I/7.1.1 The prelude-type

The prelude in E^b major is a fairly long and complex piece. Its three different segments are visibly distinct in both the use of material and the degree of virtuosity.

-	The first segment (bars 1-10) is built along the lines of a "prelude determined by motivic development", ending with a virtuoso passage and a cadential close.
-	The second segment (bars 10-25) displays polyphonic texture in which voices enter one after the other presenting a short motive. This motive is imitated in stretto right from the start, although later, this tight imitative pattern grows looser rather than denser. Structural details which might indicate one of the well-known form models (such as fugue or invention) do not materialize: there is no cadential close in a second key followed by a new beginning corresponding in some way to that in bar 10. Such a passage in free imitative style based on a single motive is usually referred to as a "fugato".
-	The third segment of the prelude (from bar 25 onward), and by far its largest, is also polyphonic. It begins with two contrapuntal voices and, as a quick glance through the remainder of the piece reveals, works with this material in many different ways. As there are several definite cadences in related keys and new presentations of the material after these cadences, this segment within the Eb major prelude must be called a "fugue".

To sum up, Bach's prelude in E^b major is conceived as an integrated three-movement composition comprising "prelude", "fugato" and "fugue".

I/7.1.2 The design of the prelude

The first cadence is completed on the middle beat of bar 4. However, as the bass has not yet begun to participate in the harmonic progression but remained locked in a tonic pedal, this cadential close cannot be regarded as a structural ending. Another reason is that the flow of the lines continues perfectly uninterrupted, without even the slightest sign of phrasing.

The next harmonic progression ends – again over a pedal note – on the downbeat of bar 10 in B^b major (dominant of E^b). This cadential close, as has been said above, definitely marks a structural caesura.

Within the "fugato", similar circumstances prevail as in the "prelude". The only structurally relevant cadence, however, appears again at the end of this segment, i.e. on the downbeat of bar 25 (cadence also in B^b major). There are, though, two earlier cadences which are worth mentioning because of the unusual way in which the listener's expectations for a resolution are deceived in the first and turned around in the second. Both cadences attempt to close in the home key of E^b major, but are prevented from doing so.

The first cadence seems to draw to a close in bars 15/16. The typical closing-formula has, however, not yet reached the resolution when three of the four voices proceed quite differently from what is anticipated. (Try and play bar 15 as the second-last bar of an E^b major cadence. The soprano would resolve onto E^b, the alto would descend to G and the tenor to E^b, and the bass would jump down to E^b. As the downbeat of bar 16 shows, this is not what happens: all voices but the alto take unexpected turns. Recognizing this subtle process seems important both for the listener and for the performer of this piece.) The second cadence occurs in bar 18. On the downbeat of bar 19, the return to the tonic seems achieved, with only a soprano appoggiatura remaining unresolved. Yet when the expected resolution materializes, it finds the inner voices moved, so that the E^b harmony appears redefined as an inverted F major seventh chord. After this second attempt at a resolution onto E^b major, this section returns to the dominant tonality from which it had set off.

Neither the "prelude" nor the "fugato" thus contain any structurally relevant cadences. The "fugue", however, is clearly subdivided. Altogether, the E^b major prelude consists of eight structural sections, each of them individual and without any analogy of design. In the table below, the key in brackets denotes the cadence in which each section closes.

I/7.1.3 Practical considerations for performers

The ideal tempo for this prelude is one which allows to accommodate the particular character of each of the three "movements" without any need for adjustments of pace. To be specific, the tempo should allow the thirty-second-notes of bars 8/9 to sound fluent enough to give the impression of an ornamental rather than that of a melodic line; at the same time, the quarter-notes of bars 10-24 should sound calm enough to express the basic character of the "fugato".

The appropriate articulation for the entire piece is mainly legato. Although in the prelude, the lively character would require any eighth-notes and longer note values to be played non legato, there are no notes to which this could apply: virtually all longer values come with tie-prolongations, and the only separate long notes (tenor bars 7-10) form a keynote / leading-note / keynote (do-si-do) group which is legato in any case.

In the rather calm character of both the "fugato" and the "fugue", only cadential-bass notes and consecutive jumps are detached. These are the groups in which non legato applies:

The only ornament in this prelude occurs in bar 9. It is a trill ending in an anticipated resolution, i.e. a "point d'arrêt" trill. The motion in this ornament should be faster than – preferably twice as fast as – the fastest regular note values appearing in the piece. (It need not, however, exceed the tempo of the spelled-out turn figure immediately preceding the trill, as closer inspection reveals that this figure is in fact part of a longer compound ornament commencing on the tied eighth-note E^b.) The trill itself thus sets out in sixty-fourth-notes from the upper auxiliary F, comes to a sudden halt ("arrêt") on its main note and ends with the anticipated resolution. The following figure gives a written-out version for the entire compound ornament.

(ex. 2)

 

I/7.1.4 What is happening in this prelude?

a) The "prelude" within the prelude

The first segment of the composition is built entirely on an eight-note motive. This motive, which will be referred to as M1, is introduced in the upper voice where it commences after a downbeat rest, describes a curve in sixteenth-notes and ends with a large leap upwards. This leap is written as a split in the voice, which emphasizes the interval it spans. (See bar 1 middle, where the tied E^b remains while the split voice proceeds on to D^b, and similarly bars 2 and 3.) The impact of the target note is further enhanced by its length which exceeds that of the entire preceding sixteenth-note group.

M1 is immediately imitated but not copied in the tenor of this four-part texture; the leap is much smaller and there is no voice splitting; instead, a pedal note E^b materializes in the bass. The subsequent two bars bring ascending sequences of the pattern established in bar 1, together with a corresponding tension-increase.

After a short resolution onto the home chord (middle of bar 4) the right hand propels M1 up to the peak C. At the same time the left-hand part develops the motive: the leap appears substituted by a note which is integrated into the sixteenth-note figure both in pitch and in note value, and the prolongation of its note value is given up. The result is a continuous run downwards which covers two octaves. In bar 6, a descending scale in the right hand joins the left, and both voices reach a C minor chord – step vi in E^b major, thus a chord with comparably high tension – on the downbeat of bar 7. Two more statements of M1 are followed in the treble by a continuous development similar to that previously heard in the lower part (compare bar 8 right hand from C onwards with bars 4-6 left hand). The "prelude" section ends with a freely virtuoso run and the afore-mentioned cadence in bars 9/10.

b) The "fugato" within the prelude

The second segment of the composition is also based on one motive. M2 is originally five notes long (see T bars 10-11m: B^b E^b D C B^b ) but soon drops its final resolution. In its four-note version it is strikingly related to the main motive of the Prelude in B minor, also from Book I of Bach's Well-Tempered Clavier. As M2 is the one and only driving force of the fugato, it seems important to identify all its statements:

While the four-note version is still very close to the original, later modifications of M2 transform it more and more. These are the variations as indicated by the asterisks above:

*	=	The third note may appear prolonged to twice its value, delaying the fourth note to a weak beat where it follows usually as yet another syncopation.
**	=	The motive may sound with its first note lengthened to a syncopation. This may then be followed either by only the third note or by the two remaining notes.
***	=	The fourth note may bend back instead of leading downwards.

 
The final portion of the fugato shows only two rudimentary statements of M2 (see S and B: bars 19-21); more influential here are the descending lines in all voices:

Each of these descending lines comes in diminuendo, so that the last five bars of this section describe a long relaxation. Not only is the ending of the fugato section thus well prepared, but, more importantly, the beginning of the third major segment, the fugue, is strongly suggested.

c) The "double fugue" within the prelude

The beginning of the fugue presents two melodic ideas simultaneously. As each of them is later used quite independently, it seems appropriate to speak of two subjects rather than of one subject and its counter-subject.

Subject 1 (S1) is introduced in the alto. It is two bars long, beginning on the second sixteenth-note in bar 25 and ending on the downbeat of bar 27. This subject is closely related to M1 from which it borrows its first seven notes.

(ex. 3)

 

Subject 2 (S2) first appears in the bass: it stretches from the first beat of bar 25 to the downbeat of bar 27. This subject is closely related to M2. The beginning recalls the first three notes of M2; these are followed, after the third note has doubled as the beginning of a new sequence, by the entire four-note version of M2.

(ex. 4)

 

The dynamic design of the two subjects is, at least at their beginnings, determined by the motives from which they stem.

-	S1 commences with a tension-increase towards what was the final note of M1; the second, longer subphrase begins anew and carries an even stronger crescendo through the varied sequence of the motive. The climax falls preferably on the quarter-note Eb and is followed by the resolution of the tension through the subsequent do-si-do figure.
-	The dynamic shape of S2 reflects its evolution from the fugato motive: a first climax on the syncopation Eb is followed – after a slight relaxation which turns out to serve as a new beginning – by a stronger second climax on the downbeat of the second bar. The descent to the keynote of the target chord brings the complementing relaxation.

The combination of both subjects in their particular phrase structure and dynamic development is depicted below:

(ex. 5)

 

In the course of the "fugue" within the E^b major prelude, S1 appears twelve times and S2 twenty-two times. The following chart lists the statements of both subjects:

bars

25-27

S1

A

+

S2

B

bars

27-29

S1

S

+

S2

T

bars

30-32

S1

B

+

S2

A

bars

35-37

S2

A

+

S2

S

bars

38-40

S2

S

+

S2

T

bars

41-44

S2

A

+

S2

T

+

S1

S

bars

46-49

S2

B

+

S2

T

+

S1

A

bars

49-51

S1

A

+

S2

B

bars

53-56

S1

S/B

+

S2

T

+

S2

A

bars

56-58

S1

B

+

S2

A

+

S1

S

bars

58-60

S1

A

+

S2

S

bars

60-63

S1

S

+

S2

A

+

S2

B

bars

64-67

S2

A

+

S2

S

+

S2

A

bars

68-70

S1

A

+

S2

T

Both subjects appear with several irregularities and variations:

S1

may come without its final note (see bars 27-29) or even without the last two notes (e.g. bars 60, 63); - it may be deprived of its entire first subphrase (see bars 30-32); - it may be shortened in the middle, so that the first subphrase leads directly into the note repetition of the ending (see bars 56/57 B); - it may, while shortened in the middle as described above, find its closing note repetition replaced by a single tied note (bars 56/57 S).

S2

may come without its final note (see e.g. bar 27-29); it may have lost both its final notes (see bars 30-32, 35-37, 38-40 etc.); its beginning may sound ornamented (see bar 60). S2 builds several strettos (see particularly bars 35-49 and bars 64-67) the last of which sounds briefly like a parallel – although it is not. In addition, there are a few interesting voice crossings which should be mentioned: - In bar 28 the tenor does not descend right away after the two rising fourths of the S2 beginning; instead it continues, using scattered M1 quotations, to climb as high as Ab (bar 29). The alto with its statement of S2 thus begins underneath the tenor and only regains its rightful position in bar 31.  - In bars 41-43 both the alto and tenor with their S2 statements climb high while the soprano with its S1 entry crosses below both voices before it corrects its position with an octave displacement (see bar 43 the compound fourth from Bb to Eb ). - Finally, in bars 53/54 the statement of S1 seems "mixed up": it begins in the soprano with a varied first subphrase, then descends correctly until Eb (bar 54 beat 1) after which it switches to the bass! This, however, does not pick up the right pitch: instead of the expected Ab Ab Ab G Ab we hear F F F Eb Ab.

As in any other fugue there are a number of subject-free passages or episodes:

The material employed derives most frequently from M1; the remainder is neutral. Features to be pointed out include typical cadential patterns (see B: at the end of E2 and E8, S: at the end of E3 and E4), as well as particular pitch patterns which engineer tension-rise in all voices, thus preparing for the entries which follow (see E5 and E6). In contrast to these six episodes with definite closures, E1 and E7 use fragments of the first subject, serving merely as links.

As for the design of the fugue, many obvious indicators help in presenting an easy overview:

-	The four-part ensemble is built up gradually, from the initial two voices (alto + bass) in bar 25 which are joined by the soprano in bar 26 and the bass in bar 30, to a first four-part cadence in bars 34/35.
-	A tonic pedal in bars 68-70 separates the coda from the fugue's "trunk".
-	The grouping of subject statements includes simple S1/S2 juxtapositions in bars 25-35, S2 strettos in bars 35-41, S2 strettos with additional S1 statements in bars 41-49, S1/S2 juxtapositions with irregular S1 entries in bars 49-58, merging entries / juxtaposition / S2 stretto in bars 58-68.

 
These groupings coincide perfectly with the sections that had been revealed in the earlier harmonic analysis:

The design of the entire Prelude in E^b major can thus be expressed as shown in ex. 6.

(A missing accidental in the Urtext, contained in several other editions, should be carefully considered: in bar 20, the tenor features B^b-A^b-B^b despite the A^b in both soprano (bar 19) and alto (bar 20). As the soprano statement of M2 suggests B^b major for these bars, adding a natural to the leading note seems essential.)

I/7.2.1 The subject

The subject of this fugue is one and a half bars long. It commences on the downbeat of bar 1 and ends on the middle beat of bar 2 (B^b). As indicated by the >ð in front of the A (see end of bar 1), the middle of the subject witnesses a modulation to the key which has only two flats: B^b major, the dominant key of E^b major. A natural is not only the leading-note to the new key but also part of a broken chord F-A-C-E^b (see bars 1/2), the dominant-seventh chord of B^b major. The subject note B^b in the middle of bar 2 brings the resolution onto the new tonic.

There are two subphrases within this subject. This can be deduced not only from the rest in its middle but much more from the varied partial sequence with which the second subphrase commences: the two prominent eighth-notes in the second half of the subject actually sound like an elevated sequence of the two eighth-notes before the rest, the preceding sixteenth-note-group is shortened here but "made up for" by the final strong-beat note.

The pitch pattern in the subject contains mainly broken chords (the use of the second eighth-note in bar 2 as a passing note is confirmed in Bach's harmonization of later subject statements; see e.g. bars 4, 7, 18):

A brief look at the remainder of the fugue shows that these and other broken-chord patterns are prevalent features throughout the piece.

The rhythm in the subject consists mainly of sixteenth-notes and eighth-notes, with the exception of the quarter-note which carries the trill. The same predominance of these two note values can be detected in the entire piece.

The subject's harmonic background is determined by the modulation which takes place within its confines. The active step (tonic to subdominant) occurs melodically immediately after the second beat, metrically confirmed only on beat 3. This subdominant harmony is sustained even when the second eighth-note of beat 3 returns to B^b (a note which, in its unaccompanied melodic version, might be heard as a return to the tonic). The pivot chord (V⁷/V) which begins melodically with the A>ð can be felt metrically either in the rest on beat 3 or on the downbeat of the second bar:

(ex. 7)

 

For several reasons, the E^b on the downbeat of bar 2 seems the obvious choice for a climax: it falls on a downbeat, it represents the metrical place of the pivot chord which triggers the modulation, and it is reached in the high-tension interval leap of a minor seventh. In addition, it is conceived in varied sequence to the process in the first subphrase which finds its climax on the C (bar 1m), the note which represents the subdominant harmony and sounds rhythmically as the first halt after the initial eight sixteenth-notes.

The tension in the entire subject thus consists of two curves. The first begins with a crescendo of moderate strength and is complemented with a relaxation in only one note (C-B^b); a second crescendo then surpasses the first and is complemented with a longer diminuendo for a more perfect resolution of the tension.

I/7.2.2 The statements of the subject

The subject appears altogether nine times in this fugue:

(ex. 8)

The subject always sounds in its complete length; its last note appears most often as a sixteenth-note but may be extended to an eighth-note (bars 27 and 30) or even to a quarter-note in the final entry (bar 35). Moreover, several statements begin with a syncopated anticipation of the first note (see bars 10/11, 25/26, 28/29 and 33/34). In addition to these small changes in the appearance of the subject, interval adjustments – between the first two notes and across the rest – occur in all tonal answers (see bar 3 etc.). No stretto or parallel of subject statements appear in this fugue.

I/7.2.3 The counter-subject

Bach has invented only one counter-subject for this fugue. CS is introduced in bars 3/4, against the second subject statement, where it commences slightly later than the subject with the eighth-note A^b and ends, together with the subject, on the G in the middle of bar 4. This counter-subject appears as a faithful companion to the subject in all but the initial and final entries, featuring only one slight variation of its beginning in bar 20. It fulfills its task of counter-balancing the subject in several ways:

-	Against the broken chord patterns which dominate the first two-thirds of the subject, CS sets stepwise motion, and against the stepwise motion at the end of the subject it sets a broken dominant-seventh chord (see bar 4 beat 2).
-	While the subject is made up of two subphrases, the counter-subject is conceived as one indivisible line.
-	While the subject has two climaxes – a softer one on the third beat and a stronger one on the fifth beat after its beginning – the counter-subject shows only one unbroken tension-curve. Its climax is either on the first eighth-note, followed in this case by a single long diminuendo, or (perhaps more likely) on the syncopation which coincides with the rest in the subject.

Sketch showing phrase structure and dynamic design (ex. 9):

 

I/7.2.4 The episodes

In this fugue, the number of episodes equals that of the subject statements:

Only E6 among all these episodes shows a relationship to the subject: its first two bars (see bars 22/23) use a variation of the first subphrase in their upper voice. All other episodes are entirely independent from the primary material. They present a number of characteristic motives which are used with great consistency:

M1	E1 introduces a half-bar motive featuring two broken chords, each with a subsequent step downwards to the next beat (see bars 2/3: F-D-Bb-Ab, F-D-Ab-G). This motive plays a leading role in all episodes of this fugue, occasionally in an extended version with a final unaccented jump upward (see in E3, E4).
M2	E2 combines a prolonged M1 in the middle voice with a figure in the upper voice which also consists of broken chords, this time in ascending direction; significant features, however, are the long syncopations. M2 also recurs (see e.g. bars 8/9), sometimes unchanged and sometimes represented only by the accented upward jump in eighth-note rhythm (see e.g. U/L: bar 9).
M3	E3, the first episode in full three-part texture, introduces the third motive (see M bars 7/8: F D Bb Eb ) which is subtly related to the other two: like M1 it begins with a descending broken chord, and like M2 it ends with an accented upward jump. Yet it is at the same time clearly distinct, as its rhythm contains only eighth-notes.

 
These three motives are used in a variety of combinations (see particularly in E3, E4, E5, E8). The second half of E6 then introduces a new pattern which recurs shortly afterwards in E7: sequences of ascending eighth-notes in the bass and a sixteenth-note dialogue with varied segments of M1 in the two higher voices create a pattern which we shall call M4.

Several relationships exist among the episodes of this fugue:

E5, E2	the shape of the two episodes is very similar though the hands appear inverted (compare bars 4/5 with bars 19/20);
E3, E4a, E8	with inverted voices but few other changes (compare bars 7-10 with bars 12-15 as well as with bars 30-33);
E6b, E7	the second half of E6 is taken up, as was mentioned above, in E7.

The only episode segments which remain without any correspondence are the cadential close of E4b (with its preparation, see bars 15-17m), the first half of E6 (for E6a see bars 22-24d), and the final episode E9.

As all episodes apart from E6a are conceived as independent in material and character from the subject and counter-subject, they should logically sound as self-contained units, in a color and intensity distinctly different from those of the subject and its counter-subject. The dynamic gestures within this contrasting and much lighter color are:

-	E1 features descending sequences which create a natural decline of tension; equally, the final episode E9 sounds in manifold falling lines.
-	E2 with its corresponding episode E5; and E3 with its corresponding episodes E4 and E8 all show relaxing tendency in descending sequences.
-	The first half of E6 also features a pitch direction which points downward; here again the dynamic tendency is decreasing.
-	The second half of E6 and, correspondingly, E7 are the only episode segments to show dynamic build-ups; these are created both by the ascending eighth-note lines in the bass and by the ascending sequences.

 

I/7.2.5 Character, tempo, articulation, ornament realization

Both the steady rhythm pattern with its predominance of sixteenth-note and eighth-note values, and the pitch pattern with its high content of broken chords, clearly characterize this fugue as rather lively.

The tempo should be fast; a conductor beating an energetic four-four meter may give a good orientation for the minimum tempo, and the tricky trills in bars 21, 27 and 35 certainly mark the upper limit. The articulation which corresponds with the character of this fugue requires a bouncing non legato for the eighth-notes and a legato which borders on leggiero for the sixteenth-notes. The only longer note values which must be played legato appear in a do-si-do formula (see bar 35 E^b -D-E^b: U); legato is optional in the two-part version of M1 in U: bars 27/28 (see D^b-C and E^b -D) and in the chromatic descent in the split-off upper part of the middle voice in the final bar (see D^b-C-C^b-B^b).

The relative tempo of the E^b major prelude to the subsequent fugue should best be kept simple: 

The only ornament in this fugue is the trill in the subject. It begins, as it is approached in stepwise motion, from the main note (which is a sixteenth-note long), then proceeds in two pairs of thirty-second-notes and ends in a suffix.. This trill has to be retained in every subject statement, even where it is not at all or only ambiguously indicated in the score, as in bar U: 12, L: bar 27 and M: bar 35. (Note that the trills in bars 7, 12, 21 and 27 come with a double note to be played in the middle of the trill motion; bar 30 becomes much easier if both middle-voice E^b are played in the right hand – which is more comfortable than one might think. In bar 35, the main part of the trill can be played with the right hand while the suffix is much smoother if taken in the left.)

I/7.2.6 The design of the fugue

The design of the fugue in E^b major reveals itself from several obvious features:

-	The entering order of the subject statements begins with a complete round of all three voices followed by one redundant entry. While all four entries are separated by episodes which steadily increase in length (E1 = 2 bar, E2 = 12 bars, E3 = 32 bars), the episode which follows the redundant entry is by far the longest (E4 = 5 bars); furthermore, it ends in a definite cadence.
-	The fifth subject statement, after E4 with its cadential close, is presented in a reduced ensemble as the bass is resting. This texture confirms that a new section begins here. The next episode is a variation of E2, the episode introduced after the two-part entry in the first section – an obvious structural correspondence.
-	The first half of E6, as has been shown above, is the only one in this fugue not to find a matching counterpart; we can therefore assume that it has some structural importance.
-	The second half of E6, with its rising tendency, not only prepares the next statement but also recurs in variation (see E7) immediately afterwards where it acts as a bridge to the subsequent subject entry. This episode-type, newly invented here, must therefore be understood as marking the beginning of the third section; the fact that it is taken up at the first opportunity strings the seventh and eighth entries closely together.
-	The subsequent group of subject entry / episode / subject entry is built in obvious symmetry to that group in the first section of the fugue which encompasses the third entry / third episode / redundant entry (compare bars 6-12 with bars 29-35).

This symmetry hints at a structural analogy between the second to fourth entries of the first section and the same number of entries in section three. Pursuing this assumption one finds that the entries in bars 3/4 and 26/27 are in fact strikingly similar.

The harmonic progression within the composition confirms this concept of a structural outline:

-	The first four subject statements all relate to the home key; only the section-concluding episode E4 modulates to the relative key of C minor.
-	The two entries which, according to the above-stated concept, make up the second section are both in minor mode. The ensuing first half of E6 modulates back to Eb major which appears firmly re-established on the downbeat of bar 24.
-	The second half of E6 as well as the three entries in the third section are again rooted in the key of Eb major.
-	The final entry is harmonically the most daring event of the entire fugue. It features additional chromaticism (see particularly bar 34 middle) and ends in an interrupted cadence (bar 35 middle = C minor).

 
For a sketch showing the design of the fugue in E^b major, see ex. 10.

I/7.2.7 The development of tension

Within the first and second sections, the tension-increase engendered by the gradually growing ensemble appears constantly interrupted by the regularly interspersed episodes of contrasting color. Thus each subsequent entry sounds only slightly louder than the previous one.

In the third section, the preparation of entry no.7 creates more tension at the very beginning (thus making up for the "missing" first statement in the recapitulation?). This process is repeated before the next subject statement so that the tension-increase within this section is more pronounced than that in the exposition.

As the first subject entry of the fugue already expresses a certain strength, due to the lively and bouncing character of the subject, the dynamic equivalent to this tension-increase might be approximately mezzoforte to poco forte. Within the second section, the change of mode results in a considerably less exuberant mood and, consequently, in a much softer touch. The third section thus not only balances the first one but even exceeds it slightly.