Steven Mithen (author of The Singing Neanderthals) does a summary of his ideas on the evolutionary basis of musicality in this open access article in the Annals of the New York Academy of Sciences.
Why does music pervade our lives and those of all known human beings living today and in the recent past? Why do we feel compelled to engage in musical activity, or at least simply enjoy listening to music even if we choose not to actively participate? I argue that this is because musicality—communication using variations in pitch, rhythm, dynamics and timbre, by a combination of the voice, body (as in dance), and material culture—was essential to the lives of our pre-linguistic hominin ancestors. As a consequence we have inherited a desire to engage with music, even if this has no adaptive benefit for us today as a species whose communication system is dominated by spoken language. In this article I provide a summary of the arguments to support this view.