In a revolutionary work of music theory, Allen Forte introduces his mathematically-based concept of pitch-class set theory as a means of analyzing atonal music, particularly the music of such composers as Schoenberg, Webern, Berg, Stravinsky, and Bartók. Formalizing groups of pitch-class set classes, Forte moves on to describe how these set classes might relate to one another through such operations as transposition and inversion. Finally, Forte applies his theory of pitch-class set relations to actual compositions.