Schenkerian readings from ^8

Continuing the newly revived theme of linear analysis graphs closely hewing to the Schenkerian tradition, here are three potential readings from ^8, none of which is particularly convincing (all would fit Culler's ideas about extravagance and the implausible in (over)interpretation).

The first two are conventional readings. They require an initial arpeggiation across C#4 and E4 to reach ^8 at the end of the first strain; thereafter, each finds its own long path back to ^1. Both begin from G# (now acting as ^7) in the second strain.

The first reading finds a path through F#, as 7 in C#:V7, and so reaches the register of ^5 and descends as in the five-line readings. This requires the "mixture" voice leading to work.

The second eight-line reading preserves Schachter's G# passing between A and F#, but then the descent occurs very late--we are left to imagine a rush downward over two bars of V7; this ^4-^3-^2 is a Leerlauf, though this one sounds less like an "unsupported stretch" than like a free fall. Overall, both of these readings exaggerate the weaknesses of the reading from ^5. The only Schenkerian who might choose such lines would be a contrarian who hears a determined passage of lines through the waltz's net of cover tones.

Nevertheless, the third reading is obviously the most contrived. This Mixolydian reading rewrites the already weak octave-line to replace ^7 with ^7-natural, the motivation being that the G-natural constitutes the only truly dramatic, unexpected moment in this waltz. That a Mixolydian modal scale exists to accommodate the G-natural helps, even though such modal scales scarcely exist in the musics of this period (and certainly not in music for social dancing!).

For this reading we take an expressive, marked moment, rather as Edward T. Cone does with his promissory note in Schubert's Moment musical in Ab or Schachter with his F#/Gb in Beethoven's Symphony No. 6, but go beyond either of these authors by elevating the distinctive pitch to the status of a member of the urlinie; that is, the reading imposes a belief that such a note should not merely point to the background, it should be the background. In this case, however, the G-natural lacks any further consequences (unless you believe that the A Major Waltz was meant to act as a trio to the previous waltz in D major, in which case there certainly are consequences, for the earlier waltz foregrounds a juxtaposition of a G-natural neighbor note in the upper voice with a G# in an inner voice).

References:
Cone, Edward T. "Schubert's Promissory Note." Nineteenth Century Music 5/3 (1982): 233-241. Reprinted in Walter Frisch, ed., Schubert: Critical and Analytical Studies, pp. 13-30. Lincoln: University of Nebraska Press, 1986.
Schachter, Carl. "Triad as Place and Action." Music Theory Spectrum 17/2 (1995): 149-169. Reprinted in Schachter, Unfoldings, 161-183.

Proto-background 6: the octave ^1-^8

Also see the proto-background introduction.

Register plays such a crucial expressive role in D779n13 that the octave, at first glance, would seem to be an appealing starting point for an interpretation. As it turns out, however, the proto-background ^1-^8 simply shuffles the priorities (levels) of the reading from ^1-^1, rather than introducing any substantially new information, as will be obvious if you compare the graphic below with the first hearing: blog entry.

Nevertheless, I am inclined to prefer this new version, if only because it takes the teleological bias (which will be a factor in any analysis of this waltz involving ^1) and pushes it to the max, making for a more consistent interpretation overall.

As a postscript to the reading from ^1-^8, here is a reading that, if possible, goes even further to declare a "universal" space of the octave (see graphic below). This hearing of D779n13 follows from an observation that the traditional octave ambitus of the modal scale continued to exert a considerable force throughout the Baroque era, but not later (Neumeyer 1987; Smyth 1999). Since the practices of European tonal music arose and were solidified in this era, it is not unreasonable to suppose that the octave might be a universal principle for tonal space, with the same status as strict counterpoint, figured bass, and the rhetorical schemata exemplified in the partimenti tradition.

If so, the result might be a fixed octave "background" with secondary motions (represented by arrows here) established in relation to it. The idea is not only retrospective but prospective since it is, of course, related to the device of absolute register in some twentieth-century musics.

References:
Neumeyer, David. "The Urlinie from ^8 as a Middleground Phenomenon." In Theory Only 9/5-6 (1987): 3-25.

Smyth, David. “Schenker’s Octave Lines Reconsidered.” Journal of Music Theory 43/1 (1999):101–33.