More to hexatonic cycles and D779n13

I referred to Richard Cohn's article on Schubert in an earlier post. This post is mainly text citations with a comment or two.

Cohn uses the astronomical metaphors more expansively than I do (earlier post). I replace the primitive earth-bound up/down metaphor with the earth's spherical center-periphery model of gravity, a common image by the early 19th century, as Cohn reports:

By Schubert's time, the spherical earth had long been acknowledged. . . . Gottfried Weber compared the components of a tritone to "antipodes, literally with the feet directly opposite to one another, as those of persons standing on the opposite sides of the globe," anticipating Tovey's comment a century later: "Harmonic space is curved like the surface of the earth, and [the] tritone is its date-line." (231)

Cohn, on the other hand, pushes the metaphors out to galactic levels:

The traditional metaphorical source for tonal relations is the solar system, where positions are determined relative to a central unifying element. A star cluster evokes a network of elements and relations, none of which hold prior privileged status. These two contrasting images of cosmic organization provide a lens through which to compare two conceptions of tonal organization in Schubert's music. (213)

The essential claims, then, are "that efficient voice leading, emphasizing semitonal displacement, furnishes a context in which to understand nineteenth-century triadic progressions that are not adequately reconcilable to diatonic tonality" (231); and that, in at least some of Schubert's late music, one finds "the intersection of plural incommensurate systems: amid tonally indeterminate triadic progressions exhibiting efficient voice leading, Schubert's [Bb major piano] sonata establishes diatonic collections, articulates cadences, and prolongs tonics by conventional means."

This "intersection" is represented in the figure below, a reworking of Cohn's Figure 3, which collapses the hexatonic cycles into a "table of tonal relations" (217). Here I have reordered the triads to fit not Bb major but the A major of D779n13.

I do think that Cohn, in his advocacy for a Riemannian historical thread, pushes the "equality" of diatonic (fifth-based) and symmetrical (third-based) systems a bit too far, suggesting a level of organized thinking that seems foreign to practical musicians in the first half (at least) of the nineteenth century. In particular, he doesn't explain why a looser narrative -- of accidental or serendipitous results from the exploration of chromatic mediant progressions common since the late 1790s -- wouldn't work just as well or better in explaining Schubert's bolder harmonic and tonal moves.

Reference:

Cohn, Richard. "As Wonderful as Star Clusters: Instruments for Gazing at Tonality in Schubert." Nineteenth Century Music 22/3 (1999): 213-32.

Hexatonic cycles, after Cohn

The LP transformation that has become a motif in this blog –- because the harmonic progression that expresses it is such a distinctive element in D779n13 -- is a segment from one of the four hexatonic cycles described by Richard Cohn ("Maximally Smooth Cycles")--see the left side of the graphic below.

Though the display of the cycle is neutral (the C# triads could just as well be shown on the right or "clockwise" side (in relation to A major) as on the left or "counterclockwise" side), the order chosen in the figure has substantial historical resonance, as progressions to the lowered sixth degree were common in the early nineteenth century (and later) but progressions to the major mediant were rare. (In "As Wonderful as Star Clusters," Cohn explores Schubert's use of harmonic and tonal progressions based on hexatonic cycles in the late Bb major piano sonata. The work is interesting even if Cohn's reading of the piece is ultimately more elegantly complex than it is convincing.)

We might speculate that D971n2 and D779n13 as published are the remainder of Schubert's experiments at mirroring the common move to the lowered sixth by going in the opposite direction. If he indeed tried this out while his friends danced near him, Schubert would quickly have discovered how awkward the return to A major was in the constrained context of 16 bars. The conventional return from a progression I - bVI was through an alteration that produced an augmented sixth chord, or I - bVI - +6 – V (as happens in the second strain of the Trauerwalzer).

If one attempted the same from III, one would end up on the dominant of bVI--in other words, the progression will always move one position counterclockwise along the cycle, which means that a second progression through an augmented sixth would have been necessary to reach I again. The simpler solution, undoubtedly, would be to close in the secondary key, then simply shift back to the main key--the solution Schubert used in D971n2--but the non-tonic opening of the reprise in D779n13 posed an additional obstacle. Under the circumstances, the solution Schubert used in the published version is the simplest one available.

(The other option would be to convert the tonic of C# major to a dominant seventh chord and use a deceptive resolution, or C#: I – f#: V7 – VI. Unfortunately, this would oblige Schubert to include in the final triad the pitch A (to resolve the seventh), which would greatly hinder the reintroduction of the theme's characteristic suspensions.)

References:

Cohn Richard. "Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late Romantic Triadic Progressions." Music Analysis 15 [1996), 9-40.

Cohn, Richard. "As Wonderful as Star Clusters: Instruments for Gazing at Tonality in Schubert." Nineteenth Century Music 22/3 (1999): 213-32.