Humans collaborate with each other on a wide variety of tasks that are often largely improvised and unscripted. In this study, we investigated the dynamics of coordination in a joint musical improvisation task, what the effect of intentions is on coordination, and how musicians propagate these intentions. To quantify coordination within musical trios, we derived per-musician time series of acoustic features to which we applied effective transfer entropy (ETE) and empirical dynamic modeling (EDM), two methods derived from complex systems science. Using ETE allowed us to investigate coordination as directional information flow between musicians, whereas through EDM we conceptualized coordination as the predictability of a complex system. We found that both techniques, when applied to root-mean-square (RMS) amplitude time series, could be used to distinguish coordinating from noncoordinating musicians. Various other feature-technique combinations, such as fractal dimension-ETE and Tonnetz distance-EDM, were also viable. Our results further suggest that coordination improves as an intention gets more shared, that is, as more musicians in the joint improvisation have the same intention. Lastly, we found evidence suggesting that musicians increase the predictability of their playing when seeking to end a performance, though our results did not provide an indication that this was done with the intention of improving coordination with partners
