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

Abstract

A musician’s spontaneous rate of movement, called spontaneous motor tempo (SMT), can be measured while spontaneously playing a simple melody. Data shows that the SMT influences the musician’s tempo and synchronization. In this study we present a model that captures these phenomena. We review the results from three previously-published studies: solo musical performance with a pacing metronome tempo that is different from the SMT, solo musical performance without a metronome at a tempo that is faster or slower than the SMT, and duet musical performance between musicians with matching or mismatching SMTs. These studies showed, respectively, that 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, musicians drifted away from the initial tempo toward the SMT, and the absolute asynchronies were smaller if musicians had matching SMTs. We hypothesize that the SMT constantly acts as a pulling force affecting musical actions at a tempo different from a musician’s SMT. To test our hypothesis, we developed a model consisting of a non-linear oscillator with Hebbian tempo learning and a pulling force to the model’s spontaneous frequency. While the model’s spontaneous frequency emulates the SMT, elastic Hebbian learning allows for frequency learning to match a stimulus’ frequency. To test our hypothesis, we first fit model parameters to match the data in the first of the three studies and asked whether this same model would explain the data the remaining two studies without further tuning. Results showed that the model’s dynamics allowed it to explain all three experiments with the same set of parameters. Our theory offers a dynamical-systems explanation of how an individual’s SMT affects synchronization in realistic music performance settings, and the model also enables predictions about performance settings not yet tested.

A framework for joint music making: behavioral findings, neural processes, and computational models

“…Temporal coordination during JMM depends on both endogenous properties of individual musicians , as well as exogenous sources of sensory information, such as auditory feedback. demonstrated that an important factor predicting the quality of interpersonal synchronization between performing musicians is the similarity of their endogenous rhythms when playing solo (see also Roman et al, 2023).…”

Pitch biases sensorimotor synchronization to auditory rhythms

“…Accordingly, we may have observed a larger effect during continuation tapping if performed in the absence of auditory feedback. Without feedback, we might expect the participant to simply continue trying to maintain the 582 ms interval they originally perceived, perhaps while also drifting towards their spontaneous motor tempo (Roman et al, 2023;Zamm, Wang, & Palmer, 2018).…”

“…In the field of music perception, there are a several dominant models of how humans synchronize their movements to rhythmic sounds (Large et al, 2023;Palmer & Demos, 2022). Rhythm refers to a series of events that are predictably organized across time, and humans-as well as some nonhuman animals (Gámez et al, 2018;Patel, Iversen, Bregman, & Schulz, 2009a, 2009b)-are able to extract a sense of underlying pulse or beat from these predictable event struc-tures.…”

“…Rhythm refers to a series of events that are predictably organized across time, and humans-as well as some nonhuman animals (Gámez et al, 2018;Patel, Iversen, Bregman, & Schulz, 2009a, 2009b)-are able to extract a sense of underlying pulse or beat from these predictable event struc-tures. Some models envision this process of perceiving and synchronizing to the beat as an emergent property of neural dynamics, in which the auditory and motor systems resonate when driven by rhythmic stimulation (Large & Snyder, 2009;Large, Almonte, & Velasco, 2010;Large, Herrera, & Velasco, 2015;Roman, Roman, Kim, & Large, 2023). Others conceptualize the brain as a Bayesian prediction engine that works to infer the structure underlying predictable patterns in time, in accordance with predictive coding theory (Cannon, 2021;Friston, 2010;Koelsch, Vuust, & Friston, 2019;Vuust & Witek, 2014).…”

Adaptive oscillators support Bayesian prediction in temporal processing

“…Specifically, period-adjusting oscillators have been proposed in the music cognition literature as a plausible mechanism underlying beat tracking [29] and general metrical structure perception [30], as well as to explain temporal attention [4]. Similarly, in a recent study Roman and colleagues show that a non-linear oscillator with Hebbian tempo learning and a pulling force toward the spontaneous individual's motor frequency is capable of predicting professional musicians' synchronization on real performance settings [31].…”