Saturday, October 24, 2009

Proto-background 1: the unison ^1

Also see the proto-background introduction.
It would have been better, perhaps, to start with a simpler reading, such as ^3-^3, ^1-^3, or the obvious ^3-^5, but the unison ^1 has the advantage of shifting the interpretive ground rather abruptly and thus emphasizing the variety induced by registrally based proto-backgrounds.
NB: The graphics are thumbnails; click on them to see the originals.

Given the alto's strong focus on ^3 and the soprano's equally dogged emphasis on ^5, a reading generated from ^1 might seem counter-intuitive, but it does a very good job of conveying the teleology in the 8-bar antecedent. After the left hand's "oompah" introduction establishes key and meter, the right hand figures unfold over unstable harmonies; the first point of stability is at the end, when the alto reaches ^1 over I (bar 9). The notation in the treble staff reflects that with unstemmed closed notes for ^5 and the line from ^3 but an open note for ^1.
The consequent repeats the harmonic progression with variants in the eighth-note groups, but its ending is a surprise as a line rises from ^5 to the upper octave (A5), overwhelming the placid repetition of the descent in the alto. The idea, then, is to make a REGistral shift, but the register of A4 is doubled -- it doesn't disappear -- and so I call the transformation ADDINV, which adds above a given interval its inverse (here, the octave above the unison).
The register change is not made directly by A4-A5, but at a later level ("foreground") by G#4 -- see the graphic below:

The density of this figure is preferable to a reading that simplifies the passage through reduction to schematic voice leading over the given harmonies.
Returning to the main graphic, I have bracketed the octave with its internal fifth (which receives direct melodic emphasis in bar 17) and then noted how the progress of the second strain takes this framework and transposes it upward twice. (These could have been labeled as diatonic transformations T2 & T3, respectively.) This is an elaboration, however: on the larger scale, the entirety of the second strain repeats (or maintains the result of) ADDINV.