Abstract
Broadly speaking, two approaches can be distinguished in the study of the timing of skilled movement behavior: the representational approach and the dynamical approach. Proponents of the former attempt to account for the timing of movements by invoking symbolic representations (i.e., motor programs with explicit timekeepers). Such models have recently been criticized for being largely data-driven and theoretically underconstrained. In contrast, proponents of the latter approach seek to explain temporal order in movement in terms of physical self-organization (i.e., time as an emergent property) rather than symbolic representations. In the present paper, bifurcations in polyrhythmic tapping are analyzed according to the branching structure of the Farey tree. This tree is a generic mathematical object that summarizes all possible mode locks that complex dynamical systems may attain. Its branching structure coincides with known bifurcation routes in both mathematical and natural systems. Data on tapping 5:2 and 5:3 polyrhythms with increasing cycling frequency reveal that cycling frequency may be conceived as a control parameter. If cycling frequency was increased, bifurcations from mode locks with larger integer ratios to mode locks with smaller integer ratios often occurred in the more skilled subjects. These transitions were generally characterized by a tendency to move to the right (1:1) flank of the Farey tree instead of to its left flank (0:1). Evidence is reported that the stability of tapping polyrhythms is also a function of training.
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© 1991 Springer Science+Business Media Dordrecht
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Peper, C.E., Beek, P.J., Van Wieringen, P.C.W. (1991). Bifurcations in Polyrhythmic Tapping: In Search of Farey Principles. In: Requin, J., Stelmach, G.E. (eds) Tutorials in Motor Neuroscience. NATO ASI Series, vol 62. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3626-6_33
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DOI: https://doi.org/10.1007/978-94-011-3626-6_33
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