Lumatone mapping for 90edo - Revision history

Lucius Chiaraviglio: /* Undevicesimal Quasitonemic + Semitonismic + Archagallismic */ Bryan Deister's 90edo improv (2026) is actually Fantasy in 90edo [short clip]

2026-04-17T08:08:32Z

Undevicesimal Quasitonemic + Semitonismic + Archagallismic: Bryan Deister's 90edo improv (2026) is actually Fantasy in 90edo [short clip]

← Older revision		Revision as of 08:08, 17 April 2026
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	== Undevicesimal Quasitonemic + Semitonismic + Archagallismic ==		== Undevicesimal Quasitonemic + Semitonismic + Archagallismic ==
	[[Bryan Deister]] has demonstrated a [[6L 6s]] (8:7 step ratio) [[6th-octave_temperaments\|6th-octave temperament]] mapping for [[90edo]], in [https://www.youtube.com/shorts/LdxUD1taOqI ''90edo ~~improv~~''] (2026). This temperament is similar to [[6th-octave_temperaments#Spoob\|spoob]], but spoob itself (which equates the werckismic tone ~[[55/49]] to 1/6 of an octave) will not actually work in the [[patent val]] of 90edo, which maps 55/49 inconsistently. ("Undevicesimal quasitonemic" is a placeholder name, pending approval of an official name for this 6th-octave temperament.) Instead, it equates the near-just quasi-tempered whole tone ~[[64/57]] (one key right, as 15\90) to 1/6 of an octave — the [[undevicesimal quasitonema]] (34359738368/34296447249, name proposed by [[User:Xenllium\|Xenllium]]) is tempered out. The down-right generator 8\90 is a near-just large septendecimal semitone ~[[17/16]]; two of them (passing a 6th-octave boundary) make a sharp (and inconsistently-mapped) Pythagorean whole tone ~[[9/8]] (the semitonisma [[289/288]] is tempered out); three of them make a somewhat sharp classic minor third ~[[6/5]] (the archagallisma [[24576/24565]] is tempered out). The range is slightly short of five octaves (which slope upwards with the rows), with many missing notes in each octave, but this is an interesting mapping nonetheless, and could shine on a hypothetical XL-sized Lumatone having at least 465 keys in a span of five octaves.		[[Bryan Deister]] has demonstrated a [[6L 6s]] (8:7 step ratio) [[6th-octave_temperaments\|6th-octave temperament]] mapping for [[90edo]], in [https://www.youtube.com/shorts/LdxUD1taOqI ''<nowiki>Fantasy in 90edo [short clip]</nowiki>''] (2026). This temperament is similar to [[6th-octave_temperaments#Spoob\|spoob]], but spoob itself (which equates the werckismic tone ~[[55/49]] to 1/6 of an octave) will not actually work in the [[patent val]] of 90edo, which maps 55/49 inconsistently. ("Undevicesimal quasitonemic" is a placeholder name, pending approval of an official name for this 6th-octave temperament.) Instead, it equates the near-just quasi-tempered whole tone ~[[64/57]] (one key right, as 15\90) to 1/6 of an octave — the [[undevicesimal quasitonema]] (34359738368/34296447249, name proposed by [[User:Xenllium\|Xenllium]]) is tempered out. The down-right generator 8\90 is a near-just large septendecimal semitone ~[[17/16]]; two of them (passing a 6th-octave boundary) make a sharp (and inconsistently-mapped) Pythagorean whole tone ~[[9/8]] (the semitonisma [[289/288]] is tempered out); three of them make a somewhat sharp classic minor third ~[[6/5]] (the archagallisma [[24576/24565]] is tempered out). The range is slightly short of five octaves (which slope upwards with the rows), with many missing notes in each octave, but this is an interesting mapping nonetheless, and could shine on a hypothetical XL-sized Lumatone having at least 465 keys in a span of five octaves.
	{{Lumatone EDO mapping\|n=90\|start=86\|xstep=15\|ystep=-7}}		{{Lumatone EDO mapping\|n=90\|start=86\|xstep=15\|ystep=-7}}

Lucius Chiaraviglio: /* Diatonic */ Insert Bryan Deister's Undevicesimal Quasitonemic + Semitonismic + Archagallismic Lumatone mapping after this

2026-04-17T07:15:55Z

Diatonic: Insert Bryan Deister's Undevicesimal Quasitonemic + Semitonismic + Archagallismic Lumatone mapping after this

← Older revision		Revision as of 07:15, 17 April 2026
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	Due to the size of the edo, this mapping does not cover all the notes. In addition, the best approximation to [[5/4]] is a ''hextuply augmented'' fifth or ''septuply-diminished'' second, which is impossible to play with the root note of the scale.		Due to the size of the edo, this mapping does not cover all the notes. In addition, the best approximation to [[5/4]] is a ''hextuply augmented'' fifth or ''septuply-diminished'' second, which is impossible to play with the root note of the scale.
	{{Lumatone EDO mapping\|n=90\|start=12\|xstep=16\|ystep=-11}}		{{Lumatone EDO mapping\|n=90\|start=12\|xstep=16\|ystep=-11}}

			== Undevicesimal Quasitonemic + Semitonismic + Archagallismic ==
			[[Bryan Deister]] has demonstrated a [[6L 6s]] (8:7 step ratio) [[6th-octave_temperaments\|6th-octave temperament]] mapping for [[90edo]], in [https://www.youtube.com/shorts/LdxUD1taOqI ''90edo improv''] (2026). This temperament is similar to [[6th-octave_temperaments#Spoob\|spoob]], but spoob itself (which equates the werckismic tone ~[[55/49]] to 1/6 of an octave) will not actually work in the [[patent val]] of 90edo, which maps 55/49 inconsistently. ("Undevicesimal quasitonemic" is a placeholder name, pending approval of an official name for this 6th-octave temperament.) Instead, it equates the near-just quasi-tempered whole tone ~[[64/57]] (one key right, as 15\90) to 1/6 of an octave — the [[undevicesimal quasitonema]] (34359738368/34296447249, name proposed by [[User:Xenllium\|Xenllium]]) is tempered out. The down-right generator 8\90 is a near-just large septendecimal semitone ~[[17/16]]; two of them (passing a 6th-octave boundary) make a sharp (and inconsistently-mapped) Pythagorean whole tone ~[[9/8]] (the semitonisma [[289/288]] is tempered out); three of them make a somewhat sharp classic minor third ~[[6/5]] (the archagallisma [[24576/24565]] is tempered out). The range is slightly short of five octaves (which slope upwards with the rows), with many missing notes in each octave, but this is an interesting mapping nonetheless, and could shine on a hypothetical XL-sized Lumatone having at least 465 keys in a span of five octaves.
			{{Lumatone EDO mapping\|n=90\|start=86\|xstep=15\|ystep=-7}}

	== Diaschismic + Charismic ==		== Diaschismic + Charismic ==

Lucius Chiaraviglio: /* 2L 8s */ Add step ratio

2026-04-15T06:51:16Z

2L 8s: Add step ratio

← Older revision		Revision as of 06:51, 15 April 2026
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	=== 2L 8s ===		=== 2L 8s ===
	With [[2L 8s]], the range is three octaves with a very mild upwards slope, but some notes are missing.		With [[2L 8s]] (13:8 step ratio), the range is three octaves with a very mild upwards slope, but some notes are missing.
	{{Lumatone EDO mapping\|n=90\|start=36\|xstep=8\|ystep=5}}		{{Lumatone EDO mapping\|n=90\|start=36\|xstep=8\|ystep=5}}

Lucius Chiaraviglio: /* Diaschismic */ Add temperament text and demo video for the 10L 2s mapping

2025-07-28T11:26:35Z

Diaschismic: Add temperament text and demo video for the 10L 2s mapping

← Older revision		Revision as of 11:26, 28 July 2025
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	{{Lumatone EDO mapping\|n=90\|start=12\|xstep=16\|ystep=-11}}		{{Lumatone EDO mapping\|n=90\|start=12\|xstep=16\|ystep=-11}}

	== Diaschismic ==		== Diaschismic + Charismic ==
	On the other hand, the golden [[diaschismic]] mapping can cover the whole gamut, has better melodic properties than the diatonic mapping and makes harmonics easier to play together, although it needs to be expanded from [[2L 8s]] to [[10L 2s]] to hit every single note.		On the other hand, the golden [[diaschismic]] mapping can cover the whole gamut, has better melodic properties than the diatonic mapping and makes harmonics easier to play together, although it needs to be expanded from [[2L 8s]] to [[10L 2s]] to hit every single note. The rightward generator 8\90 is a semitone that functions as both ~[[16/15]] and ~[[17/16]] (the charisma [[256/255]] is tempered out). Splitting the octave in half (the [[diaschisma]] 2048/2025 is tempered out) enables this generator to produce these mappings without [[contorsion]].

			=== 2L 8s ===
			With [[2L 8s]], the range is three octaves with a very mild upwards slope, but some notes are missing.
	{{Lumatone EDO mapping\|n=90\|start=36\|xstep=8\|ystep=5}}		{{Lumatone EDO mapping\|n=90\|start=36\|xstep=8\|ystep=5}}

			=== 10L 2s ===
			[[Bryan Deister]] has demonstrated the [[Diaschismic]]-[[256/255\|Charismic]] [[10L 2s]] mapping for [[90edo]] (with 8:5 step ratio), in [https://www.youtube.com/shorts/0j33e4F-4jY ''microtonal improvisation in 90edo''] (20025). The range is about 2⅔ octaves with no missed notes, with a mild upward slope.
	{{Lumatone EDO mapping\|n=90\|start=84\|xstep=8\|ystep=-3}}		{{Lumatone EDO mapping\|n=90\|start=84\|xstep=8\|ystep=-3}}

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

Yourmusic Productions: Create Page.

2025-06-09T22:18:32Z

Create Page.

New page

{{Lumatone mapping intro}}

== Diatonic ==
Due to the size of the edo, this mapping does not cover all the notes. In addition, the best approximation to [[5/4]] is a ''hextuply augmented'' fifth or ''septuply-diminished'' second, which is impossible to play with the root note of the scale.
{{Lumatone EDO mapping|n=90|start=12|xstep=16|ystep=-11}}

== Diaschismic ==
On the other hand, the golden [[diaschismic]] mapping can cover the whole gamut, has better melodic properties than the diatonic mapping and makes harmonics easier to play together, although it needs to be expanded from [[2L 8s]] to [[10L 2s]] to hit every single note.
{{Lumatone EDO mapping|n=90|start=36|xstep=8|ystep=5}}

{{Lumatone EDO mapping|n=90|start=84|xstep=8|ystep=-3}}

{{Navbox Lumatone}}