Over 140 years ago Charles Darwin first argued that birdsong and human music, having no clear survival benefit, were obvious candidates for sexual selection. Whereas the first contention is now universally accepted, his theory that music is a product of sexual selection through mate choice has largely been neglected. Here, I provide the first, to my knowledge, empirical support for the sexual selection hypothesis of music evolution by showing that women have sexual preferences during peak conception times for men that are able to create more complex music. Two-alternative forced-choice experiments revealed that woman only preferred composers of more complex music as short-term sexual partners when conception risk was highest. No preferences were displayed when women chose which composer they would prefer as a long-term partner in a committed relationship, and control experiments failed to reveal an effect of conception risk on women's preferences for visual artists. These results suggest that women may acquire genetic benefits for offspring by selecting musicians able to create more complex music as sexual partners, and provide compelling support for Darwin's assertion ‘that musical notes and rhythm were first acquired by the male or female progenitors of mankind for the sake of charming the opposite sex’.