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

[Dmitri Tymoczko]

Last night I thought of an interesting way to approach this general issue of 6/4 chord use.  We can ask: "what pairs of chords are most typically connected by a 6/4 chord?"  That is, we can search for progressions

	X -> Y -> Z

Where

	1. Y is a 6/4 chord; and
	2. Y is one of the most common intermediaries between X and Z.

When you do this, the most common category is of course cadential 6/4 formations, as when X is ii6 and Z is V and the most common intermediary is I6/4.  (That is,  ii6 -> I6/4 -> V.)  Filtering these out, we can identify the most common *noncadential* 6/4 roles.

The winner, by a mile, is the I6/4 connecting IV6 to either IV, ii6, or ii6/5.  This usually happens in a descending direction

	IV6 -> I6/4 -> IV [ii6 or ii6/5]

But can also occur ascending.

Anyway, this supports what I've been trying to say here over the past few years: the chief noncadential use of 6/4 chords is the idiomatic I6/4 connecting IV6 to a predominant on scale degree 4.  There's really nothing else that happens anywhere near as often.

Two more notes:

	1) My upcoming SMT talk will actually address the origins of this progression.

	2) It would be interesting to generalize this analysis by considering bass scale degrees: given a pair of scale degrees ^x and ^z, we could ask what chord typically connects them (giving ^x -> Y -> ^z), and how the scale degrees are typically harmonized (what chord X "goes on top of" ^x, etc.).  I'll get to work on this analysis when I have some free time, because I think it would be informative!

DT

PS. Interestingly, and quite in keeping with my own intuition, you do *sometimes* find this "passing I6/4" formulation when the initial chord is a vi:

	vi -> I6/4 -> IV [ii6]

However, it is strongly disfavored compared to

	vi -> I6 -> IV [ii6]

It is interesting to think about why -- perhaps the two common tones weaken the progression vi->I6/4.  In any case, it's interesting that vi->I6 almost always moves up by step to ii6/IV as if it were a kind of substitute for vi->I6->ii6.

Dmitri Tymoczko
Associate Professor of Music
310 Woolworth Center
Princeton, NJ 08544-1007
(609) 258-4255 (ph), (609) 258-6793 (fax)
http://dmitri.tymoczko.com