WTC II/8 in D# minor – Prelude 

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

II/8.1.1 The prelude-type

This prelude is written in consistent two-part texture, with imitation occurring regularly (see e.g. U: bar 1, L: bar 2). Techniques of counterpoint are also widely used, and there is not one moment where the feeling of strict polyphonic independence of the voices is lost.

One can speak here of either a two-part fugue or an invention. In the case of a fugue, there are several obvious irregularities. The first bar features bass notes which serve exclusively as harmonic support but do not take part in the polyphonic play. (But then, the other prelude of the Well-Tempered Clavier which is composed as a two-part fugue, the prelude in F# minor vol. I/14, also introduces its subject against a neutral accompaniment in the lower voice.) More suspicious are three other atypical features: (1) the imitation of the main idea occurs in tonic position and not, as usual in a fugue, on the dominant; (2) the main melodic idea only covers thirteen of the thirty-six bars, but its various forms of development account for much more; and (3) there are repeat signs for the first sixteen as well as the following twenty bars. It might therefore be less controversial to describe this prelude as a two-part invention.

 

II/8.1.2 The overall design of the prelude

The sections in this "invention" are defined, in addition to the usual harmonic processes, by the recurrence of the thematic material. In this first overview, however, we state only the harmonic processes.

I

bars 1- 9d

tonic to relative major

(D# minor to F# major)

II

bars 9-16

relative key to dominant

(F# major to A# minor)

III

bars 17-28d

dominant back to tonic

(A# minor to D# minor)

IV

bars 28-36

confirmation of tonic

(D# minor)

 

There is a striking number of structurally analogous bars:

compare

with

bars 1/2

bars 28/29

(same key, counterpoint varied)

bars 3/4 U,
3m-5m L

bars 21/22 L,
21m-23m U

(transposed)

bars 6-8

bars 25-27

(transposed from the relative key)

bars 154-16

bars 354-36

(transposed from the dominant)

bars 17/19

bars 32m-34m

(transposed, voices inverted)

To sum up our findings with regard to harmonic design and structural analogies, we can recognize that this invention conceals a typical Baroque binary form, found e.g. in many of Bach's suites, particularly in Allemandes.

 

II/8.1.3 Practical considerations for performers

To determine the basic character of this prelude, we must proceed in the same manner as we would in the case of a fugue or an invention: considering the pitch and rhythm patterns. The information we can derive here reads as follows. On the one hand, we can contend that the rhythmic pattern is generally simple. Most bars contain predominantly eighth-notes and sixteenth-notes. The pitch pattern encompasses frequent jumps both in the eighth-notes (see e.g. L: bars 6-8) and the sixteenth-notes (see e.g. U: bars 6-8). On the other hand, there are not only written-out thirty-second-notes but also a very large number of ornaments. The basic character of this invention is thus rather lively, but the tempo should be moderate rather than fast.

The articulation must contrast a fairly gentle non legato in the eighth-notes and quarter-notes with legato style in the sixteenth-notes. Among the eighth-notes one can distinguish melodically intensive touch (as in U: bar 2) from a more neutral touch used in accompanying groups (as in L: bars 6-8). The only occasions where eighth-notes must sound legato because of their being paired as appoggiatura-resolutions, are indicated by the composer himself (see bars 16 and 36). In the tied notes (see e.g. bars 4/5, 5/6), the sixteenth-note-extension is treated as a sixteenth-note. Wherever abbreviation of this note due to phrasing is desired, it must be guaranteed that the syncopated effect is not destroyed. (Expressing phrasing by dynamic means alone may be a better choice here.)

Among the numerous ornaments, the inverted mordents pose the smallest problem. None of them needs an accidental for an artificial leading note. (Their lower neighbor notes are regular: F# in bar 3, B and E# in bar 4, A# and G# in bar 5; G# in bar 21, C# and F# in bar 22, B in bar 23.) Trills and mordents come with and without suffixes and begin differently, too. In bars 2 and 9, the mordents in the upper voice both commence on the main note (since they are approached stepwise) and contain a single three-note shake. The trill in bar 14, by contrast, begins on the upper neighbor note (A#), shakes in three pairs and ends with the indicated suffix. Finally, the turn in bar 2 consists, after a beginning on the upper note, of four thirty-second-notes.

  

II/8.1.4 What is happening in this prelude

This prelude is best approached in the manner for analyzing a fugue or an invention. We will therefore begin by describing the main motive, listing its statements, finding and describing its polyphonic counterparts, proceeding then to the secondary material and giving an overview of the structural details – now with their proper names – at the end.

 

a) The main motive (M1)

The main melodic idea upon which this "invention" rests is a little over one bar long. It begins and ends on a downbeat. Consisting exclusively of sixteenth-notes, it describes a curved line in which a zigzagging ascent to the fifth in the first half of the bar is answered by a full descending scale in the second half. Surprising in this line are the pitches at the outset of the descent: they represent the melodic minor scale (usually used only for ascending). The dynamic shaping had certainly best follow this very straightforward curve. Thus the climax falls either on the octave D# (if the tempo is taken slow enough to feel an offbeat sixteenth-note) or on the fifth A# (which, as it represents the strong beat, is the rhythmically more convincing choice, particularly at a swifter pace).

There are altogether thirteen statements of M1 in the "invention". Most of the statements appear in pairs on the same note. The following table gives the keys of all the paired statements in brackets. (Capital letters stand for major, lower-case letters for minor keys).

1.

bars 1/2

U (d#)

7.

bars 17/18

L

2.

bars 2/3

L (d#)

8.

bars 19/20

U

3.

bars 9/10

L (F#)

9.

bars 28/29

L (d#)

4.

bars 10/11

U (F#)

10.

bars 29/30

U (d#)

5.

bars 11/12

U (a#)

11.

bars 32m-33m

U

6.

bars 12/13

L (a#)

12.

bars 33m-34m

L

13.

bars 34m-35m

U

M1 experiences a number of small changes in the course of the piece. In bars 18d, 20d, 33m and 34m, the descent in the second half of the motive begins not from the octave but only from the seventh, with the effect that it reaches the keynote on the final sixteenth-note of the bar. Consequently, the interval to the following downbeat is modified in all cases. In bars 18 and 20 it is raised to a fourth, while in bars 33 and 34 the transition to the counter-motive is such that the strong-beat note is not perceived as belonging to the motive.

 

b) The counter-motives (CM)

Bach creates two companions for M1. The first (CM1), introduced in bars 2/3, plays around the keynote and fifth. It commences with three eighth-notes (the leading-note followed by the keynote and its octave), centers in an ornamented descent, and concludes, after a rest, with another leading-note/keynote pair. The single climax of this counter-motive falls on the middle beat and thus coincides (almost or literally) with that of the main motive.

CM1 recurs several times, albeit heavily disguised. In bar 9, the sixteenth-note figure begins with F#-E# (instead of E#-F#) and ends on the octave. The ornamented descent is the same, but the resolving final pair is omitted. In bar 12, one recognizes the initial eighth-notes although the octave jump is diminished to a sixth. The descent, twice as fast as before, occurs an octave lower than expected and is followed by another jump; the ending (Gx-A#) appears faster and a little earlier than it should, with unexpected notes following. Finally in bars 28 and 29, only the descending figure, now even on a different degree of the scale, can be identified.

The second counter-motive (CM2) is introduced in the second half of the prelude (see U: bars 17/18). It is characterized by a symmetrical structure in which the second half acts as an inversion of the first. There are two broken seventh chords in the same rhythmic pattern (on beats 1 and 3 respectively), and two "turn"-figures (beats 2/3 and 4/1). Regarding its dynamic design, the rhythmic details – surprising in a composition with an otherwise so simple rhythmic pattern – demand that the climaxes fall on the two syncopations. This counter-motive thus appears much more polyphonically independent than the first. CM2 recurs four times, in L: bars 19/20, L: bars 32m-33m, U: bars 33m-34m and, considerably modified, in L: bars 34m-35m.

 

c) Other motives

The "invention" features three other motives besides M1. Naming them creates a little problem as the first obviously derives from the main motive, and the second, though not related to the main motive, derives very definitely from the previous one. To avoid confusion, they will appear here with consecutive numbering regardless of their relationships.

The initial two statements of M1 are followed by M2 (see U: bars 3/4). It commences on the second eighth-note of the bar with a fragment of the zigzag known from M1, and continues with a short descent also reminiscent of the main motive. The two segments are then complemented by a fourth leap in longer values and an ornamented tied peak note, a pattern which distinguishes this motive immediately from the preceding main material. M2 is imitated in stretto (see L: bars 3m-4m). The sequence of both the original and its imitation (see U: bars 4/5, L: bars 4m-5m) features a strongly varied first half and thus severs all ties with M1. (One could call this M2a.) A partial sequence of the fourth leap follows (see L: second half of bar 5) and can be recognized, without its ornament, at the beginning of the accompaniment figures in the three following bars. This is important as Bach creates, with these broken chords in the lower voice, a gradual descent which contributes to the shaping of this portion of the prelude: E#-G#-C# (bar 4), D#-F#-B, C#-E#-A# (bar 5), B-D#-G# (bar 6), A#-C#-F# (bar 7), G#-B-E# (bar 8), F# (bar 9).

M2 recurs, complete with imitation and varied sequence but in inverted voices, in bars 21-23. In addition, its first half which we discovered to be so closely related to M1, reappears in bars 13/14 (three times, in almost complete parallel motion) and 30-32 (four times – twice with neutral accompaniment, twice with a disguised parallel). M3 also appears in two versions: as a trunk, and with an extension. The trunk commences like M1 and M2 after the strong beat and ends on the next strong beat (see U: bar 5 E#-E#). Among the eight regular sixteenth-notes, the initial four and the last are melodic, describing a turn-figure and, after interrupting escape notes, its resolution. (The melodic idea is thus conceived as E#-D#-Cx-D#-----E#.) M3 is sequenced in this format (see bars 5-6d: D#-D#). In three further sequences, the non-melodic inner segment is extended and thus lengthens the motive to a full-bar scope (M3a see bars 6-7d: C#-C#, 7-8d: B-B, 8-9d: A#-A#).

The dynamic shaping of this motive takes the play with melodic and non-melodic components into account. The first four sixteenth-notes sound in a more intense legato and grow in tension, the broken-chord insertion is lighter both in touch (quasi legato) and in tension (diminuendo), and the final note, while soft at the end of the decrease, picks up the more intense tone color of the melodic notes.

 

d) The structure of the prelude

Section I introduces all motives, in the following order:

-

two M1 statements, the second accompanied by CM1 (bars 1-3d)

-

two M2 statements in stretto (bars 3-4m)
followed by two M2a statements in stretto (bars 4-5m)

-

two M3 statements (bars 5-6d)
followed by three M3a statements (bars 6-9d)

The upper voice is leading in presenting each new motive. After the initial statements of the main motive, the remainder of the first section is dominated by descending peak-note lines in both parts creating a protracted decrease in tension (see U bars 3-9d the final notes of each motive,: G#-F#-E#-D#-C#-B-A#; L bars 4-8 the final notes of M2 and its partial sequences: C#-B-A#-G#-F#-E#).

 
Section II combines a doubled set of M1 statements with partial quotations of M2 and a free cadential close:

-

two M1 statements in the relative major key (bars 9-11d)
followed by two M1 statements on the dominant (bars 11-13d)

-

three parallel statements of M2 (first half) (bars 13-14m)

-

complemented by free figurative work (U) over
a slightly elaborate cadential bass pattern (bars 14m-16)

As the second pair of M1 statements brings the voices in inverted order and thus creates the effect of an ascending sequence in the upper part (see bars 10/11), the beginning of this section expresses an increase in tension. The M2 sequences do not reply with the expected relaxation since Bach transposes the last segment (U: bar 14) a fifth higher. The increasing tendency is then continued through the peak notes in the upper voice (see bars 14/15: Fx-Gx-A#) and only released from bar 15m onwards. The rhythmic density of the cadential close thwarts true relaxation.


Section III combines all motives from section I as well as several features from section II in a new way:  

-

one M1 statement (L) accompanied by CM2 (bars 17-18d)
followed by one quote of M3a (U) (bars 18-19d)

-

one M1 statement (U) accompanied by CM2 (bars 19-20d)
followed by one quote of M3a (L) (bars 20-21d)

-

one parallel statement of M2 (first half) (bar 21)
followed by two M2 statements in stretto (bars 21m-22)
followed by two M2a statements in stretto (bars 22m-23)

-

one bar with free figurations (from bar 15) (bar 24)

-

followed by three M3a statements (bars 25-27)

Due to the heightened rhythmic density of CM2 and its dynamic independence from M1, the beginning of this section represents the greatest tension so far within this prelude. The alternation of this intense combination with the dynamically fairly weak M3a creates strong contrasts from bar to bar. (Note that in bar 20, the upper voice is accompanying with non-motivic material which, despite its compelling syncopations, must be softer than the leading lower voice.) This pattern of dynamic ups and downs continues in bars 21-23m (where descending sequences create diminuendo) / bars 23m-24m (where ascending sequences in L, ascending lines and intensified rhythm build up tension) / bars 24m-28d (where descending sequences create diminuendo).


Section IV presents yet another combination of thematic material:

-

two statements of M1, both with CM1 (bars 28-30d)

-

M2 (half) with sequence/neutral accompaniment (bars 30-31d)
M2 (half) with sequence, in hidden parallels (bars 31-32d)
followed by half-bar cadence (resolving into I7) (bar 32)

-

three statements of M1, all with CM2 (bars 32-35m)

-

complemented by free figurative work (U) over
a cadential bass pattern (bars 35m-36)

This section, while not as dramatic as the previous one, admits less relaxation than any section before. The development from the polyphonically less intense M1/CM1 combination to the much more dramatic M1/CM2 match alone would provide a buildup. In addition, the final three statements of M1 are conceived with growing harmonic tension. Even the M2 sequences which, in themselves, convey decreasing tendency, are here set in a pattern of increasing textural density (bars 30/31). Only the figurative close, which picks up immediately from the main motive, brings forth a degree of relaxation and thus concludes the prelude on a moderately soft note.

 

 

WTC II/8 in D# minor – Fugue

 

II/8.2.1 The subject

The scope of this subject does not pose a problem: while there are – as Bach demonstrates masterfully – a host of possible harmonizations throughout the phrase, the return to the tonic occurs unambiguously on the downbeat of the third bar. This gives the subject a very balanced length, with the final note complementing the initial rest to make exactly two bars.

The pitch pattern also displays a clear direction. Commencing on the keynote which is reinforced by a short deviation to the leading note, the subject contains three ascending motions (see the step D#-E# in bar 1 and the fourths D#-G# and E#-A# in bar 2) before ending in a downward motion (see A#-G#-F#, bars 2/3). The rhythmic pattern includes eighth-notes and sixteenth-notes as well as two dotted quarter-notes, both placed as syncopations. This rhythmic structure can be regarded as having a bearing on the perception of the melodic shape. As the second of the fourths is metrically unaccented while the preceding rising motions are reinforced by the two syncopations, we may hear the following line underlying the subject: D#-E#-G#---F#.

The harmonization of the given melodic unit is open to a variety of progressions. (Compare e.g. the entirely different solutions of the statements in bars 7/8, 21/22 and 40-42.) Thus the initial note repetitions can represent the tonic or the subdominant, while the leading note Cx may stand for the dominant or the tonic relative; the syncopations epitomize either dominant-ninth and subdominant respectively or dominant relative and dominant, and so forth. (Ample use of chromaticism due to artificial leading notes in the secondary material adds to the confusion – but also to the beauty of this fugue; see e.g. the almost complete twelve-tone content in bass and tenor of bars 21/22.) The only fact that seems unchallenged is the return to the tonic on the final note – and not a moment before. This, as well as the curve underlying the melodic shape, determines the phrase structure as simple, without subdivisions. (The following harmonic illustration can be found in L. Czaczkes' analysis.)

(ex. 22)

 

The dynamic outline follows the prominent features. The tension increases successively in the leading note, through the first syncopation which is reached in stepwise motion, until the second syncopation which is approached by the fourth interval. After this climax, the tension subsides quickly throughout the final half bar.

 

II/8.2.2 The statements of the subject

There are sixteen subject statements in this fugue.

1

bars 1-3

A

9

bars 23-25

A

2

bars 3-5

T

10

bars 25-27

B

3

bars 7-9

B

11

bars 27-29

S

4

bars 9-11

S

12

bars 30-32

A

5

bars 15-17

B

13

bars 32-34

T

6

bars 17-19

A

14

bars 40-42

B

7

bars 19-21

T

15

bars 43-45

S

8

bars 21-23

S

16

bars 43-45

T

 

(ex. 23)

 

The subject receives a real answer without any interval adjustment. The modification of the first step from a minor second to a minor third, i.e. the kind of change which is expected in the answer, occurs later in the fugue instead, in three consecutive entries (see bars 15, 17, 19). Another entry enlarges the first step only to a whole tone and lowers also the step above the keynote (see bar 32: C# and E). Two entries feature a Picardy-third modification at the end: after an entire statement in minor mode, the final note is raised to the major third (see bars 27 and 29).

The fugue contains one stretto, one parallel and one inversion. The overlapping occurs in bars 23-25 where the entry in the alto is followed first by a fake beginning in the tenor (see bar 24: E E E D# E# Fx) and then by a complete entry in the bass. The inverted subject statement is also the one which appears in parallel to another entry (see bars 43-45: soprano subject in original shape, tenor subject in inversion).

 

II/8.2.3 The counter-subjects

Bach has given this subject one companion which, however, disappears in the second half of the fugue. It is introduced in bars 3-5 against the answer. Characterized by its ascending three-note figure, it seems like an ornamentation of a simple scale (see bars 3-5, alto: E#-D#--E#--F#--G#--A#).

While it shares many features with the subject (compare e.g. the ascending three-note groups with the rising fourths), it differs significantly in that it presents only one gesture: the rise of both pitch and tension, versus the curved shape in the subject. CS1 recurs, with slight modifications, in bars 7-9, 9-11, 15-17, 19-21, and 21-23. The example shows the dynamic outline in the contrapuntal setting of subject and counter-subject (ex. 24).

 

 

II/8.2.4 The episodes

We can distinguish eight subject-free passages.

E1

bars 5-7

E5

bars 29/30

E2

bars 11-15

E6

bars 34-40

E3

bar 23 (eighth-notes 2-5)

E7

bars 42/43

E4

bar 27 (eighth-notes 2-5)

E8

bars 45/46

The episodes of this fugue establish two distinct motives. M1 is introduced in E1 where it dominates the uppermost voice (from B# in bar 5 to F# in bar 7). It recurs in E2 (see bars 11-13: T, bars 13-15: A) and in E6 (see bars 35-37: T) where its second half is sequenced (see bars 37/38). A four-note figure which accompanies this motive's first appearance (bar 5: B#-A#-A#-D#) also recurs (see bars 37/38: A). M2 appears in a preliminary shape already in E4 (see bar 27: T, from B to C#) but gains its full size only in E6 where it appears followed by its sequence (see bars 36/37: S). Its extension exposes a descending sixteenth-note group (see bars 38/39: S) which is imitated and sequenced throughout the remainder of E6.

Four of these subject-free passages suggest a harmonic conclusion, but in only one of them is this conclusion identical with the end of the episode (see E8 where the cadence ends not only the episode but the entire piece as well).

-

In E3, the soprano features a traditional closing formula (keynote – leading note – keynote), but this formula with its cadential return to D# major on the downbeat of bar 24 overlaps with the subject entry in the alto.

-

Similarly, the cadential formula in bars 29/30 (E5) of the F# major cadence concludes only on the fourth eighth-note of the next subject entry.

-

In E6, by contrast, the cadential close occurs after the first 12 bars (see bar 35 beat 3), while the episode continues for another five bars. (One should therefore here speak of E6a and E6b.)


The role each episode plays in the dynamic design of the fugue is determined by its motivic and cadential content. Thus E1, E2 and E6b all create a contrasting color which is used as a kind of negative preparation (apprehension) for the following subject statement. E3, E5, E6a, E7 and E8 all conclude the preceding entry. They bring forth a slight diminuendo, but not as a change of color.

  

II/8.2.5 Character, tempo, articulation, ornament realization

The rhythmic variety, together with the high content of leading notes and other alterations, indicate a rather calm basic character. At the same time, it is obvious that the eighth-notes and longer note values carry the melodic line while the sixteenth-notes serve as embellishments. The eighth-notes may thus not be too slow. The relative tempo of prelude to fugue must be complex, last not least because of the identical time signature in both pieces which, if combined with identical pulse, would appear dull. One good way for a translation is to use an imagined eighth-note triplet (instead of the actual four sixteenth-notes in each beat) for the proportion:

a triplet eighth-note

corresponds with

a sixteenth-note

in the prelude

in the fugue

 
(Approximate metronome settings: prelude beat = 80, fugue beat = 60.)

The "translation" is achieved by mentally continuing the quarter-note pulse of the prelude and then dividing each into a triplet. These triplet-beats are then regrouped in pairs and, as soon as they are perceived as independent pulses, each pair is converted into one of the opening eighth-notes of the fugue.

The articulation in the fugue is predominantly legato. Detached playing is only necessary in connection with the jumps in the episode motives (in M1 at least once, i.e. after the D# in bar 6 alto; in its companion twice, i.e. before and after the higher A# in bar 5 tenor; and throughout the broken chord in M2) and in the cadential bass patterns (see e.g. bars 30, 35, 43 and 46).

 

II/8.2.6 The design of the fugue

There are four sections in this fugue.

-

The first section comprises the four initial subject statements and, in the middle, the contrasting E1. The section concludes on the downbeat of bar 11 (in A# minor = minor dominant, alto with resolution of the suspension). The reduced number of voices in the subsequent bars (see the rests in A: bars 12-17, S: bars 17-21) clearly confirms this section ending.

-

The second section begins with an episode (E2) followed by four consecutive subject statements. This section concludes with the cadential extension of E3 on the downbeat of bar 24 (in D# major = tonic with Picardy third). Again the number of voices is reduced to three after this conclusion (see the soprano which rests in bars 24-27).

-

The third section commences with a stretto of which the earlier entry (alto) overlaps with the preceding cadence. (It is therefore the bass entry which has more weight with regard to the structure, and which counts as the group leader in this stretto.) Short, half-bar long episodes bridge the entries in bass and soprano as well as those in soprano and alto, while the fourth entry, in the tenor, follows without interruption. The cadential close of E6a ends this section on the middle beat of bar 35 (in A# minor = minor dominant). The ensuing episode returns once more to three-part texture.

-

The fourth section again begins with an episode (E6b) before launching its bass entry. As a first subject statement in a new section this bass entry avoids the full four-part texture. Bach does not achieve this by reducing the ensemble but by changing the texture to an almost homophonic pattern (i.e. by accompanying the statement with metrically regular chords). The bass entry is followed, after the short E7, by the parallel statements in soprano and inverted tenor. The final episode E8 concludes the fugue in D# major.


It may already have become obvious from this description that there is a remarkable symmetry in the layout of this fugue.

-

Sections I + II encompass 23 bars, as do sections III + IV.

-

Sections I and III conclude in A# minor, while sections II and IV end in the tonic with the Picardy third.

-

Sections II and IV both commence with a longer episode and terminate with the very similar one-bar cadential extensions E3 and E8 respectively.

-

One essential difference between the two halves of the fugue additionally underpins the binary effect: Almost all entries in sections I + II are supported by the counter-subject, but sections III + IV do not quote it ever.


For a sketch showing the design of the D# minor fugue, see ex. 25.

.

 

II/8.2.7 The overall dynamic outline of the fugue

The first part of the fugue (i.e. sections I + II) should be considered as a whole. It establishes a pattern of intermingled-tension increase and contrast. Two subject statements in scarce texture are contrasted with a single M1 quote. The following two subject statements, which complete the buildup of the ensemble and therefore also bring forth a buildup of tension, are contrasted with a double quote of the episode motive. The ensuing four subject entries in uninterrupted succession heighten the tension even further. They are rounded off by a concise cadential formula which contributes to the expected relaxation.

The second part begins with an overlap and a stretto, thus immediately propelling the tension upwards. Three further subject entries in four-part setting, only interspersed by half-bar episodes, retain the tension at a high level which is only abandoned at the cadential close of this section. The episode which opens section IV provides the longest span of contrasting color in the fugue. The section ends, after the cadential return to the home key which deceives as a final relaxation (see bar 43), with the climax in the parallel subject statements.