WTC II/6 in D minor – Prelude 

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

II/6.1.1 The prelude-type

This prelude is in two-part texture. The material includes components usually indicative of homophonic style (see e.g. the broken-chord accompaniment patterns in bars 2-4), as well as a number of motives developed in even distribution between the two parts. Contrapuntal techniques and imitation are amply used.

 

II/6.1.2 The overall design of the prelude

The first harmonic progression closes on the downbeat of bar 5. The close coincides with the end of the four-bar phrase which is consequently imitated; it should therefore not be regarded as a structurally relevant caesura. The same holds true and for the same reason for the cadence which closes at the end of the imitation of the initial phrase, on the downbeat of bar 9. The first structurally relevant harmonic conclusion is not reached until the downbeat of bar 26 which affirms the modulation to the dominant.

The prelude then continues uninterrupted as motives not only follow each other in succession but also develop from one another in such a way that distinguishing sections seems impossible. The subdominant field within the large-scale harmonic development is established in bar 42 but immediately gives way to a dominant pedal. This launches a liquidation process which proceeds, through various steps up to a final tonic pedal.

  

I a

bars 1- 9d

tonic confirmed

I b

bars 9-26d

modulation to the dominant

II

bars 26-42d

modulation to the subdominant

III

bars 42-61

return to the tonic

 

II/6.1.3 Practical considerations for performers

This composition is characterized, above all, by its uniquely homogeneous rhythmic pattern. The only interruptions of the continuous sixteenth-note motion occur not because of longer note values which allow breathing room, but on the contrary because of inserted groups of faster figures: ornamental runs in thirty-second-notes (see bars 22, 24). This rhythmic simplicity finds an equivalent in the pitch pattern which consists predominantly of either broken-chord figures or scale passages and ornamental figures. The basic character of this prelude is thus certainly rather lively and the tempo swift not hurried but in a pace which discourages the listener from concentrating on single sixteenth-notes but conveys patterns like those in bars 2 and 3 as units.

Articulation is very crisp. The non legato in the eighth-notes should rebound without leaving a weighty impression. Apart from the few groups which Bach marked legato (see U: bars 22 and 24; L: bars 43-45) the faster note values should appear in distinct quasi legato, resembling the tone quality that the Viennese Classical style was to call leggiero.

The only ornaments indicated for this prelude are inverted mordents. Note that their lower neighboring note uses the pitch that corresponds with the harmony of the bar: in bars 1-3, 44 and 50 where the decorated note is the tonic of D minor, the ornaments touch the leading-note C#, and in bars 27/28 where the secondary key A minor is reached, G# and not G natural is the proper auxiliary. In bars 43 and 45, however, the inverted mordents use the whole-tone step.

 

II/6.1.4 What is happening in this prelude

We count four distinct motives. One of them appears with a specific accompaniment which it retains; one is escorted by varying non-motivic note-groups; the other two are introduced in stretto imitation, thus not leaving room for any contrapuntal figure.

Before describing these motives it is necessary to mention a particularity occurring at the beginning of the prelude. The falling octave in the lower voice does not ever recur in the piece and must therefore be regarded as separate from the thematic material. Also, the descending scale is, on two strategic occasions (see bars 5 and 26), conceived as an upbeat feature which commences in a metrically weak position on the second sixteenth-note of the bar. It may thus be permitted to contend that the prelude begins with a kind of assertive "signal" the triple D and only launches its motivic material from the next weak beat.

M1

consists of a melodic part in eighth-notes (see L: bars 2-5d) and an accompaniment (M1a) in which a descending scale triggers a broken-chord motion. While M1a is harmonically determined and reaches its climax on the subdominant chord (bar 2) followed by a diminuendo until the end of the motive, the leading part of M1 follows melodic features. The rests together with the sequential layout at the beginning indicate at least one sub-phrasing. The climax of the entire motive falls on the Bb in bar 4, a note which is preceded and followed by high-tension intervals (minor sixth, diminished fifth).

In this concept, bar 3 is interpreted as a varied sequence of bar 2. It takes part in the gradual buildup to the climax and should therefore increase in intensity. Both voices come to a relaxed ending on the downbeat of bar 5 (ex. 59).

The repetition in inverted voices begins with a renewed secondary buildup of M1a, followed by a duplication of the processes described above. Later in the prelude, M1a recurs in L: bars 26-30d and U: bars 30-34d, while M1 in its original melodic shape only reappears in U: bars 27-30d. Fragments of the melodic material of this motive can also be recognized in L: bar 42, U: bar 43 and L: bar 50.

M2

is also introduced in the lower voice. Commencing on the second sixteenth-note of bar 9, it describes a curve which culminates on D (see bar 9 beat 3) and is rounded off by a broken chord also in the shape of a curve (see bars 10/11).

In an interpretation which emphasizes pitch patterns, the tension also peaks on this D, while in an interpretation which supports metric features, the climax falls on the B>ð (bar 10d). In either case, the climax is followed by a gradual decrease of tension which approaches the final note of the motive (bar 11d: C) without passing through any further accent (ex. 60).

M2 is set in stretto imitation: it recurs in U: bars 10-12d (ending varied to tied note) and in L: bars 11-13d. Furthermore strange for an imitative process we can recognize its two halves which separately fill up the spaces left vacant at the beginning and end of this stretto (see M2 second half in U: bars 9-10d, and M2 first half in U: bars 12-13d).

M3

presents itself under structural conditions very similar to those found in M2. Introduced in the lower voice, it is imitated in stretto. The first complete statement of M3 appears in the lower voice of bars 13-15d. Its initial bar consists of a two-step "upbeat" to a broken chord in zigzag (see bars 13/14: D-F-Bb-D-G) followed by a continuous sixteenth-note motion inside which close inspection can reveal a continuation of the same zigzag line (see bars 14/15: Bb-E-G-C#-E-A).

An interpretation which aims at revealing actual and hidden pitch shapes should place the dynamic climax on the note which is the outset of the descending broken-chord pattern, the D on the second beat of bar 13, whereas a performer who has chosen to focus on rhythmic and metric features will increase tension until bar 14d and decrease thereafter (ex. 61).

M3 recurs in U: bars 14-16d; in L: bars 15-17d; in U: bars 16-18d. In addition there are, as in the case of M2, half statements (see M3 second half in U: bars 13-14d, M3 first half in L: bars 17-18d).

M4

The last thematic component is introduced much later and - as the first truly melodic unit in this prelude in the upper voice (see U: bars 35-37d). In its first bar, the continuous sixteenth-notes are conceived in hidden two-part structure, displaying a peak-note line ascending against the backdrop of a repeated Eb-D-C. The harmonic resolution of the thus described diminished seventh chord F#-A-C-Eb materializes on the subsequent downbeat (with Bb-G for G minor), followed by a descending G minor scale which, after a bend, ends on C (ex. 62).

For the dynamic representation of this process there are again two options. One can emphasize the harmonic play of tension and relaxation and play the downbeat of bar 36 already softened, as the beginning of a resolution. Or one can choose the metrically oriented version in which the climax will fall on the strongest beat which here, actually, also contains a melodic "surprise" as the Bb deceives the listeners' expectations for a continuation of the ascending peak-note line.

M4 differs from the other motives in this prelude in that it does not come accompanied by a fixed figure in the second voice. The imitation sets in after the original figure has ended, and the eighth-notes of bars 35/36 never return in the same shape.

This motive recurs, with slight variations at both the beginning and the end, in L: bars 37-39d. Thereafter, only the first half of the motive appears in U: bars 39-40d. (The descending sixteenth-notes in the lower voice of bars 40/41 are easily heard as a continuation of the motive in octave displacement which, strictly speaking, they are not.)


The structure of the prelude in D minor is determined by the appearance of the four motives and their respective inherent impetus.

The first section of the prelude displays a lineup of the motivic material followed by an extended cadential figure. Bars 1-5d and bars 5-9d present the main motive in its original setting and in inverted voices respectively. This repeated statement of M1 is balanced by the two stretto-groups of M2 (see bars 9-13d) and M3 (see bars 13-18d) which induce the modulation to the dominant key. In the following pattern, which exposes a chordal progression in hidden two-part structure, four bars with an indirect pedal A (see the peak notes in the upper voice) are matched by four bars with an indirect pedal D. In bar 25, the treble D has turned into the seventh of an E major chord and thus leads to the completion of the modulation to A minor on the downbeat of bar 26.

With regard to the development of tension, M1 is clearly the strongest in this section, both because of its greater length (four bars versus only two bars in M2 and M3) and because of the extended dynamic buildup within the melodic part of the motive. The two smaller motives both feature descending sequences. While the tension may momentarily flare up at the outset, it then gradually subsides, reaching a level of quiet suspension at the beginning of the pedal-note bars. Throughout these eight cadential bars, the tension then rises, gradually but relentlessly, reinforced by the sudden thirty-second-note flushes in bars 22 and 24, until the dynamic level of the prelude's beginning is regained.

Section II commences in an intensity similar to that of section I. Yet while the immediate recurrence of M1 presents itself as triumphant as ever, its repetition in inverted voices is so strongly varied that the same character cannot be maintained. An inserted extra bar, reminiscent of the initial run of M1a, seems to launch a new attempt but leads instead into M4. The section concludes after two bars which serve both as a complement to the aborted M4 sequence and as a transition, on the downbeat of bar 42.

The decline of dynamic intensity is much more drastic in this section than in the previous one. It begins with the variation of M1 in which the dropout of the characteristic melody creates a thematic void. The impression of reduced polyphonic density continues throughout the bars dominated by M4 where only one voice seems relevant as supported by the switch to parallel texture in bars 38/39. In the transitional bars, the lower voice continues the decreasing tendency while the upper voice opposes this with a stringent increase in (mostly chromatically) rising eighth-notes.

Section III differs from the two preceding sections in almost every respect. Perhaps most importantly, none of the motives is quoted in their entirety. Instead, the initial bar with fragments of M1 is immediately followed by a development which combines faint remembrances of M1 with the extended pedal which concluded section I (see here A in L: bars 43-46 and in U: bars 47-49). Two bars of hidden two-part structure with parallels recall the end of section II (compare bars 51/52 with bars 38/39) and lead to four bars in toccata-style (bars 53-56). After the home key is reestablished in its major mode (Picardy third from bar 57 onwards), the prelude ends with four cadential bars on a bass pedal D and a final chord which, with its four voices, confirms the indirectly instituted four-part structure of all non-polyphonic passages in this prelude.

Dynamically, the third section describes a prolonged decrease of tension. Caused primarily by the absence of thematic substance, this decrease is further supported by a descending peak-note line (see upper voice E: bar 43, D: bar 44, C: bar 45, Bb: bar 46, A: bars 47-49, G: bar 50, F-Eb-D: bar 51, Eb-D-C: bar 52, Bb: bar 53). While the toccata-like bars describe superficial waves rather than a consequential increase in tension, only the final development over the tonic pedal counteracts the decreasing tendency and concludes the prelude on an assertive note.

 

 

WTC II/6 in D minor – Fugue

 

II/6.2.1 The subject

The subject begins on the downbeat and ends in bar 3 also on the downbeat, thus extending over a little more than 2 bars. The two extra eighth-notes which follow the final note have neither harmonic function nor do they ever recur; they should therefore not be regarded as part of the subject. The F on the downbeat, on the other hand, is indispensable to complete the D minor cadence.

When describing the pitch and rhythmic patterns of this fugue, the view held depends very much on the interpreter's personal preference. There are two possible interpretations which will, of course, influence how the basic character is determined. Both can be supported by sound reasons.

1.

One can describe the rhythmic pattern as consisting of a variety of note values (eighth-notes, triplet sixteenth-notes, normal sixteenth-notes, syncopations), and the pitch as containing predominantly stepwise motion.

2.

One can also argue that while there are three regularly occurring note values, the rhythmic pattern can nevertheless be regarded as simple in its overall impression. At the same time, the stepwise triplets can be recognized as having ornamental character.


The phrase structure of this subject also allows for two conflicting interpretations (plus a little variation in one of them). As each of these interpretations is clearly linked to a particular view on the character of the piece, it is vital not only to recognize the two possibilities but to be aware of the ground on which each of them stands, and the consequences that each of them triggers.

1.

The subject can be regarded as one indivisible unit.
This view is only truly convincing in a very lively character.

2.

The subject can also be interpreted as consisting of two subphrases. The first subphrase ends on the first of the eighth-notes (the A on bar 1 beat 3 which is the natural target note of the winding ascent in the sixteenth-notes). The second subphrase then comprises the descent from the octave D to the final F. This concept is possible in lively character; in rather calm character it is probably the only meaningful interpretation.

3.

On basically the same grounds, the subject can be described as encompassing three segments: a first subphrase from the beginning to the A on beat 3 (as above), a second subphrase whose main body ends on the F after the tied G, and a cadential tail.
The argument is as follows. The syncopated G embodies harmonically both the subdominant and the dominant chord, and the subsequent eighth-note F brings the return to the tonic; so there is a point for regarding the main body of the subject as ending here. Yet this is metrically unsatisfactory and would appear somewhat arbitrary as the remaining three notes provide a more convincing conclusion - mainly because of their cadential skips which are a reassuring orientation after so much chromatic mystery. To regard these notes as a "tail" might therefore not be such a bad idea: it shows that they are not essential although they belong, that they are somehow self-contained (see their harmonic background) but not weighty enough to constitute a subphrase of their own; and that they can occasionally be omitted without damage to the main body (see e.g. bars 10-12, bars 14/15, bars 17/18).


The harmonic layout used by the composer for this subject is very complex, particularly in the second half where the high degree of chromaticism creates altered chords and chords of secondary order. Bach's own realization displays harmonic changes on each eighth-note with only one exception (we shall come back to this). While this constant change makes the search for what could be determined as the main harmonic functions difficult, it certainly contains a message of its own which is worth taking into consideration. On the one hand, such dense harmonic action requires time to be appreciated and thus rules out a very fast tempo which the sixteenth-note runs might otherwise tempt us to adopt. On the other hand, the only exception from the constant change of harmony occurs on the third beat of bar 1 where both the A and the D stand for the tonic. This supports the view of a subject consisting of two subphrases, both of which display a roughly similar harmonic design (ex. 63):

 

As to the dynamic outline, any suggestion would obviously have to be in keeping with decisions made in other respects. The following options seem open:

1.

For performers who, despite the dangers for an adequate appreciation of the rich harmonic fabric, have assumed a fast tempo, with no subphrasing inside the subject, a consistent dynamic design places the climax on the highest note D, with a crescendo in the ascending runs and a diminuendo in the gradual descent. This interpretation is based on the view of the subject and, to a degree, the entire fugue as a virtuoso display in which pitch curves dominate. (Harmonic details, however, are overrun in this interpretation.)

2.

For interpreters who opted for a moderately fast tempo and a subject consisting of two subphrases, the first subphrase remains basically equal, with a crescendo in the ascent. (One can occasionally hear the very subtle version which increases only until the Bb but resolves slightly into the tonic on A. This is beautiful as long as it does not lead to a similar up-down on the first beat, which may, with one stroke, ruin the subphrase by making it sound like "emotional waves" more suitable to 19th century music.) The second subphrase can now give credit to the syncopation and its special harmonic background, so that the tension increases in the chromatic descent until the G and decreases gradually thereafter.

3.

For those who pledge that in addition to two subphrases there is a cadential tail, the final decrease after the syncopated G must be fairly abrupt, so as to allow for the following F to sound fully relaxed. The three final eighth-notes E-A-F then sound in a neutral, dispassionate tone color.


 

II/6.2.2 The statements of the subject

The D minor fugue contains nine complete subject statements.

   

1

bars 1-3

M

5

bars 14/15

M

2

bars 3-5

U

6

bars 14-17

U

3

bars 6-8

L

7

bars 17/18

M

4

bars 10-13

U

8

bars 17/18

L

9

bars 25-27

U

(ex. 64)

 

None of the further statements sounds exactly like the initial one. The second and third entries appear without major modifications, but the final note concludes the melodic cadence even more powerfully than at the beginning of the fugue by falling back to the keynote (see bar 5d: A instead of C; bar 8d: D instead of F). The fourth subject statement breaks off immediately before the expected syncopation and, after an octave displacement, sequences the eighth-note descent but alters the ending and breaks off unresolved (bar 13 C#).

Statements 5 and 6, as well as 7 and 8, are positioned in stretto, and the latter pair uses the inversion of the subject. None of these entries is complete. The fifth entry anticipates the syncopation (see M, bar 15: on A instead of G) and then breaks off suddenly. Its partner corrects the position of the syncopation (see U: bar 15) but, instead of resolving afterwards and thus bringing the subject to a close, continues and expands the chromatic descent in sequences of the rhythmic figure (see U: bars 16/17).

In the following stretto with inverted entries, the leader behaves like the leader of the preceding stretto: it anticipates the syncopation, lengthens it and then breaks off (see M: bar 18). Its partner is even less complete, as it does not reach any syncopation but gives way to another motive halfway through the second segment (see L: bar 18, middle beat). Only the statement which concludes the fugue recaptures the original version. Yet while the syncopation is in place, the cadential tail is substituted by a melodic closing formula (see U: bar 27).

 

II/6.2.3 The counter-subject

This fugue contains only one proper counter-subject. It is introduced from bar 3 onwards where it commences immediately after the middle beat. Its end is unclear. One feels that the counter-subject was meant to end with a closing formula A--G#-A; but Bach obviously decided to deviate from this expected ending, to write G instead of G# and delay the final note which now resolves late and into another key. (In M: bar 5, the resolution comes after a suspension on the second sixteenth-note and suggests not a chord on the dominant A but one on the tonic D. The ending on the sixteenth-note F is thus the logical conclusion, although it is quite impossible to convey this in performance as suspension and resolution overlap with the beginning of the next motive.)

The phrasing in this counter-subject can be interpreted, again, in two ways: either as indivisible or as consisting of two subphrases. In the concept with two subphrases, the most likely place to phrase is after the downbeat A. The dynamic layout allows for a host of possibilities several within each of the different options for the phrase structure.

-

If the counter-subject is interpreted as an indivisible phrase,

*

one may feel that the climax falls on the high-tension interval (the tritone C-F# in bar 4, F-B natural in bar 7) which is therefore preceded by a melodic, unbroken crescendo and followed by a diminuendo;

*

one may prefer the climax on the syncopation; again the crescendo up to the climax is unbroken through the various bends of the line;

*

another option is to place the climax on the subdominant harmony which falls on the downbeat;

*

finally one might regard the counter-subject as composed in hidden two-part structure; in this case, the syncopation is again the best choice for the climax. The two parts of the structure are:

"melody"

B C D E F# G

A

B C

B A G#

A G F

"background"

E

G# A

F#

E

-

If the counter-subject is interpreted as consisting of two subphrases and phrased after the first downbeat,  

*

the first climax falls on this downbeat (subdominant), the second climax on the syncopation.


(A version which is sometimes heard although it seems less logical is the phrasing after C. The climaxes, however, would remain untouched by this decision; the first climax on A (subdominant) is then followed by a diminuendo up to C (!). (Attention: If you phrase after C, C-F# is no longer a high-tension interval, simply because the two notes now belong to different subphrases and, since you "breathe" between them, form no interval at all. So phrasing after C but having the climax there at the same time is not possible.)

The following example gives the counter-subject as it sounds against the tonic version of the subject in bars 6-8. Listed here are only two of the manifold contrapuntal patterns which result from the different options for phrase-structure and dynamic outline in subject and counter-subject (ex. 65a).

 

(ex. 65b)

 

 

II/6.2.4 The episodes

There are five subject-free passages in this fugue.

  

E1

bar 5

E2

bars 8-10m

(M overlaps, commencing already in bar 7m)

E3

bars 13-14d

(M overlaps, commencing already in bar 12m)

E4

bar 16

E5

bar 18m-25m

All the material that appears in these episodes either derives immediately from subject and counter-subject or is introduced against it (as a "fake" counter-subject).

E1

consists entirely of subject-derived components. The most prominent feature is a motive with twelve triplet-sixteenth-notes and a final eighth-note; this quotes the subject's head in inversion (see M: bar 5 first half, U: bars 5/6). This motive plays a role throughout the fugue and will be referred to as Ms, for "motive derived from the subject". The counterpoint to the two statements of this motive also goes back to the subject: the four eighth-notes in the upper voice and their imitation in the middle voice represent the retrograde of the second half of bar 2.

E4

similarly derives overwhelmingly from primary material: the upper voice features partial sequences of the varied subject tail, and the lower voices accompany with partial sequences from the end of the counter-subject.

E2

features several different components. 

*

Already overlapping with the ending of the preceding subject/ counter-subject statements, an independent motive (M1) is introduced (see the middle voice of bars 7-8d).
M1 consists of seven (upbeat) sixteenth-notes followed by one (strong-beat) eighth-note, and is complemented in the course of the fugue by different extensions.

*

The first three statements of M1 feature an extension which can be recognized as an imitation of the end of the counter-subject
(see the sixteenth-note jumping up a fourth plus the two syncopations, in M, bar 8: D-G-F; L, bar 8m: G-C-Bb; U, bar 9: C-F-E).

*

In the second half of E2, the head of the subject recurs: first in a shortened version (see L: bar 9), then in the length established for Ms but still inverted (see L: bar 10 first half) and finally, in stretto, in the original shape of the motive (see U from bar 10 beat 2).

E5

corresponds in many respects with E2 but is even more complex.

*

After a beginning with the subject's head (see bars 18/19, L + U) there is a related figure which consists of only six triplet-sixteenth-notes followed by two eighth-notes in a rising third (see e.g. M: bar 19m). Sometimes there are several thirds; these are extensions. This figure appears in bars 192-21d: M, L, U, L, M, L, U.

*

This is followed by a stretto with quotations of Ms;
see bar 21: L + U.

*

A third component of this episode displays M1;
see M: bars 21/22, U: bar 22, L: bars 22/23 varied,
M: bar 23 varied, L: bars 23/24.

*

Bar 24 can either be read as two more varied sequences of M1 (M/L) or as an imitation of the head of the counter-subject in inversion; see L: A-G-F-E-D-C#-E-D.

*

Finally, the last half bar of E5 corresponds with that of E2;
compare M: bar 25 with L: bar 10 and L: bar 25 with U: bar 10.

E3

is by far the shortest of the subject-free passages and finds no correspondence in the fugue. It consists of three statements of M1, quoted here without the extension from the counter-subject;
see M: bars 12/13, L: bar 13 first half, U: bars 13/14.


The role played by each of the four episodes in the dynamic development of the fugue follows directly from the analysis of the material. E1 and E4 bridge two consecutive subject statements. E3, despite its short range, brings a relaxation with independent material. The same is true for the first half of E2 and for the M1-determined segment of E5. In both cases, the final half bar of the episode turns around and prepares the advent for what appears like (and is intended to appear like) an unexpected additional entry.

 

 

II/6.2.5 Character, tempo, articulation, ornament realization

In a polyphonic composition from the Baroque era where both the pitch pattern and the rhythmic pattern permit varying interpretations, it will hardly come as a surprise that the basic character can also be determined in two ways. If one feels that the rhythmic pattern is dominated by a variety of note values (eighth-notes, triplet sixteenth-notes, normal sixteenth-notes, syncopations) and that the pitch pattern contains predominantly stepwise motion, one would conclude that the character of the fugue is rather calm. If, on the other hand, one regards the rhythmic pattern as basically simple behind the three regularly occurring note values, and if one feels that the stepwise triplets have ornamental character, then the logical conclusion for the character is rather lively.

In case this appears puzzling, it is relieving to find out that this decision has only limited consequences for the articulation. (The way in which different dynamic designs depend on the chosen character was already explained above).

-

In rather lively character, the triplet sixteenth-notes are (quasi) legato including the link to the A on beat 3, while the eighth-notes are non legato. (Note that no slurring is needed or desirable from the syncopation to the following F since this step is not composed as appoggiatura-resolution.)

-

In rather calm character, all notes that are regarded as melodic should sound in legato. Different options are, however, open for the three final notes depending on whether or not they are taken as cadential, in which case they must be played non legato. (In this option, the subject would appear as follows: bar 1 from beat 1 D to beat 3 A: legato phrasing from upper D to F: legato after that: non legato).


The articulation in the counter-subject and in M1 is overall legato, in whichever character a performer chooses. Equally, the articulation in the broken-chord extension of bars 19/20 is non legato in any case.

The tempo in this fugue can be chosen according to the interpreter's feeling. It is, however limited on both sides by certain features: it must be fast enough to ensure that quarter-notes, and not eighth-notes, are perceived as the beats; and it must be slow enough to allow full appreciation of, on the one hand, the chromaticism and its harmonization, and on the other hand, the syncopations and complementary rhythm patterns.

As to the relative tempo of the fugue to the prelude, the most convincing proportion is one that translates the main pulse [choice a) below]. If, however, a considerably faster tempo is desired for the fugue, a more complex proportion is possible [choice b)]:

a)

one quarter-note

corresponds with

one eighth-note

in the prelude

in the fugue


b)

one bar

corresponds with

half a bar

in the prelude

in the fugue


Approximate metronome settings:
a) prelude beats = 108, fugue beats = 54 (eighth-notes = 108);
b) prelude beats = 108 (bars = 36), fugue beats = 72 (half-notes = 36).

The fugue features two ornaments; one is indicated by a trill symbol (see bar 16), the other by a mordent sign (see bar 27).

-

The trill in bar 16 represents a long (note-filling) ornament since it resolves duly - in harmonic, melodic and in metric respects. As it is approached stepwise, it commences on the main note (of one triplet-sixteenth-note duration). The following four notes are the upper/main/ lower/main notes and lead smoothly into the E on the downbeat of bar 17.

-

The cadential trill in the final bar of the fugue, by contrast, is not a note-filling ornament since its resolution falls before the strong beat (point d'arrêt trill). After a regular beginning from the upper neighbor note, the shake includes four or, preferably, six notes and stops short before the next eighth-note in middle and lower voices. (The short ornament not in the context of the polyphonic Baroque style. Bach very often uses this little this symbol for rather long trills; the fugue subjects of the Well-Tempered Clavier are full of examples.)

 

II/6.2.6 The design of the fugue

The structural layout of the D minor fugue is conveyed mainly by three features: the introduction of the subject stretto in the second section, correspondences between subject entries (and, particularly, between episodes), and the dynamic function of episodes.

-

The most obvious correspondence occurs between bars 10 and 25. In both cases, the head of the subject appears in stretto with its inversion (distance one quarter-note), thus preparing the next subject entry. While the voices are inverted and the subject statement begins earlier in bar 25 than in bar 10, we can detect a basic analogy between bars 10/11 and 25/26.

-

Bars 10 and 25 both appear at the end of an episode where, after an overall relaxation of tension, they build up newly in a last-minute preparation for another subject statement. (In bar 10 which is reached in a cadential formula this is even more obvious than in bar 25.) These two bars thus determine the following entries as part of the ongoing section.

-

Another structural correspondence exists between the main body of E2 and the latter half of E5: compare the four statements of M1 in bars 7-9 with those in bars 21-23).

-

E1 and E4 fulfill an analogous function as both consist exclusively of primary material and both bridge consecutive subject entries.

-

Finally, the two subject statements which form the stretto in bars 14/15 are identical - both in notes and with regard to the voices which present them with the two initial entries in bars 1-3 and 3-5 respectively. The counter-subject of bars 3/4 also recurs here in octave transposition.

 
As far as the number of voices is concerned, no subject statement returns to two-part texture. The prominent lower-voice rests in bar 14, however, convey this impression although the reduced ensemble is given up halfway through the stretto with the entry of the counter-subject.

The fugue thus presents itself as consisting of two structurally corresponding and equally long halves. The abbreviation achieved in the second section by the stretto is made up by the additional bars in the first half of E5:

  

subject M

stretto M + U

subject U

E1

E4

subject L

stretto Minv + Linv

E5 (1st half)

E2

E5 (2nd half)

subject U

subject U

E3

(= 13 bars)

(= 13 bars)
 

While the harmonization is very complex in its details, the overall design is as simple as could be: all statements remain in the key of D minor. The dominant is not reached in cadential confirmation, and the subdominant appears only transitorily at the end of the second stretto (see bar 18). For a sketch showing the design of the fugue in D minor, see ex. 66.

 

 

II/6.2.7 The overall dynamic outline of the fugue

This playful fugue is built in one large dynamic curve: the first half represents an overall increase and the second half an overall decrease of tension.

Within the first section, the tension rises, both due to the growing ensemble and the increase in polyphonic density. While E2 brings forth a certain decline, its final half bar with the intense preparation of the subject entry (bar 10) makes up for the loss by propelling the dynamic level up again.

The second section is governed predominantly by the opposite tendency. It commences with the subject in stretto, accompanied by the counter-subject; this combination represents the highest degree of polyphonic complexity achieved in the D minor fugue. The extension produces a protracted diminuendo, followed by the more subdued character of the inverted-entry stretto. E5 continues this tendency with a prevalence of falling lines and descending sequences. The dynamic decrease only terminates on the downbeat of bar 25 where the preparation to the final subject statement achieves a last short rise of tension.