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).
