Lumatone mapping for 52edo - Revision history

Lucius Chiaraviglio: /* Neutral thirds */ Insert Bryan Deister's Porcupine mapping after this

2026-05-03T15:47:36Z

Neutral thirds: Insert Bryan Deister's Porcupine mapping after this

← Older revision		Revision as of 15:47, 3 May 2026
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	The [[Lumatone mapping for neutral thirds scales\|neutral thirds mapping]] is probably easier to navigate.		The [[Lumatone mapping for neutral thirds scales\|neutral thirds mapping]] is probably easier to navigate.
	{{Lumatone EDO mapping\|n=52\|start=43\|xstep=7\|ystep=1}}		{{Lumatone EDO mapping\|n=52\|start=43\|xstep=7\|ystep=1}}

			== Porcupine ==
			[[52edo]] is a valid [[porcupine]] tuning (with scale [[1L 6s]] having a 10:7 step ratio), as [[Bryan Deister]] demonstrates in [https://www.youtube.com/shorts/YMjz4thpjxQ ''52edo jam''] (2026). The range with no missed notes is 4½ octaves, which slope upwards moderately.
			{{Lumatone EDO mapping\|n=52\|start=13\|xstep=7\|ystep=3}}

	== Diminished + Pseudo-Pentacircle ==		== Diminished + Pseudo-Pentacircle ==

Lucius Chiaraviglio: /* Diminished + Mothra */ Actually Pseudo-Mothra

2026-03-31T22:44:29Z

Diminished + Mothra: Actually Pseudo-Mothra

← Older revision		Revision as of 22:44, 31 March 2026
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	{{Lumatone EDO mapping\|n=53\|start=4\|xstep=9\|ystep=-5}}		{{Lumatone EDO mapping\|n=53\|start=4\|xstep=9\|ystep=-5}}

	== Diminished + Mothra ==		== Diminished + Pseudo-Mothra ==
	[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 10\52, as the near-just septimal major second ~[[8/7]] (and three of these yielding the fifth ~[[3/2]]), making this a [[Gamelismic_clan#mothra\|mothra]] ~~mapping~~, but with the [[4L 4s]] scale (10:3 step ratio) and the fact that 52edo tempers out the greater diesis [[648/625]], thereby using a quarter-octave period as in [[Diminished_(temperament)\|diminished]] temperament, without which ~~mothra~~ would otherwise be [[Saturation, torsion, and contorsion\|contorted]] ~~with 52edo~~. Octaves slant downwards (incurring a vertical wraparound), and the compass is 5⅛ octaves, with no missed notes and no repeated notes. This layout is demonstrated in [https://www.youtube.com/shorts/ovA5-YkjxWk ''52edo groove''] (2026); in the video, some notes are cut off at the left and right edges due to the use of only 2 MIDI channels.		[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 10\52, as the near-just septimal major second ~[[8/7]] (and three of these yielding the fifth ~[[3/2]]), making this a [[gamelismic clan]] mapping similar to [[Gamelismic_clan#mothra\|mothra]], but much simpler in obtaining the classic major third ~[[5/4]] at 4 generators instead of 12 (which would be the case in real mothra), and with the [[4L 4s]] scale (10:3 step ratio) and the fact that 52edo tempers out the greater diesis [[648/625]], thereby using a quarter-octave period as in [[Diminished_(temperament)\|diminished]] temperament, without which the temperament would otherwise be [[Saturation, torsion, and contorsion\|contorted]] (the quarter-octave period is required to wrap the generator stack properly). Octaves slant downwards (incurring a vertical wraparound), and the compass is 5⅛ octaves, with no missed notes and no repeated notes. This layout is demonstrated in [https://www.youtube.com/shorts/ovA5-YkjxWk ''52edo groove''] (2026); in the video, some notes are cut off at the left and right edges due to the use of only 2 MIDI channels.
	{{Lumatone EDO mapping\|n=52\|start=4\|xstep=10\|ystep=-7}}		{{Lumatone EDO mapping\|n=52\|start=4\|xstep=10\|ystep=-7}}

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

Lucius Chiaraviglio: /* Diminished + Mothra */ Accidentally left out a piece of the description

2026-03-31T12:09:26Z

Diminished + Mothra: Accidentally left out a piece of the description

← Older revision		Revision as of 12:09, 31 March 2026
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	== Diminished + Mothra ==		== Diminished + Mothra ==
	[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 10\52, as the near-just septimal major second ~[[8/7]], making this a [[Gamelismic_clan#mothra\|mothra]] mapping, but with the [[4L 4s]] scale (10:3 step ratio) and the fact that 52edo tempers out the greater diesis [[648/625]], thereby using a quarter-octave period as in [[Diminished_(temperament)\|diminished]] temperament, without which mothra would otherwise be [[Saturation, torsion, and contorsion\|contorted]] with 52edo. Octaves slant downwards (incurring a vertical wraparound), and the compass is 5⅛ octaves, with no missed notes and no repeated notes. This layout is demonstrated in [https://www.youtube.com/shorts/ovA5-YkjxWk ''52edo groove''] (2026); in the video, some notes are cut off at the left and right edges due to the use of only 2 MIDI channels.		[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 10\52, as the near-just septimal major second ~[[8/7]] (and three of these yielding the fifth ~[[3/2]]), making this a [[Gamelismic_clan#mothra\|mothra]] mapping, but with the [[4L 4s]] scale (10:3 step ratio) and the fact that 52edo tempers out the greater diesis [[648/625]], thereby using a quarter-octave period as in [[Diminished_(temperament)\|diminished]] temperament, without which mothra would otherwise be [[Saturation, torsion, and contorsion\|contorted]] with 52edo. Octaves slant downwards (incurring a vertical wraparound), and the compass is 5⅛ octaves, with no missed notes and no repeated notes. This layout is demonstrated in [https://www.youtube.com/shorts/ovA5-YkjxWk ''52edo groove''] (2026); in the video, some notes are cut off at the left and right edges due to the use of only 2 MIDI channels.
	{{Lumatone EDO mapping\|n=52\|start=4\|xstep=10\|ystep=-7}}		{{Lumatone EDO mapping\|n=52\|start=4\|xstep=10\|ystep=-7}}

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

Lucius Chiaraviglio: /* Diminished + Pseudo-Pentacircle */ Insert Bryan Deister's Diminished + Mothra after this

2026-03-31T12:06:57Z

Diminished + Pseudo-Pentacircle: Insert Bryan Deister's Diminished + Mothra after this

← Older revision		Revision as of 12:06, 31 March 2026
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	A version of the above that duplicates note 0 (as note 52, as if making a layout for [[53edo]]) keeps the octaves level. This is demonstrated in [[Bryan Deister]]'s [https://www.youtube.com/shorts/PgSsSM5pJcM ''52edo improv''] (2025).		A version of the above that duplicates note 0 (as note 52, as if making a layout for [[53edo]]) keeps the octaves level. This is demonstrated in [[Bryan Deister]]'s [https://www.youtube.com/shorts/PgSsSM5pJcM ''52edo improv''] (2025).
	{{Lumatone EDO mapping\|n=53\|start=4\|xstep=9\|ystep=-5}}		{{Lumatone EDO mapping\|n=53\|start=4\|xstep=9\|ystep=-5}}

			== Diminished + Mothra ==
			[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 10\52, as the near-just septimal major second ~[[8/7]], making this a [[Gamelismic_clan#mothra\|mothra]] mapping, but with the [[4L 4s]] scale (10:3 step ratio) and the fact that 52edo tempers out the greater diesis [[648/625]], thereby using a quarter-octave period as in [[Diminished_(temperament)\|diminished]] temperament, without which mothra would otherwise be [[Saturation, torsion, and contorsion\|contorted]] with 52edo. Octaves slant downwards (incurring a vertical wraparound), and the compass is 5⅛ octaves, with no missed notes and no repeated notes. This layout is demonstrated in [https://www.youtube.com/shorts/ovA5-YkjxWk ''52edo groove''] (2026); in the video, some notes are cut off at the left and right edges due to the use of only 2 MIDI channels.
			{{Lumatone EDO mapping\|n=52\|start=4\|xstep=10\|ystep=-7}}

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

Lucius Chiaraviglio: /* Pseudo-Pentacircle */ Add Diminished temperament

2026-03-28T12:11:56Z

Pseudo-Pentacircle: Add Diminished temperament

← Older revision		Revision as of 12:11, 28 March 2026
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	{{Lumatone EDO mapping\|n=52\|start=43\|xstep=7\|ystep=1}}		{{Lumatone EDO mapping\|n=52\|start=43\|xstep=7\|ystep=1}}

	== Pseudo-Pentacircle ==		== Diminished + Pseudo-Pentacircle ==
	[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 9\52, as ~[[9/8]] but mapped by direct approximation rather than as the version mapped by the patent val or by the 52b val, which means that it has to be constituted as {{nowrap\|(3♭ × 3♯) / 8}} to make use of the dual-fifth feature of 52edo. Two of these map to a ~[[14/11]] major third, as in [[Pentacircle clan\|~~Pentacircle~~]] but for the direct approximation mapping of ~9/8. The upward generator is ~[[16/15]]. Octaves slant down and then wrap around, but the compass is 5 full octaves, with no missed notes, which is competitive with the Diatonic and Neutral Thirds layouts. This layout is demonstrated in [https://www.youtube.com/shorts/lNJCZz7EjL0 ''microtonal improvisation in 52edo''] (2025); in the video, some notes are cut off at the right edge due to the use of only 2 MIDI channels.		[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 9\52, as ~[[9/8]] but mapped by direct approximation rather than as the version mapped by the patent val or by the 52b val, which means that it has to be constituted as {{nowrap\|(3♭ × 3♯) / 8}} to make use of the dual-fifth feature of 52edo. Two of these map to a ~[[14/11]] major third, as in [[Pentacircle clan\|pentacircle]] but for the direct approximation mapping of ~9/8. The upward generator is ~[[16/15]]. In addition, this mapping makes a [[4L 4s]] scale with 9:4 step ratio easily accessible (barring a vertical wraparound), and 52edo tempers out the greater diesis [[648/625]], making this also a [[Diminished_(temperament)\|diminished]] mapping. Octaves slant down and then wrap around, but the compass is 5 full octaves, with no missed notes, which is competitive with the Diatonic and Neutral Thirds layouts. This layout is demonstrated in [https://www.youtube.com/shorts/lNJCZz7EjL0 ''microtonal improvisation in 52edo''] (2025); in the video, some notes are cut off at the right edge due to the use of only 2 MIDI channels.
	{{Lumatone EDO mapping\|n=52\|start=4\|xstep=9\|ystep=-5}}		{{Lumatone EDO mapping\|n=52\|start=4\|xstep=9\|ystep=-5}}

ArrowHead294 at 22:57, 20 January 2026

2026-01-20T22:57:55Z

← Older revision		Revision as of 22:57, 20 January 2026
Line 2:		Line 2:

	== Diatonic ==		== Diatonic ==
	You can use the b val, which produces [[~~Syntonic–diatonic_equivalence_continuum~~#Dirt\|Dirt]], but the fifth is extremely sharp, to the point where major seconds become [[8/7]] instead of [[9/8]] and the best approximation to [[5/4]] is a doubly augmented 7th.		You can use the b val, which produces [[Syntonic–diatonic equivalence continuum#Dirt\|Dirt]], but the fifth is extremely sharp, to the point where major seconds become [[8/7]] instead of [[9/8]] and the best approximation to [[5/4]] is a doubly augmented 7th.
	{{Lumatone EDO mapping\|n=52\|start=16\|xstep=10\|ystep=-9}}		{{Lumatone EDO mapping\|n=52\|start=16\|xstep=10\|ystep=-9}}

Lucius Chiaraviglio: /* Pseudo-Pentacircle */ Add pseudo-isomorphic version of this

2025-09-27T07:21:36Z

Pseudo-Pentacircle: Add pseudo-isomorphic version of this

← Older revision		Revision as of 07:21, 27 September 2025
Line 12:		Line 12:
	[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 9\52, as ~[[9/8]] but mapped by direct approximation rather than as the version mapped by the patent val or by the 52b val, which means that it has to be constituted as {{nowrap\|(3♭ × 3♯) / 8}} to make use of the dual-fifth feature of 52edo. Two of these map to a ~[[14/11]] major third, as in [[Pentacircle clan\|Pentacircle]] but for the direct approximation mapping of ~9/8. The upward generator is ~[[16/15]]. Octaves slant down and then wrap around, but the compass is 5 full octaves, with no missed notes, which is competitive with the Diatonic and Neutral Thirds layouts. This layout is demonstrated in [https://www.youtube.com/shorts/lNJCZz7EjL0 ''microtonal improvisation in 52edo''] (2025); in the video, some notes are cut off at the right edge due to the use of only 2 MIDI channels.		[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 9\52, as ~[[9/8]] but mapped by direct approximation rather than as the version mapped by the patent val or by the 52b val, which means that it has to be constituted as {{nowrap\|(3♭ × 3♯) / 8}} to make use of the dual-fifth feature of 52edo. Two of these map to a ~[[14/11]] major third, as in [[Pentacircle clan\|Pentacircle]] but for the direct approximation mapping of ~9/8. The upward generator is ~[[16/15]]. Octaves slant down and then wrap around, but the compass is 5 full octaves, with no missed notes, which is competitive with the Diatonic and Neutral Thirds layouts. This layout is demonstrated in [https://www.youtube.com/shorts/lNJCZz7EjL0 ''microtonal improvisation in 52edo''] (2025); in the video, some notes are cut off at the right edge due to the use of only 2 MIDI channels.
	{{Lumatone EDO mapping\|n=52\|start=4\|xstep=9\|ystep=-5}}		{{Lumatone EDO mapping\|n=52\|start=4\|xstep=9\|ystep=-5}}

			A version of the above that duplicates note 0 (as note 52, as if making a layout for [[53edo]]) keeps the octaves level. This is demonstrated in [[Bryan Deister]]'s [https://www.youtube.com/shorts/PgSsSM5pJcM ''52edo improv''] (2025).
			{{Lumatone EDO mapping\|n=53\|start=4\|xstep=9\|ystep=-5}}

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

Yourmusic Productions: Wrong 5-limit extension. Dirt, not ultrapyth.

2025-05-14T12:43:44Z

Wrong 5-limit extension. Dirt, not ultrapyth.

← Older revision		Revision as of 12:43, 14 May 2025
Line 2:		Line 2:

	== Diatonic ==		== Diatonic ==
	You can use the b~~ ~~val, which ~~gives~~ [[~~ultrapyth~~]], but the fifth is extremely sharp, to the point where major seconds become 8/7 instead of 9/8.		You can use the b val, which produces [[Syntonic–diatonic_equivalence_continuum#Dirt\|Dirt]], but the fifth is extremely sharp, to the point where major seconds become [[8/7]] instead of [[9/8]] and the best approximation to [[5/4]] is a doubly augmented 7th.
	{{Lumatone EDO mapping\|n=52\|start=16\|xstep=10\|ystep=-9}}		{{Lumatone EDO mapping\|n=52\|start=16\|xstep=10\|ystep=-9}}

ArrowHead294 at 11:55, 14 May 2025

2025-05-14T11:55:10Z

← Older revision		Revision as of 11:55, 14 May 2025
Line 2:		Line 2:

	== Diatonic ==		== Diatonic ==
	You can use the b val, but it is extremely sharp, to the point where major seconds become 8/7 instead of 9/8~~. This gives [[ultrapyth]]~~.		You can use the b val, which gives [[ultrapyth]], but the fifth is extremely sharp, to the point where major seconds become 8/7 instead of 9/8.
	{{Lumatone EDO mapping\|n=52\|start=16\|xstep=10\|ystep=-9}}		{{Lumatone EDO mapping\|n=52\|start=16\|xstep=10\|ystep=-9}}

Line 10:		Line 10:

	== Pseudo-Pentacircle ==		== Pseudo-Pentacircle ==
			[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 9\52, as ~[[9/8]] but mapped by direct approximation rather than as the version mapped by the patent val or by the 52b val, which means that it has to be constituted as {{nowrap\|(3♭ × 3♯) / 8}} to make use of the dual-fifth feature of 52edo. Two of these map to a ~[[14/11]] major third, as in [[Pentacircle clan\|Pentacircle]] but for the direct approximation mapping of ~9/8. The upward generator is ~[[16/15]]. Octaves slant down and then wrap around, but the compass is 5 full octaves, with no missed notes, which is competitive with the Diatonic and Neutral Thirds layouts. This layout is demonstrated in [https://www.youtube.com/shorts/lNJCZz7EjL0 ''microtonal improvisation in 52edo''] (2025); in the video, some notes are cut off at the right edge due to the use of only 2 MIDI channels.
	[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 9\52, as ~[[9/8]] but mapped by direct approximation rather than as the version mapped by the patent val or by the 52b val, which means that it has to be constituted as (3♭~~ ~~×~~ ~~3♯)~~ ~~/~~ ~~8 to make use of the dual-fifth feature of 52edo. Two of these map to a ~[[14/11]] major third, as in [[Pentacircle clan\|Pentacircle]] but for the direct approximation mapping of ~9/8. The upward generator is ~[[16/15]]. Octaves slant down and then wrap around, but the compass is 5 full octaves, with no missed notes, which is competitive with the Diatonic and Neutral Thirds layouts. This layout is demonstrated in [https://www.youtube.com/shorts/lNJCZz7EjL0 ''microtonal improvisation in 52edo''] (2025); in the video, some notes are cut off at the right edge due to the use of only 2 MIDI channels.

	{{Lumatone EDO mapping\|n=52\|start=4\|xstep=9\|ystep=-5}}		{{Lumatone EDO mapping\|n=52\|start=4\|xstep=9\|ystep=-5}}

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

Lucius Chiaraviglio: Add Bryan Deister's Pseudo-Pentacircle 52edo mapping

2025-05-06T06:29:38Z

Add Bryan Deister's Pseudo-Pentacircle 52edo mapping

← Older revision		Revision as of 06:29, 6 May 2025
Line 8:		Line 8:
	The [[Lumatone mapping for neutral thirds scales\|neutral thirds mapping]] is probably easier to navigate.		The [[Lumatone mapping for neutral thirds scales\|neutral thirds mapping]] is probably easier to navigate.
	{{Lumatone EDO mapping\|n=52\|start=43\|xstep=7\|ystep=1}}		{{Lumatone EDO mapping\|n=52\|start=43\|xstep=7\|ystep=1}}

			== Pseudo-Pentacircle ==

			[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 9\52, as ~[[9/8]] but mapped by direct approximation rather than as the version mapped by the patent val or by the 52b val, which means that it has to be constituted as (3♭ × 3♯) / 8 to make use of the dual-fifth feature of 52edo. Two of these map to a ~[[14/11]] major third, as in [[Pentacircle clan\|Pentacircle]] but for the direct approximation mapping of ~9/8. The upward generator is ~[[16/15]]. Octaves slant down and then wrap around, but the compass is 5 full octaves, with no missed notes, which is competitive with the Diatonic and Neutral Thirds layouts. This layout is demonstrated in [https://www.youtube.com/shorts/lNJCZz7EjL0 ''microtonal improvisation in 52edo''] (2025); in the video, some notes are cut off at the right edge due to the use of only 2 MIDI channels.

			{{Lumatone EDO mapping\|n=52\|start=4\|xstep=9\|ystep=-5}}

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