Musicality can be defined as a natural, spontaneously developing trait based on and constrained by biology and cognition. Music, by contrast, can be defined as a social and cultural construct based on that very musicality. One critical challenge is to delineate the constituent elements of musicality. What biological and cognitive mechanisms are essential for perceiving, appreciating and making music? Progress in understanding the evolution of music cognition depends upon adequate characterization of the constituent mechanisms of musicality and the extent to which they are present in non-human species. We argue for the importance of identifying these mechanisms and delineating their functions and developmental course, as well as suggesting effective means of studying them in human and non-human animals. It is virtually impossible to underpin the evolutionary role of musicality as a whole, but a multicomponent perspective on musicality that emphasizes its constituent capacities, development and neural cognitive specificity is an excellent starting point for a research programme aimed at illuminating the origins and evolution of musical behaviour as an autonomous trait.