Hebbian learning with elasticity explains how the spontaneous motor tempo affects music performance synchronization

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.

Reliable estimation of internal oscillator properties from a novel, fast-paced tapping paradigm

“…Despite a focus on the natural frequency of internal oscillators in timing literature, not much attention has been given to their other primary property: flexibility (referred to as elasticity in Ref. 13 and adaptability, the compliment of stability, in Ref. 14 ).…”

“…Our first hypothesis was that tempo-matching errors calculated across both the synchronization and continuation sections of the trial (TME all ) would have a negative slope as a function of stimulus rate (IOI), arising from fast stimuli being tapped too slow and slow stimuli being tapped too fast. The dynamical systems approach predicts reduced asynchronies between stimulus and the oscillator as the difference between the stimulus frequency and the oscillator’s natural frequency (i.e., detuning) is reduced 13 since it would require more energy to coordinate motion at other frequencies 12 . In addition, since finger tapping is rate-limited due to motor and cognitive constraints 21 , and since we anticipated that most participants’ preferred rates would fall somewhere into the middle of the range, we expected tapping errors to increase at both ends of the IOI range.…”

Behavioral and Neural Dynamics of Interpersonal Synchrony Between Performing Musicians: A Wireless EEG Hyperscanning Study

“…The current findings add to a growing body of work indicating that spontaneous music performance rates reflect oscillatory processes that influence auditory-motor entrainment within and between individuals (Zamm et al, 2016(Zamm et al, , 2018Scheurich et al, 2018;Palmer et al, 2019;Roman et al, 2020). Whether the spontaneous performance rates reflect intrinsic timekeeping processes or biomechanical constraints is a topic for further research.…”

“…Third, the spontaneous rates are consistent within individuals, across their limb movements and melodies ( Zamm et al, 2016 ), across time of day ( Zamm et al, 2019 ; Wright and Palmer, 2020 ). Moreover, recent computational work ( Roman et al, 2020 ) indicates that the relationship between musical partners’ spontaneous frequencies and interpersonal synchrony can be accurately predicted from a model of biological oscillator entrainment, providing further credence to an oscillator framework of musical synchrony.…”

Rhythmic Modulation of Visual Discrimination is Dependent on Individuals’ Spontaneous Motor Tempo

“…Finally, our findings also extend current literature on the functional role of spontaneous rhythmic preferences. Previous work showed that spontaneous motor tempi can affect externally paced motor performance in personal (Bardy et al, 2015;McAuley et al, 2006;Roman et al, 2021;Scheurich et al, 2018) and inter-personal settings (Alderisio et al, 2017;Roman et al, 2021;Zamm et al, 2015Zamm et al, , 2016Zamm et al, , 2018. In addition, previous work investigating the neural markers of rhythm perception found that neural markers modulated by the presence of a rhythm were also linked to individuals' spontaneous rhythmic preferences (Schwartze & Kotz, 2015).…”