WTC II/10 in E minor – Prelude 

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

II/10.1.1 The prelude-type

This prelude is written in polyphonic two-part texture. It is clearly based on a single motive and its variations. This motive is imitated (in the octave; compare U: bar 1 with L: bar 3), sequenced entirely and partially, and developed in different ways. All these features clearly point at a familiar genre: the invention.

 

II/10.1.2 The overall design of the prelude

A perfunctory glance reveals that the prelude consists of two halves, both repeated. The first half contains forty-eight bars, the second, which is slightly longer, counts sixty bars.

Within the first half there are no outstanding closing-formulas which would facilitate structural understanding. Harmonic processes must therefore be considered here in conjunction with particularities of the thematic development. The second half of the prelude, by contrast, features two traditional closing formulas which aid the listener's orientation.

The following list only mentions the harmonic steps, leaving an investigation into the thematic details for later. The entire prelude consists of six sections:

I

bars 1-11d

i - v

(E minor to B minor)

II

bars 11-23d

v - VI

(B minor to C major)

III

bars 23-48d

VI - v

(C major back to B minor*)

IV

bars 49-72d

v - iv

(B minor to A minor**)

V

bars 73-103

return to i:

interrupted cadence

VI

bars 103-108

return to i:

perfect cadence

(* The first ending continues with a link to the repetition in bar 1. This link uses, as a representative of the dominant chord, the major third and leading-note D#.
** This section-ending cadence is followed, as was the end of section III, by a one-bar link which modulates to D major; the relative major of the dominant.)

The two halves of the prelude are linked by important structural analogies. The following portions of the first half recur in the second half in a transposition one fifth down (or one fourth up):

bars 26-29

correspond with

bars 82-85 (voices inverted)

bars 30-36

correspond with

bars 86-92

bars 41m-47

correspond with

bars 96m-102

In addition, sections IV and V (the first and second sections within the second half of the prelude) begin with analogous portions:

  

bars 49-53d

correspond with

bars 73-77d
(voices inverted, counterpoint varied)

bars 53-57d

correspond with

bars 77-81d
(voices inverted, mode changed)

Also symmetrical are the first and second sections of the prelude's first half, but here we are dealing not with literal transpositions but with structural correspondences:

bars 1-11d

correspond with

bars 11-23d

motive, imitation

motive, imitation + sequence

motive + 2 sequences

motive + 2 sequences

To sum up:

-

Both halves of the prelude feature inner correspondences between their first and second sections. These are not literal but structural, and concern mainly the leading voice in each bar.

-

The latter parts of the two halves display very close relationship. The correspondence here involves mostly both voices and consists of literal transposition.

 

II/10.1.3 Practical considerations for performers

The prelude is based on a simple rhythm pattern with a predominance of sixteenth-notes and eighth-notes. (Exceptional thirty-second-notes occur only in bars 3, 4, 12 and 22 where they must be understood as written-out ornaments – "inverted slides" – and in bars 77 and 97 where they spell out the pitches of the trill suffixes.) The basic character of this "invention" is thus rather lively. The tempo may be fairly swift; sensing whole-bar beats is preferable to counting in eighth-notes.

The appropriate articulation consists of a light non legato for the eighth-notes, a crisp quasi legato for the sixteenth-notes, and legato only for the ornamental thirty-second-notes. One exception to the non legato in eighth-notes is signified by a slur (see U: bar 51). The question whether the following bar 52 should be understood as a varied sequence – and therefore played with a similar two-note slur – remains for the individual interpreter to decide.

There are a host of ornament symbols to be read. We find mordents, inverted mordents, turns, compound ornaments and trills.

-

Mordents occur in bars 18, 20, 51, 52 and 71. In bars 18 and 20, they form an integral part of a melodic figure. In both cases they commence on the upper auxiliary and comprise four notes. The mordent in bar 51 is approached in stepwise motion and therefore begins on the main note; a three-note shake is sufficient in the swift tempo of this piece.

The remaining two mordents are given in brackets. As the circumstances differ, the two cases must be resolved independently. In bar 52, the ornament strengthens, on the one hand, the impression of sequence to the preceding bar. On the other hand, the sixteenth-note figure C-B-C is, in fact, itself a written-out ornament; therefore an additional mordent might cause over-congestion. (An additional consideration for omitting the mordent here is that this would be the only case in the entire prelude where a sixteenth-note is ornamented; all other ornaments decorate longer note values.) The mordent in bar 71 appears in a typical cadential formula which, in Bach's style, would always have been played with an ornament, regardless of whether or not this is indicated.

-

Inverted mordents appear in bars 37-41, 92, 95, 96, 102 and 107. Their lower neighbor notes are taken, without exception, from the E minor scale. As this ornament is used twice in closing formulas (see bars 102 and 107), it might be a good idea to play the corresponding note in bar 47 (C#) with the same inverted mordent.

-

Turns can be found in bars 47, 57-59, 78, 102 and 107. The first one begins on the upper neighbor B and uses the sharpened lower note G#. Structurally identical turns occur in bars 102 and 107. Both also commence on the upper neighbor, and the first also requires a sharpened lower note (see bar 102: D#-turn with C#).

The turns in bars 57-59 all appear in the context of scalar motion and therefore begin on the main note. Within their five-note figures, the lower neighbor takes up the pitch of the preceding eighth-note (e.g. in bar 57: G#). As this ornament is integrated into a motivic figure which continues in sequences, it should be transferred also to the second eighth-notes in bars 60 (L), 61 (U), 62 (L) and 63 (U). The turn in bar 78 repeats the same five-note ornament once more.

-

Trills are required in bars 29-32 and, correspondingly, in bars 33-37, 86-88 and 89-92, as well as in bar 97. The four earlier trills are different as they serve to prolong the sound in a sustained pedal note, and do not take any part whatsoever in melodic lines. They had therefore best begin on the main note and launch their shakes in thirty-second-notes right away, so that the main note – and not the auxiliary – meets the melodic notes in the other voice. (We distinguish melodic and non-melodic trills in 18th century style: The concept for melodic trills is, to heighten the interest of the ornamented note by repeated appoggiaturas; thus an approach from the upper neighbor note is generally the rule. Wherever the melodic surroundings bring about a beginning on the main note, the initial note is lengthened so that all other beats in the bar are met by the upper neighbor note. The concept for non-melodic trills is usually, as in this piece, to sustain the sound of a note which, on a keyboard instrument, would otherwise fade far too early; here the sound itself – i.e. the main note – is the issue and therefore falls on the beats.)

These extended trills all end either with a tie or before a rest. None of them requires, or even allows for, a suffix. Instead, they all end on the last main note before the bar line.

The remaining trill in bar 97 is most straightforward as it is an ornament with melodic content: it begins on the upper auxiliary E, shakes in regular thirty-second-notes and ends with the suffix as marked by the composer.

-

Compound ornaments are found in bars 43 and 77. The former begins (as indicated by the vertical stroke at the left side of the symbol) with an appoggiatura E which resolves after a eighth-note, i.e. against the B in the lower voice. The shake that follows is that of an interrupted trill; i.e. it consists of four fast notes and stops short in a metrically weak position. This ornament may be transferred to the corresponding note G in bar 98.

The second compound ornament begins, as the convex curve signifies, from the lower neighbor C#. As it is followed by a written-out suffix, it should be interpreted as a note-filling trill. This ornament therefore shakes in regular thirty-second-notes (C#-D#-E-D#-E-D#-C#-D#).

 

II/10.1.4 What is happening in this prelude

The main motive of this "invention" is two bars long. It begins after a downbeat rest and ends on the downbeat of bar 3. The motive can be regarded as consisting of two symmetrical halves: the first, from G to B, contains a four-note ascent, a skip in the opposite direction, and a final ascending step; the second half, beginning again on G, correspondingly encompasses a four-note descent followed by a skip in the opposite direction and a final descending step.

In terms of tension, the motive's first half presents the increase, with the climax on the downbeat of bar 2, and the second half adds the complementary decrease.

In its complete and unvaried shape (but including inversions), the main motive recurs fifteen times:

1.

bars 1-3

U

9.

bars 17-19

L

2.

bars 3-5

L

10.

bars 19-21

L

3.

bars 5-7

U

11.

bars 21-23

L

4.

bars 7-9

U

12.

bars 49-51

Linv

5.

bars 9-11

U

13.

bars 53-55

Uinv

6.

bars 11-13

L

14.

bars 73-75

Uinv

7.

bars 13-15

U

15.

bars 77-79

Linv

8.

bars 15-17

U


The four inversions are followed each by two partial sequences
(see L: bars 49-53, U: bars 53-57, L: bars 73-77, U: bars 77-81).

The initial statement of the main motive is accompanied by the octave jump E. This does not form part of the polyphonic pattern but only serves as a harmonic support. It should therefore be played in neutral touch. Later statements of the main motive are accompanied by various counter-motives (CM). The unifying features in all of them can be found in the second bars:

-

CM1 accompanies the climax of the main motive with an "inverted slide" followed by an ascending seventh jump. It occurs, preceded by varying figures, exclusively in the upper voice: see bars (3)-4, (11)-12 and (21)-22.

-

CM2 features three ascending eighth-notes followed by a cadential step (fifth down or fourth up) to the final downbeat. Also preceded by varying upbeats, it occurs exclusively in the lower voice; see bars (5)-7, (7)-9, (9)-11, (13)-15; also, inverted and with varied ending, in bars (53)-55, (73)-75.

-

CM3, the only melodically distinct companion to the main motive, appears only twice: see bars 17-19 and 19-21: U.

Besides its original shape, the motive of this "invention" comes in several modifications. These are at the same time immediately derived from the main idea and independent in the play of texture and phrase structure which they trigger.

  

M1a

is introduced in U: bars 23-25d. It complements the unaltered first half of the main motive with a second four-note ascent. A note lower than the beginning, it sounds as a relaxation and ties over passively to the final downbeat.
M1a is characterized by stretto setting. It can be found in U: bars 23-25, L: bars 24-26, U: bars 25-27, L: bars 26-28, U: bars 25-27 (another entry in the lower voice appears shared by bars 28/29 and 23); L: bars 81-83, U: bars 82-84 (and in the upper voice divided between bars 84/85 and 81).

M1b

also leaves the first half of the main motive intact; it modifies the relaxing second half to a simple descending scale.
M1b appears accompanied by pedal notes sustained by long trills. It occurs in U: bars 29-32, 32-33, L: bars 33-35, 35-37; U: bars 85-87, 87-89, L: bars 89-91, 91-93.

M1c

already varies the climax of the motive. The downbeat-note is displaced a fourth down and then followed by a jump of more than an octave. This leads to a syncopated and ornamented note which now takes over both the climax and, in its tie, also the relaxation.
M1c occurs seven times; see L: bars 37-39, U: bars 38-40, L: bars 39-41, U: bars 40-42; (U: bars 93-95 varied), L: bars 94-96, U: bars 95-97.

M1d

is derived from the inversion of the main motive. It combines (see L: bars 57-59) the first half of the inverted motive with an ornamented two-eighth-note ascent terminating, in all lower-voice statements, in a descending fifth, and in all upper-voice statements, in a tie-prolongation.
M1d is confined to the prelude's second half, appearing in L: bars 57-59, U: bars 58-60, L: bars 59-61, U: bars 60-62, L: bars 61-63, U: bars 62-64.

M1e

also occurs only in the second half of the prelude. It picks up a feature which is characteristic for the inversion of the main motive: the extension to four bars by partial sequences. Yet while, in the case of the main motive, the motive's second half was repeated, it is here a play with sequences of the first half which, complemented by an extension, make up the four-bar unit.
This variant occurs, with different intervals at the end of each sequence, in L: bars 63-67d and L: bars 67-71d. Interestingly, the second statement is accompanied by the same figure in contrary motion (see U: bars 67-70d). A similar contrary movement can also be recognized in the second statement (see particularly U: bars 64/65).

The dynamic impact exerted by these motive-variants is determined both by their textural density and by the direction of their sequences. The picture is, in fact, quite simple:

-

M1a, M1c and M1d appear exclusively in stretto texture and in ascending sequences. Their dynamic value is therefore that of tension increase. (The fact that the final upper-voice sequence of M1d sounds an octave lower is due to the limited range of the 18th century keyboard.)

-

M1b appears accompanied by pedal notes – thus in a polyphonically sparse setting. All sequences move in descending direction, so that M1b induces a decrease in tension.

-

M1e plays a special role both because of its extended scope and because of the almost homophonic effect created by the mirrored parallels. The overall dynamic movement is very slightly increasing in the first statement and very slightly decreasing in the second.


The structure of the "invention" can best be shown in a table:

I

main motive
with imitation and sequences

IV

main motive inverted, extended
+ M1d, M1e + cadential close

II

main motive
with imitation and sequences

V

main motive inverted, extended
+ M1a, M1b, M1c
+ extended cadential close

III

M1a, M1b, M1c
+ extended cadential close

VI

main motive (varied) + M1b
+ cadential close

The development of tension in the first half of the prelude can be described as one large curve followed by two which are smaller in scale: after a long increase in the first section and a long decrease in the second section, the third section consists of rise (M1a, bars 23-29), fall (M1b, bars 29-37), rise (M1c, bars 37-41) and a soft final curve in the cadential extension.

The fourth section consists of diminishing tension followed by a strong increase (M1d, bars 57-63) and a soft final curve (M1e + cadential close, bars 63-72). In the fifth section, the initially diminishing tension in followed by curves similar to those in the third section: rise (M1a, bars 81-85), fall (M1b, bars 85-93), rise (M1c, bars 93-96) and a soft decline in the cadential extension up to the interrupted cadence (bars 96-103). The prelude ends with a final curve (bars 103-108).

 

 

WTC II/10 in E minor – Fugue

 

II/10.2.1 The subject

This is a long and multifaceted subject. Spanning over six bars, from the upbeat to the middle beat of bar 6, it stretches over more than an octave and includes a surprising number of distinct little motivic patterns.

When investigating into its phrase structure, one can quickly acknowledge a rough division into two contrasting segments. The first of these segments ends on the middle beat of bar 2 with a return to the keynote; its outline can be described as a slightly leaning curve (leaning because it ascends slowly but falls back in less than half of the time). The second segment is characterized by three syncopations which describe a gradual descent (see bar 2: C, bar 3: A, bar 4: F#); after some suspension, they also resolve into the keynote (see bar 6: E). Within each of these larger segments, smaller subphrases are established by way of sequences. It is interesting to observe that these smallest components set out with almost minimal length (the first subphrase is less than two quarter-notes long as the upbeat features only two out of three triplet eighth-notes), then grow longer (two quarter-notes) and longer (four quarter-notes in the third, fourth and fifth subphrase) until the final subphrase extends over two bars. (The scope of this final subphrase is achieved by what we may call an indirect extension. It is indirect because it cannot be omitted without leaving the subject incomplete. However, one might wish to try playing the final subphrase (from F# in bar 4) with the eighth-notes in the first half of bar 5 transposed one note lower and the middle beat bending back and resolving onto E: the subject could very convincingly have ended here. It does not therefore come as a surprise that Bach later uses the triplet run (from C down to E) as a motive, independent of the subject.)

The pitch pattern and the rhythmic pattern in the subject are as intricate as the phrase structure. There are ornamental steps (see e.g. the written-out turns in bar 1) as well as melodious seconds (C-B and A-G in bars 2-4), a broken chord (bar 2), two jumps created by the hidden two-part texture (see below) and the diminished seventh which, in bar 5, links the "indirect extension" to the main body of the subject. Further there are sixteenth-notes, triplet eighth-notes, dotted eighth-notes, quarter-notes, a quarter-note tied to a triplet eighth-note and syncopated half-notes.

In spite of this stunning variety of six subphrases, five kinds of intervals and six different note values there is, nevertheless, a unifying force. If one strips the subject of its written-out ornaments (bar 1), its broken chord (bar 2) and its "charm notes" (the D#-E in bars 3 and 4 which, while adding particular beauty, do not contribute to the basic line), the skeleton reads like this:

(ex. 46):

 

This line constitutes an important guide for the performer who might otherwise lose sight of the whole in the face of so many enchanting parts. It is also helpful when we set out to determine the dynamic shape of the subject. Talking first of the subordinate climaxes in each little subphrase, we find that the first three subphrases consist of sequencing crescendo gestures while the remaining three subphrases feature their climaxes on the first (syncopated) note, thus expressing a diminuendo each.

The most expressive of these subordinate climaxes is the C in bar 2/3. As the first syncopation it brings a rhythmic surprise, as the peak of the simplified line it marks the natural turning point of the tension, and as the bearer of the subdominant chord it also adheres to the logic of harmony.

The following example demonstrates both the main steps of the harmonic development and the dynamic outline in the subject.

(ex. 47)

 

 

II/10.2.2 The statements of the subject

The subject appears nine times in the course of the fugue.

1

bars 0 - 6

U

6

bars 41 - 47

L

2

bars 6 - 12

M

7

bars 49 - 55

M

3

bars 12 - 18

L

8

bars 59 - 65

U

4

bars 23 - 29

U

9

bars 71 - 77

L

5

bars 29 - 35

M

(ex. 48)

 

None of these statements displays any modification.

 

II/10.2.3 The counter-subjects

Bach invents one counter-subject for this fugue which is a very faithful companion to the subject, although it develops certain modifications. CS is introduced against the answer, i.e. in the upper-voice part of bars 7-12. The last five eighth-notes of bar 6 recur more often than not (see bar 12: M, bar 41: M, bar 49: L, bar 71: U), so that one might ask whether they do not form the upbeat of CS. Yet, as they derive directly from the subject's last subphrase (compare bars 5m-6 with bars 6m-7), and as the same figure is also widely used as episode material, its connection with CS cannot be ascertained. We therefore prefer to regard the descending scale as a link between the end of the subject and the beginning of the counter-subject.

In several later statements, the counter-subject appears either split between two complementary voices (see bars 13-18: M+U, 24-29: L+M), or it switches voices halfway through the phrase (see bars 30-35: L/U, 42-47: M/U, 72-77: U/M). The only CS entry which resembles the original shape very closely occurs in bars 50-55 (L), while the entry in bars 62-64 recalls only a fragment.

Such frequent variations of the counter-subject invite investigation into what might be regarded as its basic format. To determine this simplified line is not at all difficult when one takes, e.g., the modifications occurring in bars 13-18, bars 42-47 and bars 72-77 as guidelines. The splitting into two voices and the very free variation of the unaccented eighth-notes indicates that it is the main (half-note) beats that matter. And these half-note beats bring a surprise: what appears, at the surface, as a fairly independent contrapuntal line is actually nothing but an embellished parallel (in thirds or sixths respectively) to the subject. The main dynamic outline will therefore have to be drawn in parallel to that of the subject; within the subphrases, however, independent shaping is possible.

The following examples give first the juxtaposition of simplified subject and simplified counter-subject, then a possible interpretation of the tension processes in the two thematic phrases.

(ex. 49)

 

(ex. 50)

 

 

II/10.2.4 The episodes

The E minor fugue encompasses six subject-free passages.

E1

bars 18m - 23

E4

bars 55m - 59

E2

bars 35m - 41

E5

bars 65m - 71

E3

bars 47m - 49

E6

bars 77m - 86

Several of these episodes very obviously consist of two segments; in order to make later reference easier, these are pointed out here already. A change of material and a completed modulation to the relative major key allow E1a (bars 18m-20m, concluding in G major) to be distinguished from E1b (bars 20m-23); the sudden homophonic elements of fermata and general pause separate E5a (bars 65m-70m) from E5b (bars 70m-71); and the final episode can even be chopped up into three portions: E6a (bars 77m-81m), E6b (bars 81m-83 fermata) and E6c (bars 83m-86).

None of the episodes can be described as just a cadential close. Instead, all of them use material from the subject and also develop motives which constitute unique secondary material.

Ms

The subject's final bar (see bar 5 from C to bar 6 E) is freely used in the episodes. It occurs unabridged in E1a (L: 2x), in E2 (M: 1x bars 35/36), in E3 (L: 2x), in E4 (U: 3x + M: 1x), and in E5a (M: 1x and L: 1x).
In addition, its first half (the five-note descent with upward resolution) recurs separately in E1b (M: 3x), in E2 (M: bars 36/37, all voices alternating bars 37-41), in E5a (M: 1x bar 68), in E5b (L: 2x) and in E6c (U: 1x bar 84).
Another derivation, also featuring six eighth-notes in the same metric position and in scalar motion, is the ascent which appears with varying ending; see in E1b (U: 3x), in E5a (U: bars 66/67, L and U: bars 69/70, :U bar 71), in E6a (M: bars 78/79) and in E6b (U: 1x bars 84/85).

M1

is a genuine episode motive. It is characterized by its dotted rhythm which comes either in an inverted-mordent figure plus jump (M1a, introduced in bars U: 18/19) or in a simple ascent (M1b, introduced in M: bar 19). Both versions are sequenced once in E1a and recur in the same complementary pattern in E3. M1b is also three times anticipated in the varied CS-ending just before E1, E2 and E3; furthermore, it is sequenced in E2 (U: bar 36). Finally, the rhythmic model is used in a variation with a tied note (M1c see E4 M: 3x) and in a curve (M1d see E5a M: bar 67 and E6c M: bars 84/85).


Other noteworthy features include the sequence-model in the lower part of E1b (it is not imitated in another voice or taken up anywhere later in the piece; so it is not a motive), the three-part complementary pattern over a dominant pedal in E6a (bars 79-81), and the voice-splitting in bar 83 (four-part chord) and bar 86 (four-part texture all through the bar). A most obvious relationship exists between E1a and E3.

The role played by each episode in the development of tension largely follows the direction of the sequences. E1a represents a crescendo followed by a diminuendo in E1b, thus giving this episode the shape of a closed curve. E2 describes a similar curve, despite some ambiguity in the second half (L: falling, U and M: rising in bars 39-41), as does E4. E3 recalls only the rising first half of E1 and thus gives the impression of connecting two subject statements. Strangely (or: interestingly), E5 which features a rhythmic interruption with fermata and general pause nevertheless conveys a strong feeling of link between entries; its short segment E5b fabricates a compelling rise of tension as a preparation for the final subject statement. E6 is the longest and most diverse episode. It contains true toccata features (see bars 79-83) but is united by the pedal note B which supports the first and third segments of the episode (see bars 78-81 and 84/85). Surprising are the texture and complementary rhythm of the final bar which, together with the ending on a weak beat, remind one of the key confirmations found in most allemandes and some courantes of Bach's suites.

 

II/10.2.5 Character, tempo, articulation, ornament realization

The basic character of the fugue in E minor is rather calm. Bach gives the performers of this piece a clear though somewhat unusual indication: the wedges on the quarter-notes. In lively character, these quarter-notes would be played detached anyway – and Bach can certainly not be accused of writing superfluous markings. In calm character, however, particularly the two quarter-notes in bar 1 would normally be rendered as tightly linked, and the two E's in bars 3 and 4 might be considered as interval leaps of increasing tension which would then also not allow for separation. By writing the wedges, Bach thus gives us information on several levels:

-

The first piece of information, concerning the basic character and the regular articulation resulting from it, translates as follows: Unless otherwise indicated, all melodic notes in this composition are to be played in legato.

-

The second piece of information derives from the wedges in bar 2. As they appear on a broken chord (which Bach's contemporaries would have played non legato whatever the overall articulation of the piece), they must signify slightly more than just "detached style". But then, to be very precise, there is a difference between the usual non legato playing in a composition of calm character on the one hand, and a wedged note on the other:   

*

a non legato note is separated from the next note by a natural release (on string instruments, a natural slowing down of the bow motion)

*

a wedged note is stopped abruptly and actively (on string instruments, the beginning of the bow motion is already more forceful, and a sudden stop of the motion is pre-planned)

These wedged broken-chord notes are thus shorter and more intense than we would otherwise play non-legato quarter-notes in calm character. (By contrast, the broken-chord notes of L: bars 21-23 should be rendered in a much more gently detached manner.

-

The third piece of information concerns phrasing. The wedges in bars 3 and 4 which shorten the E's deliberately create gaps after the two peak notes that are larger than normal in calm character. These articulation symbols thus make it quite clear that the melodic line does not simply continue across the interval jump, but that the high note is the end of a preceding small unit.


The tempo of the piece does not permit much individual variation. It must be fast enough to convey the alla breve time, but moderate enough to allow for transparency in the thirty-second-notes of the fugue's ornaments (see below). Thus unhurriedly swinging half-notes give a good measure.

The relative tempo of the prelude to the fugue works best as follows:

one bar (3/8)

corresponds with

half a bar (a half-note)

in the prelude

in the fugue


(Approximate metronome settings: prelude beats = 180, fugue beats = 60.)

A short word on the execution of the various rhythmic values is necessary. Both the four sixteenth-notes in the written-out turns of the subject's first bar and the triplets in the subject's final subphrase are of course to be played as noted. In the entire piece, the two rhythmic figures do not ever once coincide; thus the problem of polyrhythm does not arise here. The dotted-eighth-note figures, however, regularly sound against triplets. As Bach's manuscript very clear displays his writing of note head against note head, these dotted-note figures are obviously intended to be read in triple fraction (i.e. as the eighth-note+sixteenth-note of a triplet: 2 + 1 instead of 3 + 1). While most performers may intuitively chose this reading in bar 12 and from bar 18 onwards, many of them are unaware of playing, in the three initial statements of the subject, a different (i.e. strictly dotted) rhythm. Yet consistency requires that in bar 3, the dotted-note figure should already be given the rhythmic shape it is going to have throughout the piece. (A slightly odd though basically corresponding case occurs on the final beat of bar 83: the single sixteenth-note in the middle and lower voices also makes more sense if read in triplet rhythm – with the dotted note here substituted by rests.)

This brings us to the ornaments. The score contains both thematic and cadential ornaments as well as an additional one in neutral context.

-

The first thematic ornament appears in the subject (see bar 1d). It is an inverted mordent printed in parentheses on all three occasions where it occurs (see bars 1, 7, 13). The question is thus not so much which notes to play but rather whether or not to play it at all. The three consecutive markings indicate that the ornament is to be treated as an integral part of the subject; the omission of the symbol in further subject statements was usual practice and is therefore no contradiction. Moreover, the full print relegates the ornaments to Bach's own manuscript. (Additions in other hand copies are distinguished in the Urtext by small print.)

The parentheses, however, seem to leave an option. There are two (small) problems that the inverted mordent might cause. One is technical: it arises in cases where the subject sounds in the middle voice and the ornament must thus be played in a hand which has another voice to attend to simultaneously (see bars 30 and 50). Yet all but very narrow hands will master bar 30, and bar 50 only presents a double third.

The other problem regards speed: the three notes must be over before the second triplet eighth-note in the accompanying voice (see e.g. bar 13); so the ornament has to be played at the minimum speed of a sixteenth-note triplet – which again is only slightly more difficult in the two middle-voice entries. (In bar 43 there is one subject entry which features the inverted mordent on the first syncopation instead of the first downbeat. This seems somewhat arbitrary, and most performers seem to prefer ignoring it.)

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The second thematic ornament decorates the counter-subject. It is printed only once, though without brackets (see bar 10). Placed against a half-note, i.e. a note which must be sustained and linked to the following note, this ornament poses a much bigger problem. (See e.g. already in the second statement of the counter-subject, bar 16 M on F#: in whichever hand one plays the mordent, it seems almost impossible to sustain the note and carry on with the other voice.) The option here is therefore to play it only once – or not at all.

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The non-thematic ornaments are fairly straightforward. In bar 70, the general pause is preceded by mordents in the upper and middle voices. As these ornaments appear under fermatas, there is no hurry; one can even easily manage a double shake (i.e. five notes, beginning on the main note). An identical ornament decorates the analogous fermata note in the upper voice of bar 83. The ensuing turn which, after the rhythmic break caused by the fermata and the melodic break caused by the octave jump, appears as the beginning of a new phrase, begins on the main note (D#-E-D#-C#-D#).

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Finally, the typical leading-note decoration in bar 85 is an interrupted trill (interrupted because the resolution note is anticipated). Yet there is admittedly not much time for a trill to unfold; so four notes (E-D#-E-D#, in the rhythm of a sixteenth-note-triplet plus a eighth-note) is probably all one can do.

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There is one more ornament in the middle of an episode (see bar 37). This turn begins regularly, i.e. on the upper note, and consists of four notes. Again, a rhythmic rendition with a sixteenth-note-triplet followed by the fourth note on the second eighth-note is a good choice. (Faster executions are permitted unless they blur or require too slow a tempo for the fugue; versions slower than the one explained above are not possible.)

 

II/10.2.6 The design of the fugue

In the absence of conspicuous cadential closes in episodes and of subject statements appearing in reduced ensemble, the harmonic outline and the detailed use of material must be investigated to determine the scope of each section.

The first section does not pose a problem. Its three entries are on tonic, minor dominant and tonic respectively. As the first episode develops from the preceding statement ending by way of sequences, cutting it off would be quite unthinkable. As a result, the first section would have to end with the conclusion of E1 – which is on the downbeat of bar 24, in a two-eighth-note overlap with the next subject entry.

The second section is distinguished from the first by a change to the major mode. It contains two subject statements, in the key of the relative major and its dominant respectively, plus another episode. As before, the end of the section (on the downbeat of bar 42) overlaps with the initial upbeat of the lower-voice statement which follows.

The third section returns to the harmonic realm of E minor, with two entries on the dominant and tonic respectively. The linking episode E3 and the concluding episode E4 together make up six bars – the length of each of the episodes in the first and second sections – so that we can structurally regard E3 as an anticipated segment of this section's concluding episode.

Section IV finally presents the statement on the subdominant and thus truly confirms the return to the home key. There are again two statements but, as expounded above in detail, the episodes are much extended and expose material that might seem alien to the fugue. Yet Bach has composed these 27 bars in such a way that they clearly form one large inseparable unit – despite fermata and general pause. In fact, the entire section represents one protracted cadence in E minor. The section commences in A minor (on the subdominant, see bars 60-65). Shortly after the end of the subject entry on the subdominant, the lower voice features a chromatic descent to the dominant pedal (see bars 66-70: D---C#-C-B---A#-B). Suspended for the duration of the final subject entry, the dominant pedal is resumed in bars 78-81 and, in bars 84/85, prepares the final tonic bass.

(For a sketch showing the design of the fugue in E-minor see ex. 51.)

 

 

II/10.2.7 The overall dynamic outline of the fugue

All four sections describe an increase in tension from their initial statements to the last ones. In sections I and II, these increases are not interrupted by episodes, and E3 in section III with its rising tendency also maintains the drive from one entry to the other. Only section IV reverses these facts. The initial (subdominant) entry appears more intense than the second (tonic) entry because of (a) the harmonic release from subdominant to dominant and tonic, (b) a prevailingly relaxing attitude in E5, and (c) the three-bar reduction of the ensemble (see in bars 70m-73m) which makes this subject statement the only one in the fugue (after the full three-part texture had been established) to appear in thinned-out surroundings. The final episode, however, describes a full dynamic curve corresponding to those in the other three section-concluding episodes.

Among the four sections, the second one in major mode may be regarded as most outgoing in character. The third section is still on an elevated level, and only the final section returns to the intensity level of the fugue's beginning. The differences, however, are not dramatic. This is another playful fugue in which the thematic material as such captures the attention, and not its manifold modifications or intensifications.