Jazz improvisation is commonly understood as a conversation, a normative practice where musicians take turns and give-and-take musical motives. In this paper, we analyze the musicians’ intentions as multimodal actions directed to the other person, in phenomenological interviews with jazz duets (guitar/sax). Two temporally intertwined categories of intention were obtained, related to the thematic content of the improvised music, and to the diachronic/synchronic interactions between musicians during performance. Attributions reveal the urge of grasping one’s own and other’s mental content, an ability that goes beyond the sensorimotor descriptions of intentional actions accounted for by 4E theories.