What structural properties do language and music share? Although early speculation identified a wide variety of possibilities, the literature has largely focused on the parallels between musical structure and syntactic structure. Here, we argue that parallels between musical structure and prosodic structure deserve more attention. We review the evidence for a link between musical and prosodic structure and find it to be strong. In fact, certain elements of prosodic structure may provide a parsimonious comparison with musical structure without sacrificing empirical findings related to the parallels between language and music. We then develop several predictions related to such a hypothesis.