[Smt-talk] Bach Quiz

[Dmitri Tymoczko]

My favorite WTC parallels are the barely hidden C-G octaves in the first C minor fugue, beat 2 of measure 7.  They seem to arise from reusing the same CS against both the answer and the original subject.  The CS works fine against the answer, but when repeated against the original subject it creates the parallels.

Olli, as you guessed, I have been working on cataloging all the parallels in the chorales.  Brief summary, since it seems relevant here:

	1) At the surface level, the main source of parallels is the cadential idiom where by 2-1 in the soprano is decorated with an anticipation, against 5-4-3 in an inner voice.

	2) At the level of the "harmonic skeleton" (e.g. the chorale with all nonharmonic tones removed) there are quite a lot of parallel fifths in the upper voices (75+, or one every 5 chorales).  These are usually hidden with an inner-voice suspension (as in Brent's example from the WTC II, C# minor fugue).  Sometimes, they are hidden with anticipations, especially at cadential vii/o7/V->V progressions.  Your Art of the Fugue example is a rare case where Bach uses incomplete neighbors (which as you note are pretty rare in Bach).
	In the chorales, these sorts of parallels need not always involve parallel first-inversion chords, nor 7-6 suspensions; they come in all sorts of different varieties.  However, they almost always involve fifths (not octaves) and the upper voices (not the bass).  Interestingly, virtually all the 25+ V-iv6 progressions have these parallels in them.

	3) At the level of the "quarter-note rhythmic reduction" (i.e. the reduction you get when you remove eighth-note chordal skips from quarter-note harmonies) you get a much wider array of parallels that can involve octaves and the bass.  Allyn's example is in this category.  So chordal skips seem to be a more powerful way of hiding parallels than suspensions, anticipations, and incomplete neighbors.

The upshot is that if you want to characterize Bach's practice with respect to parallel fifths, you need different rules for different structural levels.  I find this really interesting, both methodologically and pedagogically.  One possible implication: given the prevalence of parallels of type 2 (above), it is perhaps inefficient to teach students to avoid parallels at the level of the harmonic skeleton, only to change the rules on them later and allow these parallels to be disguised with nonharmonic tones.  This is the strategy in Aldwell and Schachter, for example (which, of all the common textbooks I know, has the most accurate description of Bach's practice).

DT

PS. I know that there is extensive discussion of the "afterbeat fifths" in the Schenkerian literature -- for instance, Schenker, in his Counterpoint text, admits the upper-voice parallels of type 2 above, while Matthew Brown, in his book, seeks to banish parallels from all reduction levels.  If anyone could point me to some other relevant texts, I would be grateful.

Dmitri Tymoczko
Professor of Music
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