This paper aims at describing an approach to the music performance situation as a laboratory for investigating interactivity. I would like to present “Leçons pour un apprenti sourd-muet” [1], where the basic idea is that of two improvisers, a saxophonist and a computer, engaged in a series of musical questions and responses. The situation is inspired from the Japanese shakuhachi tradition, where imitating the master performer is a prime element in the apprentice’s learning process. Through listening and imitation, the computer’s responses get closer to that of its master for each turn. In this sense, the computer’s playing emanates from the saxophonist’s phrases and the interactivity in “Leçons” happens on the level of the composition.