Introduction
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 on
a single note perceived as tonic; 2) a harmonic organisation based on triads and
seventh chords; 3) a hierarchical organisation of functional harmonies; and 4) a
contrapuntal substructure based on the laws of species counterpoint. This
music ± by such composers as Barber, Copland, Prokofiev and Stravinsky ± has
always posed a problem for music theorists, since neither traditional tonal
analysis nor pitch-class set analysis yields satisfying analytical results.