Base-20 and the Pythagorean Limma

An essay exploring how number bases shape musical intervals. The ratio (b-1):b—the largest single-digit fraction in any base—produces approximately 89 cents in base-20 (the ratio 19:20). This lands within one cent of the Pythagorean limma (256:243), the semitone of ancient Greek tuning. The essay constructs a speculative vigesimal music theory: pitch intervals derived from factors of 20, chord structures emphasizing the 4×5 factorization, and 18-beat rhythmic cycles reflecting Maya calendrical mathematics (18×20=360). The convergence between vigesimal and Pythagorean intervals illustrates a general principle: different number bases can independently privilege the same acoustic territory.