“But Bitcoin Cash Forked Off Without Consensus!” (In 40 Equal Divisions of the Octave)

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In the permissionless system that Bitcoin is, “consensus” among developers or users is irrelevant. What matters is Nakamoto consensus, where miners vote with their proof of work to create the longest chain. This process is ongoing between BTC and BCH.

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40-edo is interesting, because it supports a super-equalized version of the diatonic scale where the major and minor second only differ by one step of 40-edo, or 30 cents. That means that the “chroma”, or sharp/flat, is also this tiny, 30 cent interval.

The major third in this scale is so flat (360 cents) that, with the chroma of 30 cents, the augmented third (at 390) cents is a much better approximation of the Just interval 5:4 (386 cents). In this piece, I use those augmented thirds when I want a pure “major third” sound and, because the chroma is so small, sharps and flats can be used liberally to create small melodic nuances. I also approximate 21:16 and 11:8 at points.

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