Lumatone mapping for 99edo: Difference between revisions

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Create Lumatone mapping for 99edo, starting with 2 tested Würschmidt-series mappings, 1 untested Amity mapping for comparison, and the obligatory diatonic mapping
 
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{{Lumatone EDO mapping|n=99|start=93|xstep=7|ystep=-2}}
{{Lumatone EDO mapping|n=99|start=93|xstep=7|ystep=-2}}


{{NavBox Lumatone}}
{{Navbox Lumatone}}

Revision as of 09:08, 24 July 2025

There are many conceivable ways to map 99edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean.

Diatonic

Due to the size of the EDO, a standard diatonic mapping will miss a large fraction of the notes.

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Würschmidt/Hemiwürschmidt/Würschmidt/Hemiwur

The Würschmidt generator, which is the classic major third ~5/4 (near-just), is 32\99 in 99edo, so it is divisible by 2 or 4 but not by 3 (seen with 65edo. Division by 2 to get 16\99 yields Hemiwürschmidt/Würschmidt/Hemiwur with a slightly flat septimal) middle whole tone ~28/25 for the divided generator, with a scale 6L 1s (16:3 step ratio). This mapping only splits the Würschmidt in half to get greater range (over four octaves) than when splitting it in quarters, but at the cost of missing many notes in each octave. Despite the missing notes, Bryan Deister has demonstrated this mapping in 99edo waltz (2025).

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Division of the generator by 2 again (for 4 overall) yields a further extension that uses this mapping's rightward generator 8\99 as a slightly sharp ptolemaic chromatic semitone (major limma) ~135/128, with a scale 12L 3s (8:1 step ratio), implying that the octave is also divided into three equal parts. As befits Würschmidt, eight classic major thirds (32\65) make a near-just 6th harmonic ~6/1. The range is just over two octaves, and the octaves slant up mildly, now with no missing notes and some repeated notes to ease vertical wraparound. Compared to the Amity (Amicable) mapping with split period, this mapping is more lopsided with the hard scale step ratio, but on the other hand gets some consonant ratios with only a few generator steps. Bryan Deister has experimented with this mapping, but no demonstration video is available yet (as of 2025-07-24).

Amity (Amicable) (currently untested, and shown for comparison)

Since 99edo falls on the Amity temperament line, it is tempting to use the generator 7\99 functioning as a near-just ~21/20 as in the Amicable extension, but with the octave split into three equal parts, giving a 12L 3s scale with 7:5 step ratio. The range is a bit over two octaves, slanting up mildly, with no missed notes and a few repeated notes to assist with vertical wraparounds. Relative to the mappings for Würschmidt and its extensions, the Amicable mapping has the advantage that the layout is less lopsided, but the disadvantage that stacking generators does not hit good ratios at low numbers of generators.

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