from Siglind Bruhn
J.S. Bach's Well-Tempered Clavier
In-depth Analysis and Interpretation
I/14.1.1 The prelude type
With the exception of very few bars, this prelude shows strict two-part polyphonic writing. When perusing the thematic material one finds that the opening idea (see U: bars 1/2) is not only imitated in the lower voice immediately after its first statement but also recurs constantly in the course of the piece. As the initial imitation is placed on the fifth, there is a strong case for suspecting that this prelude is composed in adherence to the principles of a fugue.
I/14.1.2 The overall design of the prelude
The first harmonic progression already concludes on the downbeat of bar 2. As this harmonic conclusion coincides with the initial statement of the "subject", this cadence does not represent a structural break. Similarly, any further statement will conclude in a perfect cadence. These are thus not the cadences one is looking for when trying to determine structural units. The only conspicuous cadence formulas outside the subject statements occur in bars 12, 18/19 and 21/22. The first and third are perfect cadences, one in the dominant (bar 12), the other in the tonic (bars 21/22). The third formula designates an imperfect cadence (see bars 18/19, subdominant /dominant of F# minor).
Structurally relevant analogies are scarce in this prelude. Only the two bars immediately following the two above mentioned perfect cadences are composed alike (compare bars 12m 14m with bars 22d-24d, transposed from C# to F#). Their three-part texture with a sustained note in one voice and a eighth-note and rest figures in another refer to the beginning of the piece (compare bars 12/13 and 22 with bar 1).
I/14.1.3 Practical considerations for performers
The basic character of this prelude is without doubt rather lively. This follows both from the simple rhythmic pattern which consists predominantly of sixteenth-notes and eighth-notes in a straightforward setting, and from the pitch pattern which contains leaps in the eighth-notes and a mixture of ornamental figures and broken chords in the sixteenth-note segments. In fact, there seem to be hardly any notes at all which would require emotional depth; so the tempo, reflecting this truth, should be very swift. Articulation demands a light quasi legato for the sixteenth-notes and an effortless non legato for the eighth-notes.
The only ornaments in the prelude are the three cadential trills. All of them appear in that pattern which is typical for Baroque closing-formulas, a dotted note followed by the anticipated resolution. All three trills (see bars 12, 18 and 21) are therefore point d'arrêt trills: they stop short a considerable distance before the succeeding sixteenth-note on the half beat eighth-note or slightly before. The trills in bar 12 and bar 18 both begin - on the upper auxiliary and, moving in thirty-second-notes, contain four notes. The ornament in bar 21, as it is approached stepwise, begins on the main note and features only three notes (two thirty-second-notes and a syncopated eighth-note).
I/14.1.4 What is happening in this prelude?
The prelude in F# minor has been unmasked as a composition built along the lines of a two-part fugue. How strict a fugue it is, and where it deviates from the fugal pattern, will be the main question to be discussed.
The subject is introduced in the upper voice (bar 1, second eighth-note until the return to the tonic on bar 2d. Whether the A on bar 2d itself or the third sixteenth-note F# constitute the intended melodic ending is almost impossible to decide.) This initial subject statement brings about the first deviance from the fugue model -- a deviance that is, however, frequent in preludes composed as fugues: it is not presented as an unaccompanied line but comes with two additional "voices". As was mentioned earlier, one of these voices moves in eighth-notes interrupted by eighth-note rests and doubles the peak notes of the subject in parallel compound thirds; the other consists of a sustained tonic keynote and its octave displacement. In the course of the fugue it can be detected that the two structurally analogous statements, those after the perfect cadences in bars 12/13 and 22/23, are also presented in a sudden three-part texture, each time with one voice acting as a pedal and the other moving in parallels to the subject peak notes. (For reference, this line of parallel eighth-notes will here be called "C", for "companion".)
The following two subject statements allow for two fake counter-subjects to make their appearance. Both, as will be shown, derive from the "companion".
|C1||is introduced in the expected position against the second subject entry
in bars 2/3. It consists of leaping eighth-notes and, if regarded as a hidden
two-part structure, describes in its lower part the same compound third
parallel to the subject peak notes as the companion of the opening entry.
(More clearly than in bars 2/3 where it accompanies the answer this can
be seen in bars 9/10.)
|C2||makes its first appearance in bars 4/5 against the third subject statement. It is characterized by broken chords filled each with one additional passing note. The line built by the lowest notes of these chords is, once again, a parallel to the subject's peak notes.|
The following example documents the relationship between the subject and its three companions; the undue eighth-notes in the first bar are revealed, in the light of the two following regular counter-subjects, as a feature to be taken seriously since both derive strikingly from it. For easier comparison, all examples are transposed to the tonic and appear with the subject in the upper voice (ex. 13)
A third companion to the subject is introduced only in the second half of the composition. This companion appears in block chords which strike in eighth-notes separated by eighth-note rests; its rhythmic pattern is thus that of the first-bar companion, and the descending scale derived from the compound third parallel to the subject's peak notes is also present (see in the right hand part of bars 14/15 the lowest notes E-D-C#-B). This figure thus continues the development we have so far witnessed from one mutation of the companion to the next in a logical way - from single notes via hidden two-part structure and broken chords to block chords. (As these chords show no attempt whatsoever to establish any melodic line, one would not normally give them the name of a companion. However, for the sake of easier identification and because of their striking analogy with the other companions these chords shall here be referred to as C3.)
What is truly surprising is that only this C3 accompanies the inversion of the subject, and thus does not build the usual parallel. As a consequence, the ensuing subject entry, also an inversion, is then accompanied by the compromise: one descending (originally parallel) and one ascending (now parallel) line (see bars 15/16). Finally in bars 19/20, things appear upside down in that the subject is here returned to its original shape but the scale in the accompanying chords is ascending (see bar 19 upper notes of right hand; the immediate relationship between these chords with the chords in bars 14/15 is revealed when one compares the lower notes here with the upper pitches there.)
The fourth and final step in the development of the companion is the direct parallel in compound thirds. This is accomplished in bars 20/21 and does not ever recur.
The subject statements in this "fugue" and their respective companions thus present the following picture (Sinv = subject inversion, Spar = subject parallel):
To answer the question about the structure in this "fugue" by grouping the subject statements into sections would probably mean carrying the exercise too far. The only relevant structural caesuras in this highly virtuoso piece occur at the cadential closures mentioned above; thus the performer should try to convey a polyphonic composition in two sections followed by a coda, and not the (theoretically possible) six fugal "rounds".
WTC I/14 in F# minor - Fugue
I/14.2.1 The subject
The subject of the F# minor fugue is four bars long. It begins after a rest with the second quarter-note of the 6/4 bar, thus conveying the impression of an extended upbeat. Its conclusion is reached on the downbeat of bar 4 where the melodic line returns to the keynote F# after an ornamented G# which harmonically represents the dominant. The length of the final note is exceptional in bar 4; later subject statements end frequently with only a eighth-note as the closing note.
The pitch pattern in the subject (as well as in the entire fugue) features predominantly stepwise motion, with very few skips. The rhythmic pattern is highly varied, containing eighth-notes, quarter-notes, dotted quarter-notes etc. up to the tied four quarter-note value in the subject. Syncopations appear frequently, two of them already in the subject.
Phrasing in this subject permits two options which create quite different effects.
||On the one hand, there are three similar note groups which can be interpreted
as varied sequences: F#-G#-A
is sequenced in contracted note values in G#-A#-B,
and sequenced again (after an additional A#-G#
pair) in A#-B#-C#.
It is therefore possible to view the subject as consisting of three consecutive
ascents of which only the last one is complemented in a descending motion.
In this case, subtle subphrasing after the long notes which end the first
two ascents (i.e. after A# and B in bar
2) is adequate.
||On the other hand, it is also possible to imagine these same notes as expressing one single gesture: an ascent through F#-G#-A---B---C# (or even F#-G#-A-A#-B-B#-C#), in which the long notes are directed forward (instead of serving as transitional endings), and in which the tension between one long note and the next is further enhanced by additional artificial leading notes (A#, later B#). If this is what the performer feels, the subject should not be broken into smaller units but conceived as a single curve. (By the way, the short instances of backtracking during the ascent find their equivalent in the descent which also falls in two sweeps.)|
The harmonic layout of the subject is simple in its large steps but fairly complex in the small ones; this is caused both by the artificial leading notes in the subject and by the high degree of chromaticism throughout the fugue. The main steps of the simple progression are represented by the three long notes, with A (bar 1) for the tonic, B (bar 2) for the subdominant, both C# and the ornamented G# (bar 3) for the dominant and the final F# (bar 4) for the return to the tonic. The more complex harmonic progression which Bach uses e.g. in bars 15-18 is shown in ex. 74 below. The Roman numerals show how Bach actually passes through the keys of B minor and C# major -- subdominant and dominant in his harmonization of the subject (ex. 14):
Depending on which of the two interpretations mentioned above the performer chooses, the dynamic outline of the subject will come out slightly different. The climax is the same: the goal of the ascending sequences or, in the alternative interpretation, the target of the powerful ascent with its enhancing chromaticism, lies on the highest pitch C# on the downbeat of bar 3. However, the preparation of the climax and, with it, the degree of urgency expressed in the subject, is very different in both concepts. In the first case, the climax is reached in consecutive sweeps each of which commences newly in a relatively relaxed way. (A string or wind player would decrease volume on the long notes.) In the second case, the tension grows constantly and thus much more powerfully through all notes. (A string or wind player would increase volume during the long notes so as to incorporate them into the long crescendo.) The character expressed in the two different interpretations has a considerably different impact.
I/14.2.2 The statements of the subject
The subject appears nine times throughout the F# minor fugue (ex. 15).
|1.||bars 1-4||T||6.||bars 25-28||S|
|2.||bars 4-7||A||7.||bars 29-32||T|
|3.||bars 8-11||B||8.||bars 32-35||B|
|4.||bars 15-18||S||9.||bars 37-40||S|
The subject suffers hardly any modification in the course of the fugue. The answer is real, with all intervals kept intact, and only in one statement is the beginning slightly varied (see in bar 25 the 3 eighth-note upbeat C#-F#-D# instead of the simpler 2-quarter-note approach C#-D#). However, a more significant modification, the inversion of the subject, does occur twice. It is introduced with the alto entry in bars 20-23 and recurs in the bass statement in bars 32-35. Neither stretto nor parallel are found in this piece.
I/14.2.3 The counter-subjects
The F# minor fugue contains two counter-subjects. One is conceived as a fairly regular companion to the subject while the other materializes only twice.
|CS1||is introduced against the second subject statement, in bars 4-7 (tenor).
It consists of two clearly distinct halves. The second segment presents
the extended version of a closing-formula see the typical leaps D#-G#-C#
and the do-si-do (keynote / leading-note / keynote) figure with its classic
syncopated rhythm, while the first half is characterized by frequent note
repetition. On closer inspection one detects that this pattern actually
consists of note pairs: C#-B, B-A#,
A#-B and so on. These pairs are harmonically
conceived either as main note + anticipation of the next (see bars 4/5 and
13/14) or as appoggiatura-resolution (see e.g. bars 8/9). Whichever
their harmonic background, these patterns are well known in Bach's music,
particularly in his vocal music, under the name of "sigh" figures. In the
context of this counter-subject it is important to distinguish between those
pairs which constitute genuine "sigh" figures, and those which do not and
should therefore sound different. (The two notes in a true "sigh" figure
are usually neighboring notes; they always represent different harmonic
steps. Skips and leaps, especially if they occur within a single harmony,
are therefore not "sighs" and should not be played as pairs. Examples for
such notes which appear in the context of "sigh" figures but do not belong
are: the octave jump in bar 15 middle (the lower F#
is in fact the end of one little subphrase, and the higher F#
is the beginning of the actual CS1); similarly in bar 19 middle, bar 22
middle, bar 29 middle and bar 32 middle.)
Dynamically, the first subphrase represents a gradual diminuendo to the long G#. The second subphrase follows with a crescendo up to the half-note C# and ends in a final relaxation.
first appears against the third subject statement, i.e. in bars 8-11
(tenor). It begins on the second quarter-note (C#)
and consists of three subphrases. The first ends on the dotted half-note
B; its ending is then sequenced in diminution (see bar 9: E#-C#-F#),
after which the third subphrase sets out from the syncopated C#
with an ascending portion of the melodic F#
minor scale followed by a descent in natural F#
minor. This subphrase, and with it the entire counter-subject, should
regularly end with the resolution on the downbeat of the final bar; in
this first statement, however, the resolution note A appears delayed.
The example below shows the phrase structure and dynamic design in the subject and its two counter-subjects (ex. 16):
I/14.2.4 The episodes
The F# minor fugue contains six subject-freepassages.
|E1||bars 7/8||E4||bars 23-25|
|E2||bars 11-15||E5||bars 28/29|
|E3||bars 18-20||E6||bars 35-37|
Three episode motives can be distinguished; two of them are remotely related to the primary material:
|M1||in its simple shape of four ascending notes is the most prominent episode
motive in this fugue. Both its rhythmic gesture which consists of three
eighth-notes followed by a three eighth-note value, and its pitch pattern
which contains artificial leading notes, recalls a segment from the middle
of the subject (compare E1: E-F#-G#-A,
with bars 2/3: G#-A#-B#-C#).
The dynamic shape of M1 is a crescendo.
|M2||The initial six notes of CS1 with their upbeat, two "sighs" and a final
note are employed in E3, E4 and E6. This figure will be called M2. Dynamically
it takes up, within an overall diminuendo, the subtle groupings from the
|M3||appears exclusively in E2 is only vaguely defined; it seems conceived as a concave curve with the climax in the middle, at or close to the lowest point of the curve. Ex. 17 illustrates this with the help of the extract from the score.|
The fourth episode stands out as different from the others because it emerges from the preceding subject statement without any clear beginning. The soprano in bars 23/24 continues the descent in syncopations begun towards the end of the subject entry (see bars 22/23 F# E, continued in bars 23 25: D-C#-B). At the same time, the bass presents sequences of that variation of the CS1 beginning which accompanied the end of the inverted subject (compare bars 22/23: D A# with bars 23/24: B-F# and, shorter, bars 24/25: G#-E#). Similarly, the alto also extends the end of the subject statement in varied sequences (compare bar 23: G#-A-B-C# with the ensuing groups F#-B and E-F#-G#-A). This entire episode can thus best be regarded as an extension of the preceding subject statement.
The structure of the episodes and their inter relationship is interesting.
||E1 recurs faithfully (except for the octave displacement) in E5 and thus creates a distinct symmetry.|
||E1 also reappears, slightly varied and with an accompanying voice, as the first part of E2 (see T+B: bars 11/12) and of E3 (see S+B: bars 18/19).|
||The second segment of E3 contains a parallel presentation of M2 in the outer voices (soprano and bass) followed by imitation, also in parallel, in what seems like the inner voices (but is actually the alto and the bass after an octave displacement, since the tenor is resting). This pattern is taken up in E6, in bar 35 with a sequence in bar 36. This creates a second structural analogy.|
Finally, there are two cadential formulas in this fugue, apart from the one in the final bar. One appears in bar 20 where the key of C# minor is confirmed in a perfect cadence. The other formula, with a dangerously similar looking bass line, marks the end of the above mentioned subject extension (see bar 25). This one, however, is not only an imperfect cadence but also overlaps with the beginning of a new subject statement in the soprano. It may therefore not be regarded as a structural caesura.
The features described above are also those which determine the role played by each episode in the dynamic development of the composition.
||E1 and E5 both commence slightly softer than the end of the preceding subject entry, after which they prepare the subsequent entry in a two fold crescendo.|
E2 begins with a similar build up. This is followed by a very gradual release generated by the overall descending direction of the M3 appearances. A complete relaxation is, however, held at bay by the frequent quotations of the outgoing M1 in the bass (bars 13/14).
||E3 again sets out with the same active gesture, followed by a gradual diminuendo in bar 19 and a complete relaxation in the perfect cadence.|
||E6 picks up this gradual release; it is a bridge to the subsequent entry.|
||Finally, E4 continues the diminuendo of the subject ending and thus, in a moment of particularly low tension, creates a kind of anti climax.|
I/14.2.5 Character, tempo, articulation, ornament realization
Both the pitch pattern with its overwhelming use of stepwise motion and the rhythmic organization with its variety of note values are unequivocal in determining the basic character of this fugue as rather calm. The frame for the tempo is set on the one hand by the required tranquility of character, and on the other hand by the rather long note values which still need to be perceived as "alive". In other words, the eighth-notes must be slow enough to convey serenity, but not so slow as to impede the listener from taking the entire subject on one breath, and thus cause the subject to fall to pieces.
The articulation is generally legato. Only the first half of the first counter-subject as well as the episode motive derived from it contain slurring in pairs, following the pattern of the "sigh" figures (refer back to ex. 15). The only notes to be played non legato are the consecutive leaps in the second half of the counter-subject (see e.g. bar 6: D#-G#-C#) and the cadential bass patterns in bars 20, 25 and 39/40.
For the relative tempo of the prelude to the fugue, a good and feasible solution is:
half a bar
in the prelude
in the fugue
(Approximate metronome settings: prelude beats = 112, fugue beats = 84.)
The only ornament in this composition is the trill incorporated in the subject. As it is duly complemented by its resolution, it is a note-filling trill. Approached in stepwise motion it commences on the main note, retains this for the length of a eighth-note and then shakes in sixteenth-note motion, ending with a suffix (altogether seven trill notes). This trill, being an integral part of the subject, must be transferred to
||bar 6 D# and bar 10 G# (where it is indicated in brackets);|
||bar 17 G# and bar 31 G#, i.e. on the second-to-last notes of original-shape entries;|
||bar 23 B and bar 34 E#, i.e. on the second-to-last note of inverted entries. (Students sometimes ask whether trills are also upside down in inverted statements. The answer is: no, ornaments are not to be inverted.)|
In the final statement of the subject, the Picardy third of the fugue ending impedes execution of the trill. The ordinary trill on G# would shake with A as its upper note; this A, however, clashes with the A# in the middle voice. A trill with A# is obviously also out of the question because of the preceding A natural. This subject ending must therefore go unornamented.
I/14.2.6 The design of the fugue
The entering order of the voices and their respective surrounding texture, in conjunction with the explicit cadence at the end of E3, clearly determine the binary structure of this composition:
||The full ensemble of four voices is reached in the fourth subject statement (bars 15-18).|
||The cadential formula closes this section in C# minor, the minor dominant of F# minor (middle beat of bar 20).|
||The entries which follow manifest in a very subtle way a protracted suspension before the renewed full ensemble:|
|*||bars 20-23, statement in inversion,||3 voices, no CS|
|*||bars 25-28, statement in original shape,||3 voices, with CS1|
|*||bars 29-32, statement in original shape,||3 voices, with CS1, CS2|
|*||bars 32-35, statement in inversion,||4 voices, no CS|
|*||bars 37-40, statement in original shape,||4 voices, with CS1|
The utilization of counter-subjects and the scheme of the episodes displays a certain analogy between the two sections of this fugue.
|section I||section II|
|statement 1, no CS||=||statement 1, no CS|
|statement 2, CS1||=||statement 2, CS1|
|E1 (only M1)||=||E5 (only M1, = E1)|
|statement 3, CS1 + CS2||=||statement 3, CS1 + CS2|
|(E2)||(statement 4, no CS)|
|statement 4, CS1 + 1/2 CS2||\/||E6 (M2 = 2nd segment E3)|
|E3 (M1, M2)||/\||statement 5, CS1|
The harmonic outline of the composition is very straightforward. The four subject statements of the first section are all in F# minor (on the tonic, dominant, tonic and tonic respectively); the episode which concludes this section modulates to the key of the dominant. The five statements in the second section are again all in F# minor (on the tonic, dominant, tonic, subdominant and tonic respectively). In other words, the harmonic succession is the same in both sections, with only the "additional" statement in section II on an unprecedented step.
For a sketch showing the design of the fugue in F# minor, see ex. 18.
I/14.2.7 The development of tension
In both sections of this symmetrically built fugue, the tension rises gradually but constantly from entry to entry. The episodes E1 and E5 have bridging functions with proceeding direction, while E2 and E6 have bridging functions with receding direction, and E4 is conceived as an extension of the preceding statement without any explicit change of color. Only E3 with its cadential formula has concluding character.