Long-Range Correlation in Synchronization and Syncopation Tapping: A Linear Phase Correction Model

Didier Delignières,Kjerstin Torre,Loïc Lemoine,Jan Lauwereyns

doi:10.1371/journal.pone.0007822

Didier Delignières, Kjerstin Torre + Show 2 more

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https://doi.org/10.1371/journal.pone.0007822

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Journal: PloS one	Publication Date: Nov 13, 2009
Citations: 55	License type: CC BY 4.0

Affiliation: University of Montpellier

Abstract

We propose in this paper a model for accounting for the increase in long-range correlations observed in asynchrony series in syncopation tapping, as compared with synchronization tapping. Our model is an extension of the linear phase correction model for synchronization tapping. We suppose that the timekeeper represents a fractal source in the system, and that a process of estimation of the half-period of the metronome, obeying a random-walk dynamics, combines with the linear phase correction process. Comparing experimental and simulated series, we show that our model allows accounting for the experimentally observed pattern of serial dependence. This model complete previous modeling solutions proposed for self-paced and synchronization tapping, for a unifying framework of event-based timing.

Highlights

Finger tapping has been for a long time studied to elucidate the timing processes that underlie the production of rhythmic behavior
This simple model supports a set of testable hypotheses: (1) the timekeeper variance should present a Weberian increase with target interval length, (2) motor variance should be independent on target interval length, and (3) inter-tap interval series should present a negative lag-one autocorrelation, bounded to 20.5
The aim of the present work was to collect series of asynchronies and inter-tap interval in synchronization and in syncopation conditions, and to check whether the linear phase correction model (Eq 8) and the present syncopation model (Eq 13), both enriched by providing the timekeeper with fractal properties, were able to account for the correlation properties computed from empirical series

Summary

Introduction

Finger tapping has been for a long time studied to elucidate the timing processes that underlie the production of rhythmic behavior. Each tap is performed after a motor delay, and the series of intervals produced by the timekeeper, as well as the successive motor delays are both considered as uncorrelated white noises This simple model supports a set of testable hypotheses: (1) the timekeeper variance should present a Weberian increase with target interval length, (2) motor variance should be independent on target interval length, and (3) inter-tap interval series should present a negative lag-one autocorrelation, bounded to 20.5. These hypotheses were successfully tested in experiments during which participants produced series of 30–50 successive taps following different initially prescribed tempi [1,2]

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