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.

Schachter and the rising Urlinie, Part 12

The Conclusion -- "Lewis Carroll's Trousers" (337-38) -- is decidedly disappointing, despite its apparent promise to drive the sartorial point home, from hats to trousers. Schachter does nothing more than repeat his point with a couple new images -- an art historian writing in 1969 saying much what Schachter already did but in reference to shapes in a visual field (how exactly does the visual analogy prove the validity of the visual prop for a musical analogy?). Since asymmetrical figures look different upside down, therefore it is clear that, "in tonal music, with its gravitationally charged pitch space, linear shapes are also 'non-commutative.' In principle, ascent tends to mean beginnings and intensifications, whereas descent means endings and resolutions" (337). Let the unmarked term stand for all.

I take the charitable way out: Schachter tries an argument by accumulation: repeat your point often enough and it will seem to be proven. Since he had only an opposition to work with, the pendulum could have swung at any time to the marked term (the joyful playground of the post-structuralists). Since he was wholly committed to one term, there was no real way to address the issue directly. Just as I assume he refrained from making any jokes about "upside down" to his Australian audience -- it was, after all, the experience of sailing around the world that drove home the point for once and all that gravity-as-down was a schema that cultures needed to grow out of (in favor perhaps of center-periphery, one of the schemata in Saslaw's list), or else needed to make far more complex than a simple opposition.