In recent years, there has been renewed interest in the biological and cultural evolution of music, and specifically in the role played by perceptual and cognitive factors in shaping core features of musical systems, such as melody, harmony, and rhythm. One proposal originates in the language sciences. It holds that aspects of musical systems evolve by adapting gradually, in the course of successive generations, to the structural and functional characteristics of the sensory and memory systems of learners and "users" of music. This hypothesis has found initial support in laboratory experiments on music transmission. In this article, we first review some of the most important theoretical and empirical contributions to the field of music evolution. Next, we identify a major current limitation of these studies, i.e., the lack of direct neural support for the hypothesis of cognitive adaptation. Finally, we discuss a recent experiment in which this issue was addressed by using event-related potentials (ERPs). We suggest that the introduction of neurophysiology in cultural transmission research may provide novel insights on the micro-evolutionary origins of forms of variation observed in cultural systems.