For years, a major challenge among artists and scientists has been the con- struction of music systems capable of interacting with humans on stage. In their attempt to further advance musicianship and assist humans provide better improvisations on stage, modern computer improvisation systems, that is, systems with the ability to improvise, have integrated into their de- sign various technologies. Such systems find applicability in contexts within which they are required to act both as independent, improvising agents and as instruments in the hands of a computer operator. This is widely known as the player and the instrument paradigm. This thesis studies the so-called three party interaction in the improvisation context. We use this term to refer to the ensemble of interactions arising from the onstage coexistence of three constituents participants: the human instrument player, the computer and the computer operator/performer. The purpose of this study is to investigate the requirements arising out of such interaction as well as establish the framework that will allow the computer fulfil the double mission of operating both as player and an in- strument. The initial challenge of the approach lies on the concept of machine mu- sicianship itself.