WTC II/23 in B major - Prelude

II/23.1.1 The prelude-type

This prelude consists almost exclusively of virtuoso patterns. Scale passages, interplay of hands in toccata style and superimposed peak-note lines determine the piece, while the motivic material remains negligible.

II/23.1.2 The overall design of the prelude

The first relevant cadential close occurs in bars 11/12 where it confirms the modulation from the tonic B major to the dominant F# major. Only five and a half bars later, the prelude modulates to G# minor, the relative minor key of B major. As this harmonic close coincides with a change of texture and pattern, it must be regarded as the second structural caesura.

There are altogether six sections. One of them (see the asterisk) ends in an imperfect cadence.

I   bars 1-12d I - V B major to F# major

II

bars 12-17m V - vi F# major to G# minor
III

bars 17m-23m

vi - I

G# minor back to B major
IV bars 23m-28m I - iii* B major to D# minor
V bars 28m-33d iii - V D# minor to F# major
VI bars 33-46 V - I F# major back to B major

With no more information than the harmonic progressions and the number of the sections, it is already possible to ascertain that the layout of this composition comprises a number of structural correspondences:

As the table above shows, the composition encompasses two halves of exactly equal length (bars 1-23, 23-46) describing two complete harmonic curves (departing from the tonic and returning to it).
Furthermore, the first and last sections correspond insofar as they are, with twelve and fourteen bars respectively, much longer than all other sections; they also complement each other in terms of the harmonic development (section I: tonic to dominant, section VI: dominant to tonic).
Finally, an analogy of harmonic progression can be detected between sections III and V: the modulation from G# minor to B major corresponds with that from D# minor to F# major. It will be interesting to discover that all these harmonic relationships are matched by correlations in material and texture.

II/23.1.3 Practical considerations for performers

The basic character of this piece is, without doubt, rather lively. There is a constant sixteenth-note motion which is not even once interrupted during the entire composition. Within the pitch pattern, the sixteenth-notes build almost exclusively virtuoso configurations (see e.g. the scales in bars 1 and 17-23 etc., the ornamented broken chords in bars 3-7), while the quavers are confined - with the exception of bars 12-14 and 23-27 - to accompanying broken-chord figures. The tempo which best expresses these characteristics is a very swift one; the upper limit is determined only by the ornaments which should still sound clear and crisp and not risk to loose their metric footing.

The appropriate articulation is based on a light touch. An elastically rebounding non legato for the accompanying quavers and a sparkling, light quasi legato for the sixteenth-notes are the predominant features. Broader non legato is used only for the few cases of melodic quavers, and legato is confined to the ornaments.

In the lively tempo one is likely to choose for this piece, the number of ornaments required may pose a problem. It helps considerably to imagine all trills, slides and appoggiaturas as fully-written note values; not only does it take away some of the fear, but also clarifies their metric position. The example below gives such a full version for bars 1/2 and bars 23m-28d. (It should be noticed that if a slide, as that in bar 23, forms part of a melodic figure, it must be transferred to any recurrences of the same melodic figure, in this case to the two sequences. A similar slide, in bar 26m, is spelled out, probably because of the required accidental. Another important aspect of ornamentation in pieces like this is that all trill notes should be of approximately the same speed - it is not acceptable to play trills in the right hand faster than trills in the left hand.)

(ex. 55a)

(ex. 55b)

 

II/23.1.4 What is happening in this prelude

The main features which provide melodic orientation in this prelude are to be found in the underlying peak-note lines. This is particularly true in sections I, II and VI.

Section I consists of two distinctive patterns which build two different kinds of curves.
Ia Bars 1/2 can be read as two large "hooks": in the right hand, there is an ascent over one and a half octaves (see bar 1: B-B, bars 1m-2m: B-F#) followed by a descent of only half the scope (bars 2m-3d: F#-A#). The left hand, beginning like an inverted imitation, counters with a one-octave descent (bars 1/2: B-B) followed by a half-octave ascent (bars 2-3d: B-F#). This design, which is obviously geared towards an effect of brilliance, creates corresponding dynamic curves with climaxes in bar 2 on the downbeat (left hand) and the middle beat (right hand) respectively.
Ib The following longer development is strung together by a peak-note curve in the right hand (see the ascent in bars 3-6: C#-D#-E-F# and the descent in bars 7-12d: A-G#-F#-E-D#-C#-B-A#). The left hand sets off with a hint of independence (see bars 3/4 F#-E-D#) but then resigns itself to mere accompaniment. In this homophonic pattern, the climax thus falls on the downbeat of bar 7.

Section VI uses the same building blocks as section I but combines them into a slightly different design.
VIa

The beginning constitutes a self-contained curve. The leading left-hand part presents an ascending F# major chord followed by a descent to, and an insisting repetition on, the low F#. The following half bar (see bars 36m-37d) presents a link which at the same time provides the modulation back to the home key.

 
VIb The next two bars display correspondences with bars 1/2. The lower voice combines the pitch layout of U: bars 1/2 (i.e. the ascent over one and a half octaves followed by a shorter descent) with some of the rhythmic features heard in L: bars 1/2, and the upper voice picks up the imitating run, this time without inverting it.
VIc Emerging from this right-hand run there begins, from bar 38 onwards (and thus overlapping with, not following the previous developments as in bar 3), an extended peak-note descent spanning two octaves (see bars 38-42: B-A#, bar 43: G#-F#-E, bar 44: D#-C#-B) followed by the notes of a closing formula wrapped in a still continuing sixteenth-note pattern (see bars 45/46: A#---B-A#-B). The lower voice moves partially in parallel to the upper voice (see the descent in the bass notes, bars 40-43) and ends with the notes of a cadential-bass pattern on the strong beats of each bar (see bars 44-46). The best dynamic representation for this segment of section VI - although by no means easy due to the long "breath" needed - is a single diminuendo form bar 38 to the end of the piece.

Section II presents itself as an extended version of segment Ia.
In contrast to the consistent two-part setting there, its initial four bars are conceived in three-part texture with melodically conducted quavers in the complementing upper and middle parts. (In this respect, section II anticipates the melodically determined section IV. Bach's apparently simple design of this prelude in two analogous halves thus allows for a more sophisticated observation on a higher level: Just as section II is the center and most melodious portion of the prelude's first half, section IV - much more definitely melodious - is the center of the entire prelude.) 
Going more into the details of this section, the left-hand part begins with scalar motions which describe a full curve in the key of F# major (see the direct ascent in bar 12-12m and the embellished descent in bars 12m-14d). This is followed by a shift of focus to G#, the forthcoming tonal center (see the descent D#-G# in bars 14-15d), and rounded off with the cadential steps G#-C#-D#-G# on the strong beats of bars 15/16. (This cadential-bass pattern is the same as that which ends section VI. The structural analogy it creates supports the view that section II is composed as an extension of section I.)
The right hand climbs in largely spaced steps right towards G# (see the ascending whole-bar beats in bars 13d/14d/15d which are enhanced by chromatic ascents) and plummets from there over two octaves (see bars 15-17m). The overall climax of this section falls certainly on the downbeat of bar 15, but a smaller dynamic curve may be already drawn in accordance with the left-hand F#-major arch.

Framed by these sections, Bach places two toccata patterns: sections III and V. They combine one-track increases of tension in falling and rising scales:

In bars 17m-19m, a small increase of tension leads to bar 18d which is the target of the scalar descent and comes supported by a bass note - as it turns out, the dominant of the subsequently approached F#. This is followed by a more powerful crescendo in a rising scale towards bar 19d where both the highest pitch of this phrase and the new harmonic root are reached. The complementing relaxation materializes in the form of another descending scale (F#-F#).
The same two-bar pattern is then sequenced in bars 19m-21m and in bars 21m-23m.
The pattern recurs once more, with a variation in the final relaxation, in bars 28m-30m. From there onwards, this newly varied tail, complemented by a corresponding ascent, is sequenced in one-bar groups (see bars 30m-31m, 31m-32m). These smaller arches represent their own tension curves which, in accordance with the declining direction of the sequential pattern, describe an overall decrease in tension.
Another half-bar link connects this section to the following one.

Section IV is, with only five bars, the shortest of all. This center piece of the prelude is placed between the two toccata-style sections. As was mentioned earlier, it is composed in consistent three-part texture and establishes a genuine small motive. In the upper part, a lavishly ornamented broken chord is topped by an octave jump. This grandiose gesture is complemented in the middle voice with four quavers which release some of the tension. The layout in which this two-part motive is further developed can be called classical: a first, very faithful sequence is followed by a second sequence which leads to a development with quaver-appoggiaturas and a final trill. (Note that in the middle voice of bar 27d, C#-B must also be slurred.) The attentive listener who recognizes the imperfect cadence here may expect more motives to come; but Bach decided instead to return to the virtuoso style in which this prelude set out.

The following simplified version of the prelude aims to show these processes (ex. 56):

 

WTC II/23 in B major - Fugue

II/23.2.1 The subject

The subject of this fugue spans from the downbeat of bar 1 to that of bar 4 or bar 5 respectively, since it comes with two endings: an accented (or "male") one and an unaccented (or "female") one. The "male" ending is determined by the harmonic progression. On the downbeat of bar 4, the dominant resolves into the tonic and thus concludes the perfect cadence in B major. The notes which follow until the downbeat of bar 5 serve as an extension which could be interpreted as a metric complement, i.e. as extending the subject so that it reaches a desired four-bar structure. Harmonically, however, these notes (bar 4/5 A#-D#) are not functional and only serve to prolong the tonic. It will therefore not come as a surprise that in the course of the fugue, Bach modifies this "female" ending liberally, up to a point where it assimilates shapes of episode material, and that he eventually omits it altogether.

Within the trunk up to its "male" ending, the subject consists exclusively of half-notes which describe a single, indivisible gesture. Except for the final semitone which features the resolution of the leading-note into the octave, the pitch pattern displays only intervals of a third or larger. The harmonic background is a simple cadential progression, with one harmonic step to each bar (ex. 57):

Two quite different dynamic representations of this subject are conceivable. How the development of tension is felt depends on the individual performer's susceptibility to harmonic over melodic processes.

If the melodic ascent is regarded as prevalent, then the subject should be taken as a single crescendo. This is complemented by a short diminuendo wherever the "female" ending retains its original falling line, but in cases where the "male" ending is followed directly by episode material, no relaxation occurs. (Care must be taken not to break the line momentarily in the descent G#-E-C#; such rendering would cut the subject in two.)
If the harmonic design is perceived as essential, then the increase of tension should lead to the subdominant function, the G# on the downbeat of bar 2. This climax would then be followed by a diminuendo through two bars - or through three bars in case of the "female" ending. (In this case, it is vital not to play the C# in bar 3d too softly, or risk fracturing the subject.

As can be imagined, these two contrasting interpretations of the dynamic gesture have, a far-reaching impact on the entire composition.

 

II/23.2.2 The statements of the subject

The fugue contains altogether fourteen entries of the subject. The table below indicates the "male" ending of each statement and shows an asterisk where a "female" ending similar to that in the initial bars is found.

1. bars 1- 4d B* 8. bars 42-45d S
2.

bars 5- 8d

T* 9. bars 48-51d B
3.

bars 10-13d

A* 10. bars 53-56d T
4. bars 14-17d S* 11.

bars 60-63d

T
5.

bars 19-22d

B(*) 12. bars 75-78d B
6. bars 27-30d T 13. bars 85-88d T
7. bars 35-38d A 14. bars 93-96d S

(ex. 58)

The subject's trunk as listed above remains completely unchanged throughout the fugue. Neither inversions nor stretto and parallel statements are employed.

 

II/23.2.3 The counter-subjects

The lack of modification in the subject itself leaves ample room for regular contrapuntal work. Bach has invented three counter-subjects for this fugue. Two of them appear exclusively in the first round of entries, while the third accompanies the subject for the remainder of the fugue and also pervades some of the episodes.

CS1

is introduced in B: bars 5-8d with a "female" ending until bar 9d. Its trunk consists of three bars with similar pattern, laid out in sequences. The first subphrase (bars 5-6d) commences with an upbeat to a syncopated half-note and concludes with three quavers in stepwise descent; it thus describes a perfect curve. The following two subphrases represent ascending sequences, each of them a fourth higher than the previous one. The entire group must therefore be interpreted as increasing in intensity. Phrasing between the subphrases may or may not be enhanced by actual cuts in the sound flow; their expression by dynamic means (relaxation followed by a new active rise) is, however, crucial. This trunk is complemented by a "female" ending which prolongs both the final harmony and the melodic descent at the end of the third subphrase.
CS1 recurs three times (T: from bar 10, A: from bar 14, S: from bar 19).

CS2

is first heard in B: bars 10-14d. It also begins with an upbeat to a syncopation; but both this note and its resolution are much more extended than in CS1, so that the first subphrase spans two bars. A second subphrase follows with an increase to bar 13d and a decrease to the final note.

These two early counter-subjects are designed to draw the listener's attention to the subject's "female" ending. This is particularly obvious in the case of CS2 which alterates the harmonic resolution on the final note of the subject's "male" ending into an interrupted cadence. This can be observed in bar 13d where the expected conclusion in B major is thwarted by the G# in the bass which converts the chord into a G# minor (vi of B major) and postpones the resolution to the final note of the "female" ending in bar 14d. An identical process occurs in bars 17/18. Interpreters who have opted for shaping the subject along harmonic lines, i.e. with the climax on the subdominant and the final tonic as a dynamic resolution, will find this diversion of Bach's to the deceptive chord particularly rewarding to play.

The following example shows the interplay of the subject with its first two counter-subjects, indicating phrase structure and dynamic options. (It should already be mentioned here that the second subphrase of CS2 features an interruption of its legato flow in the context of the consecutive jumps D#-G#-G# which must be played in detached style.) Ex. 59:

CS3 is introduced in S: bars 28-30d and accompanies almost all of the subject's further entries. It consists exclusively of quavers winding downwards in a pattern which can be read as an ornamented imitation of the subject's middle segment (see the example below). This imitative relationship determines the dynamic design of this counter-subject, allowing for the same two solutions that are possible in the subject (ex. 60):

 

II/23.2.4 The episodes

The B major fugue encompasses twelve subject-free passages. Owing to the design of the subject with two endings, the question arises where exactly one should assume the beginning of secondary material.

In entries accompanied by CS2, the answer is obvious since the diversion to the interrupted cadence and subsequent resolution do not allow partition of the "female" endings from the trunk of the subject and its companions.

In bar 22, however, CS2 is absent, the "female" ending of CS1 is transformed to a tie prolongation and the ending of the subject is transposed, thus changing the harmony after the return to the tonic has already taken place. In such a case, it must be assumed that bar 22 does not belong to the subject-dominated field. In many cases later in the fugue, however, no full return to the tonic occurs at all since the final tied note of CS3 often remains unresolved (see e.g. bar 30d; in fact, bars 30-35 do not contain a single downbeat without a suspension in one of the voices).

In all those entries where the subject's original "female" ending cannot be ascertained, episodes are therefore regarded as commencing after the "male" ending.

E1 bars 9-10d E7 bars 51-53d
E2 bars 18-19d E8 bars 56-60d
E3 bars 22-27d E9 bars 63-75d
E4 bars 30-35d E10 bars 78-85d
E5 bars 38-42d E11 bars 88-93d
E6 bars 45-48d E12 bars 96-104

These episodes display a variety of material. There are quotations from the counter-subjects (particularly from CS1 and CS3), small independent figures, and sequence models involving several parts at once.

E1 and E2 are both very short and serve to link subsequent subject statements. Their characteristic features include a varied imitation of the subject's "female" ending (see B: bars 9/10, A: bars 18/19) and an anticipation of the first subphrase of CS1 (see T: bars 9/10 and S: bars 18/19).

E3

combines various features. The segregated "female" ending and its sequence (S+A+B: compare bars 22-23d with 24-25d) are linked by a bar with neutral material, while the final bars of this episode, combines two quotations of the CS1-subphrase with a keynote / leading-note / keynote formula in the alto and a cadential-bass pattern. (The bracketed tie in S: bar 25 might better be ignored in order to facilitate recognition of the CS1 subphrase.)

E4

presents M1, an ascending tetrachord (see S: bars 30 and 31) in conjunction with two complete quotations of CS3 and neutral passages.

E5 and E6

feature M1 even more frequently (see B: bars 38-41, T: bars 41/42, A: bars 38/39d inverted; A: bars 45, 46, S: bars 45/46, 46/47 inverted); the motive even invades the first two bars of the intermittent subject entry (see bars 42/43). M1 is complemented by a short version of CS3 (see A: bars 39/40), a do-si-do keynote / leading-note / keynote formula (in E5) or a bar of neutral material (in E6).

E7

presents the first sequence model: bars 51-52d are repeated one note lower in bars 52-53d.

E8

combines CS3-derived material in the bass with free contrapuntal material in the other voices before it ends - the first episode so far apart from E3 - in a perfect cadence with resolution in all voices.
E9 is the longest episode in the fugue and at the same time the most independent one. It consists of three sequence models:
* Bars 63-65d are sequenced two steps lower in bars 65-67d and, shortened but again two steps lower, in bars 67-68d.
* Bars 68m-69m are followed by two ascending sequences in bars 69m-70m and 70m-71m.
* Finally, bars 71m-73d recur, two steps lower and varied, in bars 73-75d

E10

begins with several quotations of M1, mostly inverted (see bars 78-800d). These are followed by tension-building ascents (see S: bars 80/81, B: bars 81/82) and rounded off by a highly embellished three-part closing formula which will be encountered again later in the fugue (see S from bar 82m, A+B from bar 83).

E11

is taken up by another sequence model (A+T: compare bars 89-91d with bars 91-93d; B: compare bars 88m-90m with bars 90m-92m).

E12

begins with several four-note groups which appear remotely related to M1. An incomplete quotation of CS3 (see S: bars 100/101) leads to a transposition of the same embellished three-part closing formula which concluded E10 (see S from bar 101m, A+B from bar 102).

To sum up, there are three episodes in this fugue which end in a perfect cadence with complete resolution of all voices (E3, E8, E12); a fourth one (E10) must be regarded as structurally corresponding due to the immediate relationship of its close with that of the final episode.

Apart from the immediate correspondence between the two embellished closes, another analogy - structural rather than obvious - can be detected. The first two episodes which link subject entries accompanied by CS1 employ material from CS1, combined with a line derived from the subject's "female" ending; similarly, the first two episodes which connect subject entries accompanied by CS3 quote CS3, again combined with a frequently recurring short line in quavers (M1).

 

II/23.2.5 Character, tempo, articulation, ornament realization

The B major fugue represents rather calm basic character. This is indicated mainly by the complexity of the rhythmic pattern which contains not only a large variety of note values (the half-notes in the subject are complemented by quarter-notes, quavers and all kinds of syncopated and tied notes; even sixteenth-notes appear in one of the sequence models within E9), but combines them in a constant web of interlocking figures.

The tempo is determined on the one hand by the calm character, on the other hand by the alla breve time signature. Generously, even majestically swinging half-note beats may convey the idea. The relative tempo of the prelude to the fugue is complex, obeying the proportion of 3:2.

three quarter-note beats

correspond with
two half-note beats

in the prelude

 
in the fugue
(Approximate metronome settings: prelude beats = 96, fugue beats = 63.)

The articulation of this fugue needs a performer with a very conscious attitude. The basic approach in rather calm character demands general legato for all components that are essentially melodic. The two exceptions to this rule are the usual ones. The first concerns cadential-bass patterns; it applies in B: bars 25-27, 34/35, 59/60, 84/85 and 103/104. The second concerns consecutive jumps, and it is this exception which creates a special case in this fugue. As the subject, at least until its "male" ending, consists exclusively of jumps, it should be taken in a slightly detached style. To obtain the right duration of the articulated notes, together with a good expressive tone quality (a detail often badly neglected in non legato playing), it may help to imagine the first, unaccompanied subject entry played by a cellist who uses very broad bow strokes.

Apart from the subject statements and the cadential-bass patterns, all other components - counter-subjects and episode material - are legato. (Notice that the "female" ending is not only legato in itself but also linked to the final note of the subject's "trunk".) Within these, phrasing is an extremely important issue. This applies, on the one hand, to the sequences in CS1, the partitioning in the middle of CS2, and the episode segments deriving from primary material. On the other hand, phrasing is equally crucial in the context of the sequence models within the episodes.

Ornaments do not occur in this fugue.

 

II/23.2.6 The design of the fugue

The structural layout of this composition is clearly determined not only by the cadential closes observed in four of the episodes, but also by symmetries in the entering order of the voices and the consecutive build-up of the ensemble. There are four sections which present significant analogies.

Sections I and II, closing on the downbeats of bars 27 and 60 respectively, contain five subject statements each:

I: B T A S B
II: T A S B T

Both sections encompass a full round of statements plus one redundant entry.
In both sections, the voices enter in ascending order, with a return to the bass after the soprano, and the redundant entry occurs in the voice which had opened the section.
In both sections, the first three episodes are united by the use of similar material (see E1, E2 and E3 which all use fragments of the subject and CS1; and E4, E5 and E6 which all display M1).
In section I, the fourth subject statement does not sound, as could have been expected, in full four-part texture, since the bass rests from bar 14 onwards - the full ensemble is thus postponed for the redundant entry. Similarly in section II which commences in two-part setting, the completion of the ensemble is delayed twice (alto and tenor take consecutive rests from bar 42 onwards) and also materializes only with the redundant entry.

Sections III and IV both contain two subject statements each:

III: T B
IV: T S

Despite this comparatively small number of subject entries, these two sections encompass twenty-five and twenty bars respectively. The analogies are:

in both sections a tenor entry in three-part texture (see bars 60-64 and 85-88) is followed by a subject statement in a (more exposed) outer voice and in full four-part ensemble;
in both sections, the linking episodes (see E9 and E11 respectively) consist exclusively of sequence models;
in both cases, the latter statement is preceded by a four-bar variation of CS3 in the lowest voice (compare bars 71-74 with bars 88m-92m);
in both sections, the concluding episode ends with the same embellished closing formula.

Besides these analogies of material which links sections I and II on the one hand, sections III and IV on the other hand, there is a superimposed symmetry created by harmonic progresses which sheds yet a new light on the design of this fugue. Within the second half of the fugue, the progression in the harmonic development is exactly reversed.

The first section remains entirely in the home key, with entries alternating between the tonic and the dominant positions and the concluding cadence establishing the dominant key (see bars 26/27: F# major). Like the entries of section I, those of section IV are in the home key, on the tonic and dominant respectively.
In the second section it soon becomes clear that no modulation has yet taken place; F# major is re-defined as the dominant of B major and the first three entries remain once more in the home key. Just as the beginning of section II remained in B minor, so the end of section III has returned to B major.
Only the two final entries of section II change key: they sound in G# minor (the relative minor key of B major) and E major (the subdominant) respectively, and conclude the first half of this fugue in E major. Finally, both the end of section II and the beginning of section III are in E major.

One can thus state that,

while structural processes as created by the use of material and texture establish very conspicuous correspondences between each of the two pairs of sections (and thus seem to divide the fugue into two halves of very different content and density)
harmonic processes create an almost perfect axle symmetry (and thus knit the two halves inextricably together).

For a sketch showing the design of the fugue in B major, see ex. 61.

 

II/23.2.7 The overall dynamic outline of the fugue

The dynamic rendering of this fugue should represent as much as possible of the two-fold symmetry described above.

Following the detailed observations, it is clear that each of the four sections contains an increase of tension. Within the first two sections, this increase is very gradual as the full sound of the four-part ensemble is delayed until the very end. The third and fourth sections, by contrast, contain a fairly steep build-up of tension between their respective entry pairs.

Within the first half of the fugue, there is almost no interruption in the two processes of gradual increase since all intermittent episodes have bridging function. The second half of the fugue, by contrast, features episodes dominated by independent material as well as by structural processes of their own; these subject-free passages, which are also much longer than those bridging consecutive entries in the earlier sections, thus create a definite color contrast to the surrounding subject statements.

When comparing the level of intensity in the first half of the fugue, the second section appears somewhat lessened in comparison to the first. This is due, on the one hand, to the fact that the very "perfect" entering order B T A S B creates a stronger impact than that of its structural sequence T A S B T. On the other hand and perhaps more importantly, section I features its five subject statements surrounded by two independent counter-subjects, while section II only contains a single regular accompaniment of the subject which, what is more, is utterly dependent on the subject in terms of both pitch pattern and dynamic design. Last but perhaps not least, the change of mode towards the end of section II also softens the increase in this section.

Within the second half of the fugue, the converse process can be observed: section III contains longer episodes in contrasting color than section IV, thus suspending the rise of tension between consecutive entries more. Also, the bass entry in section III is not accompanied by a single counter-subject, thus forfeiting some of its climaxing power; the corresponding soprano statement in section IV, on the contrary, comes supported by CS3 in the tenor and a varied version of CS3 in the alto.

The dynamic representation should thus aim at depicting both the large-scale structural analogies between sections I/II and III/IV and the harmonic axle symmetry of the fugue with correspondences between sections I/IV and II/III.