There are many conceivable ways to map 75edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean.
Diatonic
However, Due to the size of the edo, this mapping does not cover all the notes. In addition, like 46edo, 75edo is a leapday system, so the best approximation to 5/4 is a triply-augmented unison, which makes for awkward fingerings. Despite the missing notes, Bryan Deister has demonstrated this layout in improv in 75edo (2025)
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Tetracot
The Tetracot mapping is considerably more efficient at putting harmonics close together.
Standard (6L 1s) Tetracot
However, 75edo is too large for the standard Lumatone mapping for Tetracot to include all of the notes.
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Compressed (Reversed-Chroma 1L 5s) Tetracot
Bryan Deister has demonstrated a compressed 1L 5s mapping of 75edo in microtonal improvisation in 75edo (2025-06-22). This combines the temperament of Tetracot with the idea of the compressed Lumatone mapping for Porcupine, by reversing the chroma. (This also contains the Tetracot 6L 1s scale, but playing that scale in this layout requires backtracking.) This expands the overall range to more than five octaves, but too much so for anything so large as 75edo, thereby causing missed notes (although it demonstrates how such a mapping could shine for a smaller EDO or a hypothetical XL-sized Lumatone that has room for all of the notes).
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Expanded (7L 6s) Tetracot
To cover all of the notes in 75edo, Tetracot needs to be expanded from 6L 1s to 7L 6s, which puts octaves all over the place
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Fog
To maximise range while covering the whole gamut, giving easy access to lower harmonics and keeping octaves near horizontal, slice the period into thirds to produce the Fog mapping.
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Neutral Thirds
The neutral thirds mapping has slightly less range, but skips fewer notes around the edges and keeps octaves (just over 3½) even closer to horizontal, with scale 7L 3s (step size ratio 9:4). Bryan Deister has demonstrated this mapping, in microtonal improvisation in 75edo (2025-06-24). Like 97edo, 75edo has mainly bad harmonics for its size (but with different harmonics being exceptions), so to find useful intervals, it is necessary to try to stick to primes 3, 5, and 23 (those having the least relative error) and/or take advantage of error cancellation as much as possible. Going right (9\75) 1 key is ~25/23 (error canceling, but starting out with some of the least bad harmonics); right 2 keys (18\75) is a subminor third ~625/529 (no simple ratio maps to this interval in the patent val of 75edo, but it merits mention anyway due to extensive use in the video); right 3 keys (27\75) = ~9/7 (errors only partially cancel, so somewhat flat); and right 7 keys (63\75) = ~34/19 (errors nearly cancel). Going down-right (4\75) 1 key functions as both ~27/26 and ~28/27; down-right 2 keys = ~14/13 (errors largely cancel), 3 keys = ~19/17 (errors largely cancel), and 5 keys = ~5/4 (the 5th harmonic has a small relative error). Going up (5\75) 1 key is ~23/22 (errors only partially canceling, so somewhat sharp).
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