
noteworthy, in that the second (development) section 
opens with an imitation of the same: 

(after 4 a follows the complete after-section without elision 
of the fifth measure). The second part takes up, first 
of all the concluding thought, and modulates with it 
through B\? -major to C-mitwr, then introduces the second 
theme, turning the same towards G-minor (parallel; cf. the 
repeated cadences in this key). Then the first theme is 
repeated (but not quite faithfully), and also the intermediate 
thought, which closes this time in C- minor \ thus the key 
of the under-dominant is reached, and made the most of. 
But the master cannot satisfy himself; and so after repro- 
ducing the whole of the thematic material of the first 
part, he follows on with a long development based on 
the first theme and concluding period, strictly a 3; this 
breaks off with a half-close on f 1 , while a coda, mostly a 2, 
forms a brilliant conclusion. 

The fugue (a 3) is flowing and simple, like its theme,, 
which, without ado, sinks down to the octave: 


Allegro moderate. 


e/ m/" ~~ ^ ~~> 




The turn-ornament (c bb a b) on the opening tonic 
is, according to rule, answered by the turn - ornament 
(g f efy g), and only then modulates (the rest is therefore 
transposition in the fifth). This fugue has no real counter- 
subject, but the counterpoint to the Comes: 

forms the starting-point and basis of all the other counter- 
points; both the quiet crotchet movement belonging to 
the above, and especially the syncopation of the closing 
member are repeatedly employed, the latter for the first 
time, and in a striking manner, in the alto entry of the 
second development: 


The counterpoint to the soprano entry,both in the second 
and in the third development, appears formed in a similar 
manner; the same figure, in descending form, appears in the 
episode following the latter. Many of the counterpoints, 
however, consist of plain third- and sixth-doubling of the 



theme; the fine, contrasting holding notes, as counterpoints 
to the theme, also deserve attention: 

(l st bass entry of the I st development). 

(2" d bass entry of the same) 

(Mixolydian bending) 

2 nd development, alto entry. 3 rd development, alto entry. 

3 rd development, soprano entry. last soprano entry. 

2 nd development, soprano entry. 

The construction is as follows: 

I. Section: Dux in the alto, Comes in the soprano; 
after an episode of four measures, Dux in the bass, 
with two measures of improved close (70 So), but 
with 80=2; and two more free measures which 
proceed to the dominant, so that a redundant bass 
entry (lower than the first; apparently a 4 th voice 
entry) brings a new period to a close (Dux [1] in 
F-major). But as the soprano makes the Mixolydian 
bend (el?), a new after- section becomes necessary; 
at the 8 th measure, this arrives on the second upper- 
dominant (- 7 = b?J, and hence, for a proper close, 
two more measures are required. By a confirmation 

Riemann, Analysis of Bach's "Wohltcmperirtes Clavier". 13. 


of one measure, the close in the dominant key is 
marked as a final, sectional one. 

II. Section: Dux in F-major in the alto, and a free 
after-section modulating back to the principal key; 
then, Dux in lib -major (principal keyl) in the soprano, 
and free after-section modulating to the parallel (G- 
minor); further, Dux in G-minor in the bass, and free 
after -section (with 4=5) modulating to the under- 
dominant (E& -major). With that, the theme has been 
carried through all three voices, and there begins, 
still part of the second section, a third development: 
Dux in Eh -major in the alto, free after-section (with 
4= 5) modulating to C-minor (parallel of the under- 
dominant); further, after a confirmation of two 
measures, Dux in C-minor in the soprano, but which 
already conveys the impression of C-minor as ^b 6 , 
which then, with change of meaning of the fourth 
measure to that of sixth, (1) actually comes into 
force. The period and section finally end with a 
close in B^- major. 

III. Section: A pleasing sequence, formed from 
the descending syncopation motive of the counter- 
subject, leads, by means of a free period of eight 
measures (but with elision of the fifth measure), to 


the half- close on / 7 (l>\> + eV^ [=g iu< ] ^ | 4 

eb+ a\> 6 b 7 I <?K 6 | / 7 , b^ eV* \ / 7 ), and con- 

(4) (6) (8) 

firms the same by a two-measure close in F -major 
(/' b + c 1 I/" 1 "). Now the soprano enters with the 
Comes (which had almost fallen into oblivion), but 
withdraws it from the key of the dominant by 
means of a convenient av. The after-section closes 
still again per inganno (prepared deceptive cadence 
d 1 V) in G- minor, so that a new after -section 
becomes necessary. The latter opens with an im- 
provement of the second group (30 40, breaking 
off allargando with sf on / 7 ), and then, taking the 
second upper -dominant (0 9> ) at the sixth measure, 
concludes smoothly on the tonic. There still follows 
only a cadence of one measure. 



II. 22. 


Two of the most powerful numbers of the second 
part of the work lie before us: both particularly rich in 
contrapuntal art and yet without any trace of exaggeration. 
At every nook and corner the prelude betrays the possi- 
bilities of contrapuntal formation, but from these Bach 
turned aside. For instance, only see how the opening 
motive (the turn, and the step of a second which is 
approached by interval of a 4 th ), is constantly appearing 
in the opening measures. 

Allegro risoluto. 

f I. 

\ etc. 



All these allusions, as the piece stands, do not con- 
cern us; we have merely to consider what Bach selected 
from this fulness of possibilities for the fugal treatment of 
the theme. The theme, however, is not that scanty 
fragment, but a whole period: 




T . -* ' T -0-mf^^ ^^ 

This period, with slight changes towards the close, 
rules the whole of this prelude, 83 bars in length. It is 
first repeated, after the manner of a fugue, in the dominant 
(joining on immediately, with elision of the first measure), 
and it has an improved close of two measures: 


(8 a) 

In the appended minims one easily recognizes the 
principal counterpoint to the first half of the theme. Quite 
in fugue style follows then an episode (without elision) 
of 8 measures, of which the graceful upward and down- 
ward floating crotchets form a, characteristic feature: 


The quaver counterpoint which at the same time 
attracts attention, must be looked upon as the principal 
counterpoint to the second half of the theme, and it 
appears, first of all (in the alto), in precise shape, as a 
transition from the first to the second theme entry: 



Now, after the first episode, it is combined with its 
inversion in the transition passage: 

Then bass takes the lead (Dux), while the soprano, 
with the second half of the theme, forms a counterpoint 
to the first; the conclusion of the theme, which, in the 
fifth measure, suffers the loss of its leading note (as it 
has to modulate to JDb- major), assumes the following 
appearance : 


At the eighth measure, the soprano (8 = 2) introduces 
the theme in D^- major (parallel) \ in the counterpoint, the 
appearance of the quaver motive, already to the first half 
of the theme (displaced by 2 / 4 ), should be noticed. The 
close is again somewhat changed, and modulates to Aty- 




The quaver motive now appears by itself as theme, and 
this deserves special attention, as it is imitated more than 
once, so that the 8 th measure turns back and becomes 5 th . 
At 8 a the key of A^V -major is again reached, and this is 
still confirmed by two measures, whereupon the bass enters 
with the theme (Comes) in F-minor (with 8 = 2). accompanied 



by the quaver movement, ever more intrusive, in direct 
and contrary motion. But this time the second half of 
the theme appears, not in the bass, but in the alto, and, 
indeed, lowered by one degree (ev eb \ eb d instead of 
f f \f e) y and modulates through Eb- minor to GV- major. 
At the close, the alto begins with the theme in this key, 
but yields it up to the soprano voice, by which it is 
correctly carried on to the end (with twofold acceptation 
of the quaver motive at the close); and then the same 
voice (with 8 = 2) continues with the theme in Eft -minor 
(under-dominant), and here its presentation agrees exactly, 
down to the end, with the opening one. It is relieved 
again (with elision of the first measure) by the alto, which 
introduces the theme in BV- minor, and carries it on to 
the end; but the last notes are free, and they lead to a 
half-close on / 7 , which, however, by means of an appen- 
dage of two measures, is changed into a full-close. It is 
followed by a new after-section, on the seventh measure 
of which the bass again arrives on /, whereby the cadential 
effect of the 8 th measure is frustrated (chord of 6 4); 
there follows, therefore, still a three membered period 
(three triplets of measures; the first still over the organ- 
point /); and thus the whole piece comes to a broad 
and effective conclusion. 

The fugue a 4 is of a strong, majestic character. With 
elementary power it presses forward from the fundamental 
note to the fourth, but then rises, with renewed, and more 
impetuous rush, to the sixth but only to break off 
suddenly on the fifth; 

Allegro maestoso. 

Ef rvv~ 



^ / A ^ 


^ f i r (2) ' 

if r *r 

/* " ",^ 


-t * , * 

ii= : r. 

1=5 ^ 



The mild turning towards to the third, which immedia- 
tely follows, already belongs to the counter subject, which 
is altogether of a softer character: 



- T 



As yet it only accompanies the theme with dark 
mutterings, whereas the latter bursts out into fierce anger; 
the concluding motive of this principal countersubject, as 
if in resignation, sinks down by degrees, during the episode, 
before the third voice entry: 


? +--= + 


During this third enunciation of the theme, the first 
Yoice shows traces of a second countersubject: 

i8 4 


It is as if it were gathering its strength once more, only 
to break off suddenly in short, violent sounds, similar to 
sobs. Although this second countersubject never reappears 
in complete form, still, in many passages of the fugue, we 
again meet with the syncopation of the second and third 
crotchets and the quaver spring which follows; and also 
with the sobbing crochets. 

The fugue naturally divides itself into five sub- 
sections which may be easily recognized: 

I. Development of the plain theme in the usual 
manner as Dux and Comes, accompanied by the 
counterpoints already shown. I st period: Dux in alto,. 
Comes in soprano, and, afterwards, an appendage of 
three measures (6 a 8 a) leading back to the prin- 
cipal key. 2 nd period: (with 8 = 1): Dux in bass 
with three appended measures (4 a, 3b 4b), and in 
after-section (with 4b = s), Comes in tenor. There 
follows on an episode of eight measures, leading 
back to the principal key. 

II. Stretto of the plain theme (without counter- 
subject) and, indeed, first between tenor and alto 
(bass is silent) at the distance of a minim, and at 
the interval of the upper seventh: 



IS 5 

then after a triplet of p measures (i measure of 
8 /i), which removes the close to D^- major (4b) 
with 40 = 5, between soprano and bass in D^- 
major , at the same distance and the same interval, 
but with voices reversed: 


(8va bassa) 

likewise with one appended measure (transformation 
of the half-, into a full-close [8 a]. An intermediate half 
period now cleverly prepares the way to the third sub- 
section: in it, a descending chromatic motive of one 
measure is developed, the relationship of which to the 
countersubject is unmistakable; again, the detached, 

forced out notes, and the anapests ( J"^J | J ), respec- 
tively, of the other voices are familiar to us: 



This is continued through 4 measures (Gty -major, 
C\t- major, Ab- major, DV- major}] on the cadential 
fifth (changed in meaning to that of first) measure 
begins the third subsection: 

III. Development of the inversion of the theme, 
countersubject, and secondary counterpoints a real 
inversione delta fugal Bach selected that particular 
form of inversion, which preserves the tonic triad, 
in that fundamental note and fifth exchange places, 
while the third remains; as is known (see my 
"Kontrapunkt 7 ' p. 168), the dominants in that case 
exchange roles, but the chord of diminished seventh 
of double meaning (a c eV g\?=t v " or ty? ix< ) 
remains. The Dux therefore proceeds also in 
the inversion, through the tonic triad; the Comes, 
on the other hand, not through the upper-, but 
through the under-dominant. We only notice the 
inversion of theme and countersubject, but once 
again call attention to the fact that the rest of the 
contrapuntal material, in the main, is inverted; 
this, indeed, is fairly self evident. The section 
commences in full with the 4 voices, and this 
happens well, since the former episode had already 
prepared the inversion. I st period (with 4a=i): 
inversion of the Dux in the tenor, inversion of the 
countersubject in the alto, and, after one measure 
of close-confirmation (with 4a=5), inversion of the 
Comes in the alto, inversion of the countersubject 
in the tenor (soprano is silent), and three close- 
confirmations of one measure (likewise close dis- 
placements in E^- minor, ?? -minor, D^V- major}. 
2 nd period (with 8c=i): inversion of the theme in 
the soprano, inversion of the countersubject in the 


I8 7 

alto, theme commencing on dfo (Dux in G?- major'] but 
starting with dty*, and first changing color to V -minor 
(principal key); the after-section is free, with elision 
of the 5 th measure, and modulation to the second under- 
dominant (Av -minor): g^' d? 1 j gb** [= eb 7 ] e\? 


3. period (with 8 = 1), inversion of the theme 
(Dux) in the bass, inversion of the countersubject 
in the tenor, but springing in the second measure 
to the soprano, the whole standing in the key of 
^9 -minor \ this key is confirmed by the first close 
repetition (4 a), while the second (/j.b) moves to 
D^- major (e\> lll< =0t? 7 ); the freely formed after- 
section wends its way homeward to B^ -minor (8 th 
measure) through E^ -minor (6 th measure), with the 
harmonic progression dV* }.* [=^ 9 *] > vn 
/ 7 f. The inversion of theme and countersubject 
is as follows: 

| J_J 

The character of hot impulse certainly disappears, 
but the wrath becomes deeper. 

IV. Stretto of the inverted theme. It is planned 
like that of the plain theme, /. e. at a distance of 
a minim , and in the interval of the under-seventh 
(likewise upper - 9 th ). The countersubject is also 
wanting here, but, as if by way of compensation, it 
appears in the shortened after-section, and, indeed, 

1 88 


in its original (upward) direction. i st period: inversion 
of the Dux in tenor, inversion of the theme in the 
upper 9 th beginning with gV in the soprano; 

_JjL,_J I J- J 

after- section, with elision of 5 th measure, free; from 
the 7 th to 8 th measure the chromatic countersubject. 
2 nd period (with 8 = 1): inversion of the Dux in 
F-minor (beginning with c] in the alto, inversion of 
the theme (beginning with db) in the bass. Appen- 
dage: confirmation of one measure of the close in F- 
minor, and then a new, free, and shortened after-section 
(with elision of the 5 th measure) which modulates 
to A? -major, parallel of the under- dominant (f I 


fvii [=4>7] 
us to the 

dl> 6 I *t> 7 ). 

This half-close leads 

V. Section: Stretto of the plain theme with its 
inversion. The first period introduces (with 8 = i) 
the inverted Dux in Av -major (but with eb 1 on 
the opening note *b), and the original theme 
beginning with g, as indeed would be suitable for the 
original Dux in A^ -major. Reminiscences of the 
countersubject occur in measures 3 and 4 (in the 
former, detached crotchets ; in the latter, the chromatic 
principal countersubject). The combination is as 

r 'f 


The close in A'^- major is confirmed by one 
measure, but frustrated by means of the Mixolydian 
bend in the bass (^); the after-section is a free 
episode making three leaps to the sixth measure, 
and, indeed, by means of a motive differing in 
measure (three 4 / 2 measures); 

bb 7 (6 a) 

1 0> 9> 8J 


and then there is a regular return to the principal 
key. The 2 nd period (with 8 = i) introduces the 
Dux in its original form in the bass, and, in the 
alto, the inversion from gv (as would be suitable for 
the inversion from /): 

* d 




* -. * 


The after-section is free and complete, and holds 
fast to the principal key; but, finally, the bass makes 
a deceptive progression (gb instead of bb\ so that 
a new after-section becomes necessary. This latter 
introduces (with 8 = 5) the last combination, a stretto 
of the Dux (soprano) with the inversion of the theme 
(tenor), but both with the other voices doubling in 
thirds, likewise sixths: 


No one can properly say of this fugue that anything 
in it is sacrificed to the counterpoint; for even the last 
combination, resulting directly from the character of the 
theme, is quite free. From the preceding combinations 
one might strictly conclude that Bach would have used 
the stretto of the theme and the stretto of the inversion 
at the same time; and not only these, but indeed, many 
other combinations: 



e I_s* - 

But with these Bach would not have obtained more 
than with the simple third doubling, on which these 
combinations, in the main, are based. He might also have 
tried threefold strettos, for example: 


* te 




^^^^^rjb^pg^fcczg-,-,. : 

I 3=fy&=i=i=^-i r Trr&-t==== 



ft ft* *f:** 


etc., etc. That Bach renounced all these combinations 
which, under the given conditions, lay near at hand, and 
only took what suited him for the structure of the work, 
again shows the wise self-restraint of the master 1 

ii. 23- 


A prelude of quite special warmth, and full of youth- 
ful firel and a double fugue which forms one of the 
noblest numbers of the whole work, and one which has, 
above all, a soft elegiacal character showing itself more 
and more in the second half, and giving to it the appea- 
rance of an epilogue (somewhat after the manner of Schu- 
mann's "The poet speaks"); so that one almost regrets 
that it is not the very last number of the second book. 

The prelude opens with a bold run: 

Giojoso con anima. 



cresc. (4) 



and then, like the F^-major prelude of this 2 nd book, 
remains quiet, as if rapt in thought: 

This period contains, besides, two repeated after-sections,, 
increasing in intensity (with close moved up from the key 
note to its 3 rd , likewise 5 th ). A second period, in motive 
akin to the first, but with freer combination of scale 
and chord figures (and with the under voice proceeding, 
for the most part, in quiet quaver movement, and in 
chord form), modulates to the dominant (F$-major)\ a- 
third (with elision of the first group) transfers the semi- 
quaver movement to the lower voice, and adds a third 
voice keeping company with the upper one: 



Riemann, Analysis of Bach's "Wohltempeiii tes Clavier". II. 


In it the modulatiou to the dominant is given up 
(/tf [=^ui<] g$ | ^ft [=<] f^ J*), as * a better 

one had been thought of, viz., the one to the parallel key} 
but this only appears, after C^-minor has been approach- 
ed through F\-major (rjf 7 | f* ["ffm*] $ * m 
*/$ 7 | Vj). The key is confirmed by a new after-section 
(again with only two voices). 

The next following period assumes a different cha- 
racter: it turns towards the principal key, and, with 
exception of the bass quavers on the group points of 
stress (2 nd , 4 th , 6 th , 8 th measure), consists entirely of one 

The key of E-major is reached at the 8 th measure, but 
meaning of the latter is changed to that of 4 th , and the n .-w 
after-section, somewhat strengthened (2 to 3 voices), con- 
cludes in B-major. Then comes a period, throughout in 
three voices, related to the first one a 3 (c), yet of quite 
independent formation (the lower voice has chord figuration 
in semiquaver* the upper ones have it in quavers, with appog- 
giatura ornamentation); the second group is repeated, and 
,(3a 4a) leads to a half-close in D-minor (&+ I b Q J} 7 , 

vn ni 

(4) (4) (6) 


. To this succeeds immediately a reproduction 

of the one -voice period (</), with return modulation to 

B-major(a\^ \ .. . . | Mf [ =<r #in<l Sff 7 I ^tt [=' 6 ] 

/jt 7 I ^)i an d f urtn er, a new period, based on the motives 


of the after -section of the first period (), which goes to 
B-minor, making therein a feminine half -close (/$$" 3)1 
and only then does the opening theme (a) appear again 
(in the bass). In what follows 2 periods of eight 
measures with a confirmation of four measures, nothing 
new is introduced; but the character of the opening run, 
likewise of the second period evolved from it, is maintained; 
and, with exception of a slight allusion to the under- 
dominant (E-major), there is no further modulation. 

The fugue (a 4), as already mentioned, is a double 
fugue, to which fact neither Bruyck nor Jadassohn has 
called attention; both, indeed, have given a particularly 
scanty and superficial analysis of it. 

The principal theme advances with powerful step 
the step, as it were, of iron fate: 

The Comes is a faithful transposition in the fifth, 
but, as such, accomplishes, as well as is possible, its task 
of modulating from the harmony of the tonic to the key 
of the dominant. The countersubject suggests a passionate 
wringing of hands: 


count ersubject_ 



In the first development (also in the redundant second 
entry of the bass) this counter subject is strictly adhered 
to, and gives to it that feeling of painful, intense passion, 
such as one is only accustomed to find in Bach's fugues 
in the minor key. A second countersubject (the contin- 
uation of the first voice during the third entry of the 

is once again strictly carried out in the theme entry imme- 
diately following, and then disappears entirely; whereas 
the syncopated motive of the first countersubject, a 
commanding feature in the episodes of the first section, 
makes its appearance in many other places of the fugue. 
The first section includes the four voice entries: bass 
(Dux), tenor (Comes), after two free measures (with 8a = i), 
alto (Dux), and soprano (Comes); and, after two measures 
forming an episode (with 8a=i), still another entry of 
the Dux in the bass (which during the delivery of the 
theme by the soprano, was silent). To this is annexed 
a free after-section (with a measure of triplets for 6 8) 
completing the period, and effecting a modulation to the 
dominant. It should be carefully noticed that real four- 
voice writing only begins at the second bass entry, and 
that the same is maintained in the after-section. On the 
closing note, however (with 8 = 1), the tenor starts with 
the theme (Comes), while all the other voices break off. 
It would be scarcely possible to indicate the entry of the 
second subject in a clearer manner. At once, on its first 
entry (alto), it is associated with the principal theme, for 


I 9 7 

which reason Bruyck and others have only looked upon 
it as a fresh countersubject (Jadassohn, indeed, expressly 
states that "anyhow it does not recur often"; but, as a 
matter of fact, it remains a feature of the scheme until 
the very close): 

mf dolce 

The second subject is now developed in quite regular 
order. The bass follows one measure later with the answer, 

and the soprano joins on immediately (7 a 8 a), likewise 
with the Comes of the second theme; the alto now (at 
8 a = i) enters with the first theme (Dux, but so har- 
monized as to modulate to G~minor), whereupon the 
tenor begins with the answer of the second theme, but 
abandons it in favour of the bass, which gives it out in 
the key of G- minor: 








~^~ \& ~t 

i i i r 

tf TUf ' 

Here the second theme is seen to be capable of inversion 
in double counterpoint in the 12 th ; it is indeed an in- 
version from: 

The after -section is free, and modulates from the 
parallel key to that of the dominant, with a motive which 
first appeared in the episode of one measure after the 
first delivery of the second theme, viz, a diatonic passage 
of four degrees: 

Z etc. 

which, finally, is really nothing else than the transition from 
the Dux to the first countersubject: 

91 cr~ r~ ?-*? 


I 99 

It appears repeatedly in crotchet movement in the epi- 
sodes of the first section, but towards the close of the 
same it is clearly extended to its later form: 



pzfczzs ' 


f F 

C *jt: |> : 

^ r f f 

In the delivery of the first theme (Comes) by the soprano 
which now follows (with 8 = i), this motive is carried out 
by bass and tenor, the latter, finally, in crotchets, thus 
confirming our derivation: 



The alto has the second theme, which, as compared 
with the first combination, shows inversion in double 
counterpoint in the 12 th , but as compared with the second, 
only an exchange of voices: 



The after-section consists of a free episode with the 
quaver motive of four notes, and opens up (with 8 = i) 
into a delivery of the first theme by the bass in the key 
of G$~minor, with the second theme in the soprano (the 
original combination: the latter beginning with the same 
note [g\ as the first), and, after two closes in the after- 
section, one (4 a) in Ffy-major, the other (4-b) in E-major, 
it is followed by the first theme in the tenor, with the 
second, inverted in the 12 th , in the alto: 

The harmonisation, corresponding to the first with 
transposed theme, modulates from E-major to C$-minor. 
The following period, with a fore -section free in form, 
tends back again to the key of E-major (under-dominant). 
The delivery of the first theme by the tenor (with 4 = 5) 
therefore begins in E-major, but with the 3 rd g, and 
turns at once to the parallel key of G\- minor-, and then 
the soprano introduces the second theme with quite a 
new combination, viz, beginning two crotchets earlier, and 
at the interval of a 3 rd : 

With this, a turning point in the fugue is reached; 
for an episode on an extended scale follows (a period 
with repetition of the second group [3 a 4 a], and a 
marked standing-still at the 6 th measure [6 a, 6b], and one 
which leads, by digression, definitely to the principal key. 
In order to understand its meaning, the long drawn-out 
melody line of the soprano should be carefully studied, 



which, giving out the second theme, has just passed 
downwards from the high b\ 

(with elision of ist measure) 



con fuoco 

(6b) dim. 


If, in contradistinction to the merciless principal 
theme, and to the anxious, beseeching, first countersubject, 
the second theme seems to bring heavenly consolation, 
this long episode appears as if it were a coming at length 
to rest with one last mighty sigh (cf. the triplet of 
measures with its strongly dotted rhythm). Over the now 
following closing section of the fugue is cast a holy 
peace: the principal theme appears first in the bass, 
while the tenor keeps company with it in quiet quavers 
and consonant (I) syncopations, after the manner of the 
second theme, by means of which it passed over from 
the episode; while the alto offers support to the soprano 
with its new, and wonderful melody: 



dolce e tranquillo 



The freely formed after -section, together with its 
additional three measures, continues in the same style 
as this fore-section (8 = 6 a; /. e. triplet for 6 a 8 a, not 
to be taken as hurrying on, but as a spreading out triplet 
quasi calando]. This after -section closes in D^- minor 
(parallel of the dominant), but only to render possible 
the entry of the Comes in the tenor (with 8 = 1). What 
a dignified effect is obtained here by the crossing of 
both themes (tenor and alto): 

_feq^3: | lz?2 

The first theme has quite lost its stiffness; it is now 
permeated with the consoling power of the second. And 
thus, in the same way, consolation and peace obtain the 
mastery in the free after-section which follows: 



The sequential form of this after-section necessitates 
a new after -section, which brings the Dux for the last 
time in the soprano, calmly and quietly spreading a bow 
of peace over the other, no longer contending, voices 
(2 nd theme in tenor): 



- r 



A close -confirmation of three measures (6 8) and 
one of five measures (4 a, 58) constitute the coda: the 
first with different pairs of voices moving in thirds, and, 
at the 8 th measure, a Mixolydian turning from a\ to a\\ 
and the second of wider extent (second upper -dominant 
0$ 9> ), with a free transcription of the second theme, and 
a gentle allusion to the syncopated formations of the first 

In truth this fugue is the real epilogue of the Well- 
tempered Clavier 1 

II. 24. 

Our admiration of the two preceding pieces, and 
their designation as epilogue of the whole, must in no 
way be regarded as depreciatory of the two actually 
standing at the end. But these are of much lighter 
contents, and do not in any way show that the author 
felt that he was bringing a work of the first rank to a 
close. For this, the key is not in fault, since the first 
book ends with a gigantic fugue, of most serious con- 
tents, in B-minor. 

The prelude over which Bach has himself written 
Allegro which, however, according to the custom of his 
age, only meant moderate movement (but Allabreve) 
develops a pensive thought of two measures, 




which the opening period, first of all, repeats four times, 
the two voices exchanging roles\ the second period makes 
clever use of the transition notes (general up-beat) which 
in the first period join together the first and second, and 
the third and fourth deliveries of this thought (see above 
a t NB.) in that it extends (syncopation), and makes 
them the chief motive of the further development; 

cresc. NI>. 




j-* /vv 

the after-section turns back the syncopation to the com- 
mencement of the measure, 

and leads to a half-close in the parallel key (D-major). 
The two following periods both introduce, after the 
manner of the first, the principal thought four times, both 
in D- major and, without real modulation (only with a* 
[ = ^n*r] b 1 as transition [general up-beat] between the 
eighth, and first measure) in E- minor (under -dominant). 
The following fifth period reproduces likewise, with 
exchange of voices, the second, but only the fore-section, 
which leads to G-major; the after - section presses on 
more hotly, heaps up the syncopations (without semi- 
quavers), and introduces, in place of the 6 th to 8 th measure, 
two triplet measures: 






Then the development of the principal thought (twice 
repeated) which may best be regarded as a repeated 
after-section closes in F^- minor (minor upper-domi- 
nant), and leads on to an imitation of the second period 
with half -close in the principal key; a new after -section 
(with triplet of measures in place of 68) confirms this 
in more emphatic manner, and breaks off with suspension 
and organ-point, whereupon two additional measures change 
the half-, into a full-close. At this moment (with 8 = x) the 
principal key appears, but with avoidance, by means of a 
deceptive cadence, of the half-close at the fourth measure; 
the after -section boldly intensifies the harmony of the 
third group, and brings the piece to a conclusion without 



, /it 

The fugue (a 3) is of joyous Allegretto character, 
and shows humour, almost caprice, in that the theme 
entries always elide measures i and 2, entering pertina- 
ciously with the second group; so that, indeed, the meaning 
of the 8 th measure is repeatedly changed to that of 3 rd . 



The theme keeps within the compass of the Draeseke 
Heptachord (II. 12, p. 98), though it twice skips down to 
the lower octave: 

Allegretto piacevole (J^ | J ) 


_ _ 

^7 "t3 * *** v 


The first countersubject looks, in a measure, as if 
it were of contrapuntal complication (with exception of the 
answering of the opening fifth of the key with the octave, 
the Comes is a simple transposition in the fifth): 






But it is short-lived; it is faithfully retained during 
the third entry (Dux in the bass), and is found in the 
preceding episode of two measures and the following one 
of four measures, but then disappears entirely, in favour 
of another one, which completely removes from the piece 
the contrapuntal fetters, and turns it into what (through 
the theme) it really is, a true Deutscher (Schnellwalzcr}\ 
(cf. also the Passepieds in the Katechismus der Kompo- 
sitionslehre II. p. 63). The new countersubject accom- 
panies only the after -section of the theme, and has also 
its caprices (the feminine endings): 



The perfect grace and "liveliness" (Feschheif) of this 
true Waltz, or Landler motive first makes itself prominent, 
when it appears and this occurs three times in the 
upper-voice. Of other counterpoints, only the one in the 
soprano accompanying the bass delivery of the theme 
deserves mention: 

its expressive syncopations afterwards playing an important 
role. Bewitching is the formality with which the first 
countersubject withdraws to make room for the second: 



(8c=3) NB? (4) 

Shall we enter 
structure? We trow 
has grown fond of 
three sections (I in 
III in the principal 
places. We need 
points such as the 
ment with its three 
larity to the theme: 

into further detail with regard to the 

not I Everyone, who from our account 
the piece, will easily recognize the 
the principal key, II in foreign keys, 
key), and assign to the episodes their 

only call attention to finely delicate 
first episode of the second develop- 

- measure rhythm, in spite of its simi- 

f ^^ * 


also the connecting feminine endings of the long episode 
between the second and third sections: 


and, finally, the most charming cscamotage of the theme 
(Dux) in the principal key again reached by the artful 
springing up of the bass with the theme in the under- 
dominant at the beginning of the concluding section: 

Riemann, Analysis of Bach's "Wohltemperirtes Clavier". II. j^ 




These are genuine flashes of genius (cf. also the last 
measures in which the theme gradually glides away). 

Thus I close the "treasury of polyphony" ("Schatz- 
kastlein der Polyphonic") without any other epilogue 
than the one given in the B- minor fugue. I hope, in a 
third volume, in which I propose to analyse the "Art 
of Fugue" ("Kunst der Fuge"), to make some general 
remarks on fugue composition. 






s. d. 
9171 ALEXANDER, J. " Con Amore." Poetical Introduction 

to Musical Instruction ,3 - 

10123 ANTCLIFFE, H. The Successful Music Teacher. 

Third Impression 1 6 

10124 How to Pass Music Examinations. The Successful 

Candidate. Words of Advice. Third Impression. Paper 1 6 

10125 The Amateur Singer. Woids of Advice. Second Impress. 1 - 

BACH.J. S. Analysis of J. S. Bach's "48 Preludes and 
Fugues" (Wohltemperites Clavier). By Dr. H. Riemann. 

9205 Part I. 24 Preludes and Fugues. Fifth Impression. Bound 3 - 

9206 Part II. 24 ,, ,, Fifth Impression. Bound 3 - 

to a Lady, by Dr. C. Reinecke, translated by 

E. M. Trevenen Dawson 3 9 

10091 CARSE, ADAM. Summary of the Elements of Music, 

with Exercises & Instructions on " How to Write Music" 1 6 

10092 Key to the above 1 6 

10093 Practical Hints on Orchestration 1 6 

Harmony Exercises. Figured basses, melodies and 

unngured basses for harmonization. 

10085 Book I Paper 2 6 

10086 Book II Paper 2 6 

Orchestral Conducting. A textbook for Students and 

I. The Technique of Conducting. 
II. The Instruments of the Orchestra. 
III. A Short History of Conducting ; Vocabulary of 
Orchestral terms ; Bibliography. 

iv + 100 pages. Bound 5 - 

What Mr. Carse's book does is to state in admirably 
direct language the nature of the conductors art and 
the problems that face him and to define the procedure 
of conducting. 

On Conducting School Orchestras ... 1 - 

COCKING, F. The Composer's Vade Mecum. 

(English-Italian) - 9 

Life and Letters, by W. C. Berwick Sayers. With an 
Appendix of Compositions compiled by J. H. Smither 

Jackson. Second Edition, revised 15 - 

9215 CROKER, NORRIS. Handbook for Singers. Seventh 

Impression Bound 3 - 

9199 DANNREUTHER, E. Wagner and the Reform ot the 

Opera Bound with Portrait 6 - 

10097 DAUGHTRY, O. Ear-Tests and How to prepare for 

Them. Sixth Impression 2 - 

RIEMANN, Dr. H.(Contd.) 

9203 Part II. History of Musical Form, with Biographical 

Notices. Third Impression Bound 

9204 Catechism of Pianoforte Playing. Third Impression. Bound 

9207 Catechism of Musical ^Esthetics. Second Impression. 

9209 Catechism of Orchestration Bound 

9208 Introduction to playing from Score Bound 

Analysis of J. S. Bach's " 48 Preludes and Fugues." 

9205 Part I. 24 Preludes and Fugues. Fifth Impression. 


9206 Part II. 24 Preludes and Fugues. Fifth Impression. 


9193 RUBINSTEIN, A. Music and its Masters. A Conversa- 

tion. Third Impression Bound 

9212 SCHROEDER, C. Handbook ot Violin & Viola Playing. 

Fourth Impression Bound 

9211 Catechism of Violoncello Playing. Fifth Impression. 


9213 Handbook of Conducting (J. Matthews.) Seventh Impres- 

sion Bound 

9194 SCHUMANN. Advice to Young Musicians 

10146 SHEDLOCK, J. S. Beethoven Pianoforte Sonatas. The 

Origin and Respective Values of Various Readings 
SHINN, Dr. F. G. Elementary Ear-Training. 

10148 I. Melodic. Fourth Impression ... 

10149 II. Harmonic and Contrapuntal. Third Impression ... 
A Method ot Teaching Harmony based upon Ear-Training : 

10150 I. Diatonic Harmony 

10151 II. Chromatic Harmony and Exceptional Progression. 

Second Impression 

10152 Musical Memory and its Cultivation 

10153 Examination Aural Tests and how to study them in prepa- 

ration for the tests given -in the Examination of the 
Associated Board, and in the Diploma Examinations of 

the R.A.M. and the R.C.M. Third Impression 

10121 SIBLEY, C. The Voice and its Control 

10131 SIMPSON, J. 300 Questions on the Grammar of Music. 

Based on the Syllabus of the Associated Board of the 
R.A.M. and R.C.M 

10132 Key to the above 

10133 400 Questions on the Rudiments of Music. Thirteenth Imp. 

10134 Key to the above 

10135 A concise text book on the Rudiments of Music 

9196 STEILER, J. The Great German Composers. Bio- 

~ >] 

STEILER, J. The Great 

graphical Notices, with some account of their Works. 



10109 WARREN, J. Catechism of the Harmonium 

WEST, G. F. Hints to Young Teachers of the Pianoforte 
WHITEMORE, CUTHBERT. Commonsense in 

Pianoforte Playing. Eighth Impression 

WHITTINGHAM, A. 200 Questions and Exercises on 
F. Davenport's " Elements of Music " 

s d. 

3 - 
3 - 
3 - 

3 -