Lumatone mapping for 48edo - Revision history

Lucius Chiaraviglio: /* Negri-related 8th-octave temperament */ → 8th octave temperament with rotated Negri; fix punctuation and a typo

2026-10-27T18:51:17Z

Negri-related 8th-octave temperament: → 8th octave temperament with rotated Negri; fix punctuation and a typo

← Older revision		Revision as of 18:51, 27 October 2026
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	{{Lumatone EDO mapping\|n=48\|start=7\|xstep=9\|ystep=-8}}		{{Lumatone EDO mapping\|n=48\|start=7\|xstep=9\|ystep=-8}}

	== ~~Negri-related~~ 8th-octave temperament ==		== 8th-octave temperament with rotated Negri ==
	[[Bryan Deister]] has demonstrated an [[8th-octave_temperaments\|8th-octave temperament]] mapping for [[48edo]], in [https://www.youtube.com/watch?v=UgngKVswJfI ''48edo improv''] (2026). This temperament equates the near-just Alpharabian tendoneutral second ~[[12/11]] (one key right, as 6\48) to 1/8 of an octave — the [[undecimal octatonic comma]] 214990848/214358881 is tempered out. Supported scales include [[6L 6s]] (5:1 step ratio) and rotated [[3L 3s]] (11:5 step ratio). Following the reverse chroma 5\48 downwards, which maps as a very sharp classic diatonic semitone ~[[16/15]], and bypassing the 8th-octave period, one gets the sharp approximation of the septimal major second ~[[8/7]] (requires using the 48d val) at two of these; the flat but consistent approximation of the classic major third ~[[5/4]] at three of these; and the near-just fourth ~[[4/3]] at four of these, thereby making this also a rotated [[negri]] mapping. Octaves slope up with the rows; the range is 4½ octaves, with a few repeated notes to mitigate vertical ~~wraprounds~~.		[[Bryan Deister]] has demonstrated an [[8th-octave_temperaments\|8th-octave temperament]] mapping for [[48edo]], in [https://www.youtube.com/watch?v=UgngKVswJfI ''48edo improv''] (2026). This temperament equates the near-just Alpharabian tendoneutral second ~[[12/11]] (one key right, as 6\48) to 1/8 of an octave — the [[undecimal octatonic comma]] 214990848/214358881 is tempered out. Supported scales include [[6L 6s]] (5:1 step ratio) and rotated [[3L 3s]] (11:5 step ratio). Following the reverse chroma 5\48 downwards, which maps as a very sharp classic diatonic semitone ~[[16/15]], and bypassing the 8th-octave period, one gets the sharp approximation of the septimal major second ~[[8/7]] (requires using the 48d val) at two of these, the flat but consistent approximation of the classic major third ~[[5/4]] at three of these, and the near-just fourth ~[[4/3]] at four of these, thereby making this also a rotated [[negri]] mapping. Octaves slope up with the rows; the range is 4½ octaves, with a few repeated notes to mitigate vertical wraparounds.
	{{Lumatone EDO mapping\|n=48\|start=42\|xstep=6\|ystep=5}}		{{Lumatone EDO mapping\|n=48\|start=42\|xstep=6\|ystep=5}}

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

Lucius Chiaraviglio: /* Other mappings */ Insert Bryan Deister's Negri-related 8th-octave temperament mapping after this

2026-10-27T18:46:57Z

Other mappings: Insert Bryan Deister's Negri-related 8th-octave temperament mapping after this

← Older revision		Revision as of 18:46, 27 October 2026
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	== Other mappings ==		== Other mappings ==
	There are three other mappings that reach the perfect fifth in 4 generator steps that might also be useful. These are the [[Negri]], [[Squares]], and [[Buzzard]] mappings.		There are three other mappings that reach the perfect fourth or fifth in 4 generator steps that might also be useful. These are the [[Negri]], [[Squares]], and [[Buzzard]] mappings.

	=== Negri ===		=== Negri ===
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	=== Buzzard ===		=== Buzzard ===
	{{Lumatone EDO mapping\|n=48\|start=7\|xstep=9\|ystep=-8}}		{{Lumatone EDO mapping\|n=48\|start=7\|xstep=9\|ystep=-8}}

			== Negri-related 8th-octave temperament ==
			[[Bryan Deister]] has demonstrated an [[8th-octave_temperaments\|8th-octave temperament]] mapping for [[48edo]], in [https://www.youtube.com/watch?v=UgngKVswJfI ''48edo improv''] (2026). This temperament equates the near-just Alpharabian tendoneutral second ~[[12/11]] (one key right, as 6\48) to 1/8 of an octave — the [[undecimal octatonic comma]] 214990848/214358881 is tempered out. Supported scales include [[6L 6s]] (5:1 step ratio) and rotated [[3L 3s]] (11:5 step ratio). Following the reverse chroma 5\48 downwards, which maps as a very sharp classic diatonic semitone ~[[16/15]], and bypassing the 8th-octave period, one gets the sharp approximation of the septimal major second ~[[8/7]] (requires using the 48d val) at two of these; the flat but consistent approximation of the classic major third ~[[5/4]] at three of these; and the near-just fourth ~[[4/3]] at four of these, thereby making this also a rotated [[negri]] mapping. Octaves slope up with the rows; the range is 4½ octaves, with a few repeated notes to mitigate vertical wraprounds.
			{{Lumatone EDO mapping\|n=48\|start=42\|xstep=6\|ystep=5}}

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

Yourmusic Productions: Went through all the temperaments and this is actually the one that makes simple ratios easiest to play together.

2025-04-30T18:16:34Z

Went through all the temperaments and this is actually the one that makes simple ratios easiest to play together.

← Older revision		Revision as of 18:16, 30 April 2025
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	[[Bryan Deister]] demonstrates this layout (albeit with range restricted to 1 MIDI channel) in [https://www.youtube.com/shorts/w1m9PMj0Ato ''48edo layout''] (2025).		[[Bryan Deister]] demonstrates this layout (albeit with range restricted to 1 MIDI channel) in [https://www.youtube.com/shorts/w1m9PMj0Ato ''48edo layout''] (2025).
	{{Lumatone EDO mapping\|n=48\|start=33\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=48\|start=33\|xstep=7\|ystep=-1}}

			== Doublewide ==
			If you don't mind skipping the occasional step, the [[doublewide]] mapping expands your range and is particularly efficient at spanning the 11-limit.
			{{Lumatone EDO mapping\|n=48\|start=5\|xstep=11\|ystep=-9}}

	== Other mappings ==		== Other mappings ==

ArrowHead294 at 17:26, 16 April 2025

2025-04-16T17:26:20Z

← Older revision		Revision as of 17:26, 16 April 2025
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	== Tetracot ==		== Tetracot ==
	If you want an evenly distributed heptatonic scale that gives easy access to the perfect 5th, you instead need to use the [[Tetracot]] mapping, which is probably the most efficient and intuitive way of organising its intervals. Though, the [[7L 6s]] MOS has a 6:1 step ratio, making it very lopsided. [[Bryan Deister]] demonstrates this layout (albeit with range restricted to 1 MIDI channel) in [https://www.youtube.com/shorts/w1m9PMj0Ato ''48edo layout''] (2025).		If you want an evenly distributed heptatonic scale that gives easy access to the perfect 5th, you instead need to use the [[Tetracot]] mapping, which is probably the most efficient and intuitive way of organising its intervals. Though, the [[7L 6s]] MOS has a 6:1 step ratio, making it very lopsided.

			[[Bryan Deister]] demonstrates this layout (albeit with range restricted to 1 MIDI channel) in [https://www.youtube.com/shorts/w1m9PMj0Ato ''48edo layout''] (2025).
	{{Lumatone EDO mapping\|n=48\|start=33\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=48\|start=33\|xstep=7\|ystep=-1}}

Lucius Chiaraviglio: /* Tetracot */ Add link to Bryan Deister's demonstration video

2025-04-13T07:28:02Z

Tetracot: Add link to Bryan Deister's demonstration video

← Older revision		Revision as of 07:28, 13 April 2025
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	== Tetracot ==		== Tetracot ==
	If you want an evenly distributed heptatonic scale that gives easy access to the perfect 5th, you instead need to use the [[Tetracot]] mapping, which is probably the most efficient and intuitive way of organising its intervals. Though, the [[7L 6s]] MOS has a 6:1 step ratio, making it very lopsided.		If you want an evenly distributed heptatonic scale that gives easy access to the perfect 5th, you instead need to use the [[Tetracot]] mapping, which is probably the most efficient and intuitive way of organising its intervals. Though, the [[7L 6s]] MOS has a 6:1 step ratio, making it very lopsided. [[Bryan Deister]] demonstrates this layout (albeit with range restricted to 1 MIDI channel) in [https://www.youtube.com/shorts/w1m9PMj0Ato ''48edo layout''] (2025).
	{{Lumatone EDO mapping\|n=48\|start=33\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=48\|start=33\|xstep=7\|ystep=-1}}

Lucius Chiaraviglio: /* Other mappings */ Fix typo

2025-04-13T06:55:32Z

Other mappings: Fix typo

← Older revision		Revision as of 06:55, 13 April 2025
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	== Other mappings ==		== Other mappings ==
	There are three other mappings that reach the perfect ~~fith~~ in 4 generator steps that might also be useful. These are the [[Negri]], [[Squares]], and [[Buzzard]] mappings.		There are three other mappings that reach the perfect fifth in 4 generator steps that might also be useful. These are the [[Negri]], [[Squares]], and [[Buzzard]] mappings.

	=== Negri ===		=== Negri ===

ArrowHead294 at 15:19, 23 March 2025

2025-03-23T15:19:35Z

← Older revision		Revision as of 15:19, 23 March 2025
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	{{Lumatone mapping intro}} If you want an evenly distributed heptatonic scale that gives easy access to the perfect 5th, you instead need to use the [[~~tetracot~~]] mapping, which is probably the most efficient and intuitive way of organising its intervals. Though the [[7L 6s]] MOS has a 6:1 step ratio, making it very lopsided.		{{Lumatone mapping intro}}

			== Tetracot ==
			If you want an evenly distributed heptatonic scale that gives easy access to the perfect 5th, you instead need to use the [[Tetracot]] mapping, which is probably the most efficient and intuitive way of organising its intervals. Though, the [[7L 6s]] MOS has a 6:1 step ratio, making it very lopsided.
	{{Lumatone EDO mapping\|n=48\|start=33\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=48\|start=33\|xstep=7\|ystep=-1}}

			== Other mappings ==
			There are three other mappings that reach the perfect fith in 4 generator steps that might also be useful. These are the [[Negri]], [[Squares]], and [[Buzzard]] mappings.

	~~There are three other mappings that reach the perfect fith in 4 generator steps that might also be useful. These are the [[~~Negri~~]] mapping~~		=== Negri ===
	{{Lumatone EDO mapping\|n=48\|start=4\|xstep=5\|ystep=3}}		{{Lumatone EDO mapping\|n=48\|start=4\|xstep=5\|ystep=3}}

			=== Squares ===
	~~The [[~~Squares~~]] mapping~~
	{{Lumatone EDO mapping\|n=48\|start=29\|xstep=3\|ystep=8}}		{{Lumatone EDO mapping\|n=48\|start=29\|xstep=3\|ystep=8}}

			=== Buzzard ===
	~~And the [[~~Buzzard~~]] mapping.~~
	{{Lumatone EDO mapping\|n=48\|start=7\|xstep=9\|ystep=-8}}		{{Lumatone EDO mapping\|n=48\|start=7\|xstep=9\|ystep=-8}}

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

ArrowHead294 at 18:26, 14 March 2025

2025-03-14T18:26:50Z

← Older revision		Revision as of 18:26, 14 March 2025
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	~~There are many conceivable ways to map [[48edo]] onto the [[Lumatone]] keyboard. Unfortunately, as it has multiple rings of 5ths, the [[Standard~~ Lumatone mapping ~~for Pythagorean]] is not one of them. Since it is [[Highly_composite_equal_division\|highly composite]], many other mappings will also fail to cover the entire gamut.~~ If you want an evenly distributed heptatonic scale that gives easy access to the perfect 5th, you instead need to use the [[tetracot]] mapping, which is probably the most efficient and intuitive way of organising its intervals.		{{Lumatone mapping intro}} If you want an evenly distributed heptatonic scale that gives easy access to the perfect 5th, you instead need to use the [[tetracot]] mapping, which is probably the most efficient and intuitive way of organising its intervals. Though the [[7L 6s]] MOS has a 6:1 step ratio, making it very lopsided.
	{{Lumatone EDO mapping\|n=48\|start=33\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=48\|start=33\|xstep=7\|ystep=-1}}


	There are three other mappings that reach the perfect ~~5th~~ in 4 generator steps that might also be useful. These are the [[Negri]] mapping		There are three other mappings that reach the perfect fith in 4 generator steps that might also be useful. These are the [[Negri]] mapping
	{{Lumatone EDO mapping\|n=48\|start=4\|xstep=5\|ystep=3}}		{{Lumatone EDO mapping\|n=48\|start=4\|xstep=5\|ystep=3}}

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	Or the [[Buzzard]] mapping.		And the [[Buzzard]] mapping.
	{{Lumatone EDO mapping\|n=48\|start=7\|xstep=9\|ystep=-8}}		{{Lumatone EDO mapping\|n=48\|start=7\|xstep=9\|ystep=-8}}

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

ArrowHead294 at 16:55, 11 February 2025

2025-02-11T16:55:15Z

← Older revision		Revision as of 16:55, 11 February 2025
Line 1:		Line 1:
	There are many conceivable ways to map [[48edo]] onto the [[Lumatone]] keyboard. Unfortunately, as it has multiple rings of 5ths, the [[Standard Lumatone mapping for Pythagorean]] is not one of them. Since it is [[Highly_composite_equal_division\|highly composite]], many other mappings will also fail to cover the entire gamut. If you want an evenly distributed heptatonic scale that gives easy access to the perfect 5th, you instead need to use the [[tetracot]] mapping, which is probably the most efficient and intuitive way of organising its intervals.		There are many conceivable ways to map [[48edo]] onto the [[Lumatone]] keyboard. Unfortunately, as it has multiple rings of 5ths, the [[Standard Lumatone mapping for Pythagorean]] is not one of them. Since it is [[Highly_composite_equal_division\|highly composite]], many other mappings will also fail to cover the entire gamut. If you want an evenly distributed heptatonic scale that gives easy access to the perfect 5th, you instead need to use the [[tetracot]] mapping, which is probably the most efficient and intuitive way of organising its intervals.
	{{Lumatone EDO mapping\|n=48\|start=33\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=48\|start=33\|xstep=7\|ystep=-1}}


	There are three other mappings that reach the perfect 5th in 4 generator steps that might also be useful. These are the [[Negri]] mapping		There are three other mappings that reach the perfect 5th in 4 generator steps that might also be useful. These are the [[Negri]] mapping
	{{Lumatone EDO mapping\|n=48\|start=4\|xstep=5\|ystep=3}}		{{Lumatone EDO mapping\|n=48\|start=4\|xstep=5\|ystep=3}}


	The [[Squares]] mapping		The [[Squares]] mapping
	{{Lumatone EDO mapping\|n=48\|start=29\|xstep=3\|ystep=8}}		{{Lumatone EDO mapping\|n=48\|start=29\|xstep=3\|ystep=8}}


	Or the [[Buzzard]] mapping.		Or the [[Buzzard]] mapping.
	{{Lumatone EDO mapping\|n=48\|start=7\|xstep=9\|ystep=-8}}		{{Lumatone EDO mapping\|n=48\|start=7\|xstep=9\|ystep=-8}}

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

BudjarnLambeth at 01:32, 17 November 2024

2024-11-17T01:32:28Z

← Older revision		Revision as of 01:32, 17 November 2024
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	Or the [[Buzzard]] mapping.		Or the [[Buzzard]] mapping.
	{{Lumatone EDO mapping\|n=48\|start=7\|xstep=9\|ystep=-8}}		{{Lumatone EDO mapping\|n=48\|start=7\|xstep=9\|ystep=-8}}
	~~[[Category:~~Lumatone ~~mappings]] [[Category:48edo]]~~
			{{Lumatone mapping navigation}}