WTC I/3 in C# major – Prelude

from Siglind Bruhn
J.S. Bach's Well-Tempered Clavier
In-depth Analysis and Interpretation

I/3.1.1 The prelude-type

This prelude presents itself in two-part texture. It clearly shows a number of motivic figures. These are restated after their respective first appearance in an answering voice – i.e. in imitation – before they sound again in their original voice.

The fact that some of these motives are not conceived as a one-dimensional melodic line but as a hidden two-part structure requires further attention. Similarly it should be mentioned that the secondary voice to this motive is not polyphonically independent but in fact a disguised parallel (ex. 25: bars 1-16):

(ex. 26: bars 63-75)

 

I/3.1.2 The overall design of the prelude

The first cadence ends on the downbeat of bar 7. On the one hand, this cadence ending lies embedded in a melodic flow which continues uninterrupted beyond this bar. On the other hand, a definite change of surface pattern occurs in the following bar 8 which suddenly features two melodically designed voices and leads into the inverted-voice texture of bars 9-15. In this sense, this initial cadence is only an indirect indication of a subordinate structural ending within a larger context. There is, therefore, no caesura, and no cut whatsoever after the appearance of the tonic itself.

Exactly the same holds true for the following harmonic progression which, now in the new tonal area of G# major, draws to a cadential close on the downbeat of bar 15. Here again, the melodic pattern continues through another bar before giving way to a continuation in inverted voices which marks the beginning of a new harmonic development.

Since the structural units determined by these simple cadences are fairly short, we can distinguish a great number of them. The phrase in bars 25-31 is the first not to be followed by such a link. Instead, the second half of the cadence-ending bar serves as the beginning of a new development.

The following diagram lists the phrases and their keys in the entire prelude. (Capital letters refer to major, lower-case letters to minor keys. Note that the bridging bars – i.e. those bars which link consecutive phrases by prolonging the tonic of a cadential close before a renewed change of voices and thus do not harmonically belong to either of the closed progressions – are deliberately omitted here.) The graphic arrangement tries to visualize the harmonic progressions.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  



1. bars

1-7



C#







2. bars

9-15



G#







3. bars

17-23



d#







4. bars

25-31



a#






5. bars

31-35



a#-d#





6. bars

35-39



d#-G#





7. bars

39-43



G#-C#





8. bars

43-47



C#-F#





9. bars

47-53



F#






-

10. bars

-

55-61

-
-
-

C#

-
-
-
-




11. bars

63-73



G#

pedal

note



12. bars

75-83



C#







13. bars

87-104



G#

pedal

note


with resolution in final bar to

C#


- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
This prelude contains both identical and structurally corresponding passages. With regard to untransposed recurrences, there is a stretch of seven bars in the first half of the piece which returns later (compare bars 1-7 with bars 55-61); another span of ten bars in the second half of the prelude is repeated a few bars later an octave lower (compare bars 63-72 with bars 87-96).

As for other analogies, the opening phrase of the prelude reappears altogether five times, both transposed and with its voices inverted. While the first three reappearances occur in immediate succession to the model phrase and are therefore best named imitation in inverted voices, a true recapitulation can be found after the intersecting portion with its different patterns (see bars 47- 62). These two phrases in the middle of the piece sound reminiscent of the prelude’s very beginning, particularly since they are conceived as mirror images of the first two phrases.
 

Compare:

bars 1-16

model pattern,
followed by voices inverted,

tonic
dominant

with

bars 47-62

voices inverted,
followed by model pattern,

subdominant
tonic

 
Next, there is a very interesting large-scale structural analogy in this piece: the first half of the prelude, visually distinct from the second by its uninterrupted flow of sixteenth-notes in at least one of the voices, is designed in ternary form – so indeed is the second half of the piece (with the exception of the final line). A rough scheme of the structure in this prelude (which draws only on the architectonic patterns but not yet on the motivic components) would list:

-

bars 1-31


two-part pattern,
voices interdependent




bars 31-46


contrapuntal lines


bars 47-62


two-part pattern,
voices interdependent


-

bars 63-74


homophonic pattern




bars 75-86


contrapuntal lines


bars 87-96


homophonic pattern



On a different scale, there is an analogy in the harmonic structure (see the table above): the first four phrases (eight bars each, in dependent two-part pattern) move from the tonic through the dominant and the supertonic to the relative minor. The following four phrases (four bars each, in contrapuntal texture) reverse this process (see the progression vi-ii-V) and end on the tonic.

  

I/3.1.3 Practical considerations for performers

The material in the non-contrapuntal segments of this prelude is only indirectly melodic (refer back to ex. 25.) It is this indirect melodic pattern which determines the tempo. In addition, it seems worth considering the time signature of this prelude. As we know from other pieces by Bach, 3/8 does not so much indicate a pulse in three eighth-notes but rather one in whole-bar beats. With these whole-bar pulses in mind, it should not be difficult to find the appropriate range for the tempo.

The articulation applicable in a hidden two-part structure is a little more complex than that in a one-track melodic texture. Here it is the “hidden” melodic line which is to be articulated, not the progression from note to note as it appears on the surface. Taking e.g. the secondary line in the model of the main motive: the left-hand line in the first seven bars – C#  D# E# F# E# D# C# – should, within the context of this lively character, sound non legato. This non legato effect is, however, naturally achieved by the interlocking repeated pedal note.

It would therefore be counterproductive to try to separate the first C# from its octave and so forth, because by doing this one would obtain exactly the opposite effect and hear all sixteenth-notes as belonging to one line. In other words:

In order to achieve the melodically correct results
in a “hidden two-part structure”,
the surface progression must be played legato.

In addition, the distinction in each hand between “melody” and “background” can be achieved above all by two means: by touch and by intensity. The ideal shading of the texture would consist of

an intense, dynamically molded melodic line
sounding against an almost neutral,
dynamically rather subdued background.

  

I/3.1.4 What is happening in this prelude?

Several motives can be distinguished within this prelude.

M1 has already been repeatedly referred to. Here are once more its main characteristics:

-

It is seven bars long (the eighth bar represents a link);

-

it consists of two interdependent lines;

-

each of these two lines is in itself designed as a hidden two-part structure, with a curved pitch pattern providing the melodic idea and the keynote, as indirect pedal, serving as background (In bar 6 there is a deviation from the hidden two-part structure in the right hand, and in the left hand the keynote C# is replaced by the dominant representative B#).

-

within the two melodic parts which form parallel tenths, the line rising from the third to the sixth is slightly more intense than that which starts from the keynote (i.e. in bars 1-7, the right hand leads over the left). 


It is the link between the model and its imitation in inverted voices which deserves more attention. In bar 7, the right-hand line (which has so far been leading) continues the sixteenth-note pattern, but with such a strongly declining drift that it evokes a “retreat” from the position of “leader” to that of “accompanist . At the same time, the left-hand line emancipates itself as the background note C#, with a sudden syncopation and a consequent continuation in the higher octave range, steps forward to take the lead.

M2a and M2b develop from the above-mentioned link. After the fourth appearance of M1 in bars 25-31, this link forms two new thematic units.
 

-

In the right hand the syncopation, followed by a simplified version of what was originally the bridge to the next phrase, is repeated in sequence and thus builds a four-bar motive (M2a see U: bar 31 beat 3 to bar 35d).

-

In the left hand, another feature pertaining to the link, the turn-like figure from U: bar 8, also brings about a little four-bar motive (M2b see L: bars 31-35d).


Just as M1 sounded four times in alternating voice inversions, so do these two motives; their four appearances also contain the imitation in inverted voices. However, besides this similarity there are considerable differences:

-

While in M1 each line was conceived as a hidden two-part structure, both M2a and M2b are conceived as one-track developments.

-

While M1 consisted of two interdependent lines with melodic components which formed parallels, M2a and M2b are clearly independent and polyphonic.

-

While in M1 there was only one rise and fall in tension which followed the parallel curve, M2a and M2b show completely independent dynamic outlines. On the one hand, M2b creates a two-bar crescendo followed by a two-bar diminuendo; on the other hand, the two halves of M2a both carry an accent on the syncopation which implies a subsequent relaxation.

M3 is introduced in bars 63-73. It bears a number of relationships with M1. 

-

Like M1 it is designed in homophonic texture.

-

Like M1 it contains a pedal note in both hands (G#).

-

Like M1 it determines the main part of a ternary form. (Details see above under structural analogies.)

-

Finally, like M1 it is followed by a link which this time does not connect the model with its imitation but joins this motive to the next one instead (see bars 73-75d).


On the surface, this motive may remind the listener of toccata style: the two voices only meet on the first beat of each bar and then form a complementary-rhythm pattern. (For details of the homophonic idea behind the toccata pattern of M3 please refer back to ex. 26.) It is interesting to see that later, after its repetition an octave lower, M3 develops into a different pattern, also in toccata style and also resting on the pedal note G# (see bars 97-102).

M4 determines the middle section of this second ternary form within the prelude. It features again polyphonic texture – and thus relates to the corresponding section in the first half of the composition. Here, i.e. in bars 75-83, the right hand retains its complementary-rhythm pattern but ascends in a large sweep up to B (almost the highest available note on Bach’s keyboard). From there it moves in sixteenth-notes which gradually release the tension that had previously been built up. The entire upper-voice motive is then repeated a tone lower (and slightly softer). At the same time, the left hand describes a curve which sounds like a simplified version of the same M4. It commences with the descent (i.e. in the middle of the motive) which falls over two bars from E# to the lower-octave Cx (see bars 75-77d), and then follows the right hand in stretto imitation, rising over another two bars, before sequencing the figure.

The development of tension expressed by the layout of this prelude relies mainly on two facts: the harmonic progression (particularly in the first half) and the difference of intensity between the homophonic and the polyphonic sections. The following diagram tries to show these progressions (ex. 27):

 

 

 

WTC I/3 in C# major Fugue

 

I/3.2.1 The subject

This subject is a little less than two bars long. It commences after three eighth-notes’ rest, with what is experienced by the listener as a secondary upbeat. Such an upbeat, relating to the third beat in quadruple time, is a fairly strong impulse-giving feature, particularly since it is anticipated to shift to a normal upbeat position in the course of the fugue. (Baroque polyphony – in contrast both to the contemporary dance types and also to the music of the ensuing period – knew frequent metric shifts of its thematic material. This is especially true in quadruple time where a subject or motive first introduced in the middle of the bar could, in later statements within the same piece, be placed at the beginning of a bar, and vice versa.)

The ending of the first subject statement falls on the downbeat of bar 3. The dominant harmony (G#-B#-D#) is represented by the last two eighth-notes in bar 2, and the expected resolution onto the tonic is reached with the following keynote.

At first glance, the melodic structure of the subject seems to contain two segments: in the second half of the phrase, sequencing leaps unite the last six notes, thus appearing to distinguish these from a first half. Given this assumption, such a first half would have to be seen as ending after the “inverted mordent” figure on the second beat of bar 2 (i.e. between F# and D#).

However, the straightforward harmonic motion which describes a single curve throughout the whole subject (for details see below) clearly speaks in favor of an interpretation of this subject as one indivisible phrase. This is supported by the lack of any structural indications of sub-phrasing.

The subject contains only two rhythmic values: eighth-notes and sixteenth-notes. Its pitch pattern is characterized by leaps rather than by steps; note the alternating sixth and seventh intervals at the end and the melodic broken chord at the beginning (E#-C#-G#). The only steps to be found can be identified as written-out ornaments: a turn in bar 1 and an inverted mordent in bar 2.

The subject s harmonic background is that of a simple cadence, with the active step to the subdominant taking place on the downbeat of bar 2. An analysis of the underlying chord progressions which Bach uses later in the fugue reveals the G# (bar 2d) as an appoggiatura to the following F#. These two notes – G# and F# – thus form a pair which may under no circumstances be separated by either phrasing or articulation.
(ex. 28)

The climax within this subject occurs unmistakably on the downbeat of the second bar. Here, two powerful tension-enhancing features coincide:

-

the appoggiatura

-

the active harmonic movement from the tonic to the subdominant
(or, more often in this piece, its relative minor on ii).


The peak note E# (which may tempt all those who connect strong feelings with high pitches) is in reality only part of a broken-chord pattern on the tonic and therefore melodically and harmonically insignificant.

The dynamic curve created within the subject thus begins with an energetic crescendo through the subject s first segment until G#. This crescendo should, however, develop evenly and not burst out too early, in order to give the E# and C# still enough impetus towards the appoggiatura note G#. In the fairly abrupt tension decay which follows from this appoggiatura to its resolution, approximately half of the tension is lost. The remainder is then released gradually throughout the series of jumps.

 

I/3.2.2 The statements of the subject

There are altogether twelve subject statements in this fugue:

 

1.

bars 1-3

U


7.

bars 24-26

U

2.

bars 3-5

M


8.

bars 26-28

M

3.

bars 5-7

L


9.

bars 42-44

U

4.

bars 10-12

U


10.

bars 44-46

M

5.

bars 14-16

L


11.

bars 46-48

L

6.

bars 19-21

M


12.

bars 51-53

U

 

(ex. 29)

In three of the subject entries (nos. 4, 7 and 12) the upbeat eighth-note is replaced by three sixteenth-notes, and in statement 10 it appears split into two sixteenth-notes. No other change in the shape of the subject is found in this fugue. However, metrical displacements – i.e. a beginning on the last eighth-note of a bar – occur in statements 7, 8 and 12. The subject does not appear in either stretto or parallel.

 

I/3.2.3 The counter-subjects

The C# major fugue contains three counter-subjects.
 

CS1

is introduced against the second entry of the subject (see bars 3-5: U) and remains a faithful companion to the subject thereafter. It is exactly two bars long – i.e. longer than the subject, as it begins slightly earlier in the bar. In its full scope it begins with an “inverted-mordent” figure on the keynote, followed by a five-note scale ascent and a “turn” figure on the peak. From here to its end there is a gradual descent in ornamental waves, interrupted only rhythmically by one prolonged note.

As can be seen from this description, CS1 is conceived as a unit without subdivisions. If we consider the dynamic development without, at first, taking into account the simultaneous events in the subject, there are two possible interpretations; one is based on pitch and the other on rhythmic features:

-

according to the pitch pattern the climax falls on the highest note
at the beginning of the turn figure;

-

according to the rhythmic features it lies on the longest (tied) note.

However, as soon as we stop regarding the counter-subject as an independent body and look at it as a counterpart to the subject, the choice between these two options becomes much easier. As the second solution would cause the climaxes of the subject and its first companion to coincide, this option is contrary to the polyphonic implication of greatest possible independence within the material. Therefore, the first dynamic design is the more appropriate choice. (However, while the mind may easily accept this truth, the fingers seem more reluctant and often find it difficult to resist stressing the longer note.)

In the course of the fugue, the first counter-subject undergoes one variation which deserves a mention. The turn figure is sometimes written using the leading-note to the fifth degree (see e.g. the Fx in bar 3), yet in other similar instances it retains the context of the natural scale. This results in inconsistencies in otherwise completely analogous portions (see e.g. U in bars 3 and 44, M in bars 10 and 52).

CS2

appears only six times in the course of the fugue. It is introduced at its anticipated place, i.e. against the third entry of the subject, and taken up again only in bars 19/20, 25/26 (with a shortened beginning), 26-28, 44 46 (with a varied beginning), and 46-48. Its rhythmic and harmonic features create a distinct contrast to the two components already established:

-

Rhythmically, an initial upbeat precedes three syncopations the first two of which are eight times (!) as long as the so far prevalent sixteenth-notes;

-

harmonically, the beginning of this counter-subject redefines the first notes of the subject in a V7 context, and its ending omits the resolution into the tonic (at least in the original statement; later this is “corrected”).

The layout of tension in CS2, however, is quite unequivocal: the first prolonged syncopation builds the high-tension interval of a minor seventh over the initial notes of both the subject and CS1. It thus represents a natural climax, with the ensuing descent of the line providing the relaxation.

CS3

– an unexpected further companion in this three-part fugue – appears only twice. In bars 10-12 it sounds against the fourth subject statement; in bars 51-53 against the last. Its characteristic features are the eighth-note upbeat followed by a descent in longer note values. These features and the long release of tension resulting from this melodic shape reveal its relationship with CS2. This impression, however, is weakened both by the harmonic progression and by the concluding cadential-bass steps.

The sketch shows the phrase structure and dynamic design in the primary material of this fugue (ex. 30):

 

 

I/3.2.4 The episodes

The subject statements in the C# major fugue are interspersed six times with subject-free passages; a seventh closes the fugue. These differ surprisingly in length.

 

E1

bars 7-102


E5

bars 28m-422

E2

bars 12-142


E6

bars 48-514

E3

bars 16-191


E7

bars 53m-55

E4

bars 21-244




 

Several elements within these episodes are closely related to the subject:
  

in E4

from bar 22 (end) to bar 24, the upper voice recalls the first half of the subject twice;

in E5

from bar 34 (end) to bar 37, the upper voice quotes the subject’s first segment three times;
from bar 38 (end) to bar 41, the lower voice imitates the threefold quotation of the subject’s initial segment.


The very first episode of the fugue introduces a motive (M1) which plays a major role in the course of the fugue (see bars 7/8 U: from G#-E# to tied note A#). M1 is imitated in stretto, with a slight interval adjustment, in the middle voice of the same bar. Both the model and its imitation are then sequenced (see bars 8/9). In a second sequence (see bars 9/10), both voices show a variation in the second half of the motive, and the upper voice is completed by means of an extension which provides the harmonic resolution to its tied-note appoggiatura.

In the original version, the dynamic curve expressed in M1 is obvious: the jump upwards creates a rise in tension followed by a release in the falling broken chord. In the extended version, however, what is enlarged is actually the upward motion. It would therefore seem logical that, consequently, the rise in tension should also be increased.

During the same first episode, the lower voice presents a motive which can be traced back to the first counter-subject. It sets out with the same inverted-mordent figure, followed by ornamental waves which recall the final groups of CS1 in inversion. This motive is also frequently used within the fugue and will be called M2. In terms of tension, M2 contains very little active power. The short upbeat-like impulse in the inverted-mordent figure is followed by a long, subdued drop in tension.

The second episode (bars 12-14) is thematically related to the first. However, both M1 and M2 recur in considerable transformation. The significant changes which together create an entirely different character are principally the following:
 

In M1,

-

the leader of the imitative pattern is now the middle voice;

-

the tie prolongations in the motive are replaced by rests, thus interrupting the continuation of tension very definitely;

-

the imitating voice does not really follow its leader but restates the second, relaxing half of the motive;

-

towards the end of the episode, both voices abandon the motivic context altogether and join in a cadential figure (see M + L bars 13/14).

M2

-

sounds in the upper voice where it no longer appears as a sequencing one-bar figure, but is extended to a two-bar curve. In free inversion, it is pushed upwards to a slide-decorated peak;

-

the effect of this climax is further enhanced by the fact that it sounds in a diminished- seventh interval to the Cx in the lower voice;

-

the ensuing release ends in a so-called “female extension”

-

a melodic tail after the harmonically resolved strong beat – on the fifth sixteenth-note of bar 14.


Neither of the subject-free passages in this fugue serves exclusively as a cadential close; however, the final two and a half bars (E7) and the first one an a half bars of E4 both present non-motivic material leading to perfect cadences with distinct closing formulas (see L bars 21/22 and 55: the cadential-bass patterns; U bars 22 and 55: two typical, though different, melodic formulas). In the case of E4, the cadential close divides the episode into two segments (see E4a: bars 21-22m, E4b: bars 22m-244). Another episode in this fugue, E5, is subdivided even further (see E5a: bars 28m-30m, E5b: bars 30m-344, E5c: bars 344-422).

Several of the episodes, or their segments, are varied repetitions of earlier models.
  

1.

E1 recurs in three varied repetitions:

E3

uses mainly the tension-extended version of M1 from bar 9;

E6

is closest to the model but begins with a half-bar extension (see bar 48, first half);

E5b

appears most remote from the model in its use of the motivic material. The voices are completely exchanged, with the lower voice in the lead, the middle voice reduced to a broken-chord figure and the upper voice recalling M2. (Despite the varied beginning, the statements of M1 in the lower voice should nevertheless retain the tension curve characteristic for this motive (with e.g. a crescendo in bars 304-31d followed by a diminuendo until bar 31m), while the figure in the middle voice is too removed from the original to take part in any subtle dynamic shaping).

2.

E2 recurs once:

E5a

recalls the model in inverted voices. The lower voice now sounds the dramatic ascent (a slide is to be added on the peak note E>ð, see bar 29 beat 3); the upper voice, partly crossing over the middle voice, recalls the developed version of M1, and the middle voice is just filling in.

3.

E5c, the last segment of the longest episode, contains an internal correspondence:

-

Bars 35 38 U (with 3-sixteenth-note upbeat)
are taken up, voices inverted, in

-

bars 39 42 L (with 3-sixteenth-note upbeat). The variation ends in the upper voice on beat 2, in the lower voice on beat 3

.
One may acquire a clearer picture of what is happening in these episodes by completing the earlier diagram as follows:

E1

E2


|

E4b

E5 (= E2 + E1 + E4b)


E3 (= E1)


E4a

|


E6 (= E1)

E7

The role these episodes and their segments play in the dynamic development which shapes the entire fugue is both relevant in each case and significant with regard to the understanding of the overall structure.

-

E1, as it is determined by the introduction of new material, demands a register or color change. (The same holds true for its three variations.) Its sequences progress downwards, thus bringing a relaxation which suggests that a section is drawing to its close. (In fact, all three voices have already stated the subject.) The last sequence, however, extends the rise within M1 and reestablishes a higher level of tension, thus preparing the listener for more to come, i.e. a redundant entry.

-

The first variation of E1 , i.e. E3, shows even more of this extended rising. The ascending trend within the melodic units counterbalances the relaxation implied in the descending sequences and thus clearly defines this episode as one linking adjacent subject entries.

-

By contrast, the second variation of E1 , i.e. E5b stresses exclusively the declining direction. Its role in the overall development of tension is therefore one of announcing the forthcoming end of a section.

-

Finally, the third variation of E1, i.e. E6, returns to the pattern of the original: the smooth tension decay in the descending sequential pattern is arrested at the last moment, thus granting the following (redundant) subject entry to be perceived as still being part of the section.

-

Both the original E2 and its variation E5a are self-contained units. In a color distinctly different from that of the subject-determined passages, their dynamic outline is shaped in curves; within each, a rise to the climax and a subsequent relaxation are concluded by means of a perfect cadence ending.

-

Compared to the relaxing E1 type and the self-contained E2 type, E4b represents the type of episode which conveys a feeling of preparation for the next entry. The incomplete subject statements serve to suspend the tension before the ensuing full entry. This impression is further enhanced by three facts: (1) This episode segment sets off after a cadential close; (2) it is presented in reduced ensemble (the lower voice is resting most of the time); (3) the secondary voice is confined to non-motivic material.

-

E5c seems to repeat this pattern in a heightened version: It also begins after a complete decline in tension; it is also presented in reduced ensemble (this time it is the middle voice which is resting); its secondary voice is not only non-motivic but actually displays a barely disguised prelude-style accompaniment pattern. This last fact especially sets this episode portion furthest apart from the remainder of the fugue. Most of the active strength and tension otherwise present in this fugue seems as if temporarily retreated.

-

Finally, the two cadential formulas within the episodes both form, together with their extended preparations, dynamic curves.

In E4a,

the climax falls on the downbeat of bar 22.

E7,

the closing episode of the fugue, is launched from the interrupted cadence at the end of the final subject statement (see bar 53m where an A# minor chord replaces the expected C# major) and describes an increase towards the dominant bass note G# (bar 54m). Whether the very ending, with its quotation from the subject s tail and its voice splitting, is interpreted as a relaxation or as a triumphant close, is at the discretion of the individual performer.

 

I/3.2.5 Character, tempo, articulation, ornament realization

The basic character of this fugue is certainly rather lively. Both the pitch pattern with its many written-out ornaments, leaps and broken chords, and the rhythmic pattern with its predominance of two note values support this impression. The only element to introduce a hint of contrast is the second counter-subject with its long note values, repeated syncopations and stepwise motion.

The tempo should be fast enough to allow the written-out embellishments in the primary material to retain a touch of their ornamental character – i.e. the four notes of the “turn” at the beginning of the subject should be heard as one entity rather than as separate notes.

The appropriate articulation in this rather lively composition consists of non legato eighth-notes and legato sixteenth-notes. It is possible and gives the fugue a lovely depth (while admittedly increasing acrobatic demands) to play the contrasting CS2 with the characteristics of the rather calm character, i.e. with legato articulation and singing touch. But it is obviously also possible to opt for unity of character in all components of the material and play this counter-subject with long but slightly detached notes.

A good tempo balance between the prelude and its fugue is reached by transforming a triplet (i.e. three eighth-notes in the pulse of the prelude) into a duplet (i.e. into two quarter-notes in the pace of the fugue). The proportion thus reads:

one bar

corresponds with

half a bar

in the prelude


in the fugue.


(Approximate metronome settings: 72-80 for one prelude bar, 108-120 for one beat in the fugue.)

The fugue features three ornaments: the slide in E2 (and, correspondingly, in E5a), the cadential mordent in U: bar 22 (not included in the fair copy but deriving from a copy, presumably because Bach regarded this very conventional ornament as self-evident), and the compound ornament towards the end of E5 (see U: bar 38).

The slide often presents a dilemma, probably because of its conventional writing slightly left of the note head it ornaments. Yet, just like other Baroque embellishments, this one also begins on the beat (the visual presentation may have its origin in the fact that, unlike mordents and turns, the slide reaches the (printed) main note truly only at the end of the ornament). Thus in bar 13, the right-hand downbeat is G# (which falls together with the left-hand Cx). This G# is followed, in thirty-second-notes or faster, by A#-B, and the B is then sustained for the remainder of the note value. Correspondingly, in bar 29m the left hand plays C#-D#-E; the C# (not the E) coincides with the middle-voice Fx.

The cadential ornament in bar 22 is a simple mordent, beginning on the upper neighbor note and consisting of a double shake E#-Dx-E#-Dx. The symbol for the complex ornament in bar 38 represents a turn plus a trill. Because of its tied ending and delayed resolution this trill ends without a suffix. The result is, in sixteenth-note motion, an initial A#-G#-Fx-G#. (The pitch of the lower auxiliary needs a comment. The harmony underlying these bars of retransition is normally interpreted as the dominant, represented by an alternation of dominant-six-four (C# major with G# in the bass) and dominant-seventh chords. If this interpretation is adopted, i.e. if G# major acts as a dominant, its seventh is F# (heard repeatedly in these bars), whereas its leading note in ornaments should be Fx). This is followed by six A#-G# groups. (In order to further enhance the suspension it is possible to play only five A#-G# groups and stop short a little earlier before the bar line.)

  

I/3.2.6 The design of the fugue

The most prominent feature of this fugue, in terms of design, is the striking analogy of bars 1-12 and bars 42-53. Here are the details:
 

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the order, position and key of the three initial entries recurs identically;

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the surrounding counter-subjects also correspond (although bars 42 46d now feature an additional voice, due to the fact that the ensemble in a fugue never drops back to one voice);

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the subsequent episode (E6, bars 48-51) is, as has been shown above, a variation of E1, with its initial half-bar extension serving to modulate;

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the subject entry which follows also corresponds with the redundant entry in the first section although, as a result of the modulation in the episode, bars 51-53 now sound on the tonic and not on the dominant (as bars 10-12 did). However, the order and position of the voices are the same. The analogy of these two entries is additionally enhanced by the fact that they are the only ones in the entire fugue to be accompanied by CS3.


This prominent analogy lays out the major structural traits of the fugue. In addition, the episodes play an important role in determining the design. There are three instances in the C# major fugue where the concluding force of an episode sheds light on Bach s intention of partitioning into sections:
 

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the first is the cadential close which ends E2 at the beginning of bar 14; 

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the second is the explicit cadence in the middle of bar 22 which has already been mentioned repeatedly.

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While these appeared straightforward in their implications, the third is more complex. In E5a, the variation of E2 seems to conclude something in the middle of bar 30. However, this cadence is followed by the variation of E1 which, as has been shown, makes no attempt to launch any kind of new development; neither does the ensuing segment in which the tension is suspended. To see these three episode segments follow each other is already unusual enough; to see them trying to surpass each other in “tensionlessness” is even stranger. However, it is this very strangeness, this long retreat from the active striving in the piece, which gives this portion its particular effect: as an arresting buffer before the last section of the fugue it succeeds in highlighting the symmetrical design.


Finally, looking for features which might indicate section beginnings we find that two subject entries in this fugue appear in reduced ensemble. They are the first minor mode statement in bars 14-16 (which is thus triply justified in being regarded as a section beginning) and the first entry in the recapitulating final section. For a sketch showing the design of the fugue in C# major, see ex. 31.

The harmonic outline in this fugue confirms the other findings:
 

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The first four subject statements remain in the home key of C# major.

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The following two are in minor mode – the relative minor keys of the tonic and the dominant respectively. E# minor, the relative of the dominant G# major, is also the key in which Bach concludes this section with a very distinct full cadential formula.

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The episode segment E4b modulates back to C# major, and all remaining subject entries are presented in the home key, in the conventional alternation of tonic and dominant.

  

I/3.2.7 The development of tension

There are analogous dynamic layouts in the first and the (corresponding) last sections of this fugue. Both times, the first three entries sound gaily bouncing, with a slight increase caused by the growing number of voices. The redundant fourth subject statements regain this mood after the very timely pickup of tension at the end of the respective episodes. The second section also shows a slight tension increase between its two subject statements, mainly because of the growth from two to three voices.

In the third section, however, it is most probably the first of the two entries which contains more tension than its successor. The two main reasons are that it appears at a point of heightened expectancy (after the two incomplete subject statements) and that, in unmodified ensemble strength, the subject appears in the upper voice, possibly making it sound more powerful than when in the middle-voice position of the following statement. This decreasing tendency is then continued through the string of episode segments which, as has been shown above, become ever lighter.

Among the four sections of this fugue, the analogous outer ones clearly take the lead. The second section sounds softened, due both to its minor mode and its shorter length. In the third section, the four bars containing the two subject statements have returned to the home (major) key but contain no special features which would emphasize them in any way. While they may sound more self-assured than the preceding minor mode entries, this mood is overshadowed by the nearly sixteen bars of surrounding episodic material.

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expectancy (after the two incomplete subject statements) and that, in unmodified ensemble strength, the subject appears in the upper voice, possibly making it sound more powerful than when in the middle-voice position of the following statement. This decreasing tendency is then continued through the string of episode segments which, as has been shown above, become ever lighter.

Among the four sections of this fugue, the analogous outer ones clearly take the lead. The second section sounds softened, due both to its minor mode and its shorter length. In the third section, the four bars containing the two subject statements have returned to the home (major) key but contain no special features which would emphasize them in any way. While they may sound more self-assured than the preceding minor mode entries, this mood is overshadowed by the nearly sixteen bars of surrounding episodic material.