|
|
| Line 4: |
Line 4: |
| Due to the size of the EDO, a standard diatonic mapping will miss a large fraction of the notes. | | Due to the size of the EDO, a standard diatonic mapping will miss a large fraction of the notes. |
| {{Lumatone EDO mapping|n=99|start=6|xstep=17|ystep=-10}} | | {{Lumatone EDO mapping|n=99|start=6|xstep=17|ystep=-10}} |
| | |
| | == 49L 1s MOS subset pseudo-isomorphic pseudo-diatonic == |
| | |
| | [[Bryan Deister]] has demonstrated a pseudo-isomorphic mapping for a [[49L 1]] MOS subset of [[99edo]] in [https://www.youtube.com/shorts/GNio1PMp9BA ''99edo improv''] (2026). Since the step size is quite small, and yet the step ratio is 2:1, this enables playing a highly diatonic sound even though the layout is not truly diatonic, instead approximating a warped version of [[50edo]]. As with the standard diatonic mapping that it approximates, the the range is just short of five octaves, with no notes missing from the 49L 1s MOS scale. |
| | |
| | {{Lumatone EDO mapping|n=100|start=92|xstep=16|ystep=-6}} |
|
| |
|
| == Misty == | | == Misty == |
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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49L 1s MOS subset pseudo-isomorphic pseudo-diatonic
Bryan Deister has demonstrated a pseudo-isomorphic mapping for a 49L 1 MOS subset of 99edo in 99edo improv (2026). Since the step size is quite small, and yet the step ratio is 2:1, this enables playing a highly diatonic sound even though the layout is not truly diatonic, instead approximating a warped version of 50edo. As with the standard diatonic mapping that it approximates, the the range is just short of five octaves, with no notes missing from the 49L 1s MOS scale.
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Misty
Keeping the same generator but dividing the period in three gives you Misty. The 3L 9s mapping covers nearly all the notes with the occasional skip, while the 12L 3s one does cover the whole gamut, but has a smaller range and a very lopsided step size.
3L 9s
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12L 3s
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Würschmidt and extensions thereof
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.
Hemiwürschmidt/Würschmidt/Hemiwur
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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Würschmidt unnamed extension with generator divided by 4
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).
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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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Ennealimmal (currently untested)
This mapping uses ennealimmal temperament; it maps one axis to 1\9 and one axis to ~21/20, an ennealimmal generator.
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