Timing of Two-Handed Rhythmic Performancea

In this paper we present a simple stochastic model for the study of timing of skilled performance. The model is based on the notion that temporal variability and serial dependence observed in behavior sequences depend on the precision of a hypothetical central timing system as well as on the temporal jitter generated by the executing motor system. Within the theoretical framework of such a model it is possible to determine, for example, how much of the temporal variability in skilled performance is generated centrally, and how much is due to the precision lost during the execution of the motor program by the motor system. This general approach has been used first by Wing and Kristofferson’ in their study of timing in simple tapping situations. We have proposed extensions of the basic model to repetitive rhythmic tapping; our goal was to determine whether rhythmic performance is controlled by hierarchically organized timing mechanisms, as contrasted to simple serial mechanisms.* Analyses of actual musical performance in terms of such a model have been reported by Shaffer.’ A major problem with these models is that they rest on rather strong assumptions which are not easily accessible to empirical test. Of course, the conclusions reached from applications of the models remain dubious if the validity of the underlying assumptions can be questioned. In the following, we show how to overcome some of these problems by extending the model to synchronous two-handed performance. The model we propose rests on weaker and testable assumptions; moreover, it permits rather strong inferences about the structure of the postulated timing system given that the model’s validity can be established. It should be noted that several independent investigators have discovered recently how powerful the analysis of two-handed performance is in the study of timing and motor c o n t r ~ l . ~ . ~ In this paper we focus on the properties of the central timing structures underlying synchronous rhythm production; in a companion paper’ we investigate the statistical aspects of the motor system in more detail. The outline of the paper is as follows. First, we present the model and derive a testable prediction which is checked on data from an experiment involving two-handed rhythmic tapping. The model is then used as a