Thursday, November 12, 2009

Proto-background 5: the fifth ^1-^5

Also see the proto-background introduction.

The fifth space ^1-^5 re-introduces a teleological element into the reading, but by no means so radically as when we hear the background as ^1-^1. Here, the upper part of the interval receives attention at the beginning, but the interval as a whole is only defined at the end of the first phrase (see the third staff below). The contrast between upper and lower voices in the right hand, thus, is more striking even than in the reading ^3-^5 (entry to be posted later this week), in that the definition or the concrete presentation of each background tone is situated at opposite ends of the phrase. And the teleological hearing of the alto voice is a good mirror of the listening experience for a string of suspensions, which constantly push forward, ahead, towards a goal, the resolution of the last suspension in the series (here, the 4-3 suspension that brings the secure arrival of ^1).

The fifth space also coordinates nicely with the C# major section (in fact, more simply and directly than any other reading): a WEDGE transformation pulls the notes apart by a half step, to G#-E#, then its inverse pushes them back together again for the reprise/ending. (WEDGE here can be understood as inversion about C/C#; it is a variant of Lewin's transformation W -- see 1987, 124 ff.; see also 2006, 332 ff.)

In a performance of the waltz, of course, the WEDGE is distorted as the G# is G#5, not G#4. We would include the registral shift in a fourth staff/level (not shown here).

Lewin, David. Generalized Music Intervals and Transformations. New Haven: Yale University Press, 1987.
Lewin, David. Studies in Music with Text. New York: Oxford University Press, 2006.