more to diachrony and synchrony

This is an addition to the post on Timothy Jackson's diachronic/synchronic extension of Schenkerian analysis. There I noted that "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." Let's take a look at that possibility. Here is the score:

Note that the design is very similar to -- but much simpler than -- D779n13: the first strain is a straightforward 8-bar period (though Caplin would call it a hybrid theme because the pedal point tonic precludes cadential definition); the second strain consists of a contrasting middle that is a slight variation of the first strain transposed to III, and a literal and complete reprise of the first strain. All of these are elements that are present in D779n13, too, but in distorted form.

The resemblances are strengthened by the fact that the two dances come from the same time period: D 779 was published in 1825, and three German dances of D971 appeared as Schubert's contribution to a Carneval collection in early 1823.

Ternary form designs with the contrasting-middle-as-transposition may be found throughout Schubert's dances, though by no means in large numbers. In D365, only n32 is a ternary design and it follows the model of D971n2 (see graphic below). In the waltzes of D145, n7 fits the model (Eb-c-Eb); in the ländler, n2 (Eb-Bb-Eb). And so on.

It's very easy to imagine these designs originating in improvisation: one uses the same musical material and maintains the phrase design for the dancers while introducing a note of variety and extending the basic 16-bar form from 32 measures (with repeats) to 48. At the same time, for Schubert, the blocking out of key areas by 8-bar thematic units would give an opportunity to "absorb" the sound of a particular modulatory pairing, both going and coming, so to speak.

Dialectic of continuity/discontinuity (after Kielian-Gilbert)

In the MTS article, I write about Timothy Jackson’s juxtaposition of conflicting linear readings and also about similar work by Marianne Kielian-Gilbert (294). Her opposed pair, prolongational and translational relationships, can cover a wide range of event types and levels (refer to Figure 2: Tendencies of prolongational and translational parallelism, in her article, p. 70) but her interest lies particularly in contexts where ambiguous harmonies are linked with recurring themes, motives, or other figures.

In D779n13, there is no obvious instance of this kind of event, but Kielian-Gilbert's categories do give interesting results when applied to one crucial, "generative" moment and its varied repetitions in subsequent phrases, the result being what she calls an “oscillation” between ii6 and IV. The C# dissonance in measure 3 clearly belongs to a 7-6 suspension figure that stretches from the firmly established tonic triad of measures 1-2 to the ii6 chord in measures 3-4 (see the top system of the graphic below). The inversion of clichéd voice leading in the upper voices—see the top system, middle, combined with the firm bass motion from ^1 to ^4, however, enables a possible reading of a 7-8 suspension against subdominant harmony (top system, righthand side).

The 7-8 suspension itself is not unduly problematic (mid-seventeenth century theorist Christoph Bernhard already includes it as an acceptable syncopatio, though he also says it is rare, a statistic that still applies in the early nineteenth century)--but of course it would have radically different implications for the alto voice's movement out of C#5 (^3). Still, the context favors the supertonic and the common 7-6 suspension. On repetition of the figure in measures 10-12, however, the added G-natural, which replaces the C# that gave a literal, if short, preparation for the suspension figure in measures 2-3, shifts the two possible ways to hear measure 11 into balance (graphic, middle system). One can still hear A: I—ii6, but an applied dominant with deceptive resolution, A: V7/IV-ii (as if D: V7-vi), would surely be much more plausible with a bass motion from A2 to B2--it is easier to hear an applied dominant moving to A: IV (middle system, righthand side).

By the time the opening phrase reappears after the C# major section, the force of the tonic key is nearly attenuated: if ii6 was more difficult to hear in measure 12, it is all the more difficult in measure 31, after two measures of an A7 chord that is equally plausible as a German Sixth chord in C# major (bottom system). Now the subdominant seems much stronger, even to the point of raising the question whether the resolution to B5 does not invoke a triad with an added sixth (dominant ninth chords do arise accidentally over V7-I progressions in waltzes of the 1820s, but the added sixth is exceedingly rare before its appearance in French and Austrian ballet, operetta, and dance music in the 1860s). If one can indeed hear this moment as a triad with added sixth, then the implications for voice leading are again strong, as the added sixth would lead upward to C# in a return to I or would be stationary in a move to V.

Over the course of the waltz, then, the translational parallelisms of voice leading motives in the phrase openings can be heard gradually to undermine the stability, not of the prolongation (the subdominant function can be served equally well by ii or IV) but of the voice leading implications. The hegemony of the suspension-led motions is not so secure as it seemed. I would argue that, by measures 29-32, we do oscillate between one hearing and the other, first favoring IV (because of its applied dominant), and only later ii (because of the expanded context that ties the subdominant function into the cadence progression).

References:

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.

Kielian Gilbert, Marianne. "Interpreting Schenkerian Prolongation." Music Analysis 22/1-2 (2003): 51-104.

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.

References:

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.