Options to follow C# major

At (a) in the graphic below is a chordal reduction of the basic progression in D779n13. At (b) through (d) are three alternatives that in fact would have been statistically more likely results for a waltz that is firmly in A major in its first strain, then shifts abruptly to a C# major triad at the beginning of the second strain. Version (b) does not tonicize C# major, as does D779n13, but instead converts the triad into a seventh chord and moves smoothly through a cycle of fifths progression, devoting roughly equal time to each step. Version (c) tonicizes not C# major, but the F# minor that would have been a more likely goal of a C# chord in this context. Version (d) plays out the other implication of version (b) -- here a cycle of fifths progression leads to a close on E major. It is assumed that the close comes as the end of a contrasting middle section, because the articulation is necessary to explain an otherwise awkward retrogression to B minor for the reprise.

Version (d) follows through the implications of the hexatonic cycle and supposes a direct movement from C# major to F major (with an intermediate respelling of the C# triad as Db), and again from F major to A major.

I have worked all of these out in improvisation sessions. Not surprisingly, versions (b) and (c) are the easiest to manage, particularly in the close quarters of an 8-bar strain, but also as an 8-bar contrasting middle leading to a full reprise. Version (d) is not so successful; to make it sound plausible, I had to, as it were, override the close on E by following it with an A major triad -- that additional step on the cycle of fifths made for an uncomplicated move into the D7/b6 dissonance of the reprise. Version (e) sounded quite strange if I attempted to make it compact (fit it in 8 bars), but at least plausible if I stretched it out as a series of tonicizations.

The idea of a close look at chromatic harmonies as an addition to or corrective to linear analyses in the Schenkerian tradition was explored in a convincing way more than twenty years ago by Charles J. Smith (who was reacting to a tendency toward somewhat radically linearized -- and therefore sometimes harmonically obtuse -- readings among the first generation of American post-Schenkerists). More recently, Marianne Kielian Gilbert has given sustained attention to the issue in several articles -- see this post.

References:

Smith, Charles J. "The Functional Extravagance of Chromatic Chords." Music Theory Spectrum 8 (1986): 94-139. See also David Beach, "On Analysis, Beethoven, and Extravagance: A Response to Charles J. Smith," Music Theory Spectrum, 9 (1987): 173-185; and Charles J. Smith, "A Rejoinder to David Beach," Music Theory Spectrum 9 (1987): 186-194.

Kielian Gilbert, Marianne. "Interpreting Schenkerian Prolongation." Music Analysis 22/1-2 (2003): 51-104.

Kielian Gilbert, Marianne. "Inventing a Melody with Harmony: Tonal Potential and Bach’s "Das alte Jahr vergangen ist." Journal of Music Theory 50/1 (2006): 77-101.