Frequency-induced phase transitions in bimanual tapping.

The stability of bimanual performance of the frequency ratios 3:8 and 5:8 was examined from the perspective of the sine circle map and the associated Farey mode-locking hierarchy. By gradually increasing movement frequency, abrupt transitions from the initial frequency ratios to other frequency ratios were induced. In general, transitions occurred to frequency ratios that were near the initial frequency ratio but lower in the Farey ordering, and, hence, of higher stability in the sine circle map. A fair percentage of these transitions were to unimodularly related ratios. The transition routes from 3:8 and 5:8 remained largely unaffected by extensive practice of the lower-order ratios 2:5 and 3:5. Collectively, these results suggest that (i) bimanual tapping occurs in a domain in which frequency-locked states either overlap or are located sufficiently close to each other to make stochastic switching possible (coupling parameter K > 1 or close to 1); (ii) the overall stability of these frequency-locked states decreases as movement frequency increases (due to a decrease in K); and, consequently, (iii) the probability of transitions to nearby frequency ratios increases as movement frequency increases, due to the differential stability of the frequency locks.