[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
help!
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 ...
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
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