[Smt-talk] Nature and Labeling of the Cadential Six-Four

[Dmitri Tymoczko]

On Feb 13, 2012, at 10:54 AM, Devin Chaloux wrote:

> There are hundreds of exceptions to root functionality "rules" (if you want to call them that.) You displayed a good example of one at your talk at SMT this year where clearly there is a paradigm that V6 goes to IV6. Certainly, it's not common, but it happens. In your case, V6 leads to IV6 as a descending bass harmonization. 

Maybe I'm more optimistic than you! 

I believe that one can give a pretty simple compact set of rules that accounts for something like 95-97% of the progressions you find in the standard repertoire (described in the opening of Chapter 7 of my book).  So I would say that to describe the large majority of the progressions you find in functionally-tonal music, you need a small handful of rules (a dozen or so, not hundreds), including special rules about I6/4, special rules about progressions like V (or V6)->IV6, and vi->I6, and some rules about sequences and fauxbourdon.

In thinking about this subject, it's probably useful to get really specific about the various senses in which something can be "common" or "uncommon."  Is V6->IV6 uncommon?  In an important sense, the answer is "no" -- in the Bach chorales as a whole, about 10% of the V chords move to IV6, meaning that at least 1% of the total progressions are V->IV6.  There are about as many V->IV6 progressions as there are vi->IV progressions, with the latter being "syntactic" under almost anybody's definition.  (Other composers, like Mozart, use V->IV6 less often than Bach; Brahms uses it a lot.)

Now to be sure, there are lots of progressions that are truly, truly uncommon, in that they happen only very, very rarely: V->ii6/4 is almost completely absent from the chorales (and classical-style sonatas, etc.).  If you find it, it's really an exception.  (And these exceptions do happen!)  But I think it's important to distinguish things that happen only very, very occasionally (0.1% of all progressions, say) from those that happen pretty regularly (V->IV6).  When I teach, I try to teach the reasonably common stuff, including progressions like V6->IV6.

> However, I think you misunderstood my original point. First off, I was raising the question beyond the classroom level as this--as demonstrated by the recent flurry of emails on the SMT-talk list--is clearly an issue among us theorists as well. Certainly, anyone who sees every 6/4 chord built on scale-degree 5 as a I6/4 may curiously wonder why this debate has gone on for as long as it has. The conundrum comes when there are those of us who attach function to Roman numerals and thus, label such a chord as V6/4. It is important to note that the recent additions to the theory textbook repertoire (Marvin/Clendenning, Roig-Francoli, and Laitz) all use this nomenclature. Thus, for the many of us who have adapted this style of labeling the cadential 6/4, this is a valid issue. 

I probably did misunderstand your point, and probably am still doing so.  For instance, I'm a little confused by the idea that functions attach to Roman numerals.  On almost anybody's account, Roman numerals are functionally ambiguous -- iii can be both Tonic and Dominant, vi can be both Tonic and Subdominant.  Who knows, perhaps IV6 can be a tonic substitute, the L of P of T?  

My view is that it is a mistake to try to make Roman Numerals do too much.  In particular, it's not a great idea to use Roman Numerals to convey complex, subtle, and subjective features of perception, features which we access only through the unreliable means of introspection.  

Think about it this way: in many cases, we will all agree that there's a chord there with scale degrees 1 and 3 above 5.  But we will disagree radically about its function, meaning, and significance: some of us may hear this as a "dominant with displaced voices"; others may be more likely to hear it as a tonic chord with an unusual bass.  (See Rick Cohn's nice post on this.)  These differences are not going to be bridged no matter how much we argue and debate.  There's a certain wisdom in using the Roman numeral notation to capture those more-objective facts that we can all agree about, rather than the more-subjective facts that will always divide us.

This is particularly important when teaching: I would be very reluctant to force upon my students the view that a certain I6/4 chord is *necessarily* (or objectively) a "dominant-functioning" sonority.  I would feel really uncomfortable marking them wrong for disagreeing with me about function, and hearing it as having a tonic quality where I heard dominant (or vice versa).  Instead, I would try to be as open as possible to the incredible variety of musical experience, avoiding anything even remotely like indoctrination.

From this point of view, there is a real difference between the labels "V6/4" and "I6/4."  The former imposes a particular interpretation upon the notes, while the latter says simply that we have scale degrees 1 and 3 over 5.  We can still have our theory that says that "I6/4" is a displacement of the dominant chord (or that it is a genuine-but-weird tonic), etc., but we are not encoding that theory into the very terms of our analysis.  The very existence of people who hear I6/4 as tonic-functioning, suggests that we don't want to do that.

DT

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