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.
