[Smt-talk] Classical Form and Recursion

[Fred Lerdahl]

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.)

Another way to articulate this result is to say that, just as many 
aspects of human behavior are unconscious, listeners do not directly 
perceive hierarchy in music; rather, they experience hierarchy as waves 
of tension and relaxation. Our tension method circumvents 
methodological difficulties in previous attempts to test hierarchical 
perception, such as Dibben's "foil" approach in the 1990s. Our musical 
examples do not exceed 50 events, however. Once the tension model is 
implemented computationally, it will be easier to address tension and 
hierarchy in longer pieces. We have already shown that the perception 
of hierarchical structures goes deeper in music than what is usually 
supposed for language. But some of the very embedded structures 
postulated in Schenker (and in GTTM) are surely difficult to perceive 
without special training. Behind this question lies not only the hoary 
distinction between competence and performance but also the issue of 
artistic compared to everyday response. I doubt that the average person 
on the street would find it easy to parse complex sentences in Proust 
or Mann.

The related issue of recursion is fraught partly because the term is 
used in different ways. Sometimes it is intended just to mean 
hierarchy, but more correctly it means self-embedded structures. Music 
manifests recursion, not only in pitch structure but also in grouping 
and metrical structures. The issue of recursion would not be of 
particular interest except for the high-profile and controversial paper 
by Hauser, Chomsky, & Fitch in 2002 (Science, 298, 1569-1579) in which 
they claim that the distinguishing feature of the narrow faculty of 
language (i.e., not possessed by other faculties) is recursion. This 
untenable claim arose out of Chomsky's recent "minimalist" theory of 
syntax.

Fred Lerdahl
Columbia University
awl1 at columbia.edu