Lumatone mapping for 91edo - Revision history

Lucius Chiaraviglio: /* Diatonic */ Add demo video for flat fifth version

2026-05-14T16:45:10Z

Diatonic: Add demo video for flat fifth version

← Older revision		Revision as of 16:45, 14 May 2026
Line 2:		Line 2:

	== Diatonic ==		== Diatonic ==
	The large number of notes results in both the flat ([[patent val]]) and sharp (b val) fifths failing to cover the gamut, with both skipping many notes. If not for this problem, the flat version would be a respectable [[Schismic–Pythagorean_equivalence_continuum#Python\|Python]] or [[Meantone]] (91c) mapping, while the sharp version would be a respectable mapping for [[Quasiultra]] (as 91bd).		The large number of notes results in both the flat ([[patent val]]) and sharp (b val) fifths failing to cover the gamut, with both skipping many notes. If not for this problem, the flat version would be a respectable [[Schismic–Pythagorean_equivalence_continuum#Python\|Python]] or [[Meantone]] (91c) mapping, while the sharp version would be a respectable mapping for [[Quasiultra]] (as 91bd). Despite the missing notes, [[Bryan Deister]] has used the flat (patent) fifth diatonic mapping (the first mapping below) in {{W\|Maretu}}'s [https://www.youtube.com/shorts/7RDvArkSJrk ''Aishite ita no ni''] (2023) – microtonal cover in 91edo by [[Bryan Deister]] (2026)
	{{Lumatone EDO mapping\|n=91\|start=89\|xstep=15\|ystep=-7}}		{{Lumatone EDO mapping\|n=91\|start=89\|xstep=15\|ystep=-7}}


	{{Lumatone EDO mapping\|n=91\|start=22\|xstep=17\|ystep=-14}}		{{Lumatone EDO mapping\|n=91\|start=22\|xstep=17\|ystep=-14}}

ArrowHead294 at 13:50, 23 June 2025

2025-06-23T13:50:56Z

← Older revision		Revision as of 13:50, 23 June 2025
Line 4:		Line 4:
	The large number of notes results in both the flat ([[patent val]]) and sharp (b val) fifths failing to cover the gamut, with both skipping many notes. If not for this problem, the flat version would be a respectable [[Schismic–Pythagorean_equivalence_continuum#Python\|Python]] or [[Meantone]] (91c) mapping, while the sharp version would be a respectable mapping for [[Quasiultra]] (as 91bd).		The large number of notes results in both the flat ([[patent val]]) and sharp (b val) fifths failing to cover the gamut, with both skipping many notes. If not for this problem, the flat version would be a respectable [[Schismic–Pythagorean_equivalence_continuum#Python\|Python]] or [[Meantone]] (91c) mapping, while the sharp version would be a respectable mapping for [[Quasiultra]] (as 91bd).
	{{Lumatone EDO mapping\|n=91\|start=89\|xstep=15\|ystep=-7}}		{{Lumatone EDO mapping\|n=91\|start=89\|xstep=15\|ystep=-7}}


	{{Lumatone EDO mapping\|n=91\|start=22\|xstep=17\|ystep=-14}}		{{Lumatone EDO mapping\|n=91\|start=22\|xstep=17\|ystep=-14}}

ArrowHead294 at 13:50, 23 June 2025

2025-06-23T13:50:47Z

← Older revision		Revision as of 13:50, 23 June 2025
Line 1:		Line 1:
	~~There are many conceivable ways to map [[91edo]] onto the onto the Lumatone keyboard. However, the [[Standard~~ Lumatone mapping ~~for Pythagorean]] is unable to cover the full gamut of every octave, with the flat ([[patent val]]) and sharp (b val) versions having many skipped notes.~~		{{Lumatone mapping intro}}

	== Diatonic ==		== Diatonic ==
	~~If not for~~ the ~~problem of~~ failing to cover the ~~complete~~ gamut ~~(such as on a hypothetical XL-size Lumatone having at least 485 keys within the span of five octaves)~~, the flat version would be a respectable [[Schismic–Pythagorean_equivalence_continuum#Python\|Python]] or [[Meantone]] (91c) mapping, while the sharp version would be a respectable mapping for [[Quasiultra]] (as 91bd).		The large number of notes results in both the flat ([[patent val]]) and sharp (b val) fifths failing to cover the gamut, with both skipping many notes. If not for this problem, the flat version would be a respectable [[Schismic–Pythagorean_equivalence_continuum#Python\|Python]] or [[Meantone]] (91c) mapping, while the sharp version would be a respectable mapping for [[Quasiultra]] (as 91bd).
	{{Lumatone EDO mapping\|n=91\|start=89\|xstep=15\|ystep=-7}}		{{Lumatone EDO mapping\|n=91\|start=89\|xstep=15\|ystep=-7}}

Line 8:		Line 8:

	== Quartkeenlig-related rank-3 mappings ==		== Quartkeenlig-related rank-3 mappings ==

	=== Pseudo-isomorphic ===		=== Pseudo-isomorphic ===
	[[Bryan Deister]] has demonstrated a pseudo-isomorphic mapping for [[91edo]] in [https://www.youtube.com/shorts/HaYUAg30298 ''microtonal improvisation in 91edo''] (2025). This layout is numbered as for [[92edo]], but note 91 is actually a duplicate of note 0. The range is just one note short of 3 full octaves, with octaves sloping down gently, unlike the fully isomorphic version below, which avoids the interruption from the duplicated note 0 and has slightly greater range, but at the cost of greater (and opposite) octave slope and a vertical wraparound of note 0 with ascending octaves (as well as producing a discontinuity in scales). This mapping has the same generators as the fully isomorphic version, as described below.		[[Bryan Deister]] has demonstrated a pseudo-isomorphic mapping for [[91edo]] in [https://www.youtube.com/shorts/HaYUAg30298 ''microtonal improvisation in 91edo''] (2025). This layout is numbered as for [[92edo]], but note 91 is actually a duplicate of note 0. The range is just one note short of 3 full octaves, with octaves sloping down gently, unlike the fully isomorphic version below, which avoids the interruption from the duplicated note 0 and has slightly greater range, but at the cost of greater (and opposite) octave slope and a vertical wraparound of note 0 with ascending octaves (as well as producing a discontinuity in scales). This mapping has the same generators as the fully isomorphic version, as described below.

Lucius Chiaraviglio: /* Isomorphic */ Fix typo in ~15/14

2025-06-23T08:27:36Z

Isomorphic: Fix typo in ~15/14

← Older revision		Revision as of 08:27, 23 June 2025
Line 14:		Line 14:

	=== Isomorphic ===		=== Isomorphic ===
	[[Bryan Deister]] has demonstrated an isomorphic [[9L 2s]] mapping for [[91edo]] in [https://www.youtube.com/shorts/z6PeEocYMV8 ''improv 91edo''] (2025). The range is just one note beyond 3 full octaves, with octaves sloping up mildly (which results in a wraparound of note 0). The rightward generator 9\91 is the septimal diatonic semitone ~[[15\14]]. The upward generator 4\91 is a quartertone that functions as ~[[32/31]], ~[[33/32]], ~[[34/33]], and ~[[36/35]]; two of them make the minor diatonic semitone ~[[17/16]]; six of them make a near-just minor third ~[[6/5]]. The use of this generator makes this a mapping for [[Quartkeenlig]]; however, since stacking the upward generator quickly leads to wraparounds, and attempting to get the perfect fifth in 91edo with this generator yields 52\91, which is the [[7edo]] (91bb) fifth. Therefore, this mapping really needs to be treated as a rank-3 temperament mapping; for instance, to get the patent fifth 53\92 (a mildly flat ~[[3/2]], almost exactly [[1/7-comma meantone]]), it is easiest to stack five rightward generators and two upward generators.		[[Bryan Deister]] has demonstrated an isomorphic [[9L 2s]] mapping for [[91edo]] in [https://www.youtube.com/shorts/z6PeEocYMV8 ''improv 91edo''] (2025). The range is just one note beyond 3 full octaves, with octaves sloping up mildly (which results in a wraparound of note 0). The rightward generator 9\91 is the septimal diatonic semitone ~[[15/14]]. The upward generator 4\91 is a quartertone that functions as ~[[32/31]], ~[[33/32]], ~[[34/33]], and ~[[36/35]]; two of them make the minor diatonic semitone ~[[17/16]]; six of them make a near-just minor third ~[[6/5]]. The use of this generator makes this a mapping for [[Quartkeenlig]]; however, since stacking the upward generator quickly leads to wraparounds, and attempting to get the perfect fifth in 91edo with this generator yields 52\91, which is the [[7edo]] (91bb) fifth. Therefore, this mapping really needs to be treated as a rank-3 temperament mapping; for instance, to get the patent fifth 53\92 (a mildly flat ~[[3/2]], almost exactly [[1/7-comma meantone]]), it is easiest to stack five rightward generators and two upward generators.
	{{Lumatone EDO mapping\|n=91\|start=0\|xstep=9\|ystep=-4}}		{{Lumatone EDO mapping\|n=91\|start=0\|xstep=9\|ystep=-4}}

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

Yourmusic Productions: Patent mapping should go first.

2025-06-08T09:03:43Z

Patent mapping should go first.

← Older revision		Revision as of 09:03, 8 June 2025
Line 2:		Line 2:

	== Diatonic ==		== Diatonic ==
	If not for the problem of failing to ~~cove~~ the complete gamut (such as on a hypothetical XL-size Lumatone having at least 485 keys within the span of five octaves), the ~~sharp~~ version would be a respectable ~~mapping for~~ [[~~https://en.xen.wiki/w/Archytas_clan~~#~~Beatles~~\|~~Beatles~~]] (~~as 91bcd~~); while the ~~flat~~ version would be a respectable [[~~Meantone~~]] (~~91c~~) ~~or [[Schismic–Pythagorean_equivalence_continuum#Python~~\|~~Python]] [[patent val]] mapping.~~		If not for the problem of failing to cover the complete gamut (such as on a hypothetical XL-size Lumatone having at least 485 keys within the span of five octaves), the flat version would be a respectable [[Schismic–Pythagorean_equivalence_continuum#Python\|Python]] or [[Meantone]] (91c) mapping, while the sharp version would be a respectable mapping for [[Quasiultra]] (as 91bd).
			{{Lumatone EDO mapping\|n=91\|start=89\|xstep=15\|ystep=-7}}

	{{Lumatone EDO mapping\|n=91\|start=22\|xstep=17\|ystep=-14}}		{{Lumatone EDO mapping\|n=91\|start=22\|xstep=17\|ystep=-14}}


	~~{{Lumatone EDO mapping\|n=91\|start=89\|xstep=15\|ystep=-7}}~~

	== Quartkeenlig-related rank-3 mappings ==		== Quartkeenlig-related rank-3 mappings ==

Lucius Chiaraviglio: Add Bryan Deister's 2 Lumatone mappings for 91edo, along with the obligatory diatonic mappings

2025-06-08T07:54:00Z

Add Bryan Deister's *2* Lumatone mappings for 91edo, along with the obligatory diatonic mappings

New page

There are many conceivable ways to map [[91edo]] onto the onto the Lumatone keyboard. However, the [[Standard Lumatone mapping for Pythagorean]] is unable to cover the full gamut of every octave, with the flat ([[patent val]]) and sharp (b val) versions having many skipped notes.

== Diatonic ==
If not for the problem of failing to cove the complete gamut (such as on a hypothetical XL-size Lumatone having at least 485 keys within the span of five octaves), the sharp version would be a respectable mapping for [[https://en.xen.wiki/w/Archytas_clan#Beatles|Beatles]] (as 91bcd); while the flat version would be a respectable [[Meantone]] (91c) or [[Schismic–Pythagorean_equivalence_continuum#Python|Python]] [[patent val]] mapping.
{{Lumatone EDO mapping|n=91|start=22|xstep=17|ystep=-14}}

{{Lumatone EDO mapping|n=91|start=89|xstep=15|ystep=-7}}

== Quartkeenlig-related rank-3 mappings ==

=== Pseudo-isomorphic ===
[[Bryan Deister]] has demonstrated a pseudo-isomorphic mapping for [[91edo]] in [https://www.youtube.com/shorts/HaYUAg30298 ''microtonal improvisation in 91edo''] (2025). This layout is numbered as for [[92edo]], but note 91 is actually a duplicate of note 0. The range is just one note short of 3 full octaves, with octaves sloping down gently, unlike the fully isomorphic version below, which avoids the interruption from the duplicated note 0 and has slightly greater range, but at the cost of greater (and opposite) octave slope and a vertical wraparound of note 0 with ascending octaves (as well as producing a discontinuity in scales). This mapping has the same generators as the fully isomorphic version, as described below.
{{Lumatone EDO mapping|n=92|start=0|xstep=9|ystep=-4}}

=== Isomorphic ===
[[Bryan Deister]] has demonstrated an isomorphic [[9L 2s]] mapping for [[91edo]] in [https://www.youtube.com/shorts/z6PeEocYMV8 ''improv 91edo''] (2025). The range is just one note beyond 3 full octaves, with octaves sloping up mildly (which results in a wraparound of note 0). The rightward generator 9\91 is the septimal diatonic semitone ~[[15\14]]. The upward generator 4\91 is a quartertone that functions as ~[[32/31]], ~[[33/32]], ~[[34/33]], and ~[[36/35]]; two of them make the minor diatonic semitone ~[[17/16]]; six of them make a near-just minor third ~[[6/5]]. The use of this generator makes this a mapping for [[Quartkeenlig]]; however, since stacking the upward generator quickly leads to wraparounds, and attempting to get the perfect fifth in 91edo with this generator yields 52\91, which is the [[7edo]] (91bb) fifth. Therefore, this mapping really needs to be treated as a rank-3 temperament mapping; for instance, to get the patent fifth 53\92 (a mildly flat ~[[3/2]], almost exactly [[1/7-comma meantone]]), it is easiest to stack five rightward generators and two upward generators.
{{Lumatone EDO mapping|n=91|start=0|xstep=9|ystep=-4}}

{{Navbox Lumatone}}

Lumatone mapping for 91edo - Revision history

Lucius Chiaraviglio: /* Diatonic */ Add demo video for flat fifth version

ArrowHead294 at 13:50, 23 June 2025

ArrowHead294 at 13:50, 23 June 2025

Lucius Chiaraviglio: /* Isomorphic */ Fix typo in ~15/14

Yourmusic Productions: Patent mapping should go first.

Lucius Chiaraviglio: Add Bryan Deister's *2* Lumatone mappings for 91edo, along with the obligatory diatonic mappings

Lucius Chiaraviglio: Add Bryan Deister's 2 Lumatone mappings for 91edo, along with the obligatory diatonic mappings