Lumatone mapping for 93edo

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There are many conceivable ways to map 93edo onto the onto the Lumatone keyboard. However, it has 3 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them. Only the the sharp fifth (93b val) can be used with this layout, because the flat fifth (93 patent val) is shared with 31edo, and the large number of notes means the diatonic mapping and many others will fail to cover the entire gamut.

Diatonic (sharp fifth)

The 93b val has a moderately sharp fifth. On a hypothetical XL-sized Lumatone having enough keys to avoid skipping notes (465 required in the space of five octaves), the diatonic mapping would be a good mapping for Superpyth.

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58

Unidentified rank-3 temperament mapping

Bryan Deister has demonstrated a mapping for 93edo in microtonal improvisation in 93edo (2025). The rightward generator 6\93 represents 21/20, 23/22, and 25/24, producing a 15L 1s scale as in Valentine, although 93edo is contorted with this scale (L = 6 and s = 3) and temperament; choosing the scale 13L 3s avoids contortion, although neither the bright version (64\93) nor the dark version (29\93) of its generator maps to a convenient ratio, so the following discussion instead uses the generators for the mapping itself. Going right 2 keys makes a ~35/32 neutral second (abundantly used in the later part of the video); 3 right = ~8/7; 5 right = ~5/4; and 8 right = ~10/7. To avoid contortion, it is necessary to use a second generator, making this a rank-3 temperament mapping; the upward generator 7\93 is ~20/19; 4 steps up makes ~16/13; 5 steps up makes ~13/10, and 9 steps up (which always involves a vertical wraparound) makes ~8/5. Down-right is −1\93, enabling easy glissandos (demonstrated in the beginning of the video). In order to avoid having notes of the first note 0 to note 0 octave chopped off at the left edge, the first note 5 is placed half way down the left edge, and note 0 is 5 down-right from that. The range is just over an octave and a half, and the octaves slope from near to far.

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