Annotation for Todd, Neil

A Model of Expressive Timing in Tonal Music

Annotation (by Jonathan D. Flowers):

In musical performance, as in speech, slight decelerations and pauses frequently occur at the ends of phrases. This phenomenon, called phrase-final lengthening, forms the point of departure for Todd's study. Todd incorporates Lerdahl and Jackendoff's (1983) technique of time-span reduction (TSR) into his own mathematical model for generating a preferred duration structure for performances of a tonal composition. In Todd's algorithm, the degree of phrase-final lengthening increases at higher levels of the TSR. For example, a greater deceleration should occur at the end of an eight-bar parallel period than at the half cadence of the period's antecedent phrase.

The duration structures Todd generates for three piano pieces agree extensively with the timings he measures in live performances. He hypothesizes that the slight deviations from his model arise from structural factors that interact with time-span hierarchies. In performing the theme from Mozart's Piano Sonata in A Major, K. 331, first movement, both of the pianists tested took slightly more time than suggested by the model at imperfect authentic cadences occurring midway through eight-bar periods. Todd hypothesizes that the tonal stability of these cadences may override their low weight in the TSR. In studying a performance of the Adagio from Haydn's Piano Sonata No.59, Todd concludes that the model can incorporate an additional factor to account for slowing at prolongational boundaries within a cadenced group. The timings in a performance of Chopin's Nouvelle Etude No.3 in A-flat Major suggest that phrase-final lengthening may decrease from the model within tonally unstable sections. Todd concludes that his model generates an accurate first approximation of performed duration structures. A complete theory of expressive timing in tonal music, however, would need to account for prolongational structure in addition to time-span reduction.
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