A generative model for the characterization of musical rhythms

Sioros, George; Davies, Matthew E. P.; Guedes, Carlos

doi:10.1080/09298215.2017.1409769

Cited by 19 publications

(18 citation statements)

References 29 publications

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“…Such effects could be readily incorporated into the phase inference framework by adding history dependence to the expectation template λ, though that is beyond the scope of this work. The precise details of this history dependence in rhythm parsing could be based on any suitable formal model for rhythmic grammar (e.g., [ 61 – 63 ]), and for speech applications could include whatever aspects of the co-dependence of timing and content expectations were appropriate for the task at hand.…”

Section: Discussionmentioning

confidence: 99%

Expectancy-based rhythmic entrainment as continuous Bayesian inference

Cannon

2021

PLoS Comput Biol

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When presented with complex rhythmic auditory stimuli, humans are able to track underlying temporal structure (e.g., a “beat”), both covertly and with their movements. This capacity goes far beyond that of a simple entrained oscillator, drawing on contextual and enculturated timing expectations and adjusting rapidly to perturbations in event timing, phase, and tempo. Previous modeling work has described how entrainment to rhythms may be shaped by event timing expectations, but sheds little light on any underlying computational principles that could unify the phenomenon of expectation-based entrainment with other brain processes. Inspired by the predictive processing framework, we propose that the problem of rhythm tracking is naturally characterized as a problem of continuously estimating an underlying phase and tempo based on precise event times and their correspondence to timing expectations. We present two inference problems formalizing this insight: PIPPET (Phase Inference from Point Process Event Timing) and PATIPPET (Phase and Tempo Inference). Variational solutions to these inference problems resemble previous “Dynamic Attending” models of perceptual entrainment, but introduce new terms representing the dynamics of uncertainty and the influence of expectations in the absence of sensory events. These terms allow us to model multiple characteristics of covert and motor human rhythm tracking not addressed by other models, including sensitivity of error corrections to inter-event interval and perceived tempo changes induced by event omissions. We show that positing these novel influences in human entrainment yields a range of testable behavioral predictions. Guided by recent neurophysiological observations, we attempt to align the phase inference framework with a specific brain implementation. We also explore the potential of this normative framework to guide the interpretation of experimental data and serve as building blocks for even richer predictive processing and active inference models of timing.

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Section: Discussionmentioning

confidence: 99%

Expectancy-based rhythmic entrainment as continuous Bayesian inference

Cannon

2021

PLoS Comput Biol

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“…The standard musicological definitions of pickups (also called anacruses or upbeats) and syncopation (see definitions in Refs. 31 , 32 ) indicate that each deviation type has a different musical function: (a) pickups cue the following strong beat event and then fulfill it; (b) syncopations break this bond by omitting the strong beat event 32 , 33 . In other words, or psychological terms, pickups could be analogous to a priming stimulus prior to a temporal event while a syncopation seems more akin to its omission.…”

Section: Introductionmentioning

confidence: 99%

Pupil drift rate indexes groove ratings

Spiech

Sioros

Endestad

et al. 2022

Sci Rep

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Groove, understood as an enjoyable compulsion to move to musical rhythms, typically varies along an inverted U-curve with increasing rhythmic complexity (e.g., syncopation, pickups). Predictive coding accounts posit that moderate complexity drives us to move to reduce sensory prediction errors and model the temporal structure. While musicologists generally distinguish the effects of pickups (anacruses) and syncopations, their difference remains unexplored in groove. We used pupillometry as an index to noradrenergic arousal while subjects listened to and rated drumbeats varying in rhythmic complexity. We replicated the inverted U-shaped relationship between rhythmic complexity and groove and showed this is modulated by musical ability, based on a psychoacoustic beat perception test. The pupil drift rates suggest that groovier rhythms hold attention longer than ones rated less groovy. Moreover, we found complementary effects of syncopations and pickups on groove ratings and pupil size, respectively, discovering a distinct predictive process related to pickups. We suggest that the brain deploys attention to pickups to sharpen subsequent strong beats, augmenting the predictive scaffolding’s focus on beats that reduce syncopations’ prediction errors. This interpretation is in accordance with groove envisioned as an embodied resolution of precision-weighted prediction error.

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“…Such effects could be readily incorporated into the phase inference framework by adding history dependence to the expectation template λ , though that is beyond the scope of this work. The precise details of this history dependence in rhythm parsing could be based on any suitable formal model for rhythmic grammar (e.g., [61, 62, 60]), and for speech applications could include whatever aspects of the co-dependence of timing and content expectations were appropriate for the task at hand.…”

Section: Discussionmentioning

confidence: 99%

Expectancy-based rhythmic entrainment as continuous Bayesian inference

Cannon

2020

Preprint

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When presented with complex rhythmic auditory stimuli, humans are able to track underlying temporal structure (e.g., a “beat”), both covertly and with their movements. This capacity goes far beyond that of a simple entrained oscillator, drawing on contextual and enculturated timing expectations and adjusting rapidly to perturbations in event timing, phase, and tempo. Here we propose that the problem of rhythm tracking is most naturally characterized as a problem of continuously estimating an underlying phase and tempo based on precise event times and their correspondence to timing expectations. We formalize this problem as a case of inferring a distribution on a hidden state from point process data in continuous time: either Phase Inference from Point Process Event Timing (PIPPET) or Phase And Tempo Inference (PATIPPET). This approach to rhythm tracking generalizes to non-isochronous and multi-voice rhythms. We demonstrate that these inference problems can be approximately solved using a variational Bayesian method that generalizes the Kalman-Bucy filter to point-process data. These solutions reproduce multiple characteristics of overt and covert human rhythm tracking, including period-dependent phase corrections, illusory contraction of unexpectedly empty intervals, and failure to track excessively syncopated rhythms, and could could be plausibly approximated in the brain. PIPPET can serve as the basis for models of performance on a wide range of timing and entrainment tasks and opens the door to even richer predictive processing and active inference models of rhythmic timing.

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A generative model for the characterization of musical rhythms

Cited by 19 publications

References 29 publications

Expectancy-based rhythmic entrainment as continuous Bayesian inference

Expectancy-based rhythmic entrainment as continuous Bayesian inference

Pupil drift rate indexes groove ratings

Expectancy-based rhythmic entrainment as continuous Bayesian inference

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