WTC I/20 in A minor - Prelude

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

I/20.1.1 The prelude-type

This prelude displays a contrapuntal texture, with principally two voices embarking on melodic processes. The two-part structure is, however, not strictly observed but thickens occasionally as supporting block chords are added (see bars 5, 6, 7; 9, 10, 11) or a legatissimo is spelled out, especially in the sense of an overlapping of one sound over a number of consecutive pitches (see bars 13-15, 16+18, 17+19, 26-28). With regard to material organization, the composition builds entirely on one motive, the slightly ornamented broken-chord figure introduced in U: bar 1. The prelude can therefore be regarded as conceived along the lines of a two-part invention.


I/20.1.2 The design of the prelude

The principal motive of the "invention" establishes, in conjunction with its two sequences and a complementary figure in the fourth bar, a four-bar phrase which constitutes a complete harmonic progression. The coincidence of the cadential close in bar 4 with the end of the larger melodic idea does not, however, allow this to be regarded as a caesura of larger structural bearing.

The second harmonic progression concludes in analogy to the first after the statement - now in the lower voice and in E minor - of the four-bar melodic idea (see bar 8). Yet listeners have to wait until the end of the subsequent development, again four bars long, for the relaxation and cadential close which indicate a break in the overall structural layout of the prelude. The harmonic conclusion comes after a modulation to C major and falls on the downbeat of bar 13.

Three structural sections can be distinguished in this prelude:

I bars 1 - 13 tonic - minor dominant - tonic relative
II bars 13 - 22 tonic relative - tonic*
III bars 22 - 28 confirmation of tonic

The harmonic conclusion of section II is very strange. One is expecting a return to the tonic, and the consecutive iv - vii7 (see bars 20/21: D minor and G# diminished-seventh) seem to confirm this. At the very last moment, however, the lower voice sidetracks with a jump to C (see bars 21/22). The A minor chord at the expected end of the cadence thus appears in inversion and fails to satisfy the listener's demand for a resolution.. Even more strangely, the process is repeated similarly three bars later: the left-hand progression G#-A-B (A) diverts to C, and an unusual major-seventh jump adds to the harmonic irregularity. It is only after yet another cadential bar that the downbeat of bar 26 finally presents the true tonic bass.)
No larger portion of the prelude recurs anywhere later in the piece. As was already mentioned, the initial four-bar phrase is taken up correspondingly and in inverted voices in the subsequent four bars; but as this constitutes the imitation process anticipated at the beginning of any invention, it has no further structural relevance.


I/20.1.3 Practical considerations for performers

The pitch pattern of this prelude displays primarily a combination of broken chords in eighth-notes and ornamental sixteenth-notes (see e.g. the spelled-out trills in L: bars 1-3). As in addition, the rhythmic pattern is simple, consisting predominantly of eighth-notes and sixteenth-notes, the basic character of this prelude is no doubt rather lively.

The tempo should be taken fairly swift, with the nine-eight time signature read as a convenience for three-four time with triplets. The appropriate articulation includes non legato for the eighth-notes and quasi legato for the sixteenth-notes. The score does not contain any ornament symbols.


I/20.1.4 What is happening in this prelude?

The principal motive M (see U: bar 1) consists of an A minor chord broken in zig-zag, changing direction with each of the three compound beats: up, down, up; only the very first interval leap is filled with a passing note. This one-bar motive is sequenced twice (see bar 2: one step up, bar 3: three steps up), after which the gradual ascent is complemented with the upper keynote on the downbeat of bar 4. The following passive descent consists of a run and a falling A minor chord in a complementary pattern between both hands. This descent appears more like a link than an integral part of the four-bar phrase, and later modification can easily be anticipated.

Only the very last eighth-note in bar 4 announces the shift from the tonic to the minor dominant with a D#, representative of the chord B-D#-F#-A, the dominant-seventh of E minor. It is in this key that the four-bar phrase is then imitated by the lower voice.

The link following the imitation in bar 8, features the run and broken chord in ascending direction. The final eighth-note of the bar (A#) seems again set to initiating a harmonic shift, this time to the key of B. However, the ensuing entry of the motif (see L: bar 9) renounces the modulation and commences once more on E. The shape of the four-bar phrase is modified here. The two sequences of M are descending in steps and the linking bar, instead of displaying a complementary pattern splits the original ingredients. Simultaneously featuring runs in the upper voice and broken chords in the lower, it ends the first section of the piece.

Throughout the entire initial section, the contrapuntal figure is characterized by a long note on the first compound beat in each bar followed by a trill figure on the second one. Within the initial phrase, both the long note and the trill represent a tonic pedal, while in the imitation and the developing phrase, block chords and moving trills accommodate the steps of the harmonic progression. The final three-eighth-note group in each bar seems to serve as a small-scale link, consisting of broken chords in the initial phrase but of varying runs in the second and third phrases.

The second section sets out in bar 13 with M and its original four-bar phrase back in the upper voice and the sequences once more moving upwards. There are, however, two new modifications: the contrapuntal motive here omits the trill figure and instead complements the long notes at the outset of each bar with runs throughout the remainder of the bars; and the link at the end of the phrase combines the idea of a run with that of the broken chord by retaining the chord notes from within the run in a split-voice texture (see bar 16).

This phrase ends in C major, without any sign of a modulation even in the final eighth-note of bar 16. One is thus surprised by the next bar which is unexpected both in pattern and in harmony. Over a repeated pedal note, whose pitch is that which a very mindful listener might have anticipated for the pivotal eighth-note (F#, of D-F#-A-C), the upper voice fills in the remaining chord notes in a new complementary pattern. The resolution of this modulating chord follows immediately with the pattern newly established shortly before, in the final bar of the C major phrase (compare bar 18 with bar 16); a sequence of the "pivot-chord bar" then leads to D minor (bar 20). The last two bars of the second section come full circle with the principal motive, now in the lower voice, accompanied by a free variation of the modified contrapuntal figure (compare U: bars 20/21 with L: bars 13-15). The unusual harmonic ending of the section has already been commented on (refer back to footnote 1 of this chapter).

The beginning of the third section gives the impression of a recapitulation: the upper-voice motive commences identically with the original in bar 1, and the contrapuntal motive also takes up the trill-figure familiar from the first section (compare bar 22 with bar 1). The third beat of the same bar, however, already features a variation in the motive; the second bar of the section is harmonically diverted (compare bar 23 with bar 2), and the expected third segment of the sequential pattern is substitute by a closing link which (similar to that which concluded the initial section in bar 12) leads to the reiteration of the cadential-bass deviation (see bars 24-25d). The remainder of bar 25 continues the scalar descent and, more importantly, corrects the cadential close by reiterating it with the "proper" bass steps and melodic leading note.

Finally, bars 26-28 are built upon a tonic pedal. The lower part with its splitting voice is reminiscent of the beginning of the second section (bars 13-15), while the upper voice displays a free variation of the principal motive. The trill figure, added at the very last moment in a split-half of the upper voice, recalls once more the characteristic feature of the original contrapuntal figure, and thus ends this invention with a five-part A major chord.

The dynamic presentation of the composition should be designed to reflect the structural outline as well as the varying thematic density.

The climax of the first section falls on bar 9 where, after two four-bar phrases in protracted crescendo, the developing phrase sets in with a sudden major mode, and with both voices rather highly pitched.
The second section reaches its dynamic peak already at the end of its initial phrase (see bar 16); from there onward, the tension recedes in gradual waves. (Careful: The G# on the downbeat of bar 21 often blurts out because of the preceding large leap but should actually be very soft, in keeping with the pending cadential close.)
In the third section, the dynamic curves are very gentle as long as tonal stability is still awaited. Then, however, in the final three bars with their multiplying parts, a powerful crescendo leads to a rich completion.



WTC I/20 in A minor -- Fugue

I/20.2.1 The subject

This subject is exactly three bars long. It begins on the second eighth-note of bar 1 with the keynote A and concludes with the same note on the downbeat of bar 4. The eighth-note rest in the middle of the phrase appears between, on the one side, a strong-to-weak descending third which causes a momentary relaxation of tension and, on the other side, a new upbeat; it must therefore be interpreted as an indicator of phrasing within the subject. The two subphrases divided by this rest are almost equal in length.

The pitch pattern in this subject presents two long stretches of smooth, stepwise motion, both of which end in consecutive jumps (bar 2: F-G#-E, bar 3/4: B-E-A.) The rhythm consists exclusively of eighth-notes and sixteenth-notes which appear in a simple pattern, without syncopation, tied notes or other outstanding features.

While this description of the obvious attributes is certainly correct, it does not yet convey the entire truth. Two additional observations shed light on the particularities of the melodic line. One regards the groups of sixteenth-notes. It seems interesting to notice that all of them are ornamental figures which embellish an underlying simpler line. (The first two groups, e.g., display the well-known inverted-mordent form.) The other observation regards this assumed simpler line. An investigation into the pitches documents that two of the subject's eighth-notes are of secondary relevance with respect to the melodic structure. In bar 2, the low E on the second half of beat 3 provides a harmonic foundation to the unusual diminished-seventh leap; melodically, however, it is an escape between the high tension in the G# and the resolution brought about with the A after the rest. Similarly, the E at the end of bar 3 serves to keep the eighth-note pace going: melodically it is but an escape within the descending tetrachord D-C-B-A. The result of this short melodic analysis is a skeleton which, far from being "dead and horrid", enhances the comprehension of the subject (see ex. 14):

In the course of the fugue, Bach harmonizes this subject with slight variations. In bars 8/9 e.g., the dominant already appears on the downbeat of the second subject-bar, while in bars 4/5 the tonic is retained much longer and the dominant is only reached on the middle beat. Another discrepancy in the details of the harmonic design of the same two statements occurs in the second half of the subject. Bar 3d displays a dominant, re-established after a resolution onto the tonic of only one eighth-note duration, while the analogous bar 10d is already harmonized as a subdominant representative.

The basic harmonic outline, however, affirms a progression in which the two relevant steps are (1) the short-lived resolution of the dominant onto the tonic on the last eighth-note of the second bar, and (2) the complete perfect cadence underlying beats 3 and 4 of the third subject-bar and resolving on the final downbeat (ex. 15):


I/20.2.2 The statements of the subject

This fugue contains the proud number of thirty-nine subject entries. Particularly in the final portion of the fugue, many of them appear considerably shortened. In the list below, those statements which completely lack the second subphrase are marked with an asterisk. (Note that this fugue, while basically in four parts, introduces a fifth voice from the general pause in bar 80 onwards; this new voice establishes a tonic pedal in bars 83-87. It seemed practical, however, to retain the counting of the original four voices as soprano, alto, tenor and bass during these bars of five-part texture and use "bass 2" for the additional voice.)

1. bars 1 - 4 A 21. bars 57 - 60 Sinv
2. bars 4 - 7 S 22. bars 58 - 61 Ainv
3. bars 8 - 11 B 23. bars 62/63 Binv *
4. bars 11 - 14 T 24. bars 62/63 Tinv*
5. bars 14 - 17 Sinv 25. bars 64 - 67 B
6. bars 18 - 21 Tinv 26. bars 65 - 68 T
7. bars 21 - 24 Binv 27. bars 67 - 70 Sinv
8. bars 24 - 27 Ainv 28. bars 68 - 71 Ainv
9. bars 27 - 30 S 29. bars 73 - 76 Binv
10. bars 28 - 31 T 30. bars 73 - 76 Ainv
11. bars 31 - 34 A 31. bars 76/77 Tinv*
12. bars 32 - 35 B 32. bars 77/78 A
13. bars 36 - 39 T 33. bars 77/78 S *
14. bars 37 - 40 A 34. bars 80 - 82 A
15. bars 43 - 46 S 35. bars 81/82 S
16. bars 43 - 46 B 36. bars 83-85 Binv*
17. bars 48 - 51 Ainv 37. bars 84/85 Tinv*
18. bars 49 - 52 Tinv 38. bars 84 - 86 S
19. bars 53 - 56 Binv 39. bars 85/86 A *
20. bars 53 - 56 Sinv      


In the course of the fugue, the subject experiences a number of variations, harmonic modifications and abbreviations. The most frequently occurring change of shape is the inversion; nineteen of the thirty-nine statements, i.e. almost exactly half of the total number, appear in reverse direction of intervals. Other variations can be grouped as follows:

The second-last note of the subject, earlier described as "of secondary relevance for the melodic structure", is omitted in bar 70 (A) and substituted by an ornamental figure in bars 17 (S) and 26 (A); the ornamental substitution followed by a displaced final note occurs in bars 20/21 (T), 23/24 (B) and, with a slightly different ornamental figure, in bar 60 (A). As all these variations happen in inversions, one might get the impression that they are due to the reverse interval direction. However, the four inverted entries in bars 48-56 appear without any such adjustments.
The four final eighth-notes of the subject are substituted by longer note values and harmonic deviations in bars 60 (S) and 75 (B), whereas in bar 76 (A) they are simply cut off.
Even shorter versions of the subject appear towards the end of the fugue where the second subphrase is only represented by two notes (see A: bars 80-82) or even one (see A: bars 77/78, S: bars 81/82 and bars 84-86). In two other instances, the subject statement breaks off after the eighth-note rest (see T: bars 76/77, A: bars 85/86). Still shorter, in two further statements the last two eighth-notes of the first subphrase are replaced by a quarter-note, thus supporting the interpretation that this final eighth-note is another structurally non-essential note (see S: bar 82 and A: bar 86).
Even less substance is left where not only the second subphrase is completely dropped but the end of the first subphrase is already varied. In bars 83/84 (B), only the initial eleven eighth-note beats of the subject appear intact; in bars 77/78 (S), this is reduced to ten eighth-note beats and in bars 84/85 (T) to only eight eighth-note beats. All these subject entries appear, however, as structurally important components of strettos.
The shortest of the abridged subject statements are of equal length as the episode motive which often quotes the subject's initial bar; this creates confusion - a confusion, however, which was obviously intended by the composer. Thus in bars 62/63 the stretto between bass and tenor, featuring incomplete first subphrases in both voices, does not immediately reveal whether its loyalty lies forward or backward. Only in-depth analysis will show whether these are "false entries" or structurally relevant ones.

Harmonic alterations of considerable impact occur frequently (see e.g. bars 10 (B), 19-21 (T), 44 (B), 58/59 (A), 69/70 (S), 74/75 (A)).

Strettos are a characteristic feature in this fugue; in fact, from bar 27 onwards, not a single subject statement appears without overlapping with another entry. Towards the very end of the fugue, strettos even involve three voices, as in bars 76-78 (T/A/S) or four, as in bars 83-85 (B/T/S/A). As the distance of imitation in the strettos is usually four eighth-notes - the same length as the sequence at the beginning of the subject -, a short parallel results. However, parallels of any larger segments of the subject do not occur.


I/20.2.3 The counter-subjects

In a fugue which is so essentially based on stretto work, it is certainly not surprising that a characteristic and independent counter-subject will be looked for in vain. However, there are two short accompanying figures which, since they recur, deserve to be mentioned. Their common feature is that both establish a short parallel to one fragment of the subject (and are thus not truly polyphonically independent).

In bars 4/5 the alto, having just introduced the subject, builds a counter-motive to the beginning of the subject answer. It consists of two descending tetrachords (see the eighth-notes A-G-F#-E and C-B-A-G), followed by a parallel of the first half of the second subject-bar, and ending, at the latest, with the B on the middle beat of bar 5. This counter-motive is taken up in bars 8/9 where it is shared between soprano and alto, and in bars 11/12 in the alto (where the tetrachords are reinforced by a parallel in the soprano). Later in the piece, the sequencing tetrachords alone, i.e. without the ensuing parallel turn-figure, recur frequently as a counterpart to a subject entry; see particularly bars 14-16 (B, T, A), bars 28/29 (B), bars 53/54 (T), bars 57/58 (T+B), bars 73/74 (T).
In bars 18/19, the soprano creates a short parallel to the second segment of the subject's first subphrase; similar brief parallels occur in bars 21/22 (A), 24/25 (T). As these parallels can also be read as rudimentary imitations of the subject beginning, an interesting interpretation is that they are embryonic forerunners of the stretto entries to come.


I/20.2.4 The episodes

This fairly long fugue encloses altogether sixteen subject-free passages; most of them, however, are only very short.


bars 7/8 E9 bars 52/53

bar 14

E10 bars 56/57


bars 17/18 E11 bars 61-62
E4 bar 27 E12

bars 63-64


bar 31

E13 bars 71-73


bars 35/36 E14 bars 79/80


bars 40-43 E15 bars 82/83


bars 46-48 E16 bars 86/87

In investigating the material used in these subject-free passages, two facts are outstanding: (1) many episodes are simple cadential formulas of one-bar length (or even only half-bar length), (2) several others feature the head motive from the subject. Here are the details regarding these two types.

(1) There are five episodes which consist of nothing but a cadential close:
* E2 features the cadential-bass steps A-G-E as well as a do-si-do (keynote / leading-note / keynote) figure in the alto (see E-D#-E). It concludes on the middle beat of bar 14 in E major.
* E3 combines the cadential-bass steps A-D-D-G with one of the typical closing-formulas - dotted note and anticipated resolution - in the soprano. It closes on the downbeat of bar 17 in G major.
* In E4, the dotted-note closing-formula in the alto and the do-si-do figure in the soprano join the B-E-E-A in the bass in a cadence which regains the tonic A minor in the middle of bar 27.
* The bass notes of E15 also represent the cadential steps in the home key; a typical melodic formula does not appear here.
* The final one and a half bars display a complete harmonic progression over (and between) three tonic pedal notes. The subdominant of this A major cadence is strongly perceived only on the downbeat of bar 87 although it was already fully present on the preceding eighth-note; the dominant, substituted by a vii7, alternates with the major tonic before the progression concludes on the middle beat of this bar.
  Three more episodes feature a harmonic close as their final segment:
* The second half of E8, with the bass progression D-E-F-G-G-C and the melodic formula C-B-C in the soprano, presents a cadential close, this time in C major.
* Similarly, E12 combines the cadential roots G-A-D with the dotted-note formula in the soprano.
* A special case occurs at the end of E13 where the cadential close in F major, represented by the I-IV-V roots in the tenor (bars 72/73) and the dotted-note formula in the soprano (bar 73) overlap with the beginning of the subject statement in the bass.

(2) The head motive of the subject (below referred to as Ms) occurs in seven of the episodes. It is often accompanied by a scale passage in sixteenth-notes.
* E1 features only the inverted-mordent beginning of Ms (A), accompanied by an ascending scale (S) and followed by a descending one.
* In E3, the Ms is extended to the entire first bar of the subject and thus gives the impression of a false entry.
* E6 displays three consecutive combinations of Ms with the descending scale (see bars 35/36: B/A, S/A, B/A).
* The very last segment of E8 which succeeds the cadential close in the first half of bar 48 also combines Ms with the descending scale (S/A), and an imitation of the scale figure in the bass accompanies the ensuing subject beginning.
* The second half of E10 combines an inverted Ms (T) with a scale which bends back (A).
* In E7, the inverted-mordent beginning of Ms (bar 40: T) is unaccompanied but followed by scale figures (T/A/B).
* E12 is preceded by two very much shortened entries at the characteristic stretto distance (see bars 62/63: B/T), and followed by a descending scale (S); here the scale can be interpreted as a subtle means to lead the listener, after only a bar and a half of subject material, into the next episode.
* The final episode also separates the two components; an ascending scale (S) precedes a four-fold Ms (see bar 87: the double-note split of the tenor and, with Ms inversion, the double-note split in A).
* In E5, E8 (bar 46) and E9 the scale figure appears without Ms.

Besides the two components mentioned above, only three episodes present figures which are sequenced and thus of minimum melodic importance (see E7 bars 40/41: B and A; E9 bars 51/52: the trill motive in A and T, recurring once in the soprano of E10; E13 bars 71/72: the imitations between S and T as well as the sequences in A). E8 is the only episode to incorporate an imitation of the subject's tail (see T: bars 45-47).

As a final observation concerning the episode material, it is significant that in all the components mentioned above, sixteenth-notes appear either in ornamental patterns or in broken-chord figures.

Despite the great number of subject-free passages in this fugue and the relative simplicity of the material used in them, not many are found to be immediately related. True correspondences can only be observed between the cadential episodes E2 and E4, as well as between the two short non-cadential episodes E1 and E5. Furthermore, E9 and E10 are related through their prominent motive and its continuation in a descending scale.

The role each of the episodes plays in the dynamic development of the piece is, of course, strongly determined by the presence or absence of the cadential close. The following table describes the episodes in the order of their emergence.

E1 bridges between two consecutive subject statements. It does not provide a color contrast because the Ms figure appears as a sequence of the previous bar, but might encompass a soft rise and fall with the scales.
E2 gives the impression of a close, with a definite relaxation.
E3 seems torn between the concluding power of the bass pattern and the false entry in the alto which links it closely to the ensuing subject statement.
E4 follows with an unequivocal closure and a definite release of tension.
E5 like E1, connects two entries without noticeably interrupting the tension.
E6 with its ascending sequences clearly serves as a preparation for the following subject stretto and thus represents a gradual increase in tension. (Note that in bars 36/37, the soprano sequence of Ms even overlaps with the beginning of the next statement.)
E7 as the third episode in a row without concluding components, introduces the first change of color due to its novel material. In addition, it features descending sequences and a final descending scale, thus ending softly - as if a closure was originally intended here. This closure materializes in
E8 with its extended cadential formula. Surprisingly, it is succeeded by what must be interpreted as a preparation for the ensuing subject statement.

are both conceived as dynamic bridges. As the former emerges from a figure accompanying the end of a subject entry, no definite color contrast can be intended. Also, the latter episode ends with Ms which leads directly into the next statement.

E11 similarly to E7, presents genuine episode material which, in addition, unfolds above an octave pedal. As in E7 the listener cannot anticipate whether a close is coming up or another entry might still follow. In this respect, the stretto between two drastically shortened entries in bars 62/63 appears structurally analogous to the stretto following E7 in bars 43-46.
E12 with its cadential close should then be interpreted as corresponding with the cadence in E8.
E13 also allows for a color contrast because of its genuine little motive. Its ending with the overlap of cadential close and beginning subject statement recalls E2 and distinguishes this as another bridging episode.
E14  differs from all its antecedents by its abrupt halt in a six-part chord. This unexpected halt anticipates the chord on the middle beat of bar 82 with which it corresponds in its six-part texture, its harmonic distinction as an inverted dominant-seventh chord and its rhythmic feature with ensuing general pause. E14 thus includes a genuinely dramatic element which expresses itself in a sudden rise of tension.
E15 provides a dynamic relaxation only after the second abrupt halt in which the subject stretto breaks off.
E16 set in seven-part (!) texture, has no choice but to conclude the fugue in a triumphant climax.


I/20.2.5 Character, tempo, articulation, ornament realization

Despite the apparent predominance of stepwise motion in this piece, the ornamental character of the sixteenth-notes and the overall simplicity of the rhythmic pattern indicate a rather lively basic character for this fugue. A moderately swinging quarter-note pulse is a good choice to express the pensive side of the piece. Both the surface pattern with its ornamental sixteenth-notes and the assumed underlying simpler line (refer back to ex. 14) contain a strong metrical component and express a dance-like character. In order to convey this quality, the natural metric order in four-four time, with weak second and fourth beats, should be observed. (This seems particularly important to remark as in many other strictly polyphonic compositions of this era, this pattern of accented and unaccented beats is almost neglected in favor of the distinctive melodic or harmonic quality of musical events which may often not be metrically supported.)

The appropriate articulation in this character demands non legato for the eighth-notes and all longer note values, and quasi legato for the sixteenth-notes. In the frequent cadential closes, the do-si-do figures as well as the dotted-note formulas require genuine legato. Many exceptions occur, however, in the context of notes (often suspensions) which constitute appoggiatura-resolution or closing formulas.

(For appoggiatura-resolution see bars 6/7 [alto: C-B, E-D, D-C], bar 11 [soprano: D-C], bar 26 [soprano: B-A], bars 40/41 [tenor: G-F, F-E, E-D], bar 62 [alto: F-E]; bar 64 [alto: G-F]; bar 70 [tenor: A-G]. For keynote / leading-note / keynote formulas see bars 13/14 [alto: E-D#-E], bars 16/17 [bass: G-F#-G], bar 23 [soprano: C-B-C], bars 26/27 [soprano: A-G#-A], bar 32 [tenor: E-D#-E], bar 34 [alto: E-D#-E], bars 47/48 [soprano: C-B-C], bar 60 [bass: A-G#-A], bar 64 [tenor: D-C#-D], bar 73 [alto: F-E-F], bars 75/76 [bass: G-F#-G]. There is only one closing formula in the bass which requires partially legato articulation; see bars 47/48 [D-E-F-G = legato]).

A good choice for the relative tempo of the prelude to the fugue is one which reflects the interpretation of the compound meter:

one dotted quarter-note
corresponds with
one quarter-note
in the prelude
  in the fugue

(Approximate metronome settings:
80 for both the compound beats in the prelude and the quarter-notes in the fugue.)

The A-minor fugue contains both cadential and melodic ornaments; in addition, some cadential ornaments may be added where they would have been so self-evident, in the convention of Bach's contemporaries, that putting them down seemed less imperative.

In bars 21 and 64, the dotted-note figures in the soprano carry the mordent which is so typical for this formula. The brackets indicate that the composer himself did not find it necessary to specify this obvious ornamentation, but one of his students took it down. The same brisk mordent should be added in bar 17 on the dotted F# and in bar 73 on the dotted G. Among these, only the mordent in bar 17 commences on the main note and therefore makes do with only three notes; the remaining three mordents begin on the upper auxiliary and contain the regular four notes. (In bar 27, the figure appears in the alto and thus makes ornamentation much more difficult to execute. However, for performers with a good technique it is possible to play the mordent in the left hand, then take over its sustained final note in the right thumb, the ensuing sixteenth-note A again in the left - quite without disturbing the legato required for the upper voice.)

The trill in the motive which appears in E9 and E10 represents a note-filling ornament. Commencing each time on the upper neighbor note and shaking in thirty-second-notes, this trill comprises eight notes (including the suffix which is spelled out in all cases).

Much headache has been caused by the apparent impossibility to play the fugue's final five bars with their sustained bass pedal and the texture with up to seven voices. The following excerpt attempts to help by suggesting one possible execution.

(ex. 17)

I/20.2.6 The design of the fugue

In this A minor fugue, Bach seems to play with transformations of the subject in a way which reminds one of the D#-minor fugue, also in Book I. Conclusive evidence for the structural design can therefore be derived already from an observation of the order in which the subject statements enter, from the change of shape found in a number of consecutive entries, and from the presence or absence of strettos. The data which can be collected in this respect are particularly indisputable in the first three quarters of the fugue.

The first four entries - one in each of the four voices - appear without any overlapping (see bars 1-14).
They are followed by four inverted statements - also one in each of the four voices - which equally appear neatly after one another (see bars 14-27).
The next eight entries retrieve the original shape of the subject but are grouped in pairs: every other statement enters already half a bar after its predecessor and thus overlaps for two and a half bars (see bars 27-46).
This group is followed by eight entries in inversion which feature the same kind of stretto at the same half-bar distance (see bars 48-63). (The correspondence between the two groups of four-fold stretto gives the two abridged statements in bars 63/64 more importance than their radically shortened shape would suggest. Analysis reveals that they constitute indeed the fourth, though incomplete, group of this section.)

It is reassuring to notice that each of these four groups ends with one of the episodes which were earlier recognized as cadential formulas (see E2 in bar 14, E4 in bar 27, the second segment of E8 in bars 47/48, and E12 in bar 64). The confines of sections I through IV can thus be regarded as confirmed.

The remaining subject statements, from bar 64 onwards, comprise a stretto in original shape followed by two strettos in inversion - all using the complete phrase. Immediately afterwards appear three strettos comprising, respectively, three entries (see bars 76-78), two entries (see bars 80-82) and four entries (see bars 83-86).

All these statements are drastically shortened; in fact, in each of the strettos, only one of the statements progresses at all into the second subphrase. In order to determine the intended grouping of these six strettos one had best again look for guidance in the episodes. There are two subject-free passages which end with a perfect cadence (see E13: cadential close belatedly in bar 73, and E15: cadential formula in bar 83); these should therefore be interpreted as designating section closes. The fact that in the former case, the typical closing-formulas in the soprano and alto overlap with the beginning of the subsequent bass statement indicates that the structural partition between the two final sections of the fugue is not as clear-cut as the earlier section-endings were. The cadential close of E15 in A major, on the other hand, appears strong and definite; it determines the final bars of the composition with their pedal note in the additional second bass as a coda.

The use of texture in the various sections of the fugue might give further clues for how Bach conceived the design of the fugue. The first stretto of section III (and, with some irregularities at the beginning, also that of section IV) begins with only one accompanying voice, i.e. in reduced number of voices. It is then particularly noteworthy that the first stretto of section V appears completely unaccompanied. The commencement of section VI, however, with only three moving voices gives the impression of reduced texture but actually encompasses four parts; the indirect pedal C in the soprano suddenly comes to life again in bar 75. This observation substantiates the interpretation that sections V and VI in this fugue are more closely connected than any other consecutive sections. The overall design of the fugue thus contains two pairs of corresponding sections (sections I/II and III/IV), followed by the only minimally structured larger body containing sections V/VI and a short coda.

For a sketch showing the design of the fugue in A minor, see ex. 18.

The harmonic outline of the fugue supports the structural correspondences established above.

The first section contains entries on the tonic and dominant of A minor and ends with an E major cadence. Section II begins with a dominant statement and returns to the tonic with an A minor cadence.
I/II = tonic - dominant - tonic
Section III is still firmly rooted in the home key during its three initial strettos; after the longer interruption of E7, however, the redundant entry-pair presents the relative major key which is confirmed, at the end of E8, with a cadence in C major. Section IV returns to the home key but ends, both in its second stretto and the final abridged pair, in the subdominant region, which is confirmed in E12 with a cadence in D minor.
III/IV = tonic - its relative major - tonic; end on subdominant
The two final sections of the fugue, earlier ascertained as forming a larger unit, further underscore the subdominant field. Section V begins with a stretto of entries in A minor and D minor, and were its final cadence not placed across the beginning of the sixth section, it would conclude in F major, the relative major to the subdominant. Section VI, after several harmonic adventures* ends with a perfect cadence in A major, the Picardy-third version of the tonic (bar 83). In the coda, however, the final four-part stretto is led by a soprano statement in D minor, a last reminder of the subdominant key set against on overwhelming tonic (see three A-minor entries and the A pedal). The final cadence, as expected, confirms the A major conclusion.
V/VI = subdominant - (its relative major) - major tonic
coda = subdominant/(minor) tonic - major tonic

(* Section VI contains a number of features of particular interest. Striking, among other things, is the number of pedal notes which mark this section as a concluding one; see bars 73-75: C [soprano], bars 76/77: G [bass; actually beginning already on the middle beat of bar 75 but escaping momentarily to its leading note], bars 79/80: D [bass, interrupted], and bars 83-87: A [additional second bass voice]. Another arresting highlight is presented in the two inverted dominant-seventh chords which, enhanced by the voice-splitting into six parts, precede the reiterated general pause in bars 80 and 82.)


I/20.2.7 The development of tension

The development of tension in the first section of this fugue is both normal, insofar as it describes a steady dynamic rise, and unusual, insofar as this rise seems least caused by contrapuntal complexity. The growth of tension could be described as extroverted. While volume is added by way of a gradual increase in the number of voices, the additional parts serve much more to reinforce the already introduced material than to create polyphonic intensity. The number of bars which contain parallels to segments of the subject (bars 5, 9, 11, 12) or to portions of the counter-subject (11/12) is astounding for a Bach fugue.

Similar observations can be made in the second section. As its first subject statement is accompanied by the tetrachords from the counter-subject with parallels in contrary motion, the effect is that of only two-part polyphony with a doubling voice. Further parallels or doublings in contrary motion, of the subject or a contrapuntal voice, occur in bars 18, 19, 21, 24, 25-27. Moreover, the first three of the four entries in this section remain largely in three-part texture (with only short four-part overlappings at the beginning of the second and third statements). The dynamic increase thus resembles that of the first section: it represents an extroverted growth in volume through four statements, the climax of which captures the listener directly, with the immediate force of its prolonged parallels, without claims to the intricacy of texture expected in a fugue.

The third section commences with half a bar in two-part setting; the third voice which joins soon with a complete imitation of the subject engenders the impression that now - finally - polyphonic independence of the voices is established. The second stretto involves three voices (after, again, a short four-part overlapping at the beginning) and the third stretto, four. This gradual increase in texture is supported by an increase in polyphonic complexity, and as the connecting episode E6 with its fake stretto entries keeps the tension from dropping, an almost continuous crescendo results through these three paired statements. E7, however, introduces the first pronounced color contrast in this piece. The ensuing fourth stretto of this section is not only redundant due to the entering order of the voices (its "leader", the soprano statement, is a repeat of the soprano-led stretto which opened this section); it also fails to regain the intensity interrupted by E7, owing both to a rather passive fourth voice which consequently drops out (see tenor, bars 43-45) and to the less dramatic character of the major-mode variant of the subject. The extension of this entry, created by the imitation of the second subphrase (tenor bars 45-47) prepares the upcoming section-ending in a prolonged diminuendo.

As the second section was, in many regards, similar to the first, so the fourth section reveals itself as corresponding very much to the third. While four voices are in fact involved in its first entry, there are at no point more than three actively moving. In addition, the unusual three-part parallel in bar 49, created by the two subject entries and a doubling passage in the soprano, leaves the impression of reduced polyphonic intensity. (The composition, at any rate, creates this impression - the performances rarely do. However, a thorough analysis might convince pianists that, in this fugue, parallels stand for weakened contrapuntal intensity, and the doubling voice (here the soprano) should be played as a dependent part, i.e. extra soft.) The second stretto of this section is the most powerful from a contrapuntal aspect, while the third features again extended parallels in the two accompanying voice and an ending which overlaps with the next episode. E11, just like E7, brings forth a color contrast, underscored here by the octave pedal (two voices which, although present, are markedly passive). The redundant entry pair expected in correspondence with that at the end of the third section is even less assertive here than there: it breaks off after not even half of the subject. This half-hearted entry, together with the ensuing E12, conclude this section again with a definite diminuendo.

The unaccompanied stretto which launches the fifth section constitutes the beginning of an entirely new dynamic development. The tension rises towards the second stretto, is interrupted by the color-contrast in E13, but picks up almost where it was left at the beginning of the sixth section. Thereafter, the tension grows again; gently at first while voices are still resting or passive (up to bar 77), then more steeply. Dramatic moments arise particularly in the two six-part chords preceding the general pauses. While the subsequent E15 generates harmonic relaxation in an A major close, this cadence, coming entirely in five-part texture and terminating in the final pedal, allows no dynamic subsiding.

A powerful coda, appropriately interpreted in crescendo allargando, concludes this extraordinary fugue.