[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  

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?


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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