[Smt-talk] Classical Form and Recursion
Dmitri Tymoczko
dmitri at Princeton.EDU
Mon Apr 6 10:46:24 PDT 2009
Hi Fred,
I've been wondering whether you were going to jump in!
> Those interested in empirical results relevant to the perception of
> hierarchical structures in music might take a look at F. Lerdahl &
> C. L. Krumhansl (2007), "Modeling Tonal Tension," Music Perception,
> 24.4, 329-366. This paper submits the tension model in my book
> Tonal Pitch Space to empirical investigation. Taking music from
> Bach to Messiaen, we demonstrate that if tension predictions are
> calculated sequentially, correlations between prediction and data
> are weak; but if they are done hierarchically, correlations are
> strong. Thus untrained listeners hear tonal music hierarchically.
> (This generalization does not hold in highly chromatic passages for
> which listeners find it difficult to infer a tonal schema.)
Let me say at the outset that I'm a big fan of both your work and
Carol's and I applaud this kind of attempt to test one's theoretical
assertions.
The reservation I've always had about this paper is that these
results are only as strong as the particular nonhierarchical model
you happened to choose. It remains possible that tension is
perceived nonhierarchically, but the model used in the paper isn't
the best one. It's certainly not the one I would construct.
Another issue is that (as I recall) the prolongational analyses used
in the paper are chosen to fit the data, rather than being derived
from theoretical principles -- so in essence, the conclusion is that
there *is* a prolongational hearing that models tension better than
the particular nonhierarchical model you've chosen. But this is sort
of stacking the deck, since you didn't vary the nonhierarchical model
to fit the data.
There's a more general issue, which is that the TPS system has an
awful lot of moving parts -- essentially, you have several hundred
pages of book (or books, since GTTM is in there too) which are being
boiled down to a single tension value. Now there have been some
interesting critiques of various small parts of the TPS system (such
as Richard Randall's) and it remains possible that these will affect
bottom-line tension values.
BTW, I always thought an interesting project for a grad. student
would be to try to build a really good, totally nonhierarchical model
of tension. Even if it was not cognitively accurate, it would
strengthen the sorts of comparisons that occur in that paper.
> We have already shown that the perception of hierarchical
> structures goes deeper in music than what is usually supposed for
> language.
Respectfully, I think it's fair to consider this issue still to be
open, given the issues discussed previously. Isn't it correct that a
simple opposition between diatonic and octatonic (using Ian Quinn's
Fourier-based method) predicts the Messiaen tension values about as
well as TPS?
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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