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

[Ildar Khannanov]

Dear Colleagues,
 
it is amazing how the issue of 6/4 keeps coming back into our discussion. I remember that it was not an issue in Russia where I studied harmony and voice leading. I can only make a guess that in North America the basic instrument (the one the majority of students can relate to) is guitar, and not piano. On a guitar, due to tuning by forth (at least  of first two lower strings) the forth between the bass and the next voice sounds reasonable.  Everybody is used to this sound. Perhaps that is why all my students can write a 6/4 instead of root position triad and not feel any remourse for commiting this crime. And the question of why the 6/4 cannot serve as a neighbour chord I can relate to this same issue. In fact, the 6/4 is not a neighbor chord and cannot serve this function. If you allow it to be placed between two tonic triads in root position, the next question would be why not to use it freely as a substitute for a root position triad? Both cases
 depend of your perception of this chord as a dissonant sonority, unusable as an independent member of tonal-functional structure.
 
Perhaps, this is the reflection of the fact that a chord cannot be designated as neighbor or passing. A note can. The voice exchange, in which the 6/4 sonority is commonly used, does not make it a passing chord. It simply erases its functionality and destroys its integrity. Yet, the 6/4 in this situation cannot be identified as passing. The same applies to the cadential 6/4. The latter is not a double suspension to dominant triad. There is a confusion in terminology. I suggest simply not to use the term chord in relation to these sonorities.
 
Best,
 
Ildar Khannanov
Peabody Institute
solfeggio7 at yahoo.com


________________________________
From: Dmitri Tymoczko <dmitri at Princeton.EDU>
To: Society for Music Theory <smt-talk at societymusictheory.org>
Sent: Wednesday, October 5, 2011 10:11 AM
Subject: Re: [Smt-talk] More "Neighboring" 6/4

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






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