Lumatone mapping for 83edo

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There are many conceivable ways to map 83edo onto the onto the Lumatone keyboard. However, the Standard Lumatone mapping for Pythagorean is unable to cover the full gamut of every octave, with both the sharp (patent val) and flat (b val) versions having many skipped notes.

Diatonic

If not for the problem of failing to cove the complete gamut (such as on a hypothetical XL-size Lumatone having at least 415 keys within the span of five octaves), the sharp version would be a respectable mapping for Quasisupra; while the flat version would be a respectable Flattone mapping.

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Ripple and Miracle mapping

Bryan Deister has used the 10L 1s layout for 83edo, as demonstrated in microtonal improvisation in 83edo (2025). The octaves slant downwards (with a wraparound in the first full octave) while moving to higher pitches, and the contiguous range (with all notes represented at least once, not counting non-contiguous notes in the upper left and lower right corners) is slightly over three octaves (although due to the Lumatone only being set up for a single MIDI channel in this video, the video only demonstrates approximately one and a half octaves). The generator is the semi-flat version of 27/25, as in Ripple temperament, although it is necessary to constitute it as (3♭ × 3♯ × 3♭) / 25 (using both the flat and sharp fifths in alternation) in order to map it correctly.

Alternatively, since 83edo is at the intersection of Ripple and Miracle temperaments, the generator can be constituted as a flat secor (16/15 ~ 15/14), using the 83b val—not in the optimal tuning spectrum of Miracle, but only needing to use the flat fifth.

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