Lumatone mapping for 82edo
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There are many conceivable ways to map 82edo onto the onto the Lumatone keyboard. However, it has 2 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them.
Diatonic
You can use the b val instead, but this is barely distinguishable from a circulating system of 7edo and only covers about 2/3rds of the notes due to the size of the edo.
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There is an alternate diatonic scale that makes 5-limit chords easy to play, but it has a slight octave stretch. Since that means all notes are available in at least some of the octaves, this may actually be advantageous.
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Bischismic
The Bischismic mapping can cover the whole gamut, although it needs to be expanded from 2L 8s to 10L 2s to do so.
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Other mappings
To maximise your range, you can use the 8L 2s mapping generated by 9/82 and a half octave period, but this is not particularly efficient at putting the best note combinations close to one-another.
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