from Siglind Bruhn
J.S. Bach's Well-Tempered Clavier
In-depth Analysis and Interpretation
I/16.1.1 The prelude type
This prelude is determined by three rhythmic figures. They come with varying textures and pitch curves. Jointly these three figures cover all bars of the piece, with only one short interruption (of one beat length) and two slight variations in one of the rhythmic patterns.
I/16.1.2 The overall design of the prelude
The first perfect cadence concludes on the downbeat of bar 3. This cadential close cannot, however, be regarded as a structural break since the bass has so far not taken part in the harmonic progression but remained on the tonic pedal. Also, bars 1/2 have set a pattern of material which is taken up similarly in bars 3/4 and thus generates a distinctly felt continuity. The modulation which follows this first cadential close reaches its target, i.e. a perfect cadence in the key of the dominant (D major) on the middle beat of bar 4. The moment of harmonic resolution is only one sixteenth-note long here, since the D major chord is immediately topped by its seventh and progresses to new regions. This harmonic closure again is thus not the kind of caesura one is looking for when trying to determine the structural outline of the piece. The search finally leads to the third cadential close, attained after a second modulation to the relative major key (Bb major) on the downbeat of bar 7.
There are four sections in this prelude; only the first, as has been shown above, contains within its confines several structurally less determining cadential closes.
|I||bars 1-7d||i-III||(G minor to Bb major)|
| bars 1-3d
modulation tonic to dominant
modulation dominant to relative major
|bars 7-11d||III-iv||(Bb major to C minor)|
(C minor to G minor)
|bars 18-19||i-i||(G minor confirmed)|
No segment of this prelude ever recurs later, be it varied, transposed or even in a freer understanding of structural analogies. Any seemingly recurring bars are in fact just new manifestations of one of the motivic figures.
I/16.1.3 Practical considerations for performers
The prelude contains, even if one only considers the melodically relevant segments of each voice, three different note values: eighth-notes, sixteenth-notes and thirty-second-notes; faster motion appears in the four long trills. In second order there are occasional dotted eighth-notes and dotted quarter-notes, as well as syncopations in passages with complementary rhythm. The pitch pattern, too, is complex. A predominantly stepwise motion is regularly interrupted by sudden leaps. Closer inspection reveals that these are cases of hidden two-part structure, often with a pedal note in the secondary voice. In addition there are those instances where two voices complement each other to form one of the motivic figures; this creates extra melodic intensity.
In view of this complexity, the basic character of this prelude should be interpreted as rather calm, with a tempo that is reserved enough to allow for full melodious substance in the thirty-second-notes. The corresponding articulation requires that all notes except cadential bass patterns and consecutive leaps be played legato. Cadential bass patterns can be found e.g. in bars 10/11, 17/18 and 18/19; consecutive leaps which need to be detached occur e.g. in the lowest voice in bars 5/6, whereas those in bar 14 form part of a hidden two-part structure and should be played legato thus achieving a result in which each of the two "voices" will sound disconnected.
A tricky question arises in the area of articulation with regard to the figure which is introduced in the upper voice of bar 2. The G's clearly do not belong to the main melodic line; at the same time they do not form a secondary line of their own either. Thus they can be interpreted, and played, in two ways. One possibility is to regard them as a pedal background in a hidden two-part structure; in this case they are not separated from their surroundings by articulation, but only set apart by a different tone color. Another concept is to perceive them as "charm notes" (or playful escape notes) which were to become so much more common after Bach's time, in the music of the later 18th century; in this case they are treated as integrated parts of the melodic line which sound just lighter and, because of their interval gaps at both sides, non legato.
There are five ornaments in the G minor prelude; all of them are marked as trills. Another feature shared by all five is that each sounds at a moment of harmonic affirmation (i.e. on the tonic chords of the respective keys reached by way of modulation in the course of the piece), and thus neither need nor pretend to aim for any kind of resolution. This is most obvious in connection with the trill on the very last note, but equally true in the case of the four other ornaments which all end in tie prolongation followed by the beginning of a new phrase.
Having observed this it is obvious that none of the trills concludes with a suffix. As to the beginning, a commencement on the main note is evident in the case of four of the five trills, either because of stepwise approach (see bars 3, 7 and 19) or because the trill appears at the very outset of the piece (see bar 1). Although the context of the trill in bar 11 would allow a different solution, this ornament should probably follow the example set in the three corresponding trills before and also begin on the main note.
The speed of the trill motion (twice as fast as the shorter note values) is in sixty-fourth-notes, or four notes to each accompanying sixteenth-note. In the four trills of one bar duration, the shake comes to a halt on the last main note before the bar line, i.e. on the final sixteenth-note which is then tied over. The duration of the shake in bar 19 is not fixed in any way; it could be anything from a eighth-note upward.
I/16.1.4 What is happening in this prelude?
Three rhythmic figures determine the piece:
is introduced in bar 1. Its texture consists of three parts, two of which - the upper and the lower - are unmoving pitches (see the repeated pedal note in the lower voice). The rhythmic pattern is even here, with three different values (eighth-notes, sixteenth-notes and trill sixty-fourth-notes) sounding simultaneously.
This figure recurs three times. In bar 3, the key and the order of the
voices are the same; only the upper voice is placed an octave lower. The
eighth-note pedal note, however, has been abandoned, and a complementary
pattern of the middle and lower voices provides both the eighth-note and
the sixteenth-note pulses. In bars 7 and 11, we find the figure transposed
and in inverted voices; the pedal note, however, has been redeemed and
now appears as an off beat eighth-note pulse as part of the upper voice.
is introduced in the upper voice of bar 2. Commencing on a weak beat, i.e. on the first sixteenth-note after the downbeat, it is a one track figure which in the course of the prelude appears with varying accompaniment. Although its rhythmic structure seems to allow a subdivision into four units of "long short/short long long", its melodic design with the interspersed "charm notes" counteracts such subphrasing and distinguishes the figure as extending through the entire bar. Its final note frequently overlaps with the beginning of another figure; see e.g. in bar 3.
This figure recurs five times, varied not only with regard to its pitches
but also in its length and even in details of its rhythmic design. In
bar 4, the rhythmic pattern is suspended after half of its length, only
to recommence at the end of the same bar. From here on until the downbeat
of bar 6 the pitch pattern is closely related to that in the original
figure, with only the interspersed pedal note substituted by varying pitches.
Bar 6 presents an inversion of the pitch pattern which leads, in the second
half of the bar, to a mutation of both the pitch and the rhythmic patterns.
Bar 8 takes up this inversion plus mutation and places it in the lower
voice, while bar 15 recalls the shortened figure from bar 4.
first appears in bar 9. This rhythmic figure is related to the previous one insofar as it also commences on the first off beat sixteenth-note. While in R2 the smaller units seem tightly knit to an indivisible phrase, here each unit has its own little close after one quarter bar. In its original setting the model appears with imitation (in a free adaptation of the pitch line) and sequences, thus filling two entire bars with its rhythmic pattern (see bars 9/10, imitation in U+M).
This figure recurs in two long stretches, varied not only in pitch but also in texture. Bars 12-15 comprise single track patterns (L: first halves bars 12 and 13, bar 15 beat 3; U: bars 13m 14d) as well as complementary textures in various splittings (see bars 12m 13d and bars 14m 15m: U/M). The final three and a half bars of the prelude which are entirely devoted to this figure take up both the imitation and the complementary texture. (With regard to its pitch pattern, R3 is the freest of the three figures, appearing in ten different melodic guises; see
The structure of the prelude as a whole is determined by its harmonic outline (see above under paragraph 2 of this chapter). Regarding the material displayed in each section we find that the first section encompasses the introduction of R1 and R2, followed by a first development of these two figures. The second section takes up both R1 and R2 in transposition and very close relation to the originals, and then launches into R3. The third section, which is the longest in this prelude, begins once more with R1, followed now by an extended development of R3, with R2 only once interpolated for three beats (see bars 15/16). Section IV serves as a coda; spreading a vivid three part texture over an additional fourth voice tonic pedal, it is exclusively based on R3.
The dynamic range within this rhythmically determined prelude is not large. Small scale dynamics depend exclusively on the overall pitch direction which defines each rhythmic figure. The melodically static R1 comprises only the slightest increase in tension, while R3 seems always composed in superimposed descending pitch lines and thus appears connected with dynamic relaxation. Only R2 changes melodic orientation and, with it, dynamic direction, allowing for diminuendo (as in bars 2, 5 and 15/16), crescendo (as in bars 6 and 8) or a dynamic curve (as in bar 4).
With regard to the overall development of tension, the prelude describes a soft, largely scaled dynamic curve. The second section contains more tension than the first but is surpassed by the third, while the coda returns to the level of the beginning. Two climaxes can be determined: on the downbeat of bar 9 and in the middle of bar 12. Both are motivically connected with R3 but derive their expressive power mainly from their harmonic underpinning.
WTC I/16 in G minor - Fugue
I/16.2.1 The subject
The subject of this fugue commences on the second eighth-note of the first bar and ends on the third beat of bar 2. With regard to the pitch position in the G minor scale, it sets out on the fifth degree and resolves on the third. The beginning on the second eighth-note conveys a strong impression of upbeat. The downbeat of the second bar, however, is taken up by a rest, so that the possibly strongest beat is omitted in the melodic development. As a result, the listener is most likely to perceive the middle beat as "down", and the subject as consisting of three metric units, rather than one and a half bars. The fact that the metric position of the subject statements throughout the fugue changes constantly between a beginning after the downbeat and one after the middle beat confirms that in this fugue Bach regarded the two as being equally strong. One can thus safely assume a hidden 2/4 time behind the given notation.
The G which follows on the fourth beat of bar 2 does not belong to the subject. Three reasons can be named to support this: (a) this note never recurs in subsequent statements apart from once in bar 6; (b) harmonically, the resolution onto the tonic is already completed on the Bb; (c) metrically, a subject which begins after a strong beat can usually be expected to conclude on a strong beat.
With regard to phrasing, there are two possible interpretations of the subject. The rest in its middle can be taken for an interruption after which a new little melodic unit is launched. Alternatively, the rest could equally be perceived as tension-sustaining; in this case the notes in bar 2 continue the process immediately preceding the rest.
The pitch outline in the subject consists exclusively of seconds. The only exception is the minor-sixth leap between the second and the third subject notes. This leap constitutes a high-tension interval. The rhythmic pattern includes three note values, namely quarter-notes, eighth-notes and sixteenth-notes. This rhythmic substance is confirmed throughout the fugue.
Harmonically, the subject is very interesting. It does not begin on the tonic but launches the cadential progression from a point of already heightened tension (ex. 34):
The climax within this subject falls on the fourth note (F# in the original key). All features join to support this event:
||Melodically, the F# is approached in
steps of increasing tension. The initial fifth scale degree already represents
a higher degree of intensity than would be contained in the usual first
or third degrees. This is followed by an ascending semitone step reaching
the secondary leading note, thus adding to the tension; from there the line
plunges through the high tension interval of the minor sixth to the keynote
and, continuing its direction, reaches the primary leading note in G minor,
||Harmonically, this note represents chord VI, i.e. the step which, in the
given cadence, is most remote from the tonic.
||Rhythmically, the F# is the first longer note value; and metrically, this note appears (as was expounded earlier) in the function of a downbeat.|
After this climax, two slightly different interpretations of the dynamic process are possible, depending on the choice for sub phrasing. If one chooses to regard the subject as consisting of two subphrases, the climax is followed by an abrupt and very strong decrease; the remainder of the subject will then function as an "afterthought", with a slight increase towards a secondary climax on C and a final relaxation thereafter. However, if one recognizes the subject as an undivided entity, the tension which was so powerfully built up towards the climax on F# can be resolved gradually throughout the remainder of the subject. In this case, the C is integrated into the line and not accented in any way. (Although performers continue to emotionally prefer "interrupting" rests, the harmonically more consistent rendition is the one which resolves the tension of the main climax in a single diminuendo. As the fugue progresses, more evidence arises to support the concept of an undivided entity.)
I/16.2.2 The statements of the subject
The fugue contains sixteen complete statements and in addition one "false entry".
|1.||bars 1/2||A||9.||bars 17/18||A|
|2.||bars 2/3||S||10.||bars 20/21||B|
|4.||bars 6/7||T||12.||bars 23/24||A|
|5.||bars 12/13||A||13.||bars 28/29||S|
|6.||bars 13/14||B||14.||bars 28/29||T|
|7.||bars 15/16||S||(15.||bar 29||B)|
|8.||bars 17/18||B||16.||bars 31/32||A|
The subject suffers only small modifications, most of which are inconsequential. Its answer is conceived as tonal, so its first interval is changed from a semitone to a minor third (see e.g. bar 2 G-Bb). The beginning of the subject is further varied in bar 23 where the initial eighth-note is replaced by two ascending sixteenth-notes. That the final note of the subject, being the third scale degree, appears as a Picardy third in bar 34 comes as no surprise in a minor mode fugue. One more consequential modification can be observed when, in the major mode section (see from bar 12 onwards), the two initial intervals are changed: the semitone with its particular urging quality is substituted by a major second, and the leap appears as a major sixth which, unlike its minor brother, is not a high tension interval. These two changes have considerable influence on the strength of the build up of tension.
In two instances one can find the subject appearing in stretto: bars 17/18 feature a combination of bass and alto statements at a distance of four eighth-notes, and bars 28/29 present a corresponding group of two complete entries (in soprano and tenor) fortified by a third entry at the same distance in the bass which, however, deviates immediately after the climax.
I/16.2.3 The counter-subject
The fugue features only one counter-subject; this remains a faithful companion to the subject throughout the fugue and is only omitted in the final statement. The counter-subject commences in a metrical position equivalent to that of the subject, but half a bar "late", i.e. after the subject's climax. This belated beginning is the reason why there is that additional G on the fourth beat of bars 2 and 6, a note which does not form a part of any material but whose function is to support the beginning of the subject entry when all the other voices are resting.
In pitch pattern and rhythm, the counter-subject is strikingly related to the subject, particularly to the subject answer; in fact it almost seems to read the subject answer upside down and with its two halves exchanged (see ex. 36):
In contrast to the subject, the counter-subject presents an indivisible phrase. The climax on the sixth scale degree (Bb) unites similar characteristics as did the climax of the subject: it carries melodic tension as the secondary leading note of this entry's D minor, harmonic tension as the representative of the subdominant function (for the harmonic details see above ex. 82), and a metrical accent since it falls alternatively on the middle beat or the downbeat. Due, however, to its preparation in a somewhat relaxed rhythm pattern and stepwise motion, this climax is considerably milder than that in the subject. The remaining four notes bring a gradual subsiding of the tension.
The example shows the phrase structure and dynamic design in the primary material of this fugue (ex. 37):
I/16.2.4 The episodes
The G minor fugue contains six subject-free passages.
|bars 8-12d||E5||bars 24m-28d|
|bars 16m-17d||E6||bars 30-31m|
As the ending of the final subject statement marks the close of the piece, there is neither a coda nor even a concluding final episode. All episodes in this fugue are related to the subject; the only distinction here is the degree of relationship, and the appearance or omission of independent (i.e. not subject-related) motives.
It is generally true in all polyphonic compositions that the closest bond between an episode and the surrounding primary material is achieved either by way of a sequence or imitation of the preceding ending, or by way of anticipation of the subsequent beginning. In this fugue, the former process is used frequently: E1, E2 and E3 are all linked to the preceding subject statements in sequences of the final figure while E4 and E6 pick up this figure in imitation. E5 alone shows a very subtle variation of this pattern insofar as the figure is transformed, by a mere displacement of its final note, into a bass line which no longer appears entirely melodic but conveys a hint of a cadential pattern (see bars 24-27).
The only other motive in this composition, and the only component in the entire fugue which is not in some way related to the subject, occurs also in E5; it will be referred to as M1 here. It consists of an ascending scale section in sixteenth-note motion complemented, after a syncopated halt, by a descent which returns to the note of departure in the same rhythmic pattern. In its original version (see A: bars 24m-25m), the ascent contains the second tetrachord of the melodic G minor scale and is answered by the corresponding portion of the natural G minor scale. The dynamic outline follows the curve described by the symmetrical design: a half bar crescendo is complemented by a diminuendo. (M1 has a forerunner which, consisting only of its ascending portion, appears in E2 (see the soprano in bars 8 and 9) and in E3 (see the tenor in bar 17).
In the course of E5, M1 is followed by two sequences (see M: bars 25/26 and 26/27). Moreover, it is imitated - in inversion and slightly varied - in the upper voice. This imitation should retain the dynamic curve of the model. (The frequently heard mistake which renders the descent in the imitation in diminuendo and the ascents in crescendo actually cuts the motive in two, and each half will automatically cry for a new partner. The result is usually that middle and upper voice sound as if in a single track, so that even the original motive in the middle voice is then destroyed. A good way to avoid this mistake is to play the leading voice (M) on a slightly higher level of intensity than the imitating upper voice.)
As can be seen from this overview, none of the episodes serves exclusively as a cadential close. Only one segment of an episode fulfills this purpose. In E2, the home key of the fugue is confirmed (motivically still in the context of the subject related figure) with a perfect cadence in G minor on the middle beat of bar 10. The remaining one and a half bars are neither needed for the closure of the episode, nor do they bring any (new or continued) episode material. Instead this extension clearly functions as nothing but a modulation to the related major key.
There is no structural relationship between the episodes of this fugue. The role played by each episode in the development of the composition is determined by the direction in which the motive derived from the subject ending it sequenced. The following details can be observed:
||In E1 and E3, the final half bar from the subject is taken up in ascending
sequence; both episodes thus serves as a bridge which heightens the tension
towards the ensuing subject statement.
E2 begins similarly with an ascending sequence of this figure (see
bar 8) but continues thereafter in a generally descending direction (see
bars 9/10: soprano Bb-A-G, bass E-Bb-D-G).
This descent and the cadential closure it encompasses represent a relaxation
of the tension.
||In E4 and E6, the final half bar from the subject is not sequenced but imitated (see bars 18/19: A-S and bars 29/30: T-A-S). These imitations, though ascending in pitch direction, appear as a more indirect continuation than the sequences in the previous examples; yet while they do not convey the feeling of anticipation, they succeed in slowing down the decay of tension. In both cases, however, the episode concludes with a version of the figure inverted and with a plunging final interval which generates a strong decrease (see S and A in bars 19/20, and B in the first half of bar 31). Thus a gradual diminuendo ends in a steeper drop of tension.|
I/16.2.5 Character, tempo, articulation, ornament realization
The overall step-wise motion which is interrupted only for high-tension intervals insinuates that the interpretation of the basic character of this fugue is rather calm. The rhythmic pattern seems neutral in this respect. On the one hand, the fact that three different note values are regularly used and, in the episodes, frequently supplemented by syncopations, supports this concept. On the other hand, the rhythmic structure does not seem complex enough to require real tranquility. The result is thus an inner placidity in flowing tempo.
The choice of articulation and tempo should convey what has just been observed. The tempo is flowing; the articulation, obeying the rules of rather calm basic character, requires an overall legato which is suspended only during cadential bass patterns (see in bars 10-12, 24 and 34) and patterns of consecutive leaps (e.g. B: bars 29/30); not, however, in the counter-subject intervals which, as was demonstrated above, derive from the subject answer and thus go back to essentially tension loaded intervals. The composition does not contain any ornaments.
The relative tempo of the prelude to the fugue had best be taken in complex proportion; this seems imperative not only in order to avoid too much uniformity within the closely related rhythmic patterns of the two pieces, but is also demanded by the particular character of each. A good solution is one in which three rhythmic units of the prelude equal one in the fugue; i.e.
half a bar
in the prelude
in the fugue
I/16.2.6 The design of the fugue
The most obvious indicator, in this fugue, for the partitioning into sections is the number of voices surrounding the subject statements, particularly the beginning of an entry. In two instances (bars 12 and 28), a subject entry commences unaccompanied and thus announces without any room for doubt that a new section is beginning. On another occasion (bars 20-24), three consecutive subject statements all sound in reduced ensemble and are thus set apart from the four part texture of the enries preceding and succeeding them. These observations lead to a tentative structural analysis of four sections: bars 1-12d, 12-20d, 20-28d and 28-34. This hypothesis is further supported by the cadential formula in bars 11/12, the consistent use of the major mode in all statements between bars 12 and 20, and the particular status of the fifth episode (which is set apart by its material and expresses a concluding tendency in its pattern of descending sequences in all three voices).
The harmonic outline also confirms the division into four sections. The four subject statements of the first section alternate between the tonic and its (answering) minor dominant. The five statements in the second section sound in the relative major keys to tonic and dominant respectively. The beginning of the third section is marked by two statements representing the subdominant, while the third returns to the tonic. Finally, all entries in the fourth section are built on the tonic.
For a sketch showing the design of the fugue in G minor see ex. 38.
I/16.2.7 The development of tension
Within the first section, the tension increases through the first three statements; the fourth, however, brings a set-back. This is due not only to the drastic gap in the higher pitch range but also to the dropping out of the alto and the listener's consequently deceived expectation of four-part texture. The second section pursues its increase of tension more consistently as the texture develops from two part via three and four part setting to the stretto statement.
By contrast, the third section retains both its texture and mode completely unchanged and seems to contain no features whatsoever which indicate a dynamic increase. Lastly, the fourth section sets out with a stretto which combines in the shortest possible space the build up from one to four voices and the overlapping imitation of one complete and another incomplete subject entry. After this dynamic outbreak, the remaining two statements can only fall back; one appears in three part texture and the other without its counter-subject.
The relationship between the four sections is a complex one. The second section begins, owing to the alterations of interval structure in the major-mode subject, in reduced emotional vigor; its concluding stretto may surpass the final entry of the first section in loudness but probably does not reach its passionate quality. The third section, while returning to the melodic intensity of the minor mode, is dynamically static and by this very trait falls back even behind the second section. After the additional color contrast in very soft shades brought about by the material change in E5, the beginning of section IV then presents the sudden climax.