Harmony as an underlying ingredient in the numerical search for suitable equal temperaments
L.F. Melo
Abstract:This work investigates whether there are harmonic sets which are universally prioritized when fitting the chromatic just scale with equal-tempered tunings. We design a method to find which temperaments properly and non-ambiguously fit a set of pure intervals and show that: (a) Within range N ∈ [9, 54], temperaments with 12, 19, 22, 24, 31, 34, 41 and 53 divisions are suitable for adjusting the twelve-tone chromatic just scale – in particular, 53 divisions provide the most accurate fit, (b) For M-element subset… Show more
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