How do individuals adjust their rhythms in order to tap synchronously with a partner? We compared musically trained and untrained individuals as they tapped rhythmically by themselves (Solo task) and with a partner (Joint task). We applied auto- and cross-recurrence quantification analyses to examine the tappers' trajectories through multi-dimensional phase spaces based on their intertap interval time series. Nonmusicians' recurrences in Solo performances indicated more deterministic patterns of behavior than those of Musicians. Furthermore, increased determinism in individuals' Solo tapping corresponded to increased asynchrony variability in their Joint synchronization performances. Nonmusicians' trajectories through phase space, corresponding to changes in tempo, were less flexible than those of Musicians; less flexible individuals adapted less in response to a partner in the Joint task. Future work may apply the recurrence quantifications to generate automated music tailored to accompany individuals; it may be easier to synchronize with a partner whose behaviour is equally deterministic to oneself.