[Smt-talk] function of aug. 6 chords

[Vasili Byros]

On Nov 25, 2011, at 11:14 AM, Dmitri Tymoczko wrote:

> The other difficulty I have is the idea that semitonal alteration doesn't change chord function.  This I just don't believe.  For example, IV is a subdominant, but #ivo is a viio/V chord, an applied dominant.  Your argument seems to work just as well for applied dominants as for augmented sixths -- for you, viio/V should be a subdominant, not a "dominant of the dominant" chord.  I can't follow you here -- if the term "function" is to be useful for me, then there has to be a difference between subdominant and dominant of the dominant.

> Just to be clear: my claim was that composers regularly use augmented sixths in passages where, in earlier versions of the same music, they had V/V (or vice versa), whereas you don't find the same intersubstitution of IV (or ii) and the augmented sixths.  In all honesty, this seems pretty decisive to me -- about as strong an argument as you're ever going to get in music theory.  It strongly suggests that composers conceive V/V and the augmented sixth as "basically the same" or "analogous" whereas they didn't feel that way about the augmented sixths and IV or ii.
> 
> My intuition is that V/V before V is about as common as augmented sixths are in the same spots -- and that the applied dominants appear in basically the same places, including before the I6/4 that leads to a cadenza.  

Dmitri, I would like to challenge your "pretty decisive" and "about as strong an argument as you're ever going to get in music theory." More specifically, I would invite you to dig a bit deeper into what you call chord "substitution" as evidence for your argument: in the situation you describe, both the V/V and the augmented sixth are typically (but not always) preceded by (and therefore "substitute" for) a diatonic predominant.

The textbook example is Mozart's Violin Sonata in G major, (K. 279), third movement, a theme and variations: the theme has a C–C# bass in m.  3 that leads to a half cadence in m. 4. The harmonization of the bass, in conventional Roman-numeral terms, is ii6–V6/5/V–V. The minore variation comes as number four: here the C–C# bass of the theme is repositioned to the melody. Its harmonization is now iio6/4–It.6–V. You might take this as "substitution" evidence that aug. 6th chords are "dominants," as the It. 6 appears in the same formal and syntactic context as the V6/5/V. But it's all in the eye (ear!) of the beholder. In both cases, C# appears as a chromatic alteration of ^4, so that the alleged V6/5/V (to my ear a II6/5), and the It. 6 locally "substitute" for a diatonic predominant chord. In other words, your own evidence could also suggest that composers thought of the x/V and aug. 6 chords as "analogous" predominant-function chords. The half cadence in question occurs at the end of an antecedent phrase of a period, whose consequent then modulates to the key of the dominant with a PAC. In this modulating consequent phrase, Mozart avoids ^4 (C) of the original key, allowing C# to become a leading tone.

Would you say, in the antecedent phrase of this example, that there is a change in function from "predominant/subdominant" (C) to "dominant of the dominant" (C#) and then "dominant" (D)? If so, what would this mean from a cognitive perspective? What aspect of the listening experience does "dominant of the dominant" capture better than "chromatically altered predominant/subdominant"? It seems to me unnecessary at best, and problematic at worst, to claim that the chord over C# must have a categorically different function than the chord which precedes it on "geometric" grounds: that is, the chromatic alteration produces a change in the chord's structure.

Tonal functions are not things chords or pitches have or are, but agencies that listeners ascribe them in context, in terms of expectation, implication, or what have you, and on the basis of past experience. (See the second chapter of Steve Rings' recent book for a wonderfully lucid and perceptive discussion of this, pp. 41-43 in particular). In the Mozart example, the V6/5/V and It. 6 heighten the anticipation for the half cadence in a very conventional manner. There are myriad examples of such a phenomenon in music of the long eighteenth century, where, for example, a IV6 chord becomes an augmented sixth through chromatic inflection, in minor and major, on the way to a half cadence. Off the top of my head, Beethoven's "Tempest" Sonata, opening phrase; Beethoven's "Waldstein" Sonata, first movement, transition of exposition and recap; Mozart's Don Giovanni overture, first phrase; and Beethoven's C minor variations (WoO80). 

Finally, a historical note: Vogler's first application of Roman numerals to harmonic analysis (Gründe der kuhrpfälzischen Tonschule in Beispielen, 1778!) used "IV" to represent the Ger. 6 as well as the viio7/V, and "II" for the Fr. 6. For another example of the same concept, see Joel Lester's discussion of an anonymous eighteenth-century analysis of J.S. Bach's D minor Prelude (pp. 85–86 in CTEC), where the analyst treats a C#o7 chord in a G minor context, rather than in D minor.

All best,
Vasili

*******

Vasili Byros
Assistant Professor, Music Theory and Cognition
Northwestern University
Bienen School of Music
711 Elgin Road
Evanston, IL 60208
v-byros at northwestern.edu

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