This chapter outlines a hermeneutical approach to the study and analysis of improvisational practices, particularly in relation to artistic domains. It offers a first application of this approach to the musical notion of free improvisation, although this application can plausibly be extended to other performing arts as well. The chapter shows how some elements of the notion of orientation provide fruitful hermeneutical keys that can help us characterize these two notions of free improvisation from a common perspective. The relation between improvisation and orientation has never been explicitly thematized or thoroughly investigated. The chapter presents de jure definition of free musical improvisation, and encompasses its de facto historic-musicological definition. The kairological dimension of improvisation, specifically at the artistic level, is formulated in the statement that, in jazz, and more generally musical improvisation, any mistake is potentially an opportunity.