[Smt-talk] "Core syntax" and 6/4 chords etc.

[Olli Väisälä]

Dear list (for one more time on this subject),

While Dmitri is probably right that this discussion has run long 
enough, some comments to his latest post are in order:

>  Olli clearly has little use for my approach, which aspires to be 
> empirical and which derives from traditional harmonic theory.

I would like to make clear that I greatly appreciate empirical 
approaches to theory, including Dmitri's Mozart counts. (Since I have 
studied Bach quite intensively, I have been well aware that one does 
not often [or ever?] find I–V6/4–I6 in Bach, but I found it interesting 
to realize that it is relatively rare also in Mozart.) However, I have 
suggested that for a deeper understanding of tonal structuring, one 
needs empirical studies more complex than those based on chord-to-chord 
statistics, ones that allow for aspects such as meter and voice-leading 
patterns, to which one should several others, such as design and 
register.

(For those interested, I would like to mention that my article on Bach 
Inventions (in the latest Spectrum) contains an empirical argument for 
the predictive power of the Urlinie in this repertoire and outlines a 
more general empirical argument for Schenkerianism. Hence, the notion 
of emprical justification of theory is integral to my own research 
interests.)

> In the standard IV6->I6/4->ii6 pattern, you have something like (A, C, 
> F)->(G, C, E)->(F, A, D).  Here the fourth (G, C) moves by a 
> combination of step and leap to (F, A).  (See the transition of Mozart 
> symphony #40, first movement, for example.)  It's not clear how this 
> relates to or derives from Renaissance-era norms of dissonance 
> treatment -- it certainly wouldn't be allowed in modal second-species 
> counterpoint.

How come??? A passing dissonance in the lowest voice (against a leaping 
"c.f." in the middle voice) does not violate any second-species rule I 
have heard of.

> Furthermore, I would reiterate that one needs to explain that only a 
> small number of these patterns actually occur: progressions such as 
> (G, B, D, G)->(A, A, D, F)->(G, B, D, G), which involve beautiful 
> neighboring motion in all voices, are almost unheard-of.

On the other hand, one does find V–ii6/4–V6/5, which is more 
"beautiful." Also when IV6 enlarges V, the 4^ characteristically 
prepares the seventh: V–IV6–V6/5 rather than V–IV6–V6. Observe also the 
related use of "ii6/4" in the "omnibus" progression from V7 to V6/5 (or 
vice versa) (one voice ascending chromatically from 5^ to 7^, and the 
other going the other direction). Hence, the category of passing 6/4 
comes rather handy on several occasions.

>
> So, given this one genuine nonstandard quarter-note passing 6/4 in 42 
> chorales, that gives us an expectation of about 9 such rascals in the 
> entire collection.  That sounds about right to me.  The question is: 
> how much class time (or how many textbook pages) do you want to spend 
> on a progression that occurs nine times in the entire chorales?

The point is that we need no textbook pages for that specific 
progression if the pages teach the general principle of passing 6/4 (as 
in A&S).

Olli Väisälä
ovaisala at siba.fi
Sibelius Academy