We have described our exploration of the judgment, production, and imitation of fractions of a beat by skilled musicians, illustrating our findings with data from violinist and conductor Paul Zukofsky. For small fractions we found systematic and substantial errors. In the judgment task small stimulus fractions are associated with names that are too large (overestimation). In both production and imitation tasks the fractions produced were too large (overproduction, overimitation). A summary of our findings and of the expectations they violate is provided in Figure 7. The temporal patterns we used are perhaps the simplest that qualify as rhythms, incorporating just a beat interval and a fraction. The phenomena we discovered in relation to these simple patterns, and their implications for underlying mechanisms, must be considered in attempts to understand the perception and production of more complex rhythms, as in actual music. We explored and rejected several plausible explanations for the overestimation and overproduction of small fractions. Although we have as yet no satisfactory explanations of the errors themselves, relations among the errors have powerful implications for human timing mechanisms. The relation between the errors in judgment and production requires us to reject a feedback model of production, in which a subject uses the same processes as in the judgment task to evaluate and adjust his performance in the production task. An explanation of the inconsistency between judgment and production seems most likely to lie in a change in time perception induced by the production task. Together with the existence of systematic errors in judgment, the equality of the errors in production and imitation argues that imitation is not accomplished by concatenating all the processes used in judgment and production. Our results are instead consistent with a model containing four internal transformation processes, in which judgment and production share no process, but do involve the same internal-fraction representation, and in which imitation shares one process with judgment and another with production.
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