Which features of music are universal and which are culture-specific? Why? These questions are important for understanding why humans make music but have rarely been scientifically tested. We used musical classification techniques and statistical tools to analyze a global set of 304 music recordings, finding no absolute universals but dozens of statistical universals. These include not only commonly cited features related to pitch and rhythm but also domains such as social context and interrelationships between musical features. We speculate that group coordination is the common aspect unifying the cross-cultural structural regularities of human music, with implications for the study of music evolution.