Perceptual smoothness of tempo in expressively performed music

We report three experiments examining the perception of tempo in expressively performed classical piano music. Each experiment investigates beat and tempo perception in a different way: rating the correspondence of a click track to a musical excerpt with which it was simultaneously presented; graphically marking the positions of the beats using an interactive computer program; and tapping in time with the musical excerpts. We examine the relationship between the timing of individual tones, that is, the directly measurable temporal information, and the timing of beats as perceived by listeners. Many computational models of beat tracking assume that beats correspond with the onset of musical tones. We introduce a model, supported by the experimental results, in which the beat times are given by a curve calculated from the tone onset times that is smoother (less irregular) than the tempo curve of the onsets.