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

[Dmitri Tymoczko]

Let me add some numbers, because it may interest people.

> I must say, however, I'm not sure I've found among the many worthy musings a convincing answer to my original question. Perhaps there isn't one. At the risk of repeating myself, let me rephrase the question and append some relevant commentary from three of the responses to the SMT list below.
> 
> Given that ^1-^2-^1 bass paradigms that expand tonic seem to be considerably rarer than either passing ^1-^2-^3 bass lines prolonging tonic or than ^1-^7-^1 and ^3-^4-^3 bass neighbor motions prolonging tonic for reasons many on this list have hypothesized, is it true that when ^1-^2-^1 bass lines prolonging tonic do occur, unaccented 6/4 chords above ^2 in the bass are rarer than other harmonizations of the same figure (say, with V 4/3 or vii65 chords),

Yes, this is true, at least given the data I have.

I -> V4/3 -> I appears 53 times in the Mozart sonatas, for example, but I -> V6/4 -> I does not appear.

> or is ^1-^2-^1 just such a rara avis that it almost never occurs as a tonic prolongation figure in common-practice music regardless of how it is harmonized?
 
Maybe it's not so rare, see above; 53 times is pretty common; that's an average of once per movement (I believe).

> In either case, why?

I think the absence of the progression I -> V6/4 -> I is to be explained as an instance of a very general pattern: 6/4 chords are typically avoided in favor of other alternatives.  Almost every progression using a 6/4 is uncommon; the exceptions conform to a very small number of types, which can be understood as idioms.

You see the same thing in the case of I -> V6/4 -> I6, which appears just three times (I believe just repeats of one progression), while I -> V4/3 -> I6 is common (62 times).

Interestingly, looking again at the data I see eight instances of I6 -> V6/4 -> I.  I will examine the original scores when I have more time.

> Is mode a factor?

Don't think so; statistics for minor look pretty similar.

> Using this nomenclature, is there such a thing as a "neighboring" 6/4 in which a harmonized upper neighbor in the bass line serves to prolong a given sonority? (A related—one might say "inverted"—question is do unaccented passing tones in the soprano harmonized by 6/4 chords appear with any regularity as prolongational devices in common-practice music?) Does anyone have a database that could begin to answer such questions?

According to my database, the only progressions X->Y6/4->X that appear with any frequency (more than 10 times) are:

I -> IV6/4 -> I (53 times)
V -> I6/4 -> V (22 times)
V7 -> I6/4 -> V7 (39 times)

Hope this helps!

DT

Dmitri Tymoczko
Associate Professor of Music
310 Woolworth Center
Princeton, NJ 08544-1007
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