Music is a universal, diverse cultural trait shaped by cultural and biological evolution. The extent to which global musical diversity traces the historical movements of people and their cultures is unresolved, with regional studies producing mixed results. Using a global musical dataset of 5,242 songs and 719 societies we identify five axes of musical diversity and show that musical traits contain geographically constrained patterns of between-society diversity. We pair musical data to genetic and linguistic datasets spanning 121 societies containing 981 songs, 1,296 individual genetic profiles, and 121 languages, showing that musical traditions contain similar, albeit weaker, patterns of spatial decay to linguistic diversity and genetic diffusion. However, the structure of musical similarity is different to linguistic or genetic histories. Musical relationships correlate with genetic and linguistic relationships within some regions, but not globally. Our results suggest that global musical traditions are distinct from non-musical aspects of human history.