Schachter and the rising Urlinie, Part 4

In his article on the Prelude from J. S. Bach's Eb-Major Cello Suite, Carl Schachter makes a serious attempt to weigh the merits of a rising Urlinie, but the direction of his argument is nevertheless obvious from the outset, as he weighs the three possibilities for a reading of the upper voices in the first section (mm. 1-10). [For reference, a copy of the score appears at the bottom of this post]  He addresses the question of the rising Urlinie head on only in the closing pages, and then only briefly. Still, the answer he comes to -- the Urlinie as one among equals rather than an obvious and controlling line -- responds in a sensitive way to the circumstances of the Prelude even as it preserves the theoretical priorities dictated by Schenkerian theory. His "first among equals" construct here is in fact almost indistinguishable from Channan Willner's four-part Ursatz model: see the item "Polyphonic Ursatz" under the year 2007 on his publications page.

I don't hear the Prelude quite the same way, but mainly with respect to the middle strand on ^5 (Schachter labels this "y" -- "x" is the upper Eb, and "z" the Urlinie G3). The idea of continuing voice leading strands certainly makes sense, given the static quality of the registers (so static they have to be broken up radically by the cadenza-figures), though I might want to experiment with the five or even six voices implied by the arpeggio figures, rather than the four Schachter follows (bass plus x, y, and z).

In the graphic below, at (a) I have pulled out early-middleground/background features for Schachter's reading in terms of score fragments and at (b) have produced an analogous graphic for my own view of it. Remember that the graphic is a thumbnail -- click on it to see the original size.

I would essentially flip the priorities of Schachter's textural model, with an ^8-^7-^8 figure as the background and Schachter's "y" and "z" as the other "equals." Probably because of the lack of typical emphasis on V, a relatively common figure that combines descent and ascent (from ^8 down to ^5, then back up) really doesn't work at all here. And in any case, I can't hear the ascent in Schachter's strand "y", especially in phrases 3 and 4 (mm. 27-62), where a rise from C4 through C#4 to D seems forced, too much at cross purposes with the underlying harmonic progression.

Posts in a series starting next week will look in detail at the article in which Schachter addresses the theoretical questions of the rising Urlinie directly: "Schoenberg's Hat and Lewis Carroll's Trousers: Upward and Downward Motion in Musical Space."

References:

Schachter, Carl. "The Prelude from Bach's Suite No. 4 for Violoncello Solo: The Submerged Urlinie." Current Musicology 56 (1994): 54-71.

Neumeyer, David. "The Ascending Urlinie." Journal of Music Theory 31/2 (1987): 275-303.