[Smt-talk] "Neighboring" 6/4 chords

[Dmitri Tymoczko]

Edward Klorman writes:

> But the passing progression I  V 6/4 I6 is extremely common and idiomatic (as in the first three measures of the Op. 2/3 trio and many similar examples).

We actually discussed this progression on the list back in January, 2010.  (What, you think it's weird to remember two-year old SMT-list discussions?)  It turns out that I -> V6/4 -> I6 is actually pretty rare in Bach and Mozart.  (There's just one example in the Mozart sonatas, for instance, and the progression is virtually absent in the Bach chorales.)  There are a few examples in Beethoven, but not a ton -- for instance the Op. 2/3 trio comes up repeatedly.  (I had thought Charles Smith mentioned it to the list in January 2010, but it turns out it was in a private email.) 

In any case, the passing V6/4 between I and I6 is much rarer than the passing I6/4 between IV6 and IV (or ii6), even in Beethoven.  I wish I had better data about Beethoven, but I only have a few pieces.  Nevertheless, it's a pretty clear asymmetry: the most common "passing I6/4" is I6/4 between IV6 and IV/ii6, not V6/4 between I and I6.

Olli writes:

> But what, exactly, do you mean by stating that the explanation is "harmonic rather than contrapuntal"? Certainly there are crucial contrapuntal constraints for the use of 6/4 chords, the essential reason for which is the dissonance of the fourth. Obviously we cannot just take any common harmonic progression and arbitrarily invert chords to 6/4s (like I–VI6/4–IV6/4–V–I6/4). The use of the fourth in 6/4 chords is regulated by similar voice-leading principles than dissonances in general. In my view, the labels "neighboring" and "passing" are indispensible for describing these principles, both in scholarly discussion and elementary instruction.

Oh, I just meant to be referring to that old tradition that asserts that certain progressions are "not truly harmonic" and are "merely of contrapuntal origin."  I think this is demonstrably false: vi->ii6/4->vi is just as contrapuntally sound as I->IV6/4->I but is virtually unknown.  What explains the difference in frequency is not anything contrapuntal, but rather the harmonies involved.  As I recall, you agree that local harmonies are governed by harmonic constraints, which puts you in the "compatibilist" camp (as discussed in Chapter 7 of my book).

You are right that every progression is subject to contrapuntal constraints.  The question is whether these "neighboring 6/4 chords" are particularly constrained contrapuntally.  It's not clear that they are.  (For instance, in IV6->I6/4->IV, the upper voice often leaps away from the fourth; now you can explain this away, but it is a little awkward.)  It might be that they are constrained, but this would be worth showing in detail.  Intuitions, I suspect, are of limited utility here.

It's certainly true that one can decide to describe, not what actually happens in actual music, but what one personally thinks it would be OK to do.  So, maybe for you, ii->V6/4->ii would make sense.  I prefer not to go down this road, since I'm tolerant of a very wide range of music (including atonal music, aleatoric music, and music that uses 6/4 chords all over the place) and anyway, I find it more fun to try to describe what actually does happen.  But this is definitely a matter of taste.

And:

> What is written above does not help much to explain the original question in this thread. Why does I–V6/4–I occur so rarely, even though the progression would seem correct in both harmonic and contrapuntal terms?

To me, this is very simple: in general 6/4 chords are avoided in the style, with only a few exceptions.  So we should expect that a given progression, using 6/4 chords, is very uncommon.

A problem only appears to arise if you believe that a bass note, part of an apparently syntactical progression, can be "a neighbor."  That gives the impression that I->V6/4->I should occur frequently.  (After all, why not?  It's "correct in both harmonic and contrapuntal terms!")  In Chapter 7 of my book, I argue that you should not think in this way -- that the Schenkerian "neighbor chord" is not at all like the uncontroversial "neighbor note."  Once you recognize this difference, the problem evaporates, and you're left with the simple fact that virtually all conceivable progressions using 6/4 chords are unused.

So I really don't see a problem here; the absence of this progression is part of a more general absence of 6/4 chords.  Of course, I have given up the idea that "neighbor chord" is a grammatical category, and interpret it what I guess is an unusual (psychological/intentional) way.

BTW, I recognize that I've pontificated about this issue several times here, so I won't press the point anymore.  I did try to take up these issues in "A Geometry of Music," and I suspect that my views about these issues are pretty clear by now ... 

DT

Dmitri Tymoczko
Associate Professor of Music
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