There are many conceivable ways to map 67edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean. However, due to the size of the edo, this mapping does not quite cover all the notes.
The smallest mapping that does cover all the notes in a clear fashion with octaves kept near horizontal and a minimum of repetition is the 2L 7s one generated by 30/67.
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Negri
The 1L 8sNegri mapping has a greater octave slope and uses the second best approximation to the 5th harmonic, but still makes familiar intervals easier to play.
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Lesser Tendoneutralic
Bryan Deister has demonstrated a 7L 3s (7:6 step ratio) layout for 67edo that uses the tempering out of the Lesser tendoneutralisma (70368744177664/69894255367443, more conveniently described as [46 -1 0 0 0 -12⟩), in microtonal improvisation in 67edo (2025). The underlying generator of the temperament is two steps right and one step down-right on the keyboard, which is 20\67, which is a near-just ~16/13 (octave-reduced 13th subharmonic). Twelve of these are tempered together to make ~12/1, which is then octave-reduced to the twelfth ~3/1, and thence to the fifth ~3/2. The range is a bit under 3⅓ octaves, and the octaves are almost level, having a barely perceptible downward slant. Although very efficient, this mapping takes a very xenharmonic approach 67edo — the notes of a complete meantone diatonic scale are not situated for easy access (being widely spaced vertically and always requiring a vertical wraparound to play the complete diatonic scale).
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Infraorwell (gramitonic)
Bryan Deister has tested forward and reverse chroma 4L 5s (gramitonic, 8:7 step ratio) mappings for 67edo. Both get all notes in each octave and have a range of a bit over 3½ octaves. Apart from straight right (forward chroma version) or straight down-right (reverse chroma version, the most accessible generator is 15\67, which is a near-just septimal minor third ~7/6. This would suggest Orwell, except that the septimal minor third of 67edo is too close to just for actual Orwell temperament, and so a stack of it manages to miss all of the intervals characteristic of Orwell, other than a fairly flat classic minor sixth ~8/5. Instead, this yields Infraorwell.
Forward chroma
The forward chroma version, demonstrated in 67edo prelude (2025), also lends itself somewhat to an 8L 3s scale (8:1 step ratio), although both types of scale are likely to go through a vertical wraparound, depending upon root note, with this dependence being different in the octaves as they alternate between mid, near, and far.
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Reverse chroma
Bryan Deister has tested a 4L 5s (8:7 step ratio) mapping for 67edo that produces octaves (and the 4L 5s scale) closer to level (at the cost of having a reverse chroma and slightly less range), but currently no demo video is available.
