The paper focuses on analytical and theoretical problems of improvised music in relation to the graphical representation of improvised music and the ways of communicating its structural dimension. On the one hand, free improvisation has the doubtful reputation of having no structure, presumably no theoretical background and therefore being not suitable to analysis. On the other hand, a concentrate listener perceives constructive strategies and formal processes which can be described and qualified. Moreover, the publication of some improvisatory sessions on recorded media (for example Gruppo di Improvvisazione Nuova Consonanza, Improvisationen, LP Deutsche Grammophon 137 007 (1968) or New Phonic Art (Begegnung in Baden-Baden, LP Wergo 60060 (1971)) induced in the audience the sense of a work character which was mostly non intentionally premeditated, but that will become an essential component in their subsequent reception, with consequences ranging from aesthetic evaluation to stylistic emulation. The research will focus on two different approaches and their limits: 1) the graphic material used by improvisation groups as a guide in formal dimension, for the definition of musical material etc.; 2) the graphic score realized during the analysis of improvisations in order to make the discourse about structure, time, gestures, sound, performance possible.