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.
