Sixteen right-handed participants without formal musical training performed a rhythmic multifrequency coordination task for several hours over a one-week period. Two groups were studied with respect to the assignment of hand to frequency: 1L:2R, in which the preferred right hand performed the higher frequency, and 2L:1R in which the non-preferred left hand performed the higher frequency. Performance asymmetries in terms of relative phase stability were initially expected and confirmed. The 1L:2R pattern was more stable than 2L:1R. It has been suggested that performance asymmetries result from asymmetrical coupling between the limbs as influenced by handedness. This study examined whether the acquisition of 2L:1R, the less stable of the two patterns, required the formation of asymmetrical coupling such that the faster hand would exert a greater forcing on the slower hand than vice versa, a supposition put forth in many studies of bimanual polyrhythmic tapping. The present data provide quantitative evidence that, in terms of stability (as quantified by relative phase uniformity, transition pathways, and lead-lag relations), handedness asymmetries, as well as acquired asymmetries, can be captured by low-dimensional dynamics consisting of symmetric and asymmetric coupling terms.