Lumatone mapping for 99edo - Revision history

Inthar: /* Ennealimmal (currently untested) */

2026-04-08T23:43:53Z

Ennealimmal (currently untested)

← Older revision		Revision as of 23:43, 8 April 2026
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	== Ennealimmal (currently untested) ==		== Ennealimmal (currently untested) ==
	This mapping uses [[ennealimmal]] temperament; it maps one axis to 1\9 and one axis to ~21/20, an ennealimmal generator.		This mapping uses [[ennealimmal]] temperament; it maps one axis to 1\9 and one axis to ~21/20, an ennealimmal generator.
	{{Lumatone EDO mapping\|n=99\|start=0\|xstep=11\|ystep=-18}}		{{Lumatone EDO mapping\|n=99\|start=0\|xstep=11\|ystep=-7}}

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

Inthar: /* Amity (Amicable) (currently untested, and shown for comparison) */

2026-04-08T23:20:00Z

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

← Older revision		Revision as of 23:20, 8 April 2026
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	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 [[Amity_family#Amicable\|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.		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 [[Amity_family#Amicable\|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.
	{{Lumatone EDO mapping\|n=99\|start=93\|xstep=7\|ystep=-2}}		{{Lumatone EDO mapping\|n=99\|start=93\|xstep=7\|ystep=-2}}

			== Ennealimmal (currently untested) ==
			This mapping uses [[ennealimmal]] temperament; it maps one axis to 1\9 and one axis to ~21/20, an ennealimmal generator.
			{{Lumatone EDO mapping\|n=99\|start=0\|xstep=11\|ystep=-18}}

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

Lucius Chiaraviglio: /* Würschmidt/Hemiwürschmidt/Würschmidt/Hemiwur */ Reorganize, and fix previous botched edit that left out second mapping

2025-11-02T21:40:35Z

Würschmidt/Hemiwürschmidt/Würschmidt/Hemiwur: Reorganize, and fix previous botched edit that left out second mapping

← Older revision		Revision as of 21:40, 2 November 2025
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	{{Lumatone EDO mapping\|n=99\|start=12\|xstep=8\|ystep=-7}}		{{Lumatone EDO mapping\|n=99\|start=12\|xstep=8\|ystep=-7}}

	== Würschmidt~~/Hemiwürschmidt/Würschmidt/Hemiwur~~ ==		== 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]]. Division by 2 to get 16\99 yields [[Hemimean_clan#Hemiwürschmidt\|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 [https://www.youtube.com/shorts/p9OUaFuTUek ''99edo waltz''] (2025).		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 [[Hemimean_clan#Hemiwürschmidt\|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 [https://www.youtube.com/shorts/p9OUaFuTUek ''99edo waltz''] (2025).
	{{Lumatone EDO mapping\|n=99\|start=40\|xstep=16\|ystep=-13}}		{{Lumatone EDO mapping\|n=99\|start=40\|xstep=16\|ystep=-13}}

			=== 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]] ([[Amity family#Amicable\|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).		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]] ([[Amity family#Amicable\|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).
			{{Lumatone EDO mapping\|n=99\|start=12\|xstep=8\|ystep=-7}}

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

Yourmusic Productions: Play Misty for me

2025-07-24T11:13:40Z

Play Misty for me

← Older revision		Revision as of 11:13, 24 July 2025
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	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}}

			== 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 ===
			{{Lumatone EDO mapping\|n=99\|start=79\|xstep=8\|ystep=1}}
			=== 12L 3s ===
			{{Lumatone EDO mapping\|n=99\|start=12\|xstep=8\|ystep=-7}}

	== Würschmidt/Hemiwürschmidt/Würschmidt/Hemiwur ==		== Würschmidt/Hemiwürschmidt/Würschmidt/Hemiwur ==

Lucius Chiaraviglio: Fix Navbox Lumatone

2025-07-24T09:08:50Z

Fix Navbox Lumatone

← Older revision		Revision as of 09:08, 24 July 2025
Line 15:		Line 15:
	{{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}}

Lucius Chiaraviglio: Create Lumatone mapping for 99edo, starting with 2 tested Würschmidt-series mappings, 1 untested Amity mapping for comparison, and the obligatory diatonic mapping

2025-07-24T09:08:09Z

Create Lumatone mapping for 99edo, starting with 2 tested Würschmidt-series mappings, 1 untested Amity mapping for comparison, and the obligatory diatonic mapping

New page

{{Lumatone mapping intro}}

== Diatonic ==
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}}

== 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 [[Hemimean_clan#Hemiwürschmidt|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 [https://www.youtube.com/shorts/p9OUaFuTUek ''99edo waltz''] (2025).
{{Lumatone EDO mapping|n=99|start=40|xstep=16|ystep=-13}}

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]] ([[Amity family#Amicable|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 [[Amity_family#Amicable|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.
{{Lumatone EDO mapping|n=99|start=93|xstep=7|ystep=-2}}

{{NavBox Lumatone}}