Allowing that "the fourth from ^5 to ^8 is among the most important structures that produce rising contours, sometimes spanning whole formal sections and, especially in short pieces, often forming the high point of an entire melodic line," Schachter says that its close on the tonic note accounts for its status, in part at least. Equally important, however, is the play of registers within the Urlinie and the balance of registers that complements upper with lower. It is these – and not Schoenberg's notion of unitary space -- that bring formal and expressive treatment of "inversion" into tonal music. Thus, for Schachter, "the interest and beauty [of such treatments] result as much from the structural and expressive differences between rising and falling lines as from the similarities of shape."
His examples are Bizet, Carmen, Act III, "Card Trio"; Bach, WTC 1, Fugue in C-minor; and Chopin, Prelude in E-major. In the first, contrast of direction is linked to an expressive life/death reversal. In the second, the gap opened in the subject is filled by the rising fourth line that leads to the fugue's highest pitch in the third episode; the line reappears in the structural cadence. The "^5-^8 fourth . . . serves as a foil both to the essentially descending subject and to the structural descent of the upper voice as a whole" (335). Finally, the E-major Prelude's obvious closing cadence figure is set into context as follows:
Although each phrase contains a primarily rising melodic line, the Prelude as a whole maintains a remarkable balance between upward and downward motion. This effect results from the second phrase's powerful climax on Ab (G#), which provides a focal point for the right-hand part. Thus the first phrase and most of the second seem to rise up to this tone, which then falls to the E at the end of the Prelude. The large-scale motion from climax to final note, then, is a descent, even though the immediate path to the final note is an ascent. (337)
I read the last of these the same way in my "Three-Part Ursatz" article (27-28), which Schachter does not cite.
Schachter, it seems to me, mixes together the notion of up/down with registral contrast, which can often be linked with timbral differences and functions of textural layers. In other words, rather as I have argued earlier, Schachter wants to maintain a simple opposition down/up so that he can the more easily choose the first, unmarked term and set it against an expressive marked term. As a device for interpretation, that tends to oversimplify (constrain) the treatment of register. In the MTS article, I discuss how the emphasis on balance of tension (along with a tendency to "naturalize" interpretive goals) links Schachter's practice to that of the literary New Critics.
Reference:
Neumeyer, David. "The Three-Part Ursatz." In Theory Only 10/1-2 (1987): 3-29.
