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Lumatone mapping for 49edo

Revision as of 05:58, 9 April 2026 by Lucius Chiaraviglio (talk | contribs) (→Didacus: Insert Bryan Deister's Archipelago + Catalan mapping after this — even more efficient and with less severely sloping octaves)

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 are a good 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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Archipelago + Catalan

The most efficient mapping for 49edo, having a range of 5¼ octaves (which slope down moderately) with no missed notes and no repeated notes, is Bryan Deister's 4L 3s (10:3 step ratio) mapping that functions for both a rank-2 or rank-3 archipelago-related temperament and catalan temperament, demonstrated in 49edo improv (2026). The rank-2 archipelago-related temperament (which is not currently on the archipelago page) uses one key right (10\49) as a slightly sharp tridecimal semifourth ~15/13 (in the 49f val) for its generator; two of them make the fairly flat fourth ~4/3; four of them make the sharp septimal minor seventh ~7/4; six of them (after octave reduction) make a slightly sharp septimal minor third ~7/6; thirteen of them (after more octave reduction) make a near-just undecimal minor sixth ~11/7; and fourteen of them make a sharp classic minor seventh ~9/5. Although this is a respectable list of intervals, by itself the rank-2 version of the temperament does not make a very good MOS scale — instead it makes for scales in which the small interval is only 1\49. Therefore, for facility in making scales, including the aforementioned 4L 3s, a second generator is needed (thus elevating this to a rank-3 temperament that tempers out 364/363, 540/539, and 847/845); that generator uses one key down-right (3\49) as the slightly sharp classic chromatic semitone ~25/24, which 49edo actually uses as a diatonic semitone. Catalan uses one key right plus one key down-right (13\49) as a slightly sharp classic minor third for its generator; two of them make a very flat Axirabian paraminor fifth ~16/11; four of them (after octave reduction) make a somewhat sharp classic chromatic semitone ~25/24; five of them make a mildly sharp classic major third ~5/4; six of them make a sharp fifth ~3/2; seven of them make a sharp classic minor seventh ~9/5; eight of them (after more octave-reduction) make a mildly flat undecimal neutral second ~12/11; and ten of them make a near-just undecimal minor sixth ~11/7. Catalan does not need a second generator to produce usable MOS scales, including the aforementioned 4L 3s.

 
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