There are many conceivable ways to map 46edo onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean.
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31
39
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18
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42
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13
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9
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8
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Unfortunately the Leapday diatonic scale is not meantone, and makes basic 5-limit minor and major interval quite complex and often awkward to play. (For example, reaching 5/4 using only sharps and flats would require a triply-augmented unison, such as C–C𝄪♯ or C to C triple sharp). The Rodan mapping has a slightly wider range and is probably more intuitive, but has the disadvantage of skipping a chroma on some of the transitions between columns, making it impossible to play the full gamut of each octave, and each octave is substantially higher up on the keyboard.
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The expanded mapping fixes this, but now the chroma goes diagonally down, requiring an adjustment of playing style when doing chromatic runs.
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The Amity mapping is a good compromise between them, since it provides an even heptatonic scale, making the full gamut playable, puts 5-limit minor and major chords within easy reach, and has the chroma going in the correct direction.
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The Echidnic mapping does even better, giving the greatest overall efficiency at reaching harmonics while also keeping octaves close to horizontal.
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1
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