Music is definable in a broad sense as embodying, entraining and transposably intentionalising time in sound and action. Human infants, in infant–caregiver interaction, and in childhood patterns of thought and behaviour, appear universally to engage in activities that share those attributes, and musics can be construed as cultural particularisations of those infant/childhood interactive and individual behaviours. Music as defined in this way appears to be uniquely human and ancient, most likely arising with Homo sapiens sapiens, ourselves. It is notable that our primate relatives do not appear to engage in activities with all the attributes of “music” as defined here. However, several primate behaviours and attributes might constitute precursors of musicality. In particular, it is suggested here that music may have arisen in the course of evolution in part as a result of processes of progressive altricialisation (a lengthening of the pre-reproductive juvenile period) in the primate and hominid lineages; a scenario for exploring the dynamics of altriciality in computational terms is also suggested.