Sunday, November 15, 2009

Discontinuities and synchronic/diachronic tension, after Timothy Jackson

In the MTS article, I briefly discuss Timothy Jackson's "diachronic transformation" (293-94). Jackson uses this device as a way to interpret conflicting structural levels in Schenkerian analysis by locating paradoxical moments, or ruptures, in tonal design. He says that "[a] musical work may embody in its endstate a conceptually prior state, which has become the endstate through a diachronic transformation." (Jackson, 239).

We can employ the synchronic/diachronic distinction in service of another way to relate D365n6 and D779n13. To accomplish this, we will have to intuit a diachrony by appealing to waltz design statistics, which will allow us to conceive a prior "typical" version. The existing waltzes, then, may be understood as diachronic distortions; in fact, they might literally have been the case as Schubert played for a late-evening cotillon, the kind of experience I sketched in the "improvisation history" posts.

Of the three basic design models, small binary forms dominate Schubert's waltzes. Regardless of form type, however, the second section most often opens with a dominant seventh chord, which may lead to a stable key area within the phrase but more often opens a modulating sequence. The distinctive feature of the A Major Waltz is the direct modulating shift to another tonic triad, a device that I have found in only twenty four waltzes. Of these, the majority (17) move to a diatonically related key; the remaining seven use mixture or minor/major alteration: bVI (1), VI (1), bIII (2), i (1), or III (2). Five of these seven have a stable single key in the contrasting middle (the other two make abrupt modulations in the final two bars).

It would be possible to use D971n2, the only other published dance that modulates to III, as the synchronic source of D779n13's distorted second half, but for my purpose here it will be more efficient to call yet again on the relationship between D365n6 and D779n13. The first graphic below gives the first half of D365n6, above it a traditional Schenkerian reading from ^3, and above that a depiction of the "endstate"--that is, D779n13--as a reading with an Urlinie from ^5 that takes account of the ascending cadence figure.

In the first strain, two by now familiar phenomena can be interpreted as transformations in Jackson's terms: (1) the upper-voice counterpoint of D365n6, is inverted, with the effect that parallel fourths above ii6-I6/4 become the parallel fifths; (2) the single ending of D365n6, becomes two, the first of them imperfect (upper voice remains on ^5, even if the inner voice reaches ^1), the second seeking the original register of the model via a stepwise ascent. On the other hand, the regular two-bar groups of our A Major Waltz actually smooth out a metric distortion in the model (where the 6/4-5/3 movement over the dominant harmony is repeated in bars 3-7).

For the opening of the second strain (see below), the path to the major mediant key may be more complicated, but it is plausible insofar as both small binary and ternary designs at this point typically take advantage of circle-of-fifths progressions with chromatic inflections. If we expand the four bars of the contrasting middle in D365n6, to eight bars, we can start with a C major triad and move in simple steps to V, at two bars per chord: III-vi-V/v-V. But the progression needs to move one additional step, past V to I, in order to connect with the subdominant bass of the reprise. To contain a move from III to I within eight bars requires some adjustments that would make it difficult to take advantage of the waltz's suspension motive: perhaps III-V7/III-III-vi-V7/V-V7-I-V7/IV.

Under the circumstances, the radical simplification of the key-stable version in our A Major Waltz is a much more workable solution with an effect similar to the metric smoothing out in the first strain. These "simplification paths" to diachronic distortion are an alternative to the "inspired moments"--improvisation histories can be readily understood as narratives of synchronic-diachronic transformation. In this case, I think the "inspired moments" are more plausible because they reduce D365n6 to its opening gesture and formulas, rather than dragging along layers of increasingly idealized voice leading.

Neumeyer, David. "Thematic Reading, Proto-backgrounds, and Transformations." Music Theory Spectrum 31/2: 284-324. {should appear any day now]
Jackson, Timothy. "Diachronic Transformation in a Schenkerian Context: Brahms's Haydn Variations." In Carl Schachter and Hedi Siegel, eds. Schenker Studies 2, 239-75. Cambridge: Cambridge University Press 1999.