Pitch-Class Sets

Physics: Pitch-class set theory (Allen Forte, 1973): 12 pitch classes as integers mod 12. Normal form = most compact rotation. Prime form = most compact among normal form and its inversion. Interval vector [i₁,i₂,i₃,i₄,i₅,i₆] counts interval classes 1-6. Major triad: Forte 3-11B, prime form [0,3,7], iv=[001110]. Whole-tone scale = 6-35, iv=[060603]. 4096 subsets of 12 pitch classes → 208 set classes (unordered) or 224 counting distinct inversions. Chromatic cluster [0,1,2] = Forte 3-1.