[Smt-talk] Classical Form and Recursion

Ildar Khannanov solfeggio7 at yahoo.com
Mon Apr 6 15:36:27 PDT 2009

Dear Fred,
thank you very much for your links and input into this discussion. You have mentioned that the studies oftonal  tension cover music from Bach to Messiaen. I can argue that tension/relaxation can be applied also to earlier and later periods. I have heard many times from my colleauges that tension/relaxation model applies mostly to 19th century music and it does not rise up to the level of Schenkerian abstraction. Or, some say that there was no harmony in the 18th-century music, let alone in the 17th and earlier centuries. What do you think about my idea that tension/relaxation as a category directly relates to harmony in a wider sense and assuch it is universal  and can be attributed to Greek music as well as Bach and Messiaen? 
Ildar Khannanov
Peabody Conservatory

--- On Mon, 4/6/09, Fred Lerdahl <awl1 at columbia.edu> wrote:

From: Fred Lerdahl <awl1 at columbia.edu>
Subject: Re: [Smt-talk] Classical Form and Recursion
To: "smt-talk Talk" <smt-talk at societymusictheory.org>
Date: Monday, April 6, 2009, 12:06 PM

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

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