A Model for Tempo Synchronization in Music Performance
Pages 2540 - 2561
Abstract
A model is derived for the manner in which performers of music establish and maintain phase (beat) and tempo in the presence of a conductor, other performers, and noise. The model assumes that a performer sets a tempo in response to several stimuli and establishes when the next beat should fall. The tempo, or period, correction occurs as a superposition of responses of the form of sensitivity times stimulus. After establishing when the next beat is to be performed, the model assumes that each performer will commit an error in execution. The model is solved and results obtained for several cases, including similar performers, one dominant performer, and performance in sections. For a large ensemble, a stochastic differential equation model describes the phase and tempo evolution, resulting in a Gaussian probability density distribution for tempo and phase. A model for phase correction is also derived. This model assumes that a performer who has strayed sufficiently far from the correct phase or tempo performs a correction. This model is coupled with stationary results from the phase-tempo model to derive the rate of correction. The results are interpreted in terms of advice to performer and conductor on tempo-setting skills that should improve music performance.
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- A Model for Tempo Synchronization in Music Performance
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Published: 01 November 2015
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