Skilled drummers performed a 4:3:2 polyrhythm with 2 hands and 1 foot. For each pair of limbs patterns of temporal covariation were used to infer relatively independent parallel streams versus integrated timing relationships. Parallel timing was more prevalent between hand and foot than between the 2 hands, and parallel timing generally increased with tapping rate. Different combinations of integrated and parallel timing were found among the 3 limbs. A second experiment used a wider range of tapping rates and explored 3:2 tapping with 2 hands, 2 feet, or hand and foot. The latter 2 limb pairs resulted in greater prevalence of parallel timing. These results can be interpreted in terms of a Gestalt principle of grouping known as Korte’s Third Law, which can be extended from the perceptual domain to the perceptual-motor domain. This principle indicates that perceived velocity is a key factor in determining whether a sequence of events is represented as a single integrated pattern or as multiple parallel patterns. The present results put disparate previous findings on bimanual polyrhythmic tapping and rhythmic aspects of the golf swing under a common theoretical perspective.