Sunday, November 1, 2009

Proto-background 4: the third ^1-^3

Also see the proto-background introduction.

The third-interval rooted in the tonic is a rich source of linear figures, although, like the ^3-^2-^1 of Schenkerian analysis, these figures almost seem too obvious; they have a clichéd or generic feel about them, as if someone were to say that the theme of a story, poem, or film was "love." In the graphic below, I have followed this line in interpreting the second level or "middleground" as a neighbor note figure aligned with the harmony of opening-plus-final-cadence (I------V7-I).
More interesting are the details in the third and fourth level. Interval inversion converts the initial third (in the alto) to a sixth in the cadence, then ultimately inverts the inversion, so to speak, in the truncated reprise. (Strictly speaking, I suppose, the second motion inverts upwards (as shown), then shifts the resulting third down an octave.) The fourth level shows further details of the registral play.

The tonal space of the third ^3-^1 is also used in Schachter's traditional Schenkerian reading of the waltz, of course. I have reproduced the background (strictly speaking, first middleground) form an earlier posting along with my notation of the first strain.

Schachter favors the (inner-voice) descent A-G#-G-natural-F# in the contrasting middle. My own reading of the second strain is close to his but I prefer to emphasize the mixture of E-E#-E.

Differences between the traditional Schenkerian reading and the proto-background can be suggested by aligning both versions with the consequent of the 16-measure theme (mm. 11-18). (b) is the proto-background; (c) is Schenkerian.

Level (c) allows a simplification of the voice leading that is not available without overt doubling in level (b). On the other hand, the bias against register (or, to put it another way, in favor of single-octave solutions) means that (c) must cut across the clearly articulated parallel sixths in the cadence.