There are many conceivable ways to map 41edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean. Herman Miller has documented five 41edo layouts, and they are available for download here.
Diatonic
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Magic
The Magic mapping is particularly efficient at putting good intervals close to each other and dissonant ones far away, as demonstrated in more detail in the writings on the kite guitar.
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Tetracot
The Tetracot mapping also puts consonant intervals within easy reach, making major, minor, and neutral triads particularly intuitive to play. Though the 7L 6s MOS is somewhat lopsided, due to its rather hard 5:1 step ratio.
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This can be compressed down to a 1L 5s mapping that extends range, but makes fingerings for common chords slightly more awkward
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Rodan
If you want to maximise your range while having access to all notes in each octave, the compressed Rodan mapping is about as good as you can get.
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However, this puts octaves all over the place. The expanded Rodan and Baldy mappings still have a wider range than the standard one and are more ergonomic for play.
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Baldy
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38
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Miracle (Miraculous) Lumatone mappings
It is possible to map 41edo as a Miracle (Miraculous) tuning, with a 8L 3s scale (4:3 step ratio), using a secor (~15/14 tempered together with ~16/15) which is in turn tempered together with ~14/13 (as per the Miraculous 13-limit extension). In this mapping, the range is only three octaves, but the octaves are perfectly level, each note is repeated at least twice, with a few being repeated three times, thus enabling the use of two manuals if the layout is offset appropriately. Bryan Deister has used this layout in microtonal dance in 41edo (2023), although without a color scheme that would show the layout.
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1
5
See also
