Whether it was a case of missed opportunity or simply ships passing in the night, bound for wholly different ports, I don't know, but at the time I was on my way to film and film music studies, and, when Schachter did publish an article on the rising line problem in 1996, I didn't see it. I wasn't paying attention to the music theory literature, and he chose to put the piece in an obscure place. In the meantime, William Rothstein had articulated the main objection from a traditionalist point of view:
What Neumeyer demonstrates convincingly is that a fourth-progression from ^5 to ^8 may span an entire composition; for this reason alone, the ascending progression must at least be assigned to a deep level of the middleground. Virtually always, however, the ascending fourth-progression is counterpointed by a descending linear progression from ^5 or ^3. . . . It is probably best to assign such a three-part counterpoint to a deep layer of the middleground rather than to the background. (306)
Although Rothstein is generous in making it clear that either the rising or falling line could potentially be "superior in status to the other," in practice the traditionalist view has been (and this is the nub of Schachter's position) that the descending line has priority and the rising one must ultimately be assigned to boundary play (coherent voice-leading figures above the principal line). The very rare example that is "convincing" is merely one of those exceptions that proves the rule.
Thus was set up an opposition in which the three descending Urlinien constitute the unmarked term and the rising line the marked term. ("Thus" is a bit misleading, since the question of the rising line -- and so the binary pair -- predated my JMT article by a good long while.) Schachter defended the unmarked term; I focused attention on the marked term ("flipped" the binary, that is, in a manner familiar to literary criticism since at least the 1950s). In such cases, critique cannot proceed logically, but only ideologically, a step that Schachter has steadfastly avoided (even celebrating that avoidance (2001)). He has, instead, preferred to retreat to an argument carried out as hermeneutics (in its old sense linked to Biblical exegesis).
In a series of posts over the next week, I will examine the arguments and analyses in Schachter's 1996 article and in an earlier article on Bach (1994).
References:
Neumeyer, David. "The Ascending Urlinie." Journal of Music Theory 31/2 (1987): 275-303.
Schachter, Carl. "A Commentary on Schenker's Free Composition." Journal of Music Theory 25/1 (1981): 115-42. Reprinted in Carl Schachter, ed. Joseph Straus, Unfoldings: Essays in Schenkerian Theory and Analysis, 184-205. New York/London: Oxford University Press, 1999.
Rothstein, William. "On Implied Tones." Music Analysis 10/3 (1991): 289-328.
Schachter, Carl. "Schoenberg's Hat and Lewis Carroll's Trousers: Upward and Downward Motion in Musical Space." In Brenton Broadstock, Naomi Cumming, Denise Erdonmez Grocke, Catherine Falk, Ros McMillan, Kerry Murphy, Suzanne Robinson, and John Stinson, eds. Aflame with Music: 100 Years of Music at the University of Melbourne. Parkville, Victoria: Centre for Studies in Australian Music, 327-41.
Schachter, Carl. "Beethoven's Sketches for the First Movement of op. 14, no. 1: A Study in Design," Journal of Music Theory 26/1 (1982): 1-21.
Schachter, Carl. "Elephants, Crocodiles, and Beethoven: Schenker's Politics and the Pedagogy of Schenkerian Analysis." Theory and Practice 26 (2001): 1-20.
Schachter, Carl. "The Prelude from Bach's Suite No. 4 for Violoncello Solo: The Submerged Urlinie." Current Musicology 56 (1994): 54-71.
