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

Dmitri Tymoczko dmitri at Princeton.EDU
Thu Jan 21 06:51:32 PST 2010

A bunch of people have written in to defend Aldwell and Schachter.   
Let me clarify that I'm not trying to single out their book in  
particular: every major textbook contains similar howlers.  For  
example, Kostka and Payne provide a map of acceptable progressions  
which asserts that both vi->V and vi->viio are unacceptable.  Yet in  
Mozart's piano sonatas, fully 29% of vi chords go to either viio or V.

In the case of Aldwell and Schachter, it's worth reiterating that an  
intelligent student, carefully reading their text, could scarcely  
avoid coming away with the following beliefs:

1) That V6/4 is more common than any other passing 6/4.
2) That IV6->I6/4->ii6/5 is more common than IV6->I6/4->ii6

Furthermore, this intelligent student would almost certainly infer  
that these beliefs were true of the Mozart piano sonatas -- a large  
and canonical body of tonal music.  This is because Aldwell and  
Schachter offer no qualifications along the lines of "this is not true  
of Mozart, we're talking about composer X" or "by 'important' we don't  
mean 'common.'"

Now, when we look at the only database we have -- a substantial one  
covering all the Mozart piano sonatas -- we see that the first claim  
is wrong by a factor of *more than twelve*, while the second is wrong  
by a factor of more than two.  To me, this is alarming.  We're talking  
about an introductory textbook's account of elementary tonal  
progressions, and one of the most familiar and canonical bodies of  
tonal literature.  Discrepancies of this magnitude should be  
disturbing, no?  Shouldn't we be bothered by the authors' failure to  
insert qualifications, such as those described above?

I know that many people on this list are very fond of Aldwell and  
Schachter and their book.  And I agree that their book may well be  
better, in certain ways, than the alternatives.  (I don't currently  
use it, but I have.)  I also understand that it is a little jarring to  
read someone criticize beloved teachers in such straightforward terms  
-- particularly in music theory, where people sometimes become  
emotionally invested in particular viewpoints.  (One older theorist  
told me that he senses something of a "studio mentality" in music  
theory, where people become aligned with a particular "workshop" or  
style of thinking.)  But I think we should try to put personalities  
and emotions aside, and to separate the substantive from the  
personal.  Our loyalty toward (or antagonism against) specific people  
and specific texts should not trump our interest in the truth, or our  
commitment to giving our students the most accurate information we can.

Note that I am not doubting that Aldwell and Schachter knew/know a  
vast amount of music.  What I am saying is that it is well-known that  
human beings are bad at making certain kinds of statistical  
inferences, even in the presence of massive amounts of knowledge.  You  
may have memorized the entire King James bible, but that does not make  
you an authority on whether one linguistic construction occurs more  
frequently than another within its pages.  Sometimes you just have to  
count.  Music is no different: you can know lots and lots of music,  
and still be wrong about which passing 6/4 is most common.  Indeed, I  
myself have had to realize that I had plenty of incorrect intuitions  
about Mozart -- for instance, about what sequences or seventh chords  
were most common.

I also acknowledge that it is possible that if we did a vast  
statistical study of all tonal literature, we might end up with  
different views about Aldwell and Schachter's claims.  Perhaps there  
is some familiar body of literature where passing V6/4 is more common  
than passing I6/4.  I suspect not, but that is just an informed  
guess.  (The point about ii6/5 I'm more sympathetic toward -- perhaps  
Mozart is the exception here.)  Anyone who wants to investigate this  
issue quantitatively is welcome to do it -- let's generate a database  
of Roman-numeral analyses of the Schubert quartets or something.  I'll  

The deep and important point is that, in the age of computers, a large  
range of traditional music-theoretical issues are now testable.  We  
don't have to rely solely on our intuition.  We can do the work and  
actually figure things out.  I personally suspect that we're at the  
very beginning of a new quantitative era in music theory -- someday,  
not too long from now, computers will be able to do pretty good Roman  
numeral analysis, and then we will have a vast trove of data at our  
disposal.  We will be able to chart, quantitatively, the narrowing of  
the harmonic vocabulary from Bach to Mozart, and its gradual  
broadening in the nineteenth century.   We will be able to specify  
very precisely the distinctive features of Brahms's harmonic  
practice.  We will be able to determine very quickly, with just a few  
minutes of programming, whether passing I6/4 or passing V6/4 is more  
common in the work of a particular composer.

Linguistics has already gone through this transition.  Grammarians  
used to rely on their intuition, and this is how we ended up with  
bogus prohibitions like the one on split infinitives.  There's now an  
entire subdiscipline of linguistics devoted to carefully examining  
natural languages as they actually are.  Music theory has yet to make  
this transition, but it is about to.  There's no point in pretending  
that music theorists don't have their own analogues to the prohibition  
on split infinitives.  It would be foolish to think that *our*  
intuitions are somehow reliable when everyone else's are not ...


Dmitri Tymoczko
Associate Professor of Music
310 Woolworth Center
Princeton, NJ 08544-1007
(609) 258-4255 (ph), (609) 258-6793 (fax)

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