What type of dissonant voice leading is this Bach example?

Question

Dissonances have to be resolved in Bach's style. If you don't resolve dissonance, you're writing is out of style for the period.

Bach's WTC I Fugue in C# minor, BWV 849, has a passage with unresolved dissonance in Bar 92. The soprano voice plays the third subject starting on G#. On the 4th beat, the bass interjects with an A. This forms a major seventh, one of the most dissonant musical intervals.

This has to be resolved, right? Wrong, according to Bach, who leaves this major seventh by moving the bass by a leap(a dissonant leap of an augmented fourth, no less!). This dissonant G# does not fit any non-chord tone description; It is not a passing, neighbor, auxiliary, or suspension tone, so it has to have been formed as a part of a dissonant voice leading chord.

What is this dissonant voice leading chord, and how does it work in other contexts?

Answer 1

It does resolve. On the third beat of m. 93, the soprano moves to F#, resolving a suspension that actually began in the alto part on the third beat of m. 91.

Notice also that the "real" bass in mm. 92 is the low E followed by the low D# in m. 93 and then a low C# in m. 94 (not shown). The effect is that the bass is split into two voices: one walking from E–D#–C# and the other from B–A–G# (beginning with the final pitch of m. 91). This is how Bach "gets away" with what other seems like a "forbidden" leap. It's just a diatonic sequence in the bass part: B-E, A-D#, G#-C#.

Here are mm. 91 – 93 of the fugue:

And here is a harmonic reduction of the passage from the m. 91 beat 3 to m. 93 beat 3.

Answer 2

Aaron's answer here has been bothering me a bit, not least because of this claim:

The effect is that the bass is split into two voices: one walking from E–D#–C# and the other from B–A–G# (beginning with the final pitch of m. 91).

I am quite certain that Bach wasn't thinking of this in this way because, well, look at it:

X:1
M:C|
L:1/1
K:C#m bass
[E,,B,,]|[D,,A,,]|[C,,G,,]

A progression by descending fifths and ascending fourths is a much more idiomatic way of thinking about it (and the preceding analysis doesn't explain the A in 92 or the G♯ in 93):

X:2
M:C|
L:1/2
K:C#m bass
E,,A,,|D,,G,,|[C,,

I agree with the basic conclusion that the G♯ does resolve, but I would explain it somewhat differently. Basically, measures 92 and 93 combine two common moves in a way that is perhaps less common.

The first technique is for a bass part with a sequence of descending fifths and ascending fourths to be harmonized by a voice that alternates between the third and the seventh above the bass. As with a standard V7-I or V7-i cadence, the dissonant seventh resolves with the chord change rather than before. For example:

X:3
M:C|
L:1/2
K:C#m bass
%%score {RH|LH}
V:RH clef=treble
GG|FF|E
V:LH
E,,A,,|D,,G,,|C,,
s: ~ 7 ~ 7

Also see the fugue Meine Seele harret from BWV 131:

You can also see this in the C major fugue from WTC Book I, for example at measure 5.

As a bonus, this technique can be used with an additional voice, though it seems more idiomatic for later music:

X:4
M:C|
L:1/2
K:C#m bass
%%score {RH|LH}
V:RH clef=treble
[DG][CG]|[CF][^B,F]|[CE]
V:LH
E,,A,,|D,,G,,|C,,
s: 7 7 7 7
s: ~ ~ ~ ♯

The second technique here is to delay the resolution of the seventh by suspension, which naturally yields a 4-3:

X:5
M:C|
L:1/2
K:C#m bass
%%score {RH|LH}
V:RH clef=treble
G(G|G/)F/F|E
V:LH
E,,A,,|D,,G,,|C,,
s: ~ 7 4~3 7

This is a common cadential formula in Bach's keyboard music, for example at measure 16 of the Goldberg aria. Another example may be seen in Handel's water music, in measures three and four of the D minor Andante:

This is of course the basic structure of the passage in question, with the addition of the dotted rhythm in the bass:

X:6
M:C|
L:1/2
K:C#m bass
%%score {RH|LH}
V:RH clef=treble
G(G|G/)F/F|E
V:LH
E,,>A,,|D,,>G,,|C,,
s: ~ 7 4~3 7

With the addition of melodic detail, it is a short step to

X:7
M:C|
L:1/2
K:C#m bass
%%score {RH|LH}
V:RH clef=treble
G/c/g/g/|g/f//e//f|e2
V:LH
E,,z/A,,/|D,,z/G,,/|C,,
s: ~ 7 4~3 7 4~3