Lumatone mapping for 51edo - Revision history

Lucius Chiaraviglio: /* Porcupine */ Add Bryan Deister's flipped version

2026-08-25T05:55:29Z

Porcupine: Add Bryan Deister's flipped version

← Older revision		Revision as of 05:55, 25 August 2026
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	However, the [[Porky]] mapping is probably more intuitive to people used to using a heptatonic scale and simple 5-limit ratios in chords. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/Fymg9vYO6iQ ''Northernlight - Deltarune (microtonal cover in 51edo)''] (2025).		However, the [[Porky]] mapping is probably more intuitive to people used to using a heptatonic scale and simple 5-limit ratios in chords. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/Fymg9vYO6iQ ''Northernlight - Deltarune (microtonal cover in 51edo)''] (2025).
	{{Lumatone EDO mapping\|n=51\|start=11\|xstep=7\|ystep=2}}		{{Lumatone EDO mapping\|n=51\|start=11\|xstep=7\|ystep=2}}

			=== Flipped version ===
			The flipped [[porcupine]] ([[porky]]) mapping demonstrated in [[Bryan Deister]]'s [https://www.youtube.com/shorts/-ZFMDsE8jy4 ''51edo groove''] (2026) increases the octave slope and decreases the range (to just over four octaves) relative to the normal mapping for this temperament, but might be needed for easy reach to certain chords.
			{{Lumatone EDO mapping\|n=51\|start=22\|xstep=7\|ystep=-9}}

	== Checkertonic/Flipped Superdiatonic with Porky Generator ==		== Checkertonic/Flipped Superdiatonic with Porky Generator ==

Lucius Chiaraviglio: /* Checkertonic/Flipped Superdiatonic with Porky Generator */ Insert Bryan Deister's Tritikleismic-related 2.3.25.7 subgroup temperament mapping after this

2026-05-30T02:07:22Z

Checkertonic/Flipped Superdiatonic with Porky Generator: Insert Bryan Deister's Tritikleismic-related 2.3.25.7 subgroup temperament mapping after this

← Older revision		Revision as of 02:07, 30 May 2026
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	[[Bryan Deister]] has demonstrated a mapping of [[51edo]] for a [[3L 5s]] scale rotated (checkertonic, with 7:6 step ratio), that also lends itself to a [[7L 2s]] scale (flipped superdiatonic, with 7:1 step ratio) and a [[12L 3s (4/1-equivalent)]] scale (7:6 step ratio, passing right through the octave zigzag), in [https://www.youtube.com/shorts/sTPJtuHUwkg ''51edo improv''] (2025-02-03). The rightward generator is 7\51, which is a near-just large undecimal neutral second ~[[11/10]], as in [[Porky]], but this mapping is sufficiently different from the Porky layout as to warrant a different name. The range is a bit over 4¼ octaves, and the octaves alternate between near/far and mid.		[[Bryan Deister]] has demonstrated a mapping of [[51edo]] for a [[3L 5s]] scale rotated (checkertonic, with 7:6 step ratio), that also lends itself to a [[7L 2s]] scale (flipped superdiatonic, with 7:1 step ratio) and a [[12L 3s (4/1-equivalent)]] scale (7:6 step ratio, passing right through the octave zigzag), in [https://www.youtube.com/shorts/sTPJtuHUwkg ''51edo improv''] (2025-02-03). The rightward generator is 7\51, which is a near-just large undecimal neutral second ~[[11/10]], as in [[Porky]], but this mapping is sufficiently different from the Porky layout as to warrant a different name. The range is a bit over 4¼ octaves, and the octaves alternate between near/far and mid.
	{{Lumatone EDO mapping\|n=51\|start=31\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=51\|start=31\|xstep=7\|ystep=-1}}

			== Tritikleismic-related 2.3.25.7 subgroup temperament ==
			One way of treating [[51edo]] is as three versions of [[17edo]], rearranged so as to divide the fifth and the octave also into three parts each, as demonstrated by [[Bryan Deister]] in [https://www.youtube.com/watch?v=k3NOBYbiqpo ''51edo improv''] (2026-04-22). This is very much like [[landscape]] temperament in equating the octave with a stack of three near-just quasi-tempered major thirds (~[[63/50]], as 17\51), but requires use of the 2.3.25.7 subgroup; division of the fifth (~[[3/2]], as 30\51) into three parts (slightly sharp septimal major seconds ~[[8/7]], as 10\51) also puts this temperament in the [[gamelismic clan]] (thus related to [[tritikleismic]], but again using the 2.3.25.7 subgroup). The obvious scale moving up and right is [[3L 3s]] (10:7 step ratio); the obvious scale moving right and down-right is [[9L 4s (4/1-equivalent)]] (10:3 step ratio); the upward and downward movements in the latter scale nearly cancel out so that while octaves alternate between far and near, double octaves just barely slope down. The range is 5¼ octaves with no missed notes and no repeated notes.
			{{Lumatone EDO mapping\|n=51\|start=4\|xstep=10\|ystep=-7}}

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

Lucius Chiaraviglio: /* Antidiatonic */ Fix a couple of mistakes in the description

2026-05-28T04:05:08Z

Antidiatonic: Fix a couple of mistakes in the description

← Older revision		Revision as of 04:05, 28 May 2026
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	{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}		{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}

	[[Bryan Deister]] has used a flipped antidiatonic layout for [[51edo]] in which the generator is a mid major second at 8\51, which maps in between ~[[10/9]] and ~[[9/8]] and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~[[512/459]] (~\|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a ~~slightly~~ flat ~[[5/4]] Ptolemeic major third, and nine of these generators make a slightly sharp ~[[8/3]] perfect eleventh. Octaves alternate between near and far, but the range is just one missing note #47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic ([[Mavila]]/[[Undecimation]]) and [[Porky]] mappings, and is competitive with the [[Slendric]] mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is [[2L 5s]] with a step ratio of 8:7, but the octave zigzag could be used to support an [[11L 2s (4/1-equivalent)]] scale, again with a step ratio of 8:7. [https://x31eq.com/temper-pyscript/ Graham Breed's x31eq Temperament Finder] gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to [[19edo]], L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025-05-02), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.		[[Bryan Deister]] has used a flipped antidiatonic layout for [[51edo]] in which the generator is a mid major second at 8\51, which maps in between ~[[10/9]] and ~[[9/8]] and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~[[512/459]] (~\|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a fairly flat ~[[5/4]] Ptolemeic major third, and nine of these generators make a slightly sharp ~[[8/3]] perfect eleventh. Octaves alternate between near and far, but the range is just one missing note 47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic ([[Mavila]]/[[Undecimation]]) and [[Porky]] mappings, and is competitive with the [[Slendric]] mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is [[2L 5s]] with a step ratio of 8:7, but the octave zigzag could be used to support an [[11L 2s (4/1-equivalent)]] scale, again with a step ratio of 8:7. [https://x31eq.com/temper-pyscript/ Graham Breed's x31eq Temperament Finder] gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to [[19edo]], L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025-05-02), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.

	{{Lumatone EDO mapping\|n=51\|start=32\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=51\|start=32\|xstep=8\|ystep=-1}}

Lucius Chiaraviglio: /* Porcupine */ Add Bryan Deister's mapping Checkertonic/Flipped Superdiatonic with Porky Generator

2026-01-03T09:29:25Z

Porcupine: Add Bryan Deister's mapping Checkertonic/Flipped Superdiatonic with Porky Generator

← Older revision		Revision as of 09:29, 3 January 2026
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	However, the [[Porky]] mapping is probably more intuitive to people used to using a heptatonic scale and simple 5-limit ratios in chords. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/Fymg9vYO6iQ ''Northernlight - Deltarune (microtonal cover in 51edo)''] (2025).		However, the [[Porky]] mapping is probably more intuitive to people used to using a heptatonic scale and simple 5-limit ratios in chords. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/Fymg9vYO6iQ ''Northernlight - Deltarune (microtonal cover in 51edo)''] (2025).
	{{Lumatone EDO mapping\|n=51\|start=11\|xstep=7\|ystep=2}}		{{Lumatone EDO mapping\|n=51\|start=11\|xstep=7\|ystep=2}}

			== Checkertonic/Flipped Superdiatonic with Porky Generator ==
			[[Bryan Deister]] has demonstrated a mapping of [[51edo]] for a [[3L 5s]] scale rotated (checkertonic, with 7:6 step ratio), that also lends itself to a [[7L 2s]] scale (flipped superdiatonic, with 7:1 step ratio) and a [[12L 3s (4/1-equivalent)]] scale (7:6 step ratio, passing right through the octave zigzag), in [https://www.youtube.com/shorts/sTPJtuHUwkg ''51edo improv''] (2025-02-03). The rightward generator is 7\51, which is a near-just large undecimal neutral second ~[[11/10]], as in [[Porky]], but this mapping is sufficiently different from the Porky layout as to warrant a different name. The range is a bit over 4¼ octaves, and the octaves alternate between near/far and mid.
			{{Lumatone EDO mapping\|n=51\|start=31\|xstep=7\|ystep=-1}}

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

Lucius Chiaraviglio: /* Porcupine */ Add demo video, and move note 0 right one key to get a complete first octave (as actually done in the demo video)

2026-01-03T08:55:49Z

Porcupine: Add demo video, and move note 0 right one key to get a complete first octave (as actually done in the demo video)

← Older revision		Revision as of 08:55, 3 January 2026
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	== Porcupine ==		== Porcupine ==
	However, the [[Porky]] mapping is probably more intuitive to people used to using a heptatonic scale and simple 5-limit ratios in chords.		However, the [[Porky]] mapping is probably more intuitive to people used to using a heptatonic scale and simple 5-limit ratios in chords. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/Fymg9vYO6iQ ''Northernlight - Deltarune (microtonal cover in 51edo)''] (2025).
	{{Lumatone EDO mapping\|n=51\|start=18\|xstep=7\|ystep=2}}		{{Lumatone EDO mapping\|n=51\|start=11\|xstep=7\|ystep=2}}

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

Lucius Chiaraviglio: /* Antidiatonic */ Distinguish the demo video from another one having the same name and creator

2026-01-01T10:10:34Z

Antidiatonic: Distinguish the demo video from another one having the same name and creator

← Older revision		Revision as of 10:10, 1 January 2026
Line 5:		Line 5:
	{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}		{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}

	[[Bryan Deister]] has used a flipped antidiatonic layout for [[51edo]] in which the generator is a mid major second at 8\51, which maps in between ~[[10/9]] and ~[[9/8]] and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~[[512/459]] (~\|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a slightly flat ~[[5/4]] Ptolemeic major third, and nine of these generators make a slightly sharp ~[[8/3]] perfect eleventh. Octaves alternate between near and far, but the range is just one missing note #47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic ([[Mavila]]/[[Undecimation]]) and [[Porky]] mappings, and is competitive with the [[Slendric]] mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is [[2L 5s]] with a step ratio of 8:7, but the octave zigzag could be used to support an [[11L 2s (4/1-equivalent)]] scale, again with a step ratio of 8:7. [https://x31eq.com/temper-pyscript/ Graham Breed's x31eq Temperament Finder] gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to [[19edo]], L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.		[[Bryan Deister]] has used a flipped antidiatonic layout for [[51edo]] in which the generator is a mid major second at 8\51, which maps in between ~[[10/9]] and ~[[9/8]] and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~[[512/459]] (~\|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a slightly flat ~[[5/4]] Ptolemeic major third, and nine of these generators make a slightly sharp ~[[8/3]] perfect eleventh. Octaves alternate between near and far, but the range is just one missing note #47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic ([[Mavila]]/[[Undecimation]]) and [[Porky]] mappings, and is competitive with the [[Slendric]] mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is [[2L 5s]] with a step ratio of 8:7, but the octave zigzag could be used to support an [[11L 2s (4/1-equivalent)]] scale, again with a step ratio of 8:7. [https://x31eq.com/temper-pyscript/ Graham Breed's x31eq Temperament Finder] gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to [[19edo]], L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025-05-02), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.

	{{Lumatone EDO mapping\|n=51\|start=32\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=51\|start=32\|xstep=8\|ystep=-1}}

Lucius Chiaraviglio: /* Antidiatonic */ Fix typo

2025-12-17T06:42:05Z

Antidiatonic: Fix typo

← Older revision		Revision as of 06:42, 17 December 2025
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	{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}		{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}

	[[Bryan Deister]] has used a flipped antidiatonic layout for [[51edo]] in which the generator is a mid major second at 8\51, which maps in between ~[[10/9]] and ~[[9/8]] and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~[[512/459]] (~\|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a slightly flat ~[[5/4]] ~~Ptolmeic~~ major third, and nine of these generators make a slightly sharp ~[[8/3]] perfect eleventh. Octaves alternate between near and far, but the range is just one missing note #47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic ([[Mavila]]/[[Undecimation]]) and [[Porky]] mappings, and is competitive with the [[Slendric]] mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is [[2L 5s]] with a step ratio of 8:7, but the octave zigzag could be used to support an [[11L 2s (4/1-equivalent)]] scale, again with a step ratio of 8:7. [https://x31eq.com/temper-pyscript/ Graham Breed's x31eq Temperament Finder] gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to [[19edo]], L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.		[[Bryan Deister]] has used a flipped antidiatonic layout for [[51edo]] in which the generator is a mid major second at 8\51, which maps in between ~[[10/9]] and ~[[9/8]] and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~[[512/459]] (~\|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a slightly flat ~[[5/4]] Ptolemeic major third, and nine of these generators make a slightly sharp ~[[8/3]] perfect eleventh. Octaves alternate between near and far, but the range is just one missing note #47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic ([[Mavila]]/[[Undecimation]]) and [[Porky]] mappings, and is competitive with the [[Slendric]] mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is [[2L 5s]] with a step ratio of 8:7, but the octave zigzag could be used to support an [[11L 2s (4/1-equivalent)]] scale, again with a step ratio of 8:7. [https://x31eq.com/temper-pyscript/ Graham Breed's x31eq Temperament Finder] gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to [[19edo]], L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.

	{{Lumatone EDO mapping\|n=51\|start=32\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=51\|start=32\|xstep=8\|ystep=-1}}

Lucius Chiaraviglio: Add Bryan Deister's flipped Antidiatonic 51edo mapping

2025-05-06T06:25:19Z

Add Bryan Deister's flipped Antidiatonic 51edo mapping

← Older revision		Revision as of 06:25, 6 May 2025
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	You can use the b val, which can be interpreted as either [[mavila]] or [[undecimation]], but is not a particularly great tuning for either.		You can use the b val, which can be interpreted as either [[mavila]] or [[undecimation]], but is not a particularly great tuning for either.
	{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}		{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}

			[[Bryan Deister]] has used a flipped antidiatonic layout for [[51edo]] in which the generator is a mid major second at 8\51, which maps in between ~[[10/9]] and ~[[9/8]] and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~[[512/459]] (~\|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a slightly flat ~[[5/4]] Ptolmeic major third, and nine of these generators make a slightly sharp ~[[8/3]] perfect eleventh. Octaves alternate between near and far, but the range is just one missing note #47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic ([[Mavila]]/[[Undecimation]]) and [[Porky]] mappings, and is competitive with the [[Slendric]] mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is [[2L 5s]] with a step ratio of 8:7, but the octave zigzag could be used to support an [[11L 2s (4/1-equivalent)]] scale, again with a step ratio of 8:7. [https://x31eq.com/temper-pyscript/ Graham Breed's x31eq Temperament Finder] gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to [[19edo]], L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.

			{{Lumatone EDO mapping\|n=51\|start=32\|xstep=8\|ystep=-1}}

	== Slendric ==		== Slendric ==

ArrowHead294 at 15:21, 23 March 2025

2025-03-23T15:21:38Z

← Older revision		Revision as of 15:21, 23 March 2025
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	{{Lumatone mapping intro}} You can use the b val, which can be interpreted as either [[mavila]] or [[undecimation]], but is not a particularly great tuning for either.		{{Lumatone mapping intro}}

			== Antidiatonic ==
			You can use the b val, which can be interpreted as either [[mavila]] or [[undecimation]], but is not a particularly great tuning for either.
	{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}		{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}

			== Slendric ==
	Instead, it is probably better to use one of the mappings that reaches the perfect 5th in three generator steps. Of these, the [[~~slendric~~]] mapping has the greater range.		Instead, it is probably better to use one of the mappings that reaches the perfect 5th in three generator steps. Of these, the [[Slendric]] mapping has the greater range.
	{{Lumatone EDO mapping\|n=51\|start=24\|xstep=10\|ystep=-9}}		{{Lumatone EDO mapping\|n=51\|start=24\|xstep=10\|ystep=-9}}

			== Porcupine ==
	However, the [[~~porky~~]] mapping is probably more intuitive to people used to using a heptatonic scale and simple 5-limit ratios in chords.		However, the [[Porky]] mapping is probably more intuitive to people used to using a heptatonic scale and simple 5-limit ratios in chords.
	{{Lumatone EDO mapping\|n=51\|start=18\|xstep=7\|ystep=2}}		{{Lumatone EDO mapping\|n=51\|start=18\|xstep=7\|ystep=2}}

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

ArrowHead294 at 18:27, 14 March 2025

2025-03-14T18:27:30Z

← Older revision		Revision as of 18:27, 14 March 2025
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	~~There are many conceivable ways to map [[51edo]] onto the [[Lumatone]] keyboard. Unfortunately, as it has multiple rings of 5ths, the [[Standard~~ Lumatone mapping ~~for Pythagorean]] is not one of them.~~ You can use the b val, which can be interpreted as either [[mavila]] or [[undecimation]], but is not a particularly great tuning for either.		{{Lumatone mapping intro}} You can use the b val, which can be interpreted as either [[mavila]] or [[undecimation]], but is not a particularly great tuning for either.
	{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}		{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}

← Older revision		Revision as of 04:05, 28 May 2026
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	{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}		{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}

	[[Bryan Deister]] has used a flipped antidiatonic layout for [[51edo]] in which the generator is a mid major second at 8\51, which maps in between ~[[10/9]] and ~[[9/8]] and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~[[512/459]] (~\|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a ~~slightly~~ flat ~[[5/4]] Ptolemeic major third, and nine of these generators make a slightly sharp ~[[8/3]] perfect eleventh. Octaves alternate between near and far, but the range is just one missing note #47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic ([[Mavila]]/[[Undecimation]]) and [[Porky]] mappings, and is competitive with the [[Slendric]] mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is [[2L 5s]] with a step ratio of 8:7, but the octave zigzag could be used to support an [[11L 2s (4/1-equivalent)]] scale, again with a step ratio of 8:7. [https://x31eq.com/temper-pyscript/ Graham Breed's x31eq Temperament Finder] gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to [[19edo]], L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025-05-02), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.		[[Bryan Deister]] has used a flipped antidiatonic layout for [[51edo]] in which the generator is a mid major second at 8\51, which maps in between ~[[10/9]] and ~[[9/8]] and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~[[512/459]] (~\|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a fairly flat ~[[5/4]] Ptolemeic major third, and nine of these generators make a slightly sharp ~[[8/3]] perfect eleventh. Octaves alternate between near and far, but the range is just one missing note 47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic ([[Mavila]]/[[Undecimation]]) and [[Porky]] mappings, and is competitive with the [[Slendric]] mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is [[2L 5s]] with a step ratio of 8:7, but the octave zigzag could be used to support an [[11L 2s (4/1-equivalent)]] scale, again with a step ratio of 8:7. [https://x31eq.com/temper-pyscript/ Graham Breed's x31eq Temperament Finder] gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to [[19edo]], L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025-05-02), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.

	{{Lumatone EDO mapping\|n=51\|start=32\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=51\|start=32\|xstep=8\|ystep=-1}}

← Older revision		Revision as of 10:10, 1 January 2026
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	{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}		{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}

	[[Bryan Deister]] has used a flipped antidiatonic layout for [[51edo]] in which the generator is a mid major second at 8\51, which maps in between ~[[10/9]] and ~[[9/8]] and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~[[512/459]] (~\|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a slightly flat ~[[5/4]] Ptolemeic major third, and nine of these generators make a slightly sharp ~[[8/3]] perfect eleventh. Octaves alternate between near and far, but the range is just one missing note #47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic ([[Mavila]]/[[Undecimation]]) and [[Porky]] mappings, and is competitive with the [[Slendric]] mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is [[2L 5s]] with a step ratio of 8:7, but the octave zigzag could be used to support an [[11L 2s (4/1-equivalent)]] scale, again with a step ratio of 8:7. [https://x31eq.com/temper-pyscript/ Graham Breed's x31eq Temperament Finder] gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to [[19edo]], L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.		[[Bryan Deister]] has used a flipped antidiatonic layout for [[51edo]] in which the generator is a mid major second at 8\51, which maps in between ~[[10/9]] and ~[[9/8]] and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~[[512/459]] (~\|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a slightly flat ~[[5/4]] Ptolemeic major third, and nine of these generators make a slightly sharp ~[[8/3]] perfect eleventh. Octaves alternate between near and far, but the range is just one missing note #47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic ([[Mavila]]/[[Undecimation]]) and [[Porky]] mappings, and is competitive with the [[Slendric]] mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is [[2L 5s]] with a step ratio of 8:7, but the octave zigzag could be used to support an [[11L 2s (4/1-equivalent)]] scale, again with a step ratio of 8:7. [https://x31eq.com/temper-pyscript/ Graham Breed's x31eq Temperament Finder] gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to [[19edo]], L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025-05-02), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.

	{{Lumatone EDO mapping\|n=51\|start=32\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=51\|start=32\|xstep=8\|ystep=-1}}

← Older revision		Revision as of 06:42, 17 December 2025
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	{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}		{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}

	[[Bryan Deister]] has used a flipped antidiatonic layout for [[51edo]] in which the generator is a mid major second at 8\51, which maps in between ~[[10/9]] and ~[[9/8]] and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~[[512/459]] (~\|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a slightly flat ~[[5/4]] ~~Ptolmeic~~ major third, and nine of these generators make a slightly sharp ~[[8/3]] perfect eleventh. Octaves alternate between near and far, but the range is just one missing note #47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic ([[Mavila]]/[[Undecimation]]) and [[Porky]] mappings, and is competitive with the [[Slendric]] mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is [[2L 5s]] with a step ratio of 8:7, but the octave zigzag could be used to support an [[11L 2s (4/1-equivalent)]] scale, again with a step ratio of 8:7. [https://x31eq.com/temper-pyscript/ Graham Breed's x31eq Temperament Finder] gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to [[19edo]], L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.		[[Bryan Deister]] has used a flipped antidiatonic layout for [[51edo]] in which the generator is a mid major second at 8\51, which maps in between ~[[10/9]] and ~[[9/8]] and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~[[512/459]] (~\|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a slightly flat ~[[5/4]] Ptolemeic major third, and nine of these generators make a slightly sharp ~[[8/3]] perfect eleventh. Octaves alternate between near and far, but the range is just one missing note #47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic ([[Mavila]]/[[Undecimation]]) and [[Porky]] mappings, and is competitive with the [[Slendric]] mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is [[2L 5s]] with a step ratio of 8:7, but the octave zigzag could be used to support an [[11L 2s (4/1-equivalent)]] scale, again with a step ratio of 8:7. [https://x31eq.com/temper-pyscript/ Graham Breed's x31eq Temperament Finder] gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to [[19edo]], L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.

	{{Lumatone EDO mapping\|n=51\|start=32\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=51\|start=32\|xstep=8\|ystep=-1}}