Human handedness was investigated in a 1:1 interlimb rhythmic coordination in which consistent and inconsistent left-handed and right-handed individuals oscillated hand-held pendulums. Mean phase difference (4> stable ) and its standard deviation (SD4>) were evaluated as functions of mode of coordination (in-phase vs. anti-phase) and the symmetry conditions imposed by controlling the natural frequencies of the left and right pendulums. The dependencies of stab)e and SD on coordination mode and imposed symmetry were found to be systematically affected by handedness. The data were consistent with an elaboration of the established order parameter dynamics of interlimb rhythmic coordination. The elaboration includes additional 2i7 periodic terms that break the symmetry of those dynamics when the natural frequencies of the component rhythmic units are identical.

The symmetrical dynamics of 1:1 rhythmic bimanual coordination may be specified by an order parameter equation involving the relative phase between rhythmic components, and an interlimb coupling which determines the relative attractiveness of in-phase and anti-phase patterns. Symmetry breaking of these dynamics can occur via the difference in the natural frequencies, delta omega, of the left and right rhythmic components, or by the intrinsic asymmetrical dynamics of the body. The latter is captured by additional terms that render the symmetrical coupling slightly anisotropic. A major prediction resulting from this step is that although delta omega = 0, as the frequency of coordination is increased, the asymmetrical coupling will increase and the symmetrical coupling will decrease. This results in a greater left-limb bias in left-handers and right-limb bias in right-handers. This "increased handedness" prediction was confirmed in an experiment in which 20 left-handed and 20 right-handed individuals performed 1:1 coordination with hand-held rigid pendulums. Manipulations of left and right pendulum lengths controlled delta omega, and the coupled frequency was determined by a metronome. Also confirmed was the prediction that the small shift in equilibria from in-phase and anti-phase due to the intrinsic asymmetry should be amplified in left-handers when delta omega > 0 and in right-handers when delta omega < 0. Further, the bias in left-handers was more consistent than the bias in right-handers, and a subgroup of right-handers was identified who performed similarly to left-handers. The coordination dynamics of functional asymmetry provides insights into the elementary synergy between the limbs, the dynamical mechanism that modulates it, and the nature of the asymmetry in left-handed and right-handed individuals.

The component frequencies of rhythmic patterns forming rational ratios, either simple (e.g., 1:2, 1:3) or complex (e.g., 2:3, 2:5), are known as mode locks or resonances. A general theory of resonances is provided by the circle map, the Farey series, and continued fractions. Predictions were evaluated in which rhythms (simple and poly) were established implicitly-the subject neither intended them nor knew their ratios. In Experiment 1, a prescribed unimanual frequency was performed as the primary task while hearing another frequency irrelevant to the task. In Experiments 2 and 3, a hand-held pendulum was oscillated at its natural frequency, while the other hand performed the primary task of following a metronome. The frequency ratio at the outset of a trial often changed during the trial. Consistent with the general theory, shifts were toward unimodular ratios of the Farey tree, and Fibonacci ratios tended to shift more than non-Fibonacci ratios.Rhythmic performances involve patterns of varying complexity. Polyrhythms (ratios such as 2:3, 2:5, and 3:5) are periodic patterns in which the respective events of the component rhythmic units coincide only once per cycle. For example, a 2:3 polyrhythm involves two isochronous pulse trains such that the first completes two events in the same duration that the second completes three events. Despite their prominence in the music of a number of non-Western cultures (

A coordinated rhythmic movement pattern is a dynamical activity involving many hidden layers of rhythmic subtasks. To investigate this dynamical substructure, spectroscopic concepts and methods were applied to an interlimb rhythmic movement task requiring 1:1 frequency locking of two hand-held pendulums in 180 degrees phase relation. The pendulums could be of identical or very different dimensions, thereby providing different values of the ratio omega of uncoupled frequencies. Analyses focused on the power spectrum of continuous relative phase as a function of variation in omega. Predictions were derived from the theories of mode locking and fractal time. Experimental results were in agreement with theoretical expectations and were discussed in terms of the possible recruiting of rhythmic subtasks in the assembling of interlimb absolute coordination, the interdependence of these subtasks, and the general dynamical principles that relate coordinative processes occurring at different length and time scales.