The kinematics of musical expression

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Abstract
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.

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