from Siglind Bruhn
J.S. Bach's Well-Tempered Clavier
In-depth Analysis and Interpretation
II/15.1.1 The prelude type
This prelude belongs to the virtuoso, playful category. Indicators are a very simple rhythm pattern with almost constant sixteenth-note motion, standard figures which create constant movement by means of repeated indirect pedal notes in hidden two-art structure, and a low melodic profile in all thematic components.
II/15.1.2 The overall design of the prelude
The first cadential formula within this prelude occurs in bar 13. As the downbeat of bar 14 reveals, this cadence is interrupted by a resolution to B minor instead of the expected D major. A perfect cadence in the key of the dominant is reached shortly afterwards in bar 16; this bar is clearly marked as the end of a section by the repeat sign.
The second section begins in D major and ends in bar 28, with a cadential formula very similar to that which was interrupted before (compare bar 27 with bar 13). The key reached here is E minor, the relative minor to the tonic G major. The four bars which follow are harmonically intriguing. Although the preceding cadence was a perfect one and does not need "correction", it is followed in bars 31/32 by another harmonic close, related to it by a similar bass figure, which confirms the modulation to the subdominant C major.
The return to the tonic announces itself from bar 37 onwards; the cadential formula in bar 45 - the same that had been heard already twice before - leads again into a deceptive resolution (see bar 46: E minor instead of G major) and is followed by a perfect cadence in the home key in bar 48.
The structural layout in the G major prelude can thus be regarded under two aspects.
On the one hand, consideration of all details as given above discloses a slightly irregular layout.
On the other hand, the main (expected) harmonic steps in the prelude suggest three portions of equal length:
|I||bars 1-16||I-V||I||bars 1-16||I-V|
|II||bars 17-28||V-vi||II||bars 17-32||V-IV|
|III||bars 29-48||ii-IV-I||III||bars 33-48||IV-I|
There are several important structural correspondences in the piece:
|bars 11-16||recur in||bars 43-48||(transposed)|
|bars 1-6||can be recognized in||bars 17-22 and 37-42||(strongly varied)|
|bars 9-11||can be recognized in||bars 23-25||(strongly varied)|
II/15.1.3 Practical considerations for performers
The basic character of this prelude is without doubt rather lively. The tempo should be quite flowing. The appropriate articulation distinguishes quasi legato for the sixteenth-notes in the hidden two-part structure and a denser legato for the sixteenth-notes in ornamental figures (see e.g. the written-out inverted mordent on the first beats of bars 7 11; if played in the same touch as the surrounding sixteenth-notes, the middle notes of these ornaments might appear to belong to the melodic line built in the hidden two-part structure - this should certainly not be conveyed.) Non legato is adequate for all eighth-notes. (The two only exceptions necessary for reasons of simple performance convention occur in bars 16 and 48 where the eighth-notes at the beginning of a descending scale in sixteenth-notes are traditionally included in the legato.
Several ornaments appear in the score; some of them are used consistently, some are not. The turn on the last note of the upper voice in bar 13 recurs identically in bars 27 and 45. In all cases, it begins with the upper neighboring pitch, contains four notes and must - because of the octave displacement of its resolution - be played very fast. (A feasible solution consists of a triplet in thirty-second-notes plus a sixteenth-note.)
In two cases, the same cadential formula is additionally decorated. In bar 45, we find a mordent on the third sixteenth-note. It enhances the virtuoso character of the piece and can easily be integrated (again a thirty-second-note triplet). Performers may then wish to consider transferring this mordent to the corresponding note in bar 13. The additional turn in bar 26, on the other hand, occurs in a surrounding of melodic eighth-notes which has no immediate analogy. Executing it may underscore the playful side of the piece but obscure the parallels between the two hands an interpretation left to the performer. If played, this turn commences on the main pitch and encompasses five regular notes.
The final cadence of the first section also features two ornaments. Both the accented bass note of chord V7 and the final I carry an inverted mordent. In the corresponding cadential close (see bars 47/48), the first of the two ornaments is lacking. If played in bar 15, it should also be added here. As to the pitches of the lower neighboring notes, only the D in bar 16 is ornamented with an artificially raised leading note since the modulation has brought us the key of D major. All other inverted mordents use notes belonging to the scale of G major.
Finally, there are four purely melodic ornaments. Three are taken up by the inverted mordent which enhances the long E in bar 32 and its two sequences. All are meaningful ingredients both with regard to the character and the structural clarity of the piece, and contain no problems. The fourth, a mordent, occurs in bar 20. In a pattern which otherwise always couples simple eighth-notes with a eighth-note line emerging from within a hidden two-part structure, this ornament seems at first glance confusing. A closer inspection of the left hand reveals that the melodic eighth-note lines are, in fact, interrupted here. The sudden unexpected ornament may serve to emphasize this.
II/15.1.4 What is happening in this prelude
The prelude is based on models (i.e. multi-voiced, homophonically conceived units with a distinct texture) rather than on motives (which, by comparison, would be expected to be polyphonically versatile). Three of these models determine the first two of the prelude's three sections.
|M1||unfolds on four levels which can be grouped as two pairs. There is a sustained
pedal G in the lowest voice, and a repeated indirect pedal D on the weak
beats of the hidden two-part structure in the upper voice. In between,
there are two lines moving in eighth-notes: one is written in eighth-note
values, the other forms the main beat portion of the hidden two part structure.
These lines move in strict parallel sixths. In the following three bars,
the model recurs in a mixture of sequence and imitation: The sustained pedal
D is now in the uppermost part, the repeated indirect pedal A on the weak
beats of the hidden two-part structure in the lower voice. Surrounding them
are the same two lines moving in eighth-notes: the one written in eighth-note
values is now played by the right hand, while the other forms the lowest
level. These lines move in compound thirds, the inversion of parallel sixths.
When M1 recurs in bars 17-22, the two pedal notes are joined in octaves (see bars 17-19: D D, bars 20-22: (G)-G), while the melodic lines move again in parallel sixths with, however, some deviation from the parallel lock in bars 19 and 22.
The third recurrence of M1 presents the pedal notes inverted so that
they form fourths and, as if slightly uneasy with this interval, move
from bar to bar (see bars 37-40: D/G, E/G E/A, F#/A
F#/B, G/B). The parallel eighth-note
lines are in compound thirds but display small irregularities due to the
modulation from bar to bar.
|M2||is not all that different from the previously described model. It begins
in the left hand in bar 7 and is joined by the right hand one bar later.
Again there are two pedal notes (moving in parallel) and two melodic lines,
also in parallels, which are rhythmically defined by one quarter-note value
followed by four eighth-notes. The melodic quarter-note value is complemented
by a written-out inverted mordent. When the pattern recurs (see bars 23/24),
the left-hand part is considerably changed.
|M3||is introduced in bars 11/12. It contains only three of the four textural layers and abandons the parallel conduct of the eighth-notes. It leads to the repeatedly mentioned cadential formula which marks the beginning of four bars appearing predominantly in two-part writing. M3 recurs in bars 25/26 and in 43/44, also followed by two part writing in the cadential formula and, in the latter case, the subsequent perfect cadential close.|
At the beginning of the third section, Bach invents two further models:
|M4||is presented in bars 29/30. It retains traces of the now familiar repeated
pedal note (see bar 29: A, bar 31: G) together with two eighth-note lines;
in contrast to the eighth-note lines in previous patterns, these are independent
of each other. The model is sequenced a note lower but breaks off to make
room for the subsequent one.
|M5||is the only component in this prelude to present some polyphonic independence of voices. The right hand part is characterized by an accented and ornamented note on either the downbeat (bar 32) or the immediately following syncopation, and complemented by a descending scale in sixteenth-notes (ending with a final bend back up to the downbeat). The left hand part begins after a sixteenth-note rest with a three note descent followed by a broken chord ascent in eighth-notes. The two voices thus profess independence of pitch pattern, rhythm and dynamic direction - a stark contrast to the homophonic effect of the other models.|
To sum up, the structural layout of the prelude can be depicted as follows:
|section II||section III|
|cadential close||cadential close|
WTC II/15 in G major - Fugue
II/15.2.1 The subject
Unusual both in its extremely regular rhythmic pattern and in its non melodic pitch pattern, this subject is sure to surprise all who think they know what to expect of Bach's fugues. An uninterrupted string of sixteenth-notes spans way beyond the confines of the subject itself and, were it not for the harmonic "full stop" reached with the return to the tonic on the downbeat of bar 6, would leave the listener at a complete loss.
The subject, then, is exactly five bars long; the five sixteenth-note upbeat is complemented by the final note. Each bar presents a broken chord pattern. In fact, the interval pattern contains only a single second (see bars 2/3), and even this is not perceived as a melodic step. While bars 1 and 2 play within the tonic chord, bar 3 - along with the first harmonic shift - establishes a figurative pattern which is sequenced in bars 4/5. No subphrasing is needed or even desirable in this virtuoso play of broken chords, last but not least because subphrasing is very much a melodic phenomenon and we are not dealing with a melody here. The harmonic outline describes an active step from bars 1/2 to bar 3, thus enhancing the beginning of the above mentioned sequence (ex. 29):
The dynamic line can only follow the very simple layout expressed in harmony and pitch. The result is a two bar increase up to the downbeat of bar 3, followed by a gradual decrease to the final note on the downbeat of bar 6.
II/15.2.2 The statements of the subject
This fugue contains only six subject statements:
|1||bars 1-6d||U||4||bars 33-38d||L|
|2||bars 8-13d||M||5||bars 40-45d||U|
|3||bars 15-20d||L||6||bars 65-70d||M|
Apart from the adjustment of the first interval in the answer, the subject remains completely unchanged throughout the fugue. It never appears in either inversion or stretto.
II/15.2.3 The counter-subjects
Bach invents two counter-subjects for this fugue and uses them very regularly albeit with some variation.
is introduced against the subject answer (see upper voice: bars 8-13). In its original shape this counter-subject consists of a five-sixteenth-note upbeat, followed by slower note values in an overall direction of descent. It ends weakly in bar 13 on the third sixteenth-note as the suspension E is resolved indirectly via G.
CS1 accompanies all further statements of the subject. It recurs in bars
15 20 (M) in a simplified pattern: the descent seems as if cleaned, i.e.
free of all ornaments and escape notes, and the final resolution occurs
on the downbeat of bar 20. In bars 33-38 (M), the initial sixteenth-note
run is replaced by a dotted note group, and in bar 40/41 the upbeat is
moved to another voice (L instead of M). Finally in bars 65-70 (U) the
main rhythmic pattern is also substituted by a chain of suspended notes
of which the last is broken into a chord; only the descending direction
reminds the listener of the original CS1.
is introduced in bars 16-20, i.e. against the third statement of the subject. Entering one bar late, it is characterized by a group which consists of a syncopation followed by a fifth jump and two sixteenth-notes. This group is sequenced twice in descending direction. The suspension of the final syncopation resolves belatedly on the weak beat after the completion of the subject (just as the final note of CS1 had done 7 bars earlier).
CS2 accompanies the following two subject statements but is absent in the final entry. In the course of its two further entries, it, too, is varied slightly: the one bar rest before the belated beginning is filled in with sixteenth-notes (see U: bars 33/34 and L: bars 40/41), and the ending is varied (see U: bars 37/38 and L: bars 44/45).
Having observed such a consistent use of contrapuntal material, it may come as a surprise when we detect, upon closer inspection, that the two counter-subjects lack one essential quality necessary in true polyphony: they are not independent of the subject's pitch pattern but actually disguised parallels! The following example shows the subject with its two companions (see bars 15 20) first in Bach's setting and then in a simplified version which reveals the dependency which extends to the dynamic design:
II/15.2.4 The episodes
In this fugue, each subject entry is separated from the subsequent one. We can thus count as many subject-freepassages as there are subject entries.
|E1||bars 6-8d||E4||bars 38-40d|
|E2||bars 13-15d||E5||bars 45-65d|
|E3||bars 20-33d||E6||bars 70-72|
The two long episodes can be further divided: E3 consists of E3a (bars 20-23d) and E3b (bars 23 33d), and E5 consists of E5a (bars 45-62) and E5b (bars 62-65d).
Three distinct episode motives can be identified; two of them (Ms1 and Ms2) derive directly from the subject, while a third (Mcs) is related to the beginning of CS1. They are shown here in the order of their first appearance.
is introduced as a link between the first and second subject entries (see U bars 6 8). Its first bar anticipates the upbeat of the first counter-subject, and its second bar complements this with another ascending scale portion.
Mcs recurs in a similar function in E2 where it precedes the CS1 entry
in the middle voice, and in E4 where it anticipates the "upbeat in the
wrong voice" (see above). In E3a its second half is varied; it comes accompanied
by an extension of the two counter-subjects (see U and M which in bars
20-22 just continue the descent and rhythm pattern of the previous bars)
and leads into a cadence (D major, on the downbeat of bar 23).
is the determining motive in the ten bars of E3b. It quotes the two initial bars from the subject without any modification (compare L bars 22-25d with U bars 1 3d). The motive is then imitated back and fourth between the upper and lower voices (see U bars 25-27, L bars 27-29, U bars 29-31, L bars 31 33).
The middle voice which takes no part in this imitation provides a regular
counterpart to this motive, consisting of a third jump, a suspension and
a descending resolution (see M bars 24/25, 26/27, 28/29 and, in variation
and voice splitting, bars 30/31).
fulfills a similarly important role in the other long episode of this fugue. Like Ms1 it consists of a two bar broken chord but experiences metric shifting. In its first appearance (see U bars 45-47d), it still begins on the second sixteenth-note of the bar, but it ends in a tie instead of on an accented downbeat. Its imitation ends similarly but is complemented at the beginning with an upbeat (see M bars 46-49d). The next imitation then omits the ending and terminates on the fifth sixteenth-note (see L bars 48-50). In this new format, the motive is sequenced (see L bars 50-52, 52-54) and imitated (see U bars 55-57, 57-59).
Here again, as in Ms1, there is a regular counterpart. It consists of a note repetition followed by a trill which ends first in a tie (see U bars 49-51d, M bars 51-53d); it is then replaced by another note repetition in a metrically irregular pattern (see U bars 53-55d) and finally appears again with a trill, now complete with suffix and resolution (see M bars 56-58d, L bars 58-60d and, in variation and voice splitting, M bars 60-62d).
Harmonically, the episodes contain two perfect cadences in D major, both of which are enveloped in melodic closing formulas and represent structural caesuras (see the cadence in bars 22/23 which divides E3, and that in bars 61-62 which divides E5). The harmonic development on the inner sides of these two cadences is most intriguing as the second appears as a free retrograde of the first:
In E3b, the imitations of Ms1 represent the keys
In E5a, the imitations of Ms2 represent the keys
Finally, E5b and E6 display no motivic content but introduce runs in thirty-second-notes, thus further emphasizing the virtuoso character of this fugue.
II/15.2.5 Character, tempo, articulation, ornament realization
The character of this fugue leaves no room for doubt: it is very lively. So is the tempo which is limited only by the performer's technical skills to produce crystal clear and very regular thirty-second-notes in the runs and trills.
The relative tempo of the (very lively) prelude to this (very lively) fugue sounds and looks simple:
in the prelude
in the fugue
(Approximate metronome settings: prelude beats = 108, fugue beats = 72.)
The actual effect for the listener is, however, one resembling a hemiola:
1 2 3 4 5 6
1 2 3 1 2 3
in the prelude
in the fugue
The corresponding articulation requires a light quasi legato touch for the sixteenth-notes, a detached (but not too short) non legato for the eighth-notes and quarter-notes. There are, however, two exceptions. The first occurs in the two eighth-notes which Bach explicitly marked staccato (see bars 10 and 12) and which should be well distinguished from the surrounding non legato. The second appears in those suspended notes which create harmonic tension waiting for resolution; just like the appoggiatura-resolution pair, these may under no circumstances be separated but must be played in tight legato (see U bar 20, M bar 25/27/29/31, U+M bar 38, U bar 39). In addition, the closing formula in M bars 33/34 must be legato, while the consecutive syncopations in U bars 65-69 can be detached (which emphasizes their rhythmic quality) or linked (which emphasizes their harmonic content).
The fugue contains five kinds of ornaments:
||The two inverted mordents in bars 10 and 12 pose no problem: the notes
are G-F#-G and E-D-E respectively, and
the first note of each ornament falls on the beat. (As the tempo of the
fugue is quite fast, imagining this ornament as a thirty-second-note triplet
with tie seems a good help).
||In the two trills in bars 50 and 52, the ornamented note finds no harmonic
or melodic resolution. The trill therefore does not end in a suffix but
stops short immediately before the bar line. (Both trills begin regularly
on the upper neighboring note and shake in thirty-second-notes; each trill
thus contains 12 notes of which the last is tied to the following downbeat.)
||The three trills with suffix and resolution in bars 57, 59 and 61 begin
like the other trills on the upper auxiliary; they end after five shakes
in the suffix indicated by the composer.
||The mordent in bar 62 is approached stepwise and therefore begins on the
main note. The rhythm is again a thirty-second-note triplet.
||Lastly, the final note in the upper voice is preceded by a grace note. This C represents an appoggiatura which, played on the beat together with notes of the middle and lower voices, resolves onto the main note B after one eighth-note. (The splitting of dotted notes into portions of 1/3 + 2/3 was a prevailing practice in J.S. Bach's time. His son C.P.E Bach, in his book On the True Art of Playing Keyboard Instruments, suggested a change in favor of a 2/3 + 1/3 splitting. His views should, however, not be applied retrospectively to his father's works.)|
II/15.2.6 The design of the fugue
The order of voice entry together with the design of the episodes and the harmonic organization of the piece give a clear picture of the structural layout of the fugue.
||The six subject entries appear in two complete rounds: U M L and L U M.
||The episodes also appear as 3 + 3. In the first half of the piece there
are two two bar episodes (E1 and E2) which have no other purpose but to
link subsequent entries. They are complemented by the long and complex E3.
In the second half of the piece, E4 corresponds with E1 in length, material
and purpose, while the long episode now precedes the third subject entry
for a more powerful closing effect. The final episode is again two bars
long and thus completes the analogy.
||The first group of subject statements relates to the home key, with entries in G, D and G major. The entries in bars 33-38 and 40-45 are in E minor (relative to the tonic) and B minor (relative to the dominant). The change of mode marks the beginning of a new section. The final entry returns of course to D major and concludes the second section on the tonic. (Note that as a single entry, it cannot make up a section of its own.)|
The dividing line between the two sections is somewhat hidden; one might wonder whether Bach did not want the entire fugue to appear as one virtuoso gesture, without too much obvious structuring. The cadence in the relative minor key which concludes the first section overlaps with the beginning of the second section and thus allows not the slightest new breath - either for the performer or for the listener (see the cadence in E minor bars 33/34). For a sketch of the design, see ex. 33.
II/15.2.7 The overall dynamic outline of the fugue
The development of tension in this fugue mirrors the structural simplicity. The three subject statements of the first section represent a gradual increase of tension, due both to the growing ensemble and the increasing tendency of the two linking episodes. The tension then decreases slightly in the cadential close of E3a, only to rise again in the ascending sequences of E3b. The relaxation at the end of this episode is short and incomplete, so that the second section commences on a very elevated level. (A slight change of color in the minor mode portion can here be expressed better by means of touch and articulation than by dynamics.)
In the second section, the first two entries are linked once more by the increasing Msc. At the same time, the choice of voices (L - U) and of pitch range (the highest octave available on Bach's keyboard instruments) supports another growth in tension. After this climactic moment, the long E5a with its descending sequences brings relief of the tension in a gradual relaxation. Although E5b presents a powerful rush upwards, the final subject entry comes in on a much softer note, due mainly to its weaker position (middle voice) and its reduced polyphonic density (simplified CS1 and accompanying bass instead of CS2). The concluding cadence and particularly the appoggiatura in the final bar confirm the soft ending.
This playful fugue thus presents itself dynamically in a design which is as simple as it is capturing (ex. 32):