Is it possible to retain a sense of Schubert's risky improvisations (see posts (1), (2)) in a Schenkerian graph? Only if the graph can be made to reflect the human and fallible, not just the unerring creative instinct of an idealized notion of genius. To attempt this shift, I will start with the continuo grid. William Rothstein (296) uses the construct of the "chordal scale" (derived from Lerdahl) as the repository of tones for the imaginary continuo, his term for what I will call the continuo grid.
The beginning of the first graphic below shows the chordal scale for D779n13 with respect to its tonic triad: all members of the A major triad between the lowest and highest notes struck. Out of this scale emerge the four voices of a standard part-writing progression representing measures 1-10, or the introduction and the first eight measure phrase. The analogy to a continuo keyboard part would be better if the right hand held three voices and the left just one, but I resist that because I want to preserve the textures of this waltz as much as I can.
Resisting the idealization of textures is in fact the basic strategy of this rewriting. Note that one result is the prominent set of parallel fifths. A respect for textures suggests that the pedagogically simplified, chorale-style texture of (a) is not the best solution for this passage, which after all contains several additional voices in the left hand: these are inserted in (b), the end result looking more like the textures in orchestral settings of dances in the late eighteenth and early nineteenth centuries. Note the octave doublings that have now been added to the parallel fifths. The fullness of this texture contrasts with the three-part reduction that keeps only the two imitative upper voices and the bass (c). It is this latter that Carl Schachter uses in his durational reduction of the Waltz, but Schachter corrects the parallels by texture inversion of the two melodic voices.
Instead of collapsing the texture as Schachter does, I have removed the "non-harmonic" I 6/4 chord in (a) of the next graphic below, leaving a simple ii6-V7-I harmonic progression. Level (b) expands (a) with the closing cadence.
The contents of (b) are reproduced in the lower system of the final graphic (below) and renotated to correspond more closely to my preferred Schenkerian reading, the rising line from ^5 to ^8. The alignment is not meant to suggest an equivalence, but a replacement: if maintaining textures is thematic here, then the lower system takes the place of the upper one.
The continuo grid has a quality of concreteness about it, as if the improviser is looking at the piano keyboard and making choices about register (A major, melody in the fifth octave, accompanying voices in "standard" positions for a waltz in this key). Once the fateful decision is made (at bar 3) to model this waltz on D365n6, the parallel fifths emerge very quickly, and Schubert's decision to maintain the register despite the parallels opens the door for the sublime counter-move to the downward pull of the ancient suspension figures: the sudden lift over V in the final cadence. The graphic suggests further that, having transmuted an error into the sublime, so to speak (the parallel fifths into the rising cadence gesture), Schubert adopts the rising itself as a design in the second strain: tonicizing C# major (rather than treating it as V of vi to start a cycle of fifths sequence), then the peculiar chord progression it leads to, which facilitates another expressive moment associated with upward shifts of register (in measures 31-32--not included in the example).
References:
Rothstein, William. "On Implied Tones." Music Analysis 10/3 (1991): 289-328.
Schachter, Carl. "Rhythm and Linear Analysis: Durational Reduction." Music Forum 5 (1980): 197-232.
