William Benzon is a cognitive scientist and jazz trumpeter. His book, Beethoven's Anvil: Music in Mind and Culture, is a great introduction to the psychology of music. The sources are well-researched, and Benzon makes clear distinctions between speculative theory and observed facts. This is particularly important, given his bias towards Evolutionary Psychology. Part of the book is an effort to determine why humans evolved to "musick" – Benzon's general term for all activities involving music: listening, performing, composing, dancing, etc. – with several theories presented and tied to observed phenomenon from anthropology, brain scans, and linguistics. But even if you think EP is a load of bunk, the preliminary steps Benzon makes are interesting in their own right. He discusses the triune and split-brain models of the mind, Manfred Clynes' Sentics, rhythm perception, melody perception, auditory streaming, and the creative process.
Benzon has a very interesting thesis that "music is a medium through which individual brains are coupled together in shared activity." (p. 23) While there are many activities that require social interactions between individuals, music is special with its rhythmic component. Repeated rhythmic patterns have been shown to entrain biological functions, including cognitive functions. And as music allows many people to take part in the entrainment, either as performers or as listeners, it is particularly effective in forming cohesive social bonds. This is his favorite theory of musical EP, that music evolved as a means of allowing humans to bond in larger and larger groups (demes and macrodemes, as termed by Linnda Caporeal.)
Benzon tells engaging stories of music-making, and explains the science aspects very clearly yet thoroughly. I think it is too geared to social psychology for me to adopt it as a classroom text, but I highly recommend it for anyone interested in the intersections of music and psychology.