Matthew Santa
There is a substantial body of music written in the twentieth century in which the notes of a diatonic scale predominate, but which often lacks one or more of the other basic requirements necessary to be considered tonal: 1) a centricity around a single tone perceived as tonic; 2) a harmonic organization based on triads and seventh chords; 3) a hierarchical organization of functional harmonies; and 4) a contrapuntal substructure based on the laws of species counterpoint. Such music, by the likes of Barber, Copland, Prokofiev, and Stravinsky, has always posed a problem for music theorists, since neither traditional tonal analysis nor pc-set analysis yields satisfying analytic results. In this paper, I argue that the problems inherent in analyzing post-tonal diatonic music can be solved by a careful application of set theory modulo 7, in interaction with the more familiar mod12 set theory. The paper outlines a system of mod7 set theory designed specifically for the analysis of post-tonal diatonic music, and then applies that system to a range of post-tonal diatonic works in order to demonstrate its validity.