Using a database of jazz recordings we study the collaboration network of jazz musicians. We define the network at two different levels. First we study the collaboration network between individuals, where two musicians are connected if they have played in the same band. Then we consider the collaboration between bands, where two bands are connected if they have a musician in common. The community structure analysis reveals that these constructions capture essential ingredients of the social interactions between jazz musicians. We observe correlations between recording locations, racial segregation and the community structure. A quantitative analysis of the community size distribution reveals a surprising similarity with an e-mail based social network recently studied.