This study explored the effects of musical improvisation between dyads of same-sex strangers on subsequent behavioural alignment. Participants–all non-musicians–conversed before and after either improvising music together (Musical Improvisation—MI—group) or doing a motoric non-rhythmic cooperative task (building a tower together using wooden blocks; the Hands-Busy—HB—group). Conversations were free, but initially guided by an adaptation of the Fast Friends Questionnaire for inducing talk among students who are strangers and meeting for the first time. Throughout, participants’ motion was recorded with an optical motion-capture system (Mocap) and analysed in terms of speed cross-correlations. Their conversations were also recorded on separate channels using headset microphones and were analysed in terms of the periodicity displayed by rhythmic peaks in the turn transitions across question and answer pairs (Q+A pairs). Compared with their first conversations, the MI group in the second conversations showed: (a) a very rapid, partially simultaneous anatomical coordination between 0 and 0.4 s; (b) delayed mirror motoric coordination between 0.8 and 1.5 s; and (c) a higher proportion of Periodic Q+A pairs. In contrast, the HB group’s motoric coordination changed slightly in timing but not in degree of coordination between the first and second conversations, and there was no significant change in the proportion of periodic Q+A pairs they produced. These results show a convergent effect of prior musical interaction on joint body movement and use of shared periodicity across speech turn-transitions in conversations, suggesting that interaction in music and speech may be mediated by common processes.