Lumatone mapping for 51edo - Revision history

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
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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}}

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}}

ArrowHead294 at 16:55, 11 February 2025

2025-02-11T16:55:55Z

← Older revision		Revision as of 16:55, 11 February 2025
Line 1:		Line 1:
	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.		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 EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}		{{Lumatone EDO mapping\|n=51\|start=33\|xstep=7\|ystep=1}}


	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}}


	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}}

	{{Lumatone ~~mapping navigation~~}}		{{Navbox Lumatone}}

← 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}}