During a performance, a pianist has direct control over only two variables, duration and intensity (Seashore, 1938). Other factors such as pitch and timbre are determined largely by the composer and the mechanics of the instrument. Thus expressiveness imparted to a performance lies in the departures from metrical rigidity and constant intensity. In this article, the first of the two variables is considered and it is shown how a duration structure can be generated, corresponding to the rubato in a performance, from the musical structure. The main input to the model is the time-span reduction of Lerdahl and Jackendoff's theory (1977, 1983). Also shown is an interesting analogy between this model and the algorithms of Grosjean, Grosjean, and Lane (1979). Thus the hypothesis that expression is largely determined by musical structure, and the formal parallel between time-span reduction and prosodic structure are given empirical support.

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Four experiments examined judgements of the duration of auditory and visual stimuli. Two used a bisection method, and two used verbal estimation. Auditory/visual differences were found when durations of auditory and visual stimuli were explicitly compared and when durations from both modalities were mixed in partition bisection. Differences in verbal estimation were also found both when people received a single modality and when they received both. In all cases, the auditory stimuli appeared longer than the visual stimuli, and the effect was greater at longer stimulus durations, consistent with a "pacemaker speed" interpretation of the effect. Results suggested that Penney, Gibbon, and Meck's (2000) "memory mixing" account of auditory/visual differences in duration judgements, while correct in some circumstances, was incomplete, and that in some cases people were basing their judgements on some preexisting temporal standard.

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The notion that there is an intimate relationship between musical motion and physical movement is an old one and can be traced back to antiquity. Recently this idea has again received some attention, particularly in relation to musical expression. To use a modern metaphor, one can consider expressive performance to be analogous to the problems of kinematics and trajectory planning in robotics. The trajectories referred to, however, are not those of the performers limbs in physical space, but those of an abstract movement relative to a metrical grid associated with a musical score. Recent studies have attempted to substantiate this idea by comparing a model of motion with timing measurements of the final ritardandi from actual performances. This study extends these earlier analyses to include the accelerandi as well as the ritardandi from complete performances. One conclusion is that the variation of tempo in music can be reasonably compared with velocity in the equations of elementary mechanics. Further, it is suggested that the origin of metrical space, upon which the motion concept rests, lies in the way the auditory system processes rhythm.