Revision as of 21:14, 19 August 2025 by Lucius Chiaraviglio(talk | contribs)(→Diaschismic: Add Bryan Deister's version, and add temperament description (including ergonomics))
There are many conceivable ways to map 58edo onto the onto the Lumatone keyboard. However, it has 2 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them. Due to its size, it would not cover the whole gamut even if it was.
The 2L 6s (14:5 step ratio) and 2L 8s (9:5 step ratio) Diaschismic mappings are probably the most intuitive ways of covering the whole gamut while putting well-tuned ones close together if you're used to playing 12edo. The rightward generator 5\58 functions as the classic diatonmic semitone ~16/15, the large septendecimal semitone ~17/16, and the small septendecimal semitone ~18/17, meaning that the charisma 256/255 and the semitonisma ([289/288]] are both tempered out. The rightward generator is also the minimal form of the Diaschismic generator, and indeed the diaschisma 2048/2045 is also tempered out. This generator makes a slew of intervals of reasonable prime limit that are not far from just: two of them make a near-just whole tone ~9/8; three of them make a mildly flat classic minor third ~6/5; four of them make a mildly flat undecimal major third ~14/11; five of them make a near-just classic acute fourth ~27/20; six of them pass the semioctave to make a slightly flat greater septimal tritone ~10/7; seven of them make a slightly flat septimal superfifth ~32/21; eight of them make a slightly flat tridecimal supraminor sixth ~21/13; nine of them make a near-just septimal major sixth ~12/7; and ten of them make an extremely accurate undecimal supraminor seventh ~20/11. Other common intervals such as the moderately sharp (although high in relative error) classic major third ~5/4, the near-just perfect fourth ~4/3, and the near-just perfect fifth ~3/2 are in very easy reach of the chain of rightward generators, and not very distant from the root note. This may be sufficient compensation for the reverse chroma and the range of only three full octaves (which slope only slightly upward), with large partial octaves being chopped off by the upper left and lower right corners, which may be compositionally limiting.
This mapping has close to the same full octave range as the 2L 6s mapping, but spreads the range out over more of the Lumatone keyboard to get more repeated notes (and smaller partial octave regions chopped off by the upper left and lower right corners), and the cost of putting common intervals one rightward position further away from the root note.
The 5L 3sBuzzard mapping is also another good option, although this occasionally skips a step.
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Harry
Or if you don't mind the smaller range and want to more easily exploit narrow intervals, there is the 2L 12sHarry mapping (as in Lumatone mapping for harry)
