Collective Free Improvisation (CFI) is a very challenging form of improvisation. In CFI, improvisers do not use any pre-existing structure (like the standard in straight-ahead jazz), but try anyway to produce together coherent music. This can be seen as a coordination problem: musicians' production must converge to collective sequences, defined as time frames during which each improviser achieves relative stability in his musical output while judging the overall result satisfying. In this paper, we report on an exploratory study made with free improvisers in December 2011 in order to understand the cognition of musicians placed in a CFI context, in particular the role played by their representations of the improvisation under different type of sequences into the explanation of both their behaviors and the coordination success or failure.