When jazz musicians perform an improvisational piece of music their behaviors are not fully prescribed in advance. Nonetheless their actions become so tightly coordinated and their decisions so seamlessly intertwined that the musicians behave as a single synergistic unit rather than a collection of individuals. A fundamental aspect of such musical improvisation is the bodily movement coordination that occurs among the performing musicians, with the embodied interaction of musicians both supporting and constraining musical creativity. Here we consider the ability of pairs of piano players to improvise, to spontaneously coordinate their actions with co-performers. We demonstrate the ability of the time-evolving patterns of inter-musician movement coordination as revealed by the mathematical tools of nonlinear time series analyses to provide a new understanding of what potentiates the novelty of spontaneous musical action. Cross wavelet spectral analysis is applied to the musical movements of pairs of improvising pianists, a method that isolates the strength and patterning of the behavioral coordination across a range of nested time-scales. Additionally, cross-recurrence quantification analysis is applied to the series of notes produced by each musician to assess when and how often they visit the same musical states throughout the improvisation. Revealing the sophistication of the previously unexplored dynamics of movement coordination between improvising musicians is an important step towards understanding how creative musical expressions emerge from the spontaneous coordination of multiple musical bodies