Matthew Saunders’ Blog

This post is for a friend of mine, who is trying to perfect the art of wooing women using his music theory and analysis skills. In the manner of Cyrano de Bergerac, however, he needs a little assistance. But at least he doesn’t have a big nose.

My comments refer to the Kalmus edition of Bach’s The Well-Tempered Clavier, edited by Carl Czerny.  Not the best edition ever, but fairly readable, as they don’t try to cram too much onto a page like some older editions.  I trust it fairly implicitly.

This is the only two-voice fugue in either book of the WTC.  The structure is more reminiscent of a two-part invention than a fugue, but the line between these is somewhat blurry.  The subject has a strange chromatic feel to it following the rising arpeggio that forms the head motive.  It modulates–once the subject has been played, the music is not in the same key it was when the subject began–the subject always ends on v of the key in which it began.  The first entry of the subject takes the piece from E minor to B minor (note D natural, not D sharp on the downbeat of measure 3).  The answer begins immediately, as expected.  This is a real answer, with the exception of the last note–where the subject always ends with a descending whole-step, the answer always ends with a descending half-step, meaning that after the answer, we may remain in the same key.  The half-step allows the subject to end on V (of the answer) rather than some temporary i.  Measures 1-4 are the first exposition.  A final feature of note is the material beginning on beat 2 of m. 3 in the soprano voice, which represents recurring contrapuntal material and accompanies every subsequent entry of either subject or answer.

The first episode lasts from m. 5 to m. 10, and consists of a descending-fifths sequence, with Bach’s very typical alternation of material between hands, until m. 10, when the sequence breaks down in order to tonicize the next key area, G major.  Between measures 10 and 11, there is almost a cadence–we are denied the stereotypical Baroque cadential 6-4 pattern, but harmonically, most of the pieces are there.  In particular, the last beat of measure 10 is very typical of the approach to a cadence, but the next passage begins on a first inversion chord (because the subject begins on the root of the chord and enters in the soprano). 

The second exposition lasts from m. 11 to m. 14 and presents subject and answer in G major, with both accompanied by the countersubject introduced in mm. 3-4.  This is an excellent example of Bachian use of invertible counterpoint, as the countersubject “works” either above or below the subject or answer.

Measures 15-19 constitute the second episode, again, a falling-fifths sequence until m. 19, which introduces the dominant of the next key area.  Measure 19 is also notable for the use of both hands in octaves, a practice not often seen in Bach.  Bach again uses inversion in this episode–note the alternating first-inversion and root position chords.

The third exposition is in measures 20-23.  This is the first time that the subject and answer have switch places, so that the subject appears in the bass and the answer appears in the soprano.  This exposition is in the key of a minor.  Because the subject always moves to v, the answer is in e minor, ending on V (B major).

The third episode lasts from measure 24 to measure 29.  The first four of these bars are measures 5-9 in inversion, another example of invertible counterpoint.  Like the first episode, they constitute a descending-fifths sequence.  The parallel construction would seem to suggest that C major be the next key area, but this is prevented by a minor change in m. 29.  Between the second and third sixteenth-note of the run in thirds here (inversion of the run in sixths from m. 10), Bach leaps up by a fourth instead of a third, then continues a step higher to tonicize D minor instead of C major.  Like its counterpart, m. 29 is almost a cadence.

D minor is not a closely-related key to E minor, and our arrival here requires explanation; D major or C major would be more harmonically typical.  I would suggest that, given the tight construction of this piece, Bach wished to continue in this manner.  If Bach had continued to C major, as the parallel construction would suggest, he would have found himself nearing the end of the fugue in a poor situation.  To continue the parallelism from C major, would require a move to D minor (following pattern of the second and third expositions in G major and A minor, respectively).  He finds himself moving further and further from home, when it is now necessary to head back toward the tonic.  Thus, C major was not an acceptable choice for the next exposition, as it leads away from rather than back to the home key.  D major, on the other hand, would require an answer in A major, similarly leading away from the home key.  However, since the subject modulates to its own v, a subject in D minor leads to an answer in A minor, the iv chord of the piece.  Thus, by stepping out of the key, Bach brings us back to the key.  This odd entrance of the subject (m. 30) is necessitated by the modulating properties of the subject itself, and the exposition leaves us in a very good position to end the piece.

The final episode, mm. 34-38, is an inverted version of mm. 15-19, complete with the hands in octaves (m. 38).

In m. 39, Bach uses the head motive and the characteristic “bariolage” section of the subject to suggest stretto.  Since neither the subject nor the medium of two-voice fugue are really well-suited to stretto, he reverts to the format of the two-part invention and merely reminds us of the subject.  The only true cadence in the piece occurs in the last measure.