Proto-background 8: the sixth ^3-^8

Also see the proto-background introduction.

The sixth ^3-^8 often seems more comfortably regarded as a transformation of ^1-^3 through INVersion or ADDINV (in the first case, the sixth replaces the third; in the second case, the sixth is added onto the third).

In D779n13, however, the prominent sixth ^3-^8 of the closing cadence is unavoidable; it generates a foil to the previous reading's static ^3-^5: the new reading is the most sharply teleological of the nine, as everything must be read "backwards" from the voicing of the final right-hand chord.

In the graphic below, the proto-background is at the top. The second level shows the distribution of the pitches over the form (A5 appears at the end of the first strain), along with the first elaboration by means of neighbor notes (as N-1 in both voices). The third level shows the origins of the C# major section in a temporally displaced (and registrally elaborated) INV transformation. The material below the third level shows later iterations of the same kind of registral play with the basic pitch classes.

For other examples of the ^3-^8 proto-background, see my web essays [NOTE 10 June 2016: both essays named here have been integrated into my PDF essay Proto-backgrounds in Traditional Tonal Music: link] on Beethoven WoO10n2, where ^3-^8, curiously, plays the anti-teleological role among the several readings; and Beethoven WoO10n1, in which registral shifts upward elaborate a neighbor-note pair (no commentary).

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.

Proto-background 2: the unison ^3

Also see the proto-background introduction.

The unison ^3 focuses attention on the alto voice but differs from ^1-^3 (future post) in delegating its repeated linear path to later levels. As the "foreground" figure in a previous posting showed, the potent voice leading clichés invoked by the suspensions in the alto voice and the essentially stationary ^5 in the soprano are subverted at the last moment in the cadence. I have rewritten that figure below in terms of ^3 rather than ^1 (this is a thumbnail; click on it for a larger image):

Details of the first section (bars 1-18). The first line is a "middle-level" version of the second line above, relevant only to the first strain. The second line shows how the intervals unfold. Note especially the 3-6 INV pair nested inside the main pair. The third line gives even more detail, focusing on lines and the cover tone E5.

The reading with a proto-background unison ^3 can be rewritten in more traditional Schenkerian notation (the C# major section is not included here -- it's the empty space in the middle of the graph):

Obviously, one has to allow for the possibility of a background/middleground neighbor note in order to make this work. I write about that issue briefly in the MTS article (291, 297fn30) in connection with Schenkerian readings by Arthur Komar.