The work presented in this thesis focuses on the conception and realization of a software capable of pertinent interaction with acoustic musicians in a collective free improvisation, that is an improvisation without any predetermined knowledge of structures, rules or style. It is extended at the end of our work with considerations on emerging properties such as pulse or a broad notion of harmony. The OMax project proposes to approach this problem of non-idiomatic improvisation by learning and mimicking the style of a musician with an agnostic and incremental knowledge model. We take this computer system as our work basis and examine carefully three aspects: the conceptual principles of the system, the software architectures for effective implementations and the real-life usage of this system in numerous testing and concerts situations. Besides a thorough study of all the conceptual elements of the system based on anthropomorphic decomposition of its parts, our main contribution is the design and realization of several variations of the OMax system. Our work has been also strongly coupled with the testing of our prototypes with several leading musicians.