The relationship between music and language is fiercely debated in the modern literature of neuroscience and music. Here, we argue that a musicological study of online communication between jazz musicians in combination with brain imaging studies offers a unique setting for evalu- ating communicational aspects of music practices that rarely enter the present discourse on the subject. We employ Miles Davis’ quintet of the 1960s and its use of polyrhythmic structures as a general example of a jazz group focusing on communication. First, we consider jazz in the light of Roman Jakobson’s model of communication in a broad perspec- tive. Next, we analyze polyrhythmic occurrences in Herbie Hancock ́s solo on the jazz standard “All of You” as an example of how this com- munication develops as a narrative structuring of tension and relief. We identify two typical types of polyrhythms, metric displacement and re- grouping of subdivisions. Finally, we show how these polyrhythmic structures employ brain areas hitherto associated with linguistic semantic processing, and discuss possible implications.