Lumatone mapping for 49edo

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Revision as of 04:25, 10 November 2025 by Lucius Chiaraviglio (talk | contribs) (→Other mappings: Reorganize into Didacus, and add Bryan Deister's version)
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There are many conceivable ways to map 49edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean.

Diatonic

Cam Taylor demonstrates this mapping in 49-equal: 7-equal meets superpyth (2023).

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Keep in mind that 49edo is a superpyth temperament, so 5/4 is mapped to the interval of an augmented second (e.g. a 5/4 above C is D♯).

Didacus

If you want to access single step movements in a more intuitive way and slightly extend your range, Didacus mappings may be the best compromise. Didacus uses a flat Pythagorean whole tone ~9/8 as its generator, which is the rightward generator in these mappings; it uses the direct approximation of the 9th harmonic instead of building it by stacking the 3rd harmonic. Unfortunately, these mappings put octaves all over the place.

Flipped 6L 1s (add rotated Sevond + Whitewood)

One possibility is a flipped 6L 1s mapping (8:1 step ratio, with the short step being up instead of down-right), with a range of five octaves, although with a severe upwards slope that incurs a wraparound. This version also functions as a rotated Whitewood or Sevond mapping, both dividing the octave into seven parts, and the latter using the flat fourth ~4/3 (20\49, but 1/7-octave-reduced to 1\49) as its generator, which is reached by going left one key and up-left three keys.

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3L 5s (add Catalan + Clyde)

Another possibility is a 3L 5s (8:5 step ratio) mapping for 49edo, as demonstrated by Bryan Deister in weathergirl - FLAVOR FOLEY (microtonal cover in 49edo) (2025). This mapping lends itself to three rank-2 temperaments, one of which is Didacus as explained above. Another temperament is Catalan, for which the right + down-right generator 13\49 is a near-just (slightly sharp) classic minor third ~6/5; this uses the 3rd harmonic, which is quite sharp, but has most of its error canceled by the sharp 5th harmonic. Yet another temperament is Clyde, for which the right = 2 down-right generator 18\49 is a mildly sharp septimal major third ~9/7; this also uses the (sharp) 3rd harmonic to make an even sharper patent 9th harmonic, which has most of its error canceled by the sharp 7th harmonic. The range is just over five octaves with no missed notes and a few repeated notes in each octave, but the octaves slope down severely, incurring a vertical wraparound.

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