We explore the capacity for music in terms of five questions: (1) What cognitive structures are invoked by music? (2) What are the principles that create these structures? (3) How do listeners acquire these principles? (4) What pre-existing resources make such acquisition possible? (5) Which aspects of these resources are specific to music, and which are more general? We examine these issues by looking at the major components of musical organization: rhythm (an interaction of grouping and meter), tonal organization (the structure of melody and harmony), and affect (the interaction of music with emotion). Each domain reveals a combination of cognitively general phenomena, such as gestalt grouping principles, harmonic roughness, and stream segregation, with phenomena that appear special to music and language, such as metrical organization. These are subtly interwoven with a residue of components that are devoted specifically to music, such as the structure of tonal systems and the contours of melodic tension and relaxation that depend on tonality. In the domain of affect, these components are especially tangled, involving the interaction of such varied factors as general-purpose aesthetic framing, communication of affect by tone of voice, and the musically specific way that tonal pitch contours evoke patterns of posture and gesture.