Glossary, Atonal Theory
Atonal theory, or musical set theory, as outlined by Allen Forte and others, is useful as a shared vocabulary for talking about harmony outside the common practice and for discussing the edges of tonality, but atonality in general is outside the scope of Harmonious.
Learn musical set theory starting from square one with Pitch & Intervals.
“Atonality discards all scales, and treats each tone of the octave as an independent unit with no ordered relationship between the tones.” (Britannica Home Reading Guide, Appreciation of Music, 1944, p.34)
Serialism, twelve-tone rows, and the work of Arnold Schoenberg and his students—and some really modern and dissonant material—are all out there to be studied, but for many musicians and aspiring composers, atonal music is only of academic interest, since it is often harder for audiences to grasp than more conventional, tonal styles of music.
Jazz has its own atonal approach, playing outside.
Tymoczko 2011 explains why throwing out tonality is something of a theoretical uphill battle, for multiple interconnected reasons.