Handout for SMT presentation

I presented "Schubert's 'Riemannian Hand': An Archaeology of Improvisation for Social Dancing" during last week's joint meeting of AMS/SMT in Indianapolis. I have posted a pdf file with the handout here. [NB: This link was updated on 3 July 2016]

Here is the PROPOSAL as it was sent to the program committee last spring:

Proposal for the annual meeting of the Society for Music Theory, Indianapolis, 2010

Title: Schubert's "Riemannian Hand": An Archaeology of Improvisation for Social Dancing

Research on improvisation practices in the nineteenth century has looked primarily at the fantasia. The reminiscences of Schubert's friends provide a window into another, equally important, practice: playing music at the piano for dancing. The celebrated Schubertiades varied greatly in their formats but often consisted in musical performances followed by dancing (Litschauer 245). For the latter, Schubert was obliged to string his waltzes into "endless cotillons" (Deutsch 230; also, Litschauer and Deutsch 101). A close relative of the contredanse, the cotillon required frequent repetition of strains, particularly the principal one, which acted as a kind of rondo theme. The number of repetitions depended on the dance caller (some published instructions stretch 24 bars of music across 80 or more bars of dancing).

Using the three-layer texture of the waltz (as played on a piano) and "endless cotillons" as the design, I will demonstrate with examples and through performance (1) how strict small forms, repetition, and variation can reveal pairings and groupings among Schubert's surviving waltzes, suggesting relationships that may have arisen through varied repetition in performance; and (2) how the chordal offbeats can effect transformations with parsimonious voice leading by simply moving thumb, middle finger, or little finger, thus anchoring the more distant modulations that Schubert attempted in improvisation.

During the presentation, I will provide a handout charting and comparing the dances that make use of third relations, and I will perform a "music-stretching" cotillon that will gradually transform one Schubert waltz (as the first iteration of the principal strain) into another (as the final iteration).

An instance of the pairings that emerge from this study is given in Example 1, which shows that the A Major Waltz D. 779 no. 13 (familiar to music theorists from analyses by Schachter and by Lerdahl and Jackendoff) might easily have arisen as an improvised variation on D. 365 no. 6. [ Example 1: At the top, Schubert, D. 365 no. 6, opening; at the bottom, D. 779 no. 13; in the middle, underlying voice leading pattern -- see the presentation handout for this.]

The three-layer texture is associated with the most common ensemble in tavern or small restaurant settings in Vienna about 1800: two violins and bass. The layers are clearly differentiated in Example 2 -- the second violin's double stops would simply become the offbeats in waltzes by Lanner and Strauss. [Example 2: Beethoven, Sechs ländlerische Tänze, WoO15, no. 1, first strain. -- see the presentation handout for this.] The texture of this ensemble could be appropriated for domestic settings when the piano became popular as a replacement for the traditional violin as accompaniment for dancing. For those pieces that used the Ländler-derived "oom-pah" rhythms, the result was three functionally differentiated layers, two in the left hand, one in the right.

I focus attention on patterns of the middle layer (left hand chords) in relation to upper voice figures, particularly on those that generate third-related key areas in the second strain. See Example 3, where the left hand executes an LP transformation. [Example 3: Schubert, D. 779 no. 13, move from the first to second strain, and from A major to C# major, as an LP transformation in the left hand -- see the presentation handout for this.]

By doing multiple comparisons among dances, I try to reconstruct some sense of how Schubert, during improvised performance, may have been—in Kofi Agawu's terms—"thinking in music about music."

Works cited

Agawu, Kofi. "How We Got Out of Analysis, and How to Get Back in Again." Music Analysis 23/ii-iii (2004): 267-86.

Deutsch, Otto. Rosamond Ley and John Nowell, trans. Schubert: Memoirs by His Friends. London: A. & C. Black, 1958.

Lerdahl, Fred, and Ray Jackendoff. A Generative Theory of Tonal Music. Cambridge, MA: MIT Press, 1983.

Litschauer, Walburga. "Unbekannte Dokumente zum Tanz in Schuberts Freundeskreis." Studien zur Musikwissenschaft 42 (1993): 243-249.

Litschauer, Walburga, and Walter Deutsch. Schubert und das Tanzvergnügen. Vienna: Holzhausen, 1997.

Notley, Margaret. "Schubert's Social Music: The 'Forgotten Genres'." In Christopher H. Gibbs, The Cambridge Companion to Schubert, 138-54. Cambridge/New York: Cambridge University Press, 1997.

Schachter, Carl. "Rhythm and Linear Analysis: Durational Reduction." Music Forum 5 (1980): 197-232.

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.

D779n13 embedded in D. 365

Instead of imagining performance conditions in which D779n13 might have acted as a trio to n12 (see trio), we can take the opposite tack and construct a new "suite" of waltzes by inserting the simplified 16-bar version into D. 365, to take the place of the waltz of which it may well be a variant.

In the graphic at the end of this post, I have assembled an excerpt from a "false" Opus 9: the actual waltzes, nos. 4 & 5, then the 16-bar recomposition of the A Major Waltz (transposed down to Ab major), then number 6, and the beginning of number 7. The recomposition fits comfortably in the set I am constructing, as all of the Ab major waltzes in D. 365 are in the most basic 8+8 design, with brief (or no) pickups.

The earliest extant manuscript for D365n4 (from 1817) is an incipit in A major, not Ab. The Trauerwalzer (D365n2), also in A, is included in that set of incipits, and it is only in several Albumblatt-style copies from the following year that this waltz is transposed down to Ab (to make it more "traurig," perhaps?); then, a manuscript from later the same year or early in 1819 has D. 365 nos. 1-4, all in Ab, as they were finally published in 1821 (Brown, 228, 230-31, 291-2).

Postscript: After Schott reissued the Trauerwalzer under Beethoven's name and with the title "Sehnsuchtswalzer" (Kinsky, 727), the little piece's fate was sealed, and it was republished any number of times throughout the nineteenth century. As we saw in another post, Schumann knew it in 1835 as Le Désir (it was also called Mon Désir in some editions). Already by 1831, it had acquired English words (under the title "The Maid of Elsmere"). By 1870, American publishers had attributed as many as seventy waltzes to Beethoven; a very small number were actually his, including WoO11n7, a Ländler that was Americanized as the "Cactus Waltz" (Kinkeldey, 245-46).

In the musical example below, n1=D365n4; n2 = D365n5; n3 = D779n13 (16-bar version in Ab); n4 = D365n6; and n5 = D365n7.

References:

Brown, Maurice. Essays on Schubert. London: Macmillan, 1966.

Kinkeldey, Otto. "The Beginnings of Beethoven in America." Musical Quarterly 13/2 (1927): 217-48.

Kinsky, Georg. Hans Halm, ed. Das Werk Beethovens: Thematisch-Bibliographisches Verzeichnis seiner Sämtlichen Vollendeten Kompositionen. Munich-Duisburg: Henle, 1955.

D779n13 originates in improvisation

The Opus 9 (D. 365) collection was published in 1821; as most of the waltzes of D. 779 were probably composed in 1822-23, it is entirely plausible that Schubert might have played a version of D365n6 at some point not long after the publication of Opus 9 and decided to use its distinctive opening formula to improvise a new waltz. The likelihood is increased by the fact that D365n6 was apparently among Schubert's favorites: as Litschauer reports, it is among only six Schubert waltzes that appear three times in different manuscripts and one of only two found in manuscript copies made by one of his friends (Litschauer 1995, 4). The fact that some of these are variants is all the more intriguing. The first of the three manuscript versions (in 9 Deutsche (1819)) is identical to the published version, but the second (in 2 Deutsche (1821)) is striking in that it gives a fully realized Bb minor 6/3 chord in the left hand of bars 1-2, whereas the third (in 4 Deutsche (undated)) combines the first strain of D365n6 with the second strain of No. 7 from the same set (see Litschauer 1989).

Thus, we can imagine the new waltz starting as depicted at (a) in the graphic below: as necessary, vamping to establish the waltz meter and tempo for the dancers (or to gather one's thoughts), then open with a slight rhythmic variant of the figure in D365n6. The voice leading formula (second line in (a)) is varied too from the moment that F# becomes the upper voice (by the end of the first full bar of melody), but that is also where the trouble begins (third line in (a)), also realized as an initial attempt at a complete phrase in (b), which has a rather flat ending that allows the suspensions to drag the upper-voice melody down through ^4 and ^3).

Level (c) shows this ending again with the lead-in to the repetition of the phrase. Here is the first inspired moment in what has so far been a rather dismal effort: the hemiola rhythm of the initial gesture has taken control by now and the "turn" in four eighth notes gracefully (and convincingly) gathers energy that is directed toward the F#. Finishing out this varied repetition of the first strain, Schubert brings the upper voice down from its perch on ^6 and ^5 with a conventional ländler cadence that strikes ^1 but leaves the register of ^3 open. This cadence will also close the second strain of an 8 + 8 recomposition in Example 4.34.) Like the descent to ^3 in the first statement, this cadence seems weak.

At this point, the decision has to be made whether to set the new waltz in a two or three-part form, but for our purpose here, Schubert's choice makes little difference. I will assume that he composes a contrasting second strain (in the manner of D365n5). The dancing continues, and I imagine that Schubert plays a trio (perhaps one of the Ab major waltzes from D. 365 transposed to A major), but the awkwardness of the newly invented waltz bothers him, and he returns to it. This time around, the first phrase and most of the second are as we know them in the published version, but the cover-tone-qua-melody, now much more insistent than in the first attempt, brings about the second inspired moment, the cadence that lifts the upper register to ^8 (see the lower line in (d)).

Having reached the register of ^8 (A5), Schubert decides to stay there, perhaps expecting to use G#5 to initiate a cycle of fifths sequence as in (e'). For reasons unknown (which might include a simple lapse of attention during a long evening of playing), he decides to ground the contrasting middle of a small ternary form in a tonicization of the C# major supporting that G#5. There are a few examples of this design, where the contrasting middle closes in the tonicized key, and the reprise returns to the main key without modulation, but in this case the design will not work because the theme starts on a non-tonic position one half-step above C#.The third and last inspired moment, then, is to take advantage of yet another motion upward to carry the melody into the pianoforte's thin-toned and ethereal upper octave where the reprise begins in the final version.

Schubert chose to keep the A Major Waltz and eventually found it a place in the D. 779 collection, but I fancy it was not because of its odd combination of counterpoint and dance topoi or even its dramatic tonal contrast (something Schubert is known to have liked), but instead for the sake of its charming two-tiered melody. I imagine one of his musically skilled friends, perhaps Josef von Spaun, coming over after hearing several repetitions of the Waltz and whispering, "Schön, zärtlich," while the dance continued.

References:

Litschauer, Walburga. "Franz Schuberts Tänze: Zwischen Improvisation und Werk." Musiktheorie10/1 (1995): 3-9.

Litschauer, Walburga, ed. Franz Schubert. Neue Ausgabe sämtlicher Werke, Series 7, part 2: Werke für Klavier zu zwei Händen, Band 6: Tänze I. Kassel: Bärenreiter, 1989.

Parallel fifths in D779n13

Today's reading might be described as the counterpoint student’s revenge. Schubert did write parallel fifths, those fifths are not hard to hear, and once heard it is not difficult to discern this sparse open sound scattered throughout the right-hand part as a shifting registral frame: see the example below.

In order to grasp how Schubert might have arrived at this unusual result, it's easiest to think in terms of improvisation while playing for dancing. The A Major Waltz bears a curious resemblance to a waltz in Opus 9 (D. 365): these are the only extant Schubert waltzes that open with a figure based on the supertonic harmony with a 7-6 suspension. As the graphic below shows, D365n6 (at the top) shares with the A Major Waltz not only the initial 7-6 suspension but also the subsequent 5-4 over the 6/4 initial component of a cadential dominant figure.

I discuss D365n6 briefly in the context of typical harmonic patterns here: "Description and Interpretation: Fred Lerdahl's Tonal Pitch Space and Linear Analysis," review-article, Music Analysis 25/1-2 (2006): 215. I will expand on the idea of improvisation as a source for D779n13 in tomorrow's post.

Postscript: Nicholas Cook offers a brief but trenchant account of the problem of parallel fifths in Schenkerian theory and practice. Writing about Schubert's song "Das Wandern," he concludes that a reading including middleground parallel fifths "is less satisfactory [than readings that remove the parallels] as an expression of that structure in terms of the metaphor of Fuxian counterpoint. [The fifths make] the music look ungrammatical and, therefore, incoherent. But this is not because the middleground consecutives contravene any natural law of musical organization. It is because they run counter to the representational means adopted in Schenkerian analysis. They spoil the comparison between Schubert's song and Fuxian counterpoint" (126, 128).

In that connection, here is a thoroughly "tamed" version of the waltz as a fourth-species exercise (with allowances for bass-specific leaps, of course).

Reference:
Cook, Nicholas. "Music Theory and 'Good Comparison': A Viennese Perspective." Journal of Music Theory 33/1 (1989): 117-41.