We propose a theory of gestural timing. It is a theory of how a gesture determines change in vocal tract state (e.g., change in constriction degree) based on the vocal tract state. A core postulate of the theory is that no executive time-keeper determines change in vocal tract state. That is, it is a theory of intrinsic timing. We compare the theory against others in which an executive time-keeper determines change in vocal tract state. Theories which employ an executive time-keeper have been proposed to correct for disparities between theoretically predicted and experimentally observed velocity profiles. Such theories of extrinsic timing make the gesture a nonautonomous dynamical system. For a nonautonomous dynamical system, the change in state depends not just on the state, but also on time. We show that this nonautonomous extension makes surprisingly weak kinematic predictions both qualitatively and quantitatively. We propose instead that the gesture is a theoretically simpler nonlinear autonomous dynamical system. For the proposed nonlinear autonomous dynamical system, the change in state depends nonlinearly on the state (and does not depend on time). This new theory provides formal expression to the notion of intrinsic timing. Furthermore, it predicts experimentally specific relations among kinematic variables which we can verify in datasets we have examined.
Suggested readings :
Fowler, C. A. (1980). Coarticulation and theories of extrinsic timing. Journal of Phonetics 8, 113–33.
Mottet, D., & Bootsma, R. J. (1999). The dynamics of goal-directed rhythmical aiming. Biological cybernetics 80(4), 235-245.