[Smt-talk] Passing and Neighboring 6/4s

[Dmitri Tymoczko]

In response to Michael Chinkida, I'd say that there are two different  
questions we're asking:

1) How frequent is V6/4 in a particular style?  Does it occur half as  
often as (either V4/3 or viio6)?  Or one tenth as often?  Or one  
fortieth?  Or one two-hundredth?  The answer makes a pedagogical  
difference.  If V6/4 is very infrequent in some style, then writing in  
that style involves learning to avoid the chord rather than deploying  
it too often.  In Mozart sonatas, the ratio is about 40 to 1.   
Consequently, I can't imagine criticizing someone's imitation Mozart  
sonata for failing to include enough V6/4 chords.  Particularly if  
we're talking about introductory pedagogy, but probably also in an  
advanced "Mozart imitation" class.

2) Regardless of the question of frequency, is it useful to describe  
V6/4 as "passing"?  Is it the same sort of thing as I6/4, in the IV6- 
 >I6/4->ii6 progression?  My own tentative answer to this is "no."   
Better to teach V6/4 as a variant of V4/3 or viio6, a kind of dominant  
chord.  The term "passing" will suggest a more general procedure that  
doesn't happen very often.  I think we should consider an idiom- or  
schema-based approach to the progression.

Let me also emphasize that I really don't know for certain how often  
V6/4 chords (or other "passing 6/4s") appear in particular repertoires  
-- beyond the Mozart sonatas.  It is, I think, a really interesting  
question.  My suspicion is that some of our certainties here are  
misplaced, and that we could stand to learn something from doing some  
counting.  I've been surprised at how unpopular this suggestion is,  
because it seems to me to be fairly natural.  I suspect some of this  
is the old "two cultures" issue.  For some people counting and  
statistics and math are convenient tools.  For others, they are signs  
of a foreign mindset.

BTW, the reason I emphasize the Mozart sonatas is because this is the  
only data I have.  It took years to assemble the analyses, and I'm  
still proofreading them.  I wish I had more analyses to look at -- I'd  
love Schubert songs -- but this will have to wait.

> I have been following the contributions to this recent thread with  
> interest, but have noted that there have not been any references  
> made to the literature of the Romantic period (please forgive me if  
> I have missed such a reference).  I would like to offer an example  
> from Brahm's Die Mainacht.  The B section begins in bVI, and in the  
> 3rd measure of this section (m. 17 of the score) there is the  
> progression I6 - (V6/4) - "I" with scale-degree 5 held as a common  
> tone in the r.h. of the piano, which supports the text "Taubenpaar,  
> sein..."  I have put the "I" chord in quotations because Brahms re- 
> spells the tonic chord as V6/5/ii (or V/V/V) with #1 in the bass.   
> Thus, this example demonstrates another of usage of the 'passing  
> 6/4,' specifically V6/4, this time in the Romantic period.
>
> Dmitri states: "Actually, V6/4 is a great chord to think about.  The  
> chord is much, much rarer than you would expect from reading harmony  
> textbooks.  Bach almost never uses it (preferring viio6), and it is  
> also exceedingly rare in Mozart....  I could just say that tonal  
> composers often use I->IV6/4->I, V->I6/4->V and IV6->I6/4->ii6, and  
> that would cover ~95% of the cases students encounter."
>
> While I in no way assume a comprehensive knowledge of the tonal  
> literature, the growing number of examples posted to the SMT-list  
> gives me reason to question the assumption in Dmitri's statement.

Suppose V6/4 occurs 200 times less frequently than viio6 or V4/3.   
Given how much tonal music there is, we would still expect to find  
plenty of examples.  One thing I've been trying to say is that  
traditional textbooks rely too much on the isolated example, and don't  
give a good enough sense of how common various progressions are.  Some  
progressions (like I->IV/IV->IV) may appear periodically in the  
literature, but infrequently enough so as to be considered really  
unusual.

> Thus, I believe the goal pedagocially should not be "this type of  
> 6/4 chord occurs x amount of times vs. that type of 6/4 chord which  
> only occurs y amount of times and as a result should be dismissed  
> out of hand," but rather, "isn't it interesting that this type of  
> 6/4 chord is used in this particular instance - what can we learn  
> from that?'

I apologize for giving the impression of "dismissing out of hand."  In  
my experience, students are often confused by being presented with too  
many possibilities: if one wants them to compose in the style, rather  
than merely labeling chords, they have to have a good sense of what  
happens frequently and what happens exceptionally.  Furthermore, if  
you give them the impression that chords can generally be embellished  
by "neighboring" or "passing" 6/4 chords, you get a wealth of  
nonstandard progressions like vi->ii6/4->vi.

Perhaps part of the issues here is that my pedagogy emphasizes  
composition, whereas others emphasize analysis?  If all you are doing  
is analyses, then the issue of frequency is less important -- you  
simply need to know how to label the progressions you encounter,  
rather than whether the progressions you don't encounter are typical  
or not.

In any case, I'm getting a bit worn out with the topic, so I will  
probably stop posting soon.  I've always been surprised at how out-of- 
the-mainstream my views are; when I raised this issue I had no idea  
what a flurry of disagreement I would be causing.  Apologies to anyone  
who was offended.

DT

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