Interpersonal synchrony refers to the temporal coordination of actions between individuals and is a common feature of social behaviors, from team sport to ensemble music performance. Interpersonal synchrony of many rhythmic (periodic) behaviors displays dynamics of coupled biological oscillators. The current study addresses oscillatory dynamics on the levels of brain and behavior between music duet partners performing at spontaneous (uncued) rates. Wireless EEG was measured from N = 20 pairs of pianists as they performed a melody first in Solo performance (at their spontaneous rate of performance), and then in Duet performances at each partner’s spontaneous rate. Influences of partners’ spontaneous rates on interpersonal synchrony were assessed by correlating differences in partners’ spontaneous rates of Solo performance with Duet tone onset asynchronies. Coupling between partners’ neural oscillations was assessed by correlating amplitude envelope fluctuations of cortical oscillations at the Duet performance frequency between observed partners and between surrogate (re-paired) partners, who performed the same melody but at different times. Duet synchronization was influenced by partners’ spontaneous rates in Solo performance. The size and direction of the difference in partners’ spontaneous rates were mirrored in the size and direction of the Duet asynchronies. Moreover, observed Duet partners showed greater inter-brain correlations of oscillatory amplitude fluctuations than did surrogate partners, suggesting that performing in synchrony with a musical partner is reflected in coupled cortical dynamics at the performance frequency. The current study provides evidence that dynamics of oscillator coupling are reflected in both behavioral and neural measures of temporal coordination during musical joint action.