[Smt-talk] function of aug. 6 chords

Dmitri Tymoczko dmitri at princeton.edu
Sun Nov 27 19:10:04 PST 2011

Hi Vasili,

Nice to hear from you, and sorry we didn't get to talk about this stuff back in Minneapolis.  

As I see it, there are several issues to discuss here.

1) What does the music actually show, and what claim am I actually making?
2) Does the fact that a chord Y *follows* chord X mean that Y "substitutes" for X?  (I say "no," you seem to imply "yes.")
3) Is it worth distinguishing "predominant function" from "secondary dominant" function? (I say "yes," you seem to say "no.)
4) Are functions in listener's brains or in composer's?  (I personally distinguish "syntactic function" [synfunction] from "[listener's] psychological function" [psyfunction].)

OK, in order:

>  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.

First, it is quite easy to find examples where a secondary dominant/augmented sixth pair is not preceded by a diatonic predominant.  Consider, Mozart Piano Sonata KV311/284c, II.  Here you have a beautiful, predominant-free case: viio6/V in the opening (m. 14), Italian 6 in the repeat (m. 50).  Or Beethoven Piano Sonata #1, I, m. 42 [viio7/V] and 140 [Ger6/5].

Now reconsider the structure of my argument more carefully: I claim there are *tons* of examples like this in the classical literature (having just found a few more in Haydn just last week, and you having just graciously provided a new Mozart example), but hardly any cases where you have ii or IV in the opening, with an augmented sixth in the repeat.  Note that there is both positive and negative evidence here: it's not just the *presence* of secondary dominant/augmented sixth pairs, but also the comparative absence of diatonic predominant/augmented sixth pairs.

I don't see you offering an argument against either form of evidence, and particularly not the negative sort.  Instead you seem to be saying "look, V/V and ii/IV are pretty close, since they both go to the dominant."  I agree they're close, but I still think it's worth making a distinction between them, for reasons I'll discuss in a moment.

However, I totally reject the idea that "since the augmented sixth is typically preceded by a diatonic predominant, it therefore substitutes for a diatonic predominant."  The mere presence of a schema X->Y does not imply that Y substitutes for X at all.  I6/4 is typically preceded by ii6, but it does not "substitute for" it in any way.  (Even worse, I is typically preceded by V7.)  So I think our intuitions may simply be different here.

> 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.

Exactly!  This is precisely the point I'm making.

> But it's all in the eye (ear!) of the beholder.

Here I disagree.  As we discussed in Minneapolis, I think that the term "function" is systematically ambiguous: it can be used as a way of categorizing chords by their behavior [syntactical function] or by our perception of their similarity [psychological function].  My Musurgia article (available on my website in English as "Root Motion, Function, Scale Degree," or available in the original French from your favorite dealer in back issues of Musurgia) talks about this, if you're interested.

I personally am interested in the syntactical question: is there enough of a systematic difference between V/V chords and ii6 chords to warrant postulating different categories?  I think there is plenty of good reason to do this.  For example, V6/5/V is sometimes inserted between I6/4 and V, but ii6 is hardly ever found there.  Certainly, both ii6 and V6/5/V "lead to V" and are in that sense similar.  But I think there are enough systematic differences between them (the ability to substitute for augmented sixths being just one) so as to warrant postulating different syntactic categories.

Ultimately, though, there's no fact of the matter here: it's a question of how thin we want to slice the salami.  You might prefer a generic "predominant" category that encompasses ii, IV, V/V and the augmented sixths, in which case there's no interesting question whether the augmented sixths are more like V/V or ii.  I prefer a more specific set of categories, in which case that same question becomes interesting.  In other words: if you are the sort of person who distinguishes ii from V/V, then there is very, very good reason to group the augmented sixth with V/V rather than ii.  You may not be such a person, but I certainly am!

> 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?

There is a terrible tendency to use "cognitive perspective" to mean "the listener's cognitive perspective," as if we forget that composers have brains too!  (Or as if we think that listening is just "composing in reverse.")  I am interested in composer's cognition, as we can understand it through the traces left in musical scores.

In this case, it would mean that ii and V/V belong to different grammatical categories, and that they behave differently.

> 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.

Let me just emphasize that I am not using the word "must" or resorting to geometry in any way.  I believe that there are good reasons for thinking of diatonic predominants and secondary dominants as belonging to different syntactic categories (which are in turn underwritten by systematic differences in how those chords appear in the music), and that I think it is pretty clear that the augmented sixths group with the secondary dominants.  It's a complicated story, but I do think the evidence is pretty decisive.

I'm more than happy to debate this issue, but we have to start from the same premises -- and in particular, to be willing to disentangle the psychological and syntactical meanings of "function."

> 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).

Not necessarily -- there's also a whole syntactic dimension to the term.  Tonal functions can be ways of grouping chords by their behavior, underwritten by how composers use them.  I discuss this distinction in that Musurgia article.

By the way, I have grown somewhat nervous about just how much weight we should put on the intuitions of contemporary listeners.  The worry is that our hearing is strongly colored by our education.  If you've been taught that augmented sixths are altered dominants, you will be more likely to report that you hear them that way.  (Or if you play a lot of jazz!)  If you've been taught something different, you will be more likely to report something different.  What does this show, exactly?

I don't mean to discount listener phenomenology altogether, but I think it's more subtle than we sometimes like to think.  As Milton Babbitt used to say, there's no such thing as an immaculate perception!

Best wishes,

Dmitri Tymoczko
Associate Professor of Music
310 Woolworth Center
Princeton, NJ 08544-1007
(609) 258-4255 (ph), (609) 258-6793 (fax)

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