Music exhibits some cross-cultural similarities, despite its variety across the world. Evidence from a broad range of human cultures suggests the existence of musical universals1, here defined as strong regularities emerging across cultures above chance. In particular, humans demonstrate a general proclivity for rhythm2, although little is known about why music is particularly rhythmic and why the same structural regularities are present in rhythms around the world. We empirically investigate the mechanisms underlying musical universals for rhythm, showing how music can evolve culturally from randomness. Human participants were asked to imitate sets of randomly generated drumming sequences and their imitation attempts became the training set for the next participants in independent transmission chains. By perceiving and imitating drumming sequences from each other, participants turned initially random sequences into rhythmically structured patterns. Drumming patterns developed into rhythms that are more structured, easier to learn, distinctive for each experimental cultural tradition and characterized by all six statistical universals found among world music1; the patterns appear to be adapted to human learning, memory and cognition. We conclude that musical rhythm partially arises from the influence of human cognitive and biological biases on the process of cultural evolution.