Temporal patterning in cascade juggling.

A key variable in cascade juggling is the proportion of time that a juggler holds onto a juggled object during a hand cycle, that is, the time from catch to throw in relation to the time from catch to catch. Space-time constraints and principles of frequency locking suggest 3/4 as the primary ratio and 2/3 and 5/8 as the most accessible options. In 5 experiments, object number, mass, and type (ball or scarf) were manipulated together with the frequency at which the objects were juggled. With 5 or 7 balls, the ratio was 3/4, independent of frequency. With 3 balls, the ratio decreased with frequency, with 3/4, 2/3, and 5/8 tending to predominate independently of the force variations induced by variation in object mass. With 3 scarves, ratios varied inversely with frequency and often exceeded 3/4. Implications for a dynamical theory of juggling were discussed with the issue of relative timing in coordination and the manipulation of task constraints as an experimental strategy.