3.1 Abstract
Music has a tempo (or frequency of the underlying beat) that musicians maintain throughout a performance. Musicians maintain this musical tempo on their own or paced by a metronome. Behavioral studies have found that each musician shows a spontaneous rate of movement, called spontaneous motor tempo (SMT), which can be measured when a musician spontaneously plays a simple melody. Data shows that a musician’s SMT systematically influences how actions align with the musical tempo. In this study we present a model that captures this phenomenon. To develop our model, we review the results from three musical performance settings that have been previously published: (1) solo musical performance with a pacing metronome tempo that is different from the SMT, (2) solo musical performance without a metronome at a spontaneous tempo that is faster or slower than the SMT, and (3) duet musical performance between musician pairs with matching and mismatching SMTs. In the first setting, the asynchrony between the pacing metronome and the musician’s tempo grew as a function of the difference between the metronome tempo and the musician’s SMT. In the second setting, musicians drifted away from the initial spontaneous tempo toward the SMT. And in the third setting, the absolute asynchronies between performing musicians were smaller if their SMTs matched compared to when they did not. Based on these previous observations, we hypothesize that, while musicians can perform musical actions at a tempo different from their SMT, the SMT constantly acts as a pulling force. We developed a model to test our hypothesis. The model is an oscillatory dynamical system with Hebbian and elastic tempo learning that simulates music performance. We simulate an individual’s SMT with the dynamical system’s natural frequency. Hebbian learning lets the system’s frequency adapt to match the stimulus frequency. The pulling force is simulated with an elasticity term that pulls the learned frequency toward the system’s natural frequency. We used this model to simulate the three music performance settings, replicating behavioral results. Our model also lets us make predictions of musician’s performance not yet tested. The present study offers a dynamical explanation of how an individual’s SMT affects adaptive synchronization in realistic musical performance.
Competing Interest Statement
Iran R. Roman, Adrian S. Roman declare that no competing financial interest exist. Edward W. Large declares a competing financial interest as CEO of Oscilloscape, LLC.