WTC I/18 in G# minor - Prelude

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

I/18.1.1 The prelude-type

The G#-minor prelude is composed as a strictly polyphonic piece. With the exception of the familiar voice splitting in the final chord and some irregularities of voice leading in the three initial bars, it is devised in consistent three-part texture. The predominance of a single motive (see U: bars 1-2d) and the initial imitation on the octave characterize this prelude as a three-part invention.

I/18.1.2 The overall design of the prelude

After the home key G# minor has been established in two very minimal progressions (see bars 1-2d, 2-3d), the first modulation occurs with, in bars 4/5, the cadential steps IV-V-I of B major, the relative to the tonic. As both the imitation of the motive and the first episode have been introduced by now, one must regard this cadence as the conclusion of the first structural unit. This impression is enhanced by the fact that, reminiscent of section beginnings in a fugue, the subsequent motive statement appears in reduced ensemble, i.e. with the lower voice resting. The fact, however, that the listener expects the third entry of the principal motive in the middle voice, and that this expectation is met at the beginning of the next harmonic progression, threads the two passages together to one larger unit.

The question where the second harmonic progression ends is more tricky. One could recognize a return to the tonic, with a perfect cadence concluding on bar 10d. This interpretation is supported by the fact that the ensuing M statement is the first in this piece to appear in inversion. However, one can equally base one's reading on the perfect cadence closing in bar 9d, and thus understand the progression as leading to the subdominant key area. This interpretation is supported by an observation on the structural level: The next section would now begin, as did the first one, with two statements followed by two bars which are clearly a variation of bars 3/4. As this is the only instance in this prelude where a passage is taken up with recognizable resemblance in all three voices, it seems important enough. The correspondence sheds light on the analogy between the beginnings of the first and second sections and, if one decides to take this as significant for the interpretation of the prelude's structural design, even invites a similar conclusion for the beginning of the third section.

Depending on the alternative explained above, the layout of this three-part invention can thus be read in two quite different ways, as the following tables show:

I bars 1 - 10d (1-5d, 5-10d) tonic - relative major - tonic
II bars 10 - 18d (10-13d, 13-18d) tonic - minor dominant - subdominant
III bars 18 - 27d (18-22d, 22-27d) subdominant - tonic, tonic confirmed
IV bars 27 - 29 tonic
I bars 1 - 9d (1-5d, 5-9d) tonic - relative major - subdominant
II bars 9 - 17d (9-13d, 13-17d) subdominant - minor dominant - tonic
III bars 17 - 29 tonic confirmed


I/18.1.3 Practical considerations for performers

The rhythmic pattern of this prelude is basically simple and would thus suggest a rather lively character. At the same time, the slightly subdued spirit inherent in many minor-key compositions is reinforced here by the specific melodic structure of the principal motive which peaks on the minor sixth and falls back to the minor third. To accommodate both traits, the tempo of the prelude should be fairly swift, without conveying the impression of energetic activity in the eighth-notes; rather, a desirable effect is that of a gentle swing in half-bar pulses.

The articulation which matches the basic character demands legato for the sixteenth-notes and non legato for the longer note values. In order to express the nuances hinted at above, the non legato in the principal motive and all figures immediately deriving from it should be very delicate; that in the larger jumps (see e.g. the middle voice in bars 3/4) can be slightly more pronounced, and a distinctly detached style is required in the cadential-bass patterns. As exceptions to this general rule, there are three do-si-do (keynote / leading-note / keynote) formulas among the longer note values which demand legato (see L: bars 1/2, M: bars 13/14, U: bars 2/3).

The score contains only one ornament which is represented by a mordent symbol (see U: bar 13). As the note to be ornamented resolves duly on the following downbeat, this ornament must be interpreted as a note-filling trill. It commences accordingly on the upper neighbor note, shakes in thirty-second-notes and concludes with a suffix (D#-E#).

I/18.1.4 What is happening in this prelude?

a) The material

The prelude builds entirely on its principal motive (M). This motive, as has already been shortly described above, commences with sixteenth-notes which ascend to the sixth scale degree, followed by a descent in eighth-notes to the third. What appears as a kind of counter-motive (see M: bars 1-2d) recurs only in bar 2 but never again thereafter.

As M is thus solely responsible for the character and development in this prelude, it is worth showing its statements in a diagram.

bar 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19-26 27 28 29
U M   epi-         M   Minv epi-     M   Minv   M epi-      
M     sode   M       M   sode       Minv       sode   Minv  
L   M 1     M M       1var   M       Minv   2 M    

The episodes (or M-free passages) also derive their material from the same source:

A first episode-type makes use of the sixteenth-note group from the head of M, transposing its second three-note group down a fourth and sequencing this newly-assembled figure twice in descending direction (see U: bars 3/4, and L: bars 11/12). 
A second episode-type presents the same figure (see L: bars 22/23); further can be found the inversion of the original sixteenth-note group (see M: bar 25, U: bar 26), and a version of the group in its first shape but with a broken triad at the end (see L: bars 19-21). In addition to all these transformations of the motive-head, this episode also recalls the tail of M (see bars 19-21, in imitation between U and M).


b) The development of tension

In order to determine the dynamic processes in this prelude, one may wish to distinguish a varying intensity among the statements of the motive. Intensity is created here not only, as is generally true for all polyphonic compositions, by the number of voices surrounding the statement or the mode in which it is set, but also by the nature of the accompanying material. In this prelude, Bach seems to use parallels as a characteristic means. The following hierarchy can be deduced from this observation:

Probably the lowest level of intensity is expressed in statements which present M without any kind of doubling (see in bars 9 and 10, 15 and 17, 27 and 28).
Slightly more emphasis is created by the parallel of the motive's tail (see in bars 1, 2 and 7); less, however, where the doubling is set in contrary motion (as in bars 8 and 16).
The fortification of the sixteenth-notes alone generates even greater density
(see in bars 5, 6, 14 and, somewhat more indirectly, in bar 13).
This last level of intensity is exceeded only once where both halves of M are doubled. In bar 18, the sixteenth-notes appear in parallel and the eighth-notes are matched in contrary motion.

Relating these observations to the structural features of the prelude one detects that

the endings of all sections appear in lessened intensity;
in the first and second sections, the climax appears immediately after the diminuendo of the episode with its descending sequences and the mid-section cadence;
the first section begins in moderate intensity, with two statements, while the second section which introduces the motive inversion sets out with only one statement of low intensity;
the third section contains only one complete statement of M which, appearing at the very beginning of the section, exhibits the highest level of intensity in the entire piece;
the coda returns to a very relaxed state.

Here is a graphic representation of the "invention", in the second reading with structurally analogous sections (ex. 55)


WTC I/18 in G# minor - Fugue

I/18.2.1 The subject

This subject encompasses two bars. Beginning on the second beat of bar 1, its up-beat character is attenuated by the length of the first subject note which seems to stand still rather than lead anywhere. After a modulation to the dominant key, the subject ends with a figure very unusual for a melodic line: a cadential-bass pattern (see G#-G#-A#-A#-D#).

There are two subphrases. The first one, ending on D# (bar 2 beat 2), is characterized by rhythmic variety (a quarter-note, several eighth-notes, two sixteenth-notes) and an emotional pitch line (two leading-notes: Fx-G# and Cx-D# , and one high-tension interval: G# -Cx). The second subphrase contains only regular eighth-notes in a line which is melodically very low-keyed. Phrasing is thus not determined by structural features (like sequences) or pitch level here, but by a drastic contrast in melodic intensity.

The pitch outline in the first bar of the subject displays only stepwise motion, circling around the key note. The return to G# on the downbeat of bar 2 is followed immediately by a high-tension interval, represented here by a tritone jump to the artificial leading-note of the fifth step. The resolution of this leading-note marks the end of the first subphrase, and the ensuing major-sixth leap is thus not a melodic interval but rather a rash split between the two subphrases. The second subphrase contains whole tone steps and a perfect fifth. Conspicuous note repetitions on the fourth and fifths scale degrees of D# minor enhance the impression of a cadential-bass patterns. Having observed this one understands why these notes seem to convey so little melodic message. They are in fact harmonic notes with not so much horizontal as vertical significance (as representatives of the chords they imply).

The harmonic background to the subject is most intriguing in a segment where it might be least expected: the eighth-note-descent B-A#-G#. The melodic return to the keynote on the downbeat of bar 2 is not matched by a similar return in the harmonic progression. On the contrary, after an initial alternation between tonic and dominant (G# minor and D# major, with or without its seventh) in bar 1, this downbeat represents the harmonically most active step in this phrase, i.e. that to the secondary dominant which triggers the modulation. The melodic resolution of the artificial leading-note Cx thus coincides with the harmonic resolution of the diminished chord into the new tonic. The freshly established key is then confirmed in a simple cadential progression.

(ex. 56)

The main climax of the subject must without doubt be expected in the first subphrase. Both the melodic and the harmonic development support the two eighth-notes in the first beat of the second bar; G#-Cx constitutes an interval of particularly high tension and, at the same time, represents the pivot chord of the modulation. The end of the first subphrase on the third eighth-note of the bar provides the resolution to both the harmonic tension and the melodic leading-note, thus generating a steep decrease after the gradual increase during the first bar. By comparison, the dynamic outline of the second subphrase is very gentle. The first note (F#) serves as an upbeat to the G#, representative of the subdominant; this is then followed by an even relaxation.

Considering the entire subject it is fascinating to see that the two subphrases which, as expounded above, could hardly be more contrasting, nevertheless complement one another so symmetrically with regard to the tension. The gradual rise through most of the first subphrase is answered by a gradual decay through most of the second one; the sudden release after the expressive first climax finds its counterpart in the curt upbeat to the second climax.

I/18.2.2 The statements of the subject

The subject appears altogether twelve times.


bars 1-3

T 7. bars 17 - 19 T
2. bars 3 - 5 A 8. bars 19 - 21 A
3. bars 5 - 7 S 9. bars 24 - 26 S
4. bars 7 - 9 B 10. bars 26 - 28 B
5. bars 11 - 13 T 11. bars 32 - 34 T
6. bars 15 - 17 B 12. bars 37 - 39 S

(ex. 57)

Apart from the alteration of the first interval in the answer, no modifications of shape or length occur in the subject throughout the fugue; inversions, parallel statements or strettos do not appear either.


I/18.2.3 The counter-subjects

There are two companions to the subject which appear repeatedly. However, just as the subject itself displays a somewhat unusual melodic line in its second subphrase, the counter-subjects also do not quite conform to ordinary expectations of polyphonic counter-parts.

CS1 is introduced against the second subject statement in bars 3-5. It commences with an upbeat (which is later occasionally dropped or varied). The following long note and particularly the ascending groups on the sixth and seventh eighth-notes of the bar sound so much like a parallel to the beginning of the subject that they may hardly pass as contrapuntal. Only the middle segment with sequences of the ascending figure leads a polyphonically independent life (see T: bar 3 Fx until bar 4 B), while what follows thereafter exposes a typical and very traditional closing-formula (G#-A#-Fx-G#). CS1 accompanies almost all statements of the subject; exceptions occur in the entries in bars 24-26 and 26-28 where CS1 is omitted, as well as in the final entry where its beginning and end are considerably varied.

CS2 is also first presented in its expected place, i.e. against the third subject statement (see T: bars 5-7). Its characteristic features are the syncopated fourth leap and the descent in quarter-notes which concludes in a tied-over note. The beginning, as stated in bar 5 with upbeat-eighth-note and quarter-note (this value again in rhythmic parallel to the initial note of the subject), is later dropped or varied, just like that of the first counter-subject. The suspension created by the tie at the end of CS2 redefines the harmonic surroundings of the subject's final note as still awaiting resolution; statements accompanied by this counter-subject are thus unlikely at section endings. CS2 recurs four times, in bars 11-13 (A), 15-17 (S), 19-21 (B) and 32-34 (S).

The phrase structure in the two counter-subjects is worth a closer inspection. While the way in which the material is connected in CS1 is obviously parallel to that of the subject - a melodious segment followed by a traditional formula - these segments are strung together in such a manner that they build a single curve without any need for partitioning. One step further, CS2 consists of an indivisible unit in both structure and material.

In terms of dynamics, neither of the counter-subjects engenders a tension process which is clearly independent of that found in the subject; CS1 meets the subject's second (weaker) climax, while the peak of CS2 coincides with the main climax in the subject.

The following sketch shows the phrase structure and the dynamic design:

(ex. 58)


I/18.2.4 The episodes

There are six subject-free passages in this fugue.

E1 bars 9 - 11 E4
bars 28 - 32
E2 bars 13 - 15 E5 bars 34 - 37
E3 bars 21 - 24 E6 bars 39 - 41

The material of these episodes allows for two features to be distinguished. The first, very unusual for a Bach fugue, is a homophonic formula (see bars 9-10d), made up of the cadential-bass pattern from the subject's second subphrase in the bass, a slightly extended version of CS1's second segment of in the soprano, and chordal filling notes in alto and tenor which are later (from bar 13 onwards) substituted by CS2's last two notes. The other conspicuous feature (see bars 21-23) is polyphonic in design; it is a motive which comes in an imitative setting.

The distribution of these two components of secondary material in the episodes is very straightforward:

E1 formula + sequence (ascending)
E2 formula + sequence (descending)
E3 motive in B/A + sequences (ascending)
E4 motive in A/S + sequence (ascending) = E4a
  formula + sequence (descending) = E4b
E5 formula (varied) + sequences/imitation
E6 formula (varied) + cadential closing-formula

As can be seen from the above table, there are several relationships among the episodes of this fugues. E1 serves as the model for E2 and E4b as well as for E5 and the first half of E6, while E3 is taken up in E4a.

The role played by each episode in the development of the composition also stems immediately from the material employed. The episodes that are based on the formula give a concluding impression due to the obvious cadential pattern, while those which display the imitated motive are either accompanied by a similar cadential-bass line (see bars 28-30), or are followed by an explicit cadential close (see in bar 24 the perfect cadence in A# major).


I/18.2.5 Character, tempo, articulation, ornament realization

Triggered by the two-faced subject, the character of the entire fugue is ambivalent; it changes constantly between calm, melodious lines of high expressivity and cadential patterns of almost neutral tone quality. The definition of the basic character therefore has to be attempted separately for the two segments of the subject and the material resulting from them. In the first subphrase of the subject, the pitch pattern with its poignant leading-notes and tritone interval as well as the corresponding rhythmic variety pledge a rather calm basic character; in the second subphrase, however, all melodic expressivity seems aborted in favor of a non-committal formula.

The tempo in this fugue is moderate to calm, in order to accommodate the leading-notes (Fx-G#) and high-tension intervals (G# -Cx ) which appear in eighth-note (bar 2) or even sixteenth-note rhythm (bar 21-23, 28/29). The articulation should reflect the ambiguous character depicted above. In the first subphrase of the subject, the appropriate articulation demands legato throughout. In the second subphrase, however, non legato articulation is needed to convey the cadential character; both the pitch pattern with its note repetitions and perfect-fifth interval and the regular rhythmic pattern support this interpretation.

Correspondingly, the remaining material also divides into two fields. All formulas maintain the detached cadential style, while the motive and the counter-subjects tend towards the melodious character. CS2 is basically legato; only the fourth jump may be detached; the episode motive with its complex rhythm and semitone as well as high-tension intervals is entirely legato. Only CS1 shares the ambiguity of the subject: its first segment is legato while in the second the non legato intention is enhanced by the written rests.

The most straightforward tempo proportion between the prelude and the fugue is probably also the best. It is achieved by equating

half a bar

one quarter-note
in the prelude
in the fugue

(Approximate metronome settings: 60 for the compound beats in the prelude and the quarter-notes in the fugue.)

No ornaments need to be considered in this fugue.


I/18.2.6 The design of the fugue

When trying to determine the structure of the G#-minor fugue, only the first section poses no problem. It is distinguished quite clearly by the entering order of the voices. Four subject statements, presented in uninterrupted succession by the four parts involved in this fugue, are followed by the concluding first episode. The next statement appears in reduced ensemble and thus confirms the end of the first section on the downbeat of bar 11.

In the absence of assistance from explicit cadential formulas and structural analogies in the further course of the fugue, the reduced number of voices in a subject statement as an indicator for the beginning of a section must be complemented by observations concerning the material.

Reductions of the ensemble appear two more times. In bars 19-21, the soprano is resting during the entry of the alto; in bars 24-26, the bass is temporarily suspended during much of the soprano statement, although the first two beats of the entry sound in complete four-part texture.
The recurrence of the tenor statement in bar 17 distinguishes this subject entry as a redundant one, thus signifying the imminent closure of a section.
As the final statement of the first section (see bars 7-9) and the final statement of the fugue (see bars 37-39) both appear polyphonically less intense than the statements preceding them, it may make sense to look into the appearance of counter-subjects throughout the fugue. If one assumes, as a hypothesis, that Bach may have composed lessening density of contrapuntal material towards the end of each section, the following groups can be established:
bars 1 3 5 7 11 15 17 19 24 26 32 37
CS1 - * * * * * - * - - * (*)
CS2 - - * - * * - * - - * -

The harmonic outline of this fugue describes a very simple curve. The minor dominant which serves as the secondary key is reached in bar 11. However, as the subject itself in its original version also modulates into this key, the D#-minor cadence here does not seem to establish a truly new tonal center. What is more, the statements which immediately follow still remain very closely linked to the original tonic: already the tenor entry in bars 11-13 modulates back to G# minor, the bass entry follows with a subdominant-tonic version, and the redundant tenor statement closes once again on the minor dominant. Only the third section brings new harmonic fields. Its first episode modulates from G# minor to A# major, the bass statement commences in F# major - the relative of the dominant - and concludes in B major - the tonic relative - and the second episode (E4) modulates back to the tonic G# minor. For a sketch showing the design of the fugue in G# minor see ex. 59.


I/18.2.7 The development of tension

This fugue seems singularly static with regard to tension. With the exception of the three initial subject statements, all increases in texture in the course of a section are annihilated by a simultaneous decrease in polyphonic intensity. The dynamics of this fugue thus live entirely from the contrast - particularly in the third section - between subject-dominated passages and episodes.