WTC I/24 in B minor - Prelude

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

I/24.1.1 The prelude-type

This is a piece in three-part texture. The lower voice is conceived as a thorough bass in continuous eighth-note motion which is only given up at the end of both large sections. Meanwhile, the upper and middle voices weave a polyphonic pattern with manifold imitations and occasional freer contrapuntal passages.

With regard to the material used in these two voices it is interesting to observe that the principal motive - with its rising fourth followed by a syncopation on beat 2 and a stepwise descent - is immediately related to the fugato motive in the Eb major prelude:


Prelude in Eb major, bars 10/11 tenor Bb-Eb---D-C
with Prelude in B minor, bars 1/2 middle voice F#-B---A-G#.


I/24.1.2 The overall design of the prelude

The first harmonic progression concludes in bar 4. The lower voice, after the prominent octave jump on the dominant note F#, ascends in a segment of the melodic minor scale until the keynote B on bar 4d. The upper voice, however, diverts its expected course at this very moment with a jump to the F# before reaching the keynote on the second beat, which is also where the middle voice resolves its suspension. Thematically, this cadence marks (belatedly) the end of the initial statement of the extended motive in the upper voice. In its actual position of overlap, it can certainly not be regarded as a structural caesura.

The second harmonic close occurs in the middle of bar 7. The cadential-bass pattern indicates a modulation to D, the relative major key; this is supported by a typical closing-formula in the soprano (D-C#-D). With two traditional formulas in the outer voices and the simultaneous resolution in all three parts, this cadence clearly represents a structurally relevant close. The sixteenth-note figure in the upper voice, unique in this composition, makes it possible to hear the third beat in this bar both as a resolution to the preceding cadence and as the upbeat to the subsequent syncopation, i.e. as the beginning of a new statement of the motive.

Further cadences in this prelude often make it difficult to distinguish whether a harmonic close marks the end of (only) a phrase or that of a structural section.

A progression of keys in the same order as the one just described can be found in the second half of the prelude where a phrase-ending cadence in D major on the downbeat of bar 21 is followed by a structurally more relevant one in F# minor on the middle beat of bar 27. After this, the sequence closes in E (bar 29) - the last perfect cadence for a long time.

Strangely, those harmonic closes which can be expected to be the most straightforward, i.e. the ones before the repeat sign and at the end of the composition, present themselves as evasive:

On the downbeat of bar 16, the traditional patterns - this time in the lower and middle voices - indicate the return to the tonic B minor. Yet the next two bars which, with their growing note values and eventual stop, determine a definite structural break, depart again from this tonic and end in an imperfect cadence before the repeat sign.
Towards the end of the piece, the listener's anticipation of a return to the tonic in the middle of bar 42 is deceived by the sudden twist to the chord on VI, and when B minor is finally regained (in the middle of bar 46), it takes quite a while for the higher voices to give in and settle.



I/24.1.3 Practical considerations for performers

This is a rather calm piece, with complex rhythm including manifold syncopations, and distinct melodic tension between the notes. The tempo as given by Bach, one of the very few tempo indications found in the Well-Tempered Clavier, is Andante; the articulation is legato. Interruption of the continuous sound flow occurs only in the context of phrasing.

The score contains two ornaments, both located at the end of the first large section (see lower voice: bar 16, upper voice: bar 17). The trill in the lower voice resolves properly on the next downbeat and is therefore note-filling with a suffix. As it is approached in stepwise motion, it begins on the main note. Although sixteenth-notes do not play a major role in the rhythmic pattern of this prelude, they are nevertheless the fastest note values to which the speed of the shake in the trill has to relate. The appropriate note values in the trill are therefore: an initial sixteenth-note due to the beginning on the main note, followed by thirty-second-notes. The ornament in the upper voice designates a short mordent. It, too, commences on the main note and contains either three or (better) five fast notes (C#-D-C# or C#-D-C#-D-C#).

Phrasing is a very important issue in this prelude. While the thorough-bass line in the lower voice is not conceived with melodic qualities and should obviously remain without any interruptions, the upper and middle voices require careful structuring in order to fully realize their potential. In ex. 62 below, these two parts have been written out in two staves for easier reference, with detailed indications of the thematic material, the corresponding phrasing, and the structural units.


I/24.1.4 What is happening in this prelude?

The first section of the prelude (until to the repeat sign) is built entirely on two motives, M1 and M2. Both are introduced in the middle voice and imitated in stretto, with some modifications, in the upper voice. The principal motive M1 was already described above; it consists of a fourth interval ascending to a syncopated half-note, followed by a quarter-note descending stepwise to the subsequent downbeat. (This final strong-beat note changes its value throughout the piece.) The second motive M2 commences with a two-beat syncopation and descends in two eighth-notes to the next strong beat. (That this motive does not, as M1, begin with a fourth-upbeat, may not become quite clear in the first statement of bar 2; further appearances in the prelude, however, confirm this beginning.)

The first phrase of the prelude contains two group statements: the initial middle-voice statements of M1 and M2 and their stretto imitations, starting half a bar later in the upper voice, in which the final note of M1 melts with the beginning of M2, and an M1 entry in the upper voice (bars 4/5) imitated now in the middle voice (ending rhythmically varied). A further M1 statement, this time with a rhythmically varied beginning, may be recognized in bars 6/7. The stretto statement in the upper voice bends its final note back upwards and thus creates a well-known closing-formula. (All details may be verified in ex. 62 below.)

This pattern of consecutive stretto entries with changing leadership are further developed in the second and third phrases. The second phrase features a string of ascending M1 sequences in the upper voice which follow one another in such a way that the final note of one serves simultaneously as the beginning of the next; all are imitated after half a bar. The same process can be observed, with the middle voice in the lead, in the third phrase. The latter sequences in both patterns feature variations - most are those already established in the first phrase, only one detail is new (see bar 14, middle voice). After the perfect cadence in bar 16, an extension completes the section with a closing formula. As was already mentioned, this formula ends in an imperfect cadence and thus creates a strong anticipation for a repetition of the entire first half of the prelude.

In the second section of the prelude Bach introduces seemingly new material which is, however, all related to the two earlier motives. The first motive to appear here, introduced like the two earlier ones in the middle voice, consists of three eighth-notes leading to a strong beat. The pitch pattern contains one ascending fourth followed by descending steps - i.e. M3 (as it will be called to avoid confusion) is conceived as a rhythmical variation and diminution of M1. This motive reigns, extended through a few linking notes in each voice, in the short fifth phrase of the prelude.

M4 enters after the D major close in bar 21. It is rhythmically close to M3 with three eighth-notes leading to a strong beat, but its pitch pattern points in a single direction - as in M2. The motive is introduced ascending in bar 21, but is later also presented descending, e.g. in bars 23 and 26.

After a closely knit pattern with alternations of M4, M3 and M2, the middle segment of the fifth phrase displays a complementary-rhythm pattern with half-notes and syncopated half-notes (see bars 24-26) which closes with M2. (We shall meet this again in the subsequent phrase.) The closing-formula of this phrase, as well as that of its modulating extension, presents yet another motive, made up this time of the three ascending eighth-notes from M4 and a diminution of M1"' (that was the variation of the first motive which sounded like the traditional closing-formula). This new motive, here called M5, also serves to indicate a cadential close (see M5 in bars 27 and 29, middle voice).

The sixth phrase (which begins on the fourth beat of bar 29) sets out with motives that are by now familiar: in the upper voice, M2 gives way to a variation of M5 and partial sequences thereof, followed by a string of M4 sequences. The middle voice, however, having accompanied for several bars, presents a sixth motive which is to play an important role in this phrase. Related to M2, it commences with a syncopation followed by three eighth-notes leading to a strong beat; the direction, however, is changed to describe a curve, with the interval of a third between syncopation and first eighth-note. This motive, M6, soon takes over all activities and from bar 36 onwards appears in stretto between the two voices. The phrase ends similarly to the preceding one: a segment with complementary rhythm (half-notes and syncopated half-notes) ending with M2 statements (compare bars 39-41 with bars 24-26) is followed by a closing-formula featuring M5 in the middle voice (compare bars 41/42 with bars 26/27).

After the interrupted cadence in bar 42, the final phrase presents the last motive of this prelude: M7 consists of a syncopated quarter-note followed by a eighth-note which jumps up to the strong beat in the interval of a fourth (perfect, diminished and augmented fourths alternate here). Introduced in the middle voice of bar 42, this motive is then imitated and sequenced in ascending direction, before giving way to the final closing-formula.

As a conclusion it may be stated that this prelude builds on a number of motives which are introduced one by one, and which all betray some kind of relationship with the two initial ones. These motives are confined to the two higher voices, while the lower voice maintains a steady pace of eighth-notes in thorough-bass style. The piece thus conveys unity and development in a unique blend.

Asked to describe the structural design in a simplified pattern one might make the following comparison.

The first section of the prelude consists of three phrases plus a cadential extension in - roughly - an a b b' c pattern.
* The initial thematic phrase introduces the first two motives as well as the rhythmic pattern (which, for the melodic voices, consists primarily of quarter-notes and syncopated half-notes).
* The two phrases in the center of this section display structural analogies, particularly in their first halves.
* A short closing-formula leading to an imperfect cadence completes the section.
The second section of the prelude consists of four phrases; a roughly similar design can be recognized.
* The initial phrase introduces the third motive with the diminution of the principal figure; at the same time it announces a shift in the predominant rhythmic values, from quarter-notes and half-notes to eighth-notes and quarter-notes.
* The two phrases in the center of this section display structural analogies, particularly in their second halves.
* A shorter phrase with a new motive and a different closing-formula completes the prelude.

At the same time, the second section must be comprehended as an intensified development of the first.
It is much longer (30 bars against the 17 bars of the first section)
It uses far more motivic material (M3, M4, M5, M6, M7 are new, and M2 recurs in addition, against only M1 and M2 in the first section)
The introduction of new material is spread through the entire section, with motives being introduced in bars 18, 21, 26/27, 32/33 and 42/43, while in the first section, the two initial motives were both presented already in bars 1-3
Two of the phrases in the second section comprise distinct subphrasing with cadential closes (see bar 19m: E minor preceding the D major close in phrase IV, and bar 27m: F# minor preceding an E minor close in phrase V); similar subphrasing in the sixth phrase is impeded at the last moment by a raised upper-voice note (see bar 32m the G major chord with G#); finally, even the final phrase reaches the subdominant key E minor in a V-I progression (see bar 44m) before terminating in B minor. In the first section, only the initial phrase contains such subphrasing (on the downbeat of bar 4), yet conversely to all other subphrases mentioned, this one is not harmonically active but simply confirms the tonic.

In terms of the development of tension in each phrase, the composition contains:

In the first section

a rounded phrase I, with two gentle increases and decreases,
followed by two dynamically active phrases which, in the ascending patterns of their sequencing stretto, raise the level of tension considerably and climax in bar 14, in the middle of the third phrase,
and an extending subphrase bringing a relaxation which, due to the imperfect cadence, remains somewhat incomplete.

In the second section

two phrases (IV and V) both commencing with heightened tension but featuring predominantly descending lines (see particularly in bars 22-26 the upper-voice descent from B2 to E#1; similarly in the middle voice),
followed by phrase VI which begins again with descending lines but surprises, after its thwarted G-major subphrasing, with a large-scale ascent in both voices, intensified in its latter portion by chromatic steps in the upper voice (see in bars 32-38, U: G#1 to B2, M: E1 to F#2). It is interesting to notice that these seven bars are also the only ones in the prelude where the lower voice emancipates itself from a mere accompanying function and develops figures of its own (see the eight-eighth-note figure in bars 32 (D) to 33 (B) and the inverted curve in bars 36 (B) to 37 (C#) both of which are sequenced twice). This passage must be regarded as the climax of the prelude. Its position in the structural layout of the prelude corresponds with the (lighter) first climax: one occurs in the middle of phrase III, the other in the middle of phrase VI, the third phrase of the second section.
The final phrase is not restricted to a simple closing-function but builds up its own little climax on the middle beat of bar 45. The metrically unusual cadential close (in which the tonic is reached on the middle beat; see bar 46), combined with the obvious reluctance of the upper voices to give in to a final release of all tension, create a closure to this prelude which can be interpreted either as hesitant or as fairly powerful - and be played accordingly, with either a return to complete piano or a rich, mezzoforte ending.


WTC I/24 in B minor - Fugue

I/24.2.1 The subject

The subject of this fugue is exactly three bars long. It begins after a eighth-note rest and ends on the downbeat of bar 4. This downbeat seems, at first glance, like a melodic return to the note from which the subject started. At the beginning, however, the F# was the fifth degree of the tonic chord (as can clearly be seen in the first half bar), whereas the same pitch in bar 4 serves now as the root of the minor-dominant harmony to which the subject has modulated. (For more details on the harmonic background see below.)

Pitch and rhythm within this phrase constitute very special cases. The rhythm consists, with the exception of the ornamented penultimate note, exclusively of eighth-notes. This rhythmic pattern is, however, not characteristic of the entire fugue where sixteenth-notes, quarter-notes and a variety of tied notes abound. The subject's pitch pattern, particularly if considered for a moment without Bach's slurs, includes a great number of large intervals besides the two obvious broken chords, and an almost equally large number of semitone steps besides only two whole-tone steps (before and after the trill). This unusual combination of intervals is again not shared by other components of the fugue's material; outside the subject, stepwise motion in regular diatonic progression prevails.

With regard to its phrase structure, this subject can be split into two very unequal segments. Both begin with a falling broken chord (compare bar 1 eighth-notes 2-4 with bar 3 eighth-notes 2-4). The first subphrase then winds its way through six note-pairs before coming to a halt on the only unpaired note, the B# on the downbeat of bar 3. The second subphrase is much more concise, comprising only the target note to the broken-chord upbeat and its harmonic resolution.

When investigating the harmonic background of the subject it is vital first to determine the nature of the note-pairs. Slurred by Bach himself, each pair reveals the relationship of appoggiatura-resolution. Having found this, one can safely claim that only the resolutions (i.e. the second note under each slur) are essential for the harmonic outline, while the appoggiaturas create additional harmonic relationships of secondary order. The example visualizes the two layers of harmonic events and analyzes Bach's harmonization as found e.g. in bars 21-24 of the fugue (ex. 63).

When determining the dynamic outline of the subject, one is looking for tension-enhancing features in each of the two sub-phrases, and will then establish a relationship between the two climaxes. The highest degree of harmonic tension within the initial two bars is reached in the chord which marks the modulation, i.e. in the C#7 which determines the second half bar 2. Within this half bar, the D natural particularly captures attention. This note is further exceptional in two respects. In terms of structure, it appears as the peak of the ascending sequences (B-A#, C-B, D-C#). With regard to its scale degree it represents the sixth in F# minor which serves as a secondary leading-note.

The climax of the second subphrase is the long G#. This note again stands out for several reasons. It is not only much longer in duration than all other notes in the subject, but also incorporates the two most essential steps of the target-key cadence: the subdominant (as a six-five chord) and the dominant of F# minor. Balancing these two climaxes against each other, one can observe that the second represents natural tension which is resolved immediately afterwards, while the first expresses artificial tension which, due to the structural cut between B# and C#, is only indirectly released. On a higher structural level one could thus claim that the first subphrase creates tension which is resolved in the second one.


I/24.2.2 The statements of the subject

This fugue contains thirteen full subject entries. Another seven are incomplete; they are marked with asterisks in the table below:


bars 1 - 4

A 11. bars 42/43 A*
2. bars 4 - 7 T 12. bars 43/44 B*
3. bars 9 - 12 B 13. bars 44 - 47 T
4. bars 13 - 16 S 14. bars 47 - 50 B
5. bars 21 - 24 A 15. bars 53 - 56 T
6. bars 30 - 33 T 16. bars 57 - 60 B
7. bars 34/35 A* 17. bars 60 - 63 T
8. bars 35/36 S* 18. bars 69/70


9. bars 38 - 41 B 19. bars 70 - 73 B
10. bars 41/42 S* 20. bars 74/75


(ex. 64)

The most prominent modification of the subject is of course the shortened version, particularly since the fragment Bach chooses is of exactly the same length each time, breaking off after the third note-pair. Another expected change occurs in the tonal answer which adjusts the intervals in the initial broken chord and in the first note-pair. Further alterations include the final resolution which may be delayed (see bars 46/47) or omitted (see bars 15/16, 55/56, 62/63). Strettos are not used; all apparent combinations feature an abridged first entry in the lead (see nos. 7/8, 10/11, 12/13, 18/19).


I/24.2.3. The counter-subject

Bach has invented one counter-subject for this fugue; it is introduced against the second subject statement, in the alto part of bars 4-7. Consisting of three segments which are often used separately, it is extremely versatile and plays a vital role both as an accompaniment to the subject and, represented by its components, in the episodes. (The segments will be referred to as CSa, CSb and CSc.)

CSa (see bar 4: E#-F#) contains two irregular ascents in sixteenth-notes
CSb (see bars 4-6: F#-B) includes a diatonic descent in quarter-notes ending in a do-si-do (keynote / leading-note / keynote) figure
CSc (see bars 6/7: C#-D) moves again in sixteenth-notes.

While in the initial statement of the counter-subject CSa and CSb have one note in common (the F#), Bach often later separates the two segments and allocates them to different voices. (See e.g. bars 9-12 where an inversion of CSa appears in the currently highest voice which is the alto; the tenor follows with CSb/CSc. Similarly in bars 13-15: CSa inversion in tenor, CSb/CSc in bass.)

All three segments suffer modifications. CSa, more varied than the other two, appears shortened (see e.g. bar 30) or lengthened (see e.g. bar 38), inverted or even completely altered in pitch; CSb is frequently shortened at the beginning and/or varied at the end, while CSc changes only its final interval.

Here is a complete listing of the CS-segments:

CSa: bar 4 9 13 21 30 34 38
42 43 44     53/54   57/58
B S S     A   A
CSb: bar 4/5 9-11 13-15 21-23 30-32   39/40      
A T B S S   S      
CSc: bar 5/6 11/12 15/16 23/24
    40/41       46/7 50   56
    S       A S   S

Concerning dynamic shape, the first two segments (whether occurring in the same voice or split into two) build one curve with a crescendo in CSa and a very gradual diminuendo in CSb. The third segment CSc creates its own little build-up and relaxation within the few notes it comprises, due to the very prominent pitch ascent and subsequent fall. This counter-subject acts as a fairly regular companion to the subject; it accompanies (in more or less complete version) the subject entries in bars 4-7, 9-12, 13-16, 21-24, 30-33, 38-41, 44-47, 47-50, 53-56, 57-60 and 70-73.

Besides this counter-subject, there is another short motive which serves several times to support the beginning of a subject entry. As this motive materializes only in the context of a subject entry but never in an episode, it must be regarded as a fragmentary second counter-subject and will therefore be referred to as CSd. This motive is easily recognizable: with its syncopation and ensuing sixteenth-note figures it constitutes a single relaxing gesture. It is introduced in bar 21 (S), against the beginning of the fifth subject entry, where its relationship to CSa becomes most obvious. It recurs in bars 34 (S), 35 (A), 38 (T), 41 (A) and 42 (S), almost exclusively against incomplete subject entries. The sketch shows the phrase structure and the dynamic design in the primary material of this fugue (ex. 65):


I/24.2.3 The episodes

This fugue contains twelve subject-free passages*.


bars 7 - 9 E7 bar 47
E2 bars 12/13 E8 bars 50 - 53
E3 bars 16 - 21 E9 bars 56/57
E4 bars 24 - 30 E10 bars 63 - 69
E5 bars 33 - 34 E11 bars 73 - 74
E6 bars 36 - 38 E12 bars 75/76

*The incomplete subject entries have here been counted among the essential subject statements, both because of their substantial material and because they appear accompanied by counter-subject segments. This is, of course, a matter of interpretation. The theoretically equally possible concept of regarding these incomplete statements as subject-related episode material would lead to slightly different results in the counting of the episodes:

E4 bars 24 - 30 E10 bars 63 - 70
E5 bars 33 - 38 E11 bars 73 - 74
E6 bars 41 - 44 E12 bars 73 - 76

There are only particles in these episodes which derive from the subject. Two are "fake entries": in bar 19, the alto (which is otherwise silent in bars 17m-21d, i.e. during almost the entire E3) presents the falling broken triad from the subject beginning; it thus anticipates the true alto entry in bar 21. Exactly the same occurs with the fake tenor entry in bar 28; the tenor had withdrawn in bar 21 and only resurfaces in bar 30. In a third instance (see bar 16), the tenor imitates the falling broken chord, the half-note and its resolution from the subject's second subphrase, but with the pitch pattern of the subject beginning (see the sixth interval).

The first counter-subject is all the more active in the episodes, contributing its third segment (CSc) to each and every one of them. Even the extremely short E7 features a partial sequence of CSc (see S: bar 47), and the episodes E2, E5 - E9 and E11/E12 are determined exclusively by this sixteenth-note figure. In the first part of the fugue, however, the CS-segment is complemented by three genuine episode motives.

M1 is introduced in E1, in imitation between alto and tenor, and recurs in E4, in parallels (see S+A: bars 24-26). It consists of three eighth-notes leading to a longer note on the strong beat.
M2 is first heard in E3 (in the bass part of bars 17-21), and recurs, likewise in the bass, in E4 (bars 26-30). It is very similar to M1: rhythmically it also consists of three eighth-notes leading to the strong beat, and its pitch only differs in the first note (an ascending instead of a descending step).


is also presented in E3. From the first sequence onwards a curved shape is established (see S: bars 17/18 E-D-C#-D-E) which then remains consistent. This motive consists primarily of sixteenth-notes. Its gentle climax falls on the strong beat in the middle of the respective curves.

None of the episodes equals a disguised cadential close. In fact, none of them contains any obvious cadential features. It needs a closer analysis to reveal those harmonic closes which do occur. Investigating the episode endings one finds that only E5 with its half-bar modulation and E12 terminate with a complete harmonic close; all others end with a suspension in one of the voices, a suspension which is resolved only at the beginning of the subsequent subject entry and thus prevents a feeling of closure.

In addition to these cadences there are two others which materialize half-way through an episode; in both cases, this occurs after a subject entry which remains somewhat "open". In bar 16, the soprano entry of the subject ends unresolved. The subject-derived fragment which follows in the tenor at the beginning of E3 determines the harmonic background as F# minor, and this key -the minor dominant in B minor - is confirmed with a perfect cadence in the first half of bar 17.

Similarly, the tenor entry in bars 60-63 ends without resolving its trill; instead, the ensuing episode E10 contains a cadential close in the home key (see bar 65, third eighth-note). In the course of any further investigation it would thus be meaningful to distinguish the following segments: E3a / E3b (bars 16-17m-21), E10a / E10b (bars 63m-65m-70). If thus two of the episodes consist of two structurally detached portions, one should go ahead and have a closer look at the others. There is in fact a third episode which can be thus divided: E4 also consists of segments E4a and E4b (bars 24-26-30).

With regard to the relationship between the episodes, it is easy to discover that E3b, E4b and E10b are very much alike; all contain M2 in the lowest voice and M3 in a pattern of imitations of the two higher voices. A more remote analogy can be found between E1 and E4a, both of which contain M1 in connection with CSc (though the pattern does not quite correspond).

The role played by each episode in the development of tension can be described as follows:


crescendo : ascending sequences


diminuendo: descending sequences


..... E3b diminuendo after a new start: descending sequences
E4a crescendo : ascending sequences
..... E4b diminuendo: descending sequences
E5 closing
E6 diminuendo: descending peak notes
E7 almost like an extension - releasing
E8 self-contained, with crescendo / diminuendo
E9 resolving previous S, building up anew
E10a closing
..... E10b diminuendo: descending sequences
E11 crescendo : ascending sequences




I/24.2.5 Character, tempo, articulation, ornament realization

A calm character and a slow tempo are clearly indicated by the heading Largo. The relative tempo to the prelude must be complex since both pieces are in calm four-four time and simple proportion would therefore give a somewhat monotonous result. There are two possible solutions between which the individual performer may choose.


three eighth-notes
correspond with
one quarter-note
in the prelude
in the fugue




one assumed triplet quarter-note
corresponds with
one eighth-note

in the prelude

in the fugue

Approximate metronome settings: prelude beats = 64, fugue beats (a) = 42, (b) = 48.

The articulation requires legato in all notes except for the few cadential-bass patterns and consecutive leaps; this means that the two broken chords in the subject are to be played gently detached. Another aspect of articulation to be pondered in the subject is the connection between the note-pairs. These should also be slightly disconnected from one another, not only because this allows the appoggiatura-resolution structure in the pair to become clearer, but also because of the underlying pattern of consecutive jumps (refer back to the melodically reduced version given earlier). By contrast, the counter-subject segments and the three episode motives all require unbroken legato.

The sole ornament in this fugue is the trill in the subject. This trill always begins on the main note as it is introduced stepwise. After an initial note of double duration it moves in thirty-second-notes (i.e. twice as fast as the faster note values in the piece). Wherever the subject ends regularly, i.e. with the resolution following the ornamented note on the subsequent strong beat, the trill is a note-filling one and ends with a suffix; in this case it would encompass fifteen trill-notes to the half-note.

The trill forms an integral part of the subject. In this fugue as in most others, the composer does not specify the trill in later subject statements, just as he stops indicating the slurs in the middle of the third entry. Both articulation and ornamentation in the subject of a fugue are such characteristic features that a performer could be trusted to observe them where applicable, without further reminders from the composer. Regarding the trill, the key word is: "where applicable". It is necessary to study the melodic and harmonic surroundings of a subject-ending (and not just the technical feasibility!) to find out where a trill is needed, where it might have to be modified and where it should be omitted. The rule of the thumb is:


if the originally ornamented note is resolved on time,
play the original trill;

if the originally ornamented note is resolved early or belatedly,
play an interrupted trill without suffix, stopping short

* immediately before the bar line (for delayed resolution)
* or before the dot (for anticipated resolution);

if the originally ornamented note is not resolved,
no trill is needed.

In this fugue, however, there are two instances where an ornament is thwarted by a literally crossing line from another voice. (In these cases, the trill may be pianistically impossible but would be played in, say, a string-quartet rendition. These cases are marked with an asterisk in the table below.) Trills in the subject-endings are thus as follows:

bar 6 (a), bar 11 (a), bar 15 (c), bar 23 (a)*,
bar 32 (a), bar 40 (a), bar 46 (b)*, bar 50 (a),
bar 56 (c), bar 60 (a), bar 63 (c), bar 72 (a).


I/24.2.6 The design of the fugue

The structural layout of this fugue cannot be deduced quite as easily as that of others.

On the one hand, this is due to the texture which is quite peculiar: although the fugue is written in four voices, only two of the thirteen complete subject entries appear in four-part setting (see the fourth statement, bars 13-16, and the last unabridged one in bars 70-73). As the latter full-texture entry only confirms what the listener already knows, i.e. that it is the final complete statement in the fugue and thus of structural importance, the former four-part statement assumes a crucial position.
On the other hand, the slightly complex appearance of this fugue is due to the absence of very ear-catching cadential closes at the end of an episode. Instead, structural understanding must rely here on the earlier investigations regarding the three cadential closes occurring within the episodes, and on the usage, so striking in this piece, of incomplete subject statements.

As has been shown, the first of the mid-episode perfect cadences occurs half-way through E3, in bar 17 beat 2. It concludes the first section and confirms that the four-part texture in the statement of bars 13-16 indeed marks the pending close of this structural entity. Section I thus contains four statements, A T B S, and encompasses the episodes E1, E2 and E3a. (This in itself would not be remarkable at all. What does appear both unusual and ingenious is the fact that E2 displays a clearly relaxing tendency - an attentive listener gets the impression that the exposition of the ensemble is completed after the third entry! Correlating this observation to the fact that four-part entries are in fact an exception in this four-part fugue, it seems as if Bach consciously created the impression of a three-part composition with only occasionally enhanced density in chosen spots.)

The second section thus commences with the episode segment (E3b ) which is significantly characterized by episode-material: the interplay of M2 with the M3 imitations. The corresponding episode segment which presents the same material in a very similar setting (E4a) precedes the next subject statement. These two pairs of episode segment plus subject statement are linked by material which was already in the first section identified as bridging: the rising sequences of M1 (compare E4a with E1). The section is closed by the only episode in the entire fugue which ends in a fully resolved perfect cadence (see E5 in bars 33/34).

The third section embarks on incomplete subject statements from its very outset. Including these abridged statements, this section contains altogether eight entries, i.e. A* S* B, S* A* B* T, B. Its confines are determined by the entering order of the complete statements: when the bass which had provided the first unabridged entry (in bars 38-41) sets in again (in bars 47-50), the signal is given that this round is closed. The actual closure occurs here on the final note of the bass entry which falls into a fully resolved D major chord (see bar 503).

Looking back on these three sections of the B minor fugue one could go as far as to suggest that they represent three expositions - in the sense that an exposition "exposes" new material which will later be taken up. This can be supported as follows:

The first section obviously exposes the primary material (subject and counter-subject), the episode-use of CSc (in E1, E2 and E3a), the first episode motive and its ascending sequences; last but not least it introduces the intended texture by presenting the fourth entry in four-part setting.
The second section exposes that episode-type which relies on the extended sequence pattern of M2 and M3 and which is conceived to precede, rather than follow, a subject statement.
The third section then introduces the pattern of several incomplete subject entries preceding a complete one.

The fourth section is comparably easy to determine. Its third subject statement appears, as did that in the third section, as a redundant entry (here: T B T). Moreover, this third entry is followed by the episode which was recognized as analogous to E3 in the first section: E10 also consists of two segments, the first of which concludes in a perfect cadence (bar 65 beat 2). The fact that the remainder of this episode then opens the ensuing final section is consistent as it displays the M2 / M3 combination which in section II also preceded the entries.

Seen from the same angle which earlier revealed three expositions, one now finds that sections IV and V develop that which has been presented earlier.

Section IV returns to the uncluttered structure with no incomplete entries (thus leaning on sections I and II), but imitates the entry pattern of section III (B T B becomes T B T).
Section V, on the other hand, takes up the abridged entries from section III but also the beginning with M2 / M3 from section II, and the four-part statement from section I.

The harmonic development in the fugue encompasses the following steps which confirm the layout described above:

Section I contains exclusively entries which modulate from the tonic to the minor dominant and back.
The two entries of section II are both conceived in original tonal setting (i.e. neither of them contains the features of the tonal answer). They are harmonically arranged in such a way that a return to the tonic is nevertheless granted: the first modulates i-v, the second reciprocates with iv-i.
The third section commences once more in the i - v environment but then modulates for good, so that the remaining two entries move from the relative major of the tonic to the relative major of the dominant, and back again, concluding this section in the major mode.
The fourth section begins and ends on v, leaving the crucial return to the home key in a iv - i modulation to the fifth section.

For a sketch of the design showing the fugue in B minor, see ex. 66.



I/24.2.7 The development of tension

The dynamic outline is quite different in each of the five sections.

Section I is characterized by a build-up of tension which is gradual though interrupted. The superimposed increase of tension occurs from the single-voiced entry to the four-part statement. The first episode, after an initial drop in intensity, contributes to the impression of mounting tension in its ascending sequences. Only the second episode decreases and thus suggests deceivingly (as was observed earlier) that this might be a three-part fugue and any further entry would be redundant. The full four-part texture of the fourth subject statement, however, defies this. The section thus ends on a high level of intensity which, due to the "fake entry" and the fully maintained ensemble of four voices in the concluding episode segment, hardly dwindles before the cadence.
The second and third episodes are each made up of two very nearly corresponding halves (compare bars 17-21 with 26-30 / bars 21-24 with 30-33; and bars 34-36 with 41-43 / bars 38-41 with 47-50). In the case of section II, the protracted episodes with their descending motion prepare two relatively soft statements, so that the entire section remains somewhat subdued. In section III the apparent density of material - with eight occurrences of the subject beginning - raises the overall tension level. At the same time, the incompleteness of five of the entries and the fact that they appear accompanied by the relaxing CSd restrict the dynamic development, so that only the final consecutive entries of T and B (bars 44-50) gain momentum.
Sections IV and V both begin with longer spans of diminishing tension (see e.g. the descending line in the bass of E8, bars 51-53: F# E, C# B A G# F#, and the descending sequences in E10b, bars 65-69). In section IV, the final entry is the sole statement in the fugue to do without any segment of the counter-subject; instead it is accompanied by ascending sequence patterns in two voices (see bars 60-62, soprano and alto) which help create a certain intensity. Section V, having recalled section II with its opening episode, then jumps directly to the final statement of section I. Prepared only by the incomplete tenor entry, the bass entry in bars 70-73 soon gains full four-part texture and thus provides the fugue with a glorious ending. The full texture is maintained throughout the ensuing E11 (which builds up tension in ascending sequences) and the incomplete entry, and surpassed in the five-part setting of bars 75/76.

When relating the climaxes of the sections to one another, it seems irrefutable that the endings of sections I and V represent the overall highlights. Regarding the sections in-between, a possible interpretation is to take section II as the softest, and the climax of section III to be surpassed by that of section IV.