Harmonic Distance

Harmonic Distance is how far a ratio p/q lies from the fundamental in the lattice of prime harmonics, in octaves: Tenney's height. Consonance falls as a ratio grows complex: 3/2 lies at about 2.6, 5/4 at 4.3, 7/4 at 4.8 and 11/8 at 6.5, and the ear holds the harmonics to 7 in tune but not 11, the 7-limit. A universe that holds harmonics in tune to a greater distance holds more primes and so more actual dimensions; the distance allowed at each level is the open binding rule. Formally, H = ln(p · q) / ln(2), where H [∅] is the harmonic distance and p and q [∅] the ratio's numerator and denominator in lowest terms: [∅] = [∅]. It connects to Prime Harmonic Dimensions, Etheric Harmonics and Dimensional Saturation Threshold.

Category: Manuscript

Chapter: Chapter 4

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