Lumatone mapping for 36edo - Revision history

Lucius Chiaraviglio: /* Baladic */ Insert Bryan Deister's Niner + Diminished after this

2026-06-26T18:51:33Z

Baladic: Insert Bryan Deister's Niner + Diminished after this

← Older revision		Revision as of 18:51, 26 June 2026
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	Another good option is the [[4L 2s]] [[Baladic]] mapping, which divides the octave in two to add easily accessible ratios of 13 & 17 to slendrics 2.3.7 subgroup and keeps octaves near horizontal, while keeping the less well tuned ratios of 5 and 11 distant from one-another.		Another good option is the [[4L 2s]] [[Baladic]] mapping, which divides the octave in two to add easily accessible ratios of 13 & 17 to slendrics 2.3.7 subgroup and keeps octaves near horizontal, while keeping the less well tuned ratios of 5 and 11 distant from one-another.
	{{Lumatone EDO mapping\|n=36\|start=34\|xstep=7\|ystep=-3}}		{{Lumatone EDO mapping\|n=36\|start=34\|xstep=7\|ystep=-3}}

			== Niner + Diminished ==
			It is possible to use the [[blackwood]] + [[whitewood]] mappings of [[35edo]] as inspiration for mapping [[36edo]] as a lattice, using its factors of closest size to those of 35edo, which are 4 and 9, as in [[niner]] + [[Diminished_(temperament)\|diminished]] temperaments, with a [[4L 4s]] scale of step ratio 5:4 running right and down. Similarly to blackwood and whitewood, the octaves slope upwards with the rows, but even so the mapping works to give 5 octaves with some repeated notes to mitigate vertical wraparounds, with no missed notes except for one missed note 35 in the top otherwise contiguous octave. [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/KCtEYSkEK8U ''36edo improv''] (2026).
			{{Lumatone EDO mapping\|n=36\|start=2\|xstep=4\|ystep=5}}

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

Yourmusic Productions: /* 5L 1s (7:1 step ratio, large reverse chroma, down-right-divided octave) */ fix spelling mistake.

2026-01-04T13:00:29Z

5L 1s (7:1 step ratio, large reverse chroma, down-right-divided octave): fix spelling mistake.

← Older revision		Revision as of 13:00, 4 January 2026
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	=== 5L 1s (7:1 step ratio, large reverse chroma, down-right-divided octave) ===		=== 5L 1s (7:1 step ratio, large reverse chroma, down-right-divided octave) ===
	The [[5L 1s]] (7:1 step ratio, upside-down scale) large reverse chroma mapping uses a slightly larger but very hard scale to compact the standard diatonic scale into two strings of single-step movements (although still rotated from the ~~custmoary~~ orientation), while also making offset strings of [[6edo]] into compact down-right key sequences, thereby dividing each octave into six parts, which may be useful for playing divided-octave temperaments. However, this makes fingerings for many chords somewhat awkward while putting octaves all over the place.		The [[5L 1s]] (7:1 step ratio, upside-down scale) large reverse chroma mapping uses a slightly larger but very hard scale to compact the standard diatonic scale into two strings of single-step movements (although still rotated from the customary orientation), while also making offset strings of [[6edo]] into compact down-right key sequences, thereby dividing each octave into six parts, which may be useful for playing divided-octave temperaments. However, this makes fingerings for many chords somewhat awkward while putting octaves all over the place.
	{{Lumatone EDO mapping\|n=36\|start=21\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=36\|start=21\|xstep=7\|ystep=-1}}

Lucius Chiaraviglio: /* Squirrel */ Make wording consistent with that for other demo video

2025-11-09T22:45:40Z

Squirrel: Make wording consistent with that for other demo video

← Older revision		Revision as of 22:45, 9 November 2025
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	== Squirrel ==		== Squirrel ==
	If you want an evenly distributed heptatonic scale that gives easy access to the perfect fifth, you instead need to use the [[Squirrel]] mapping. [[Bryan Deister]] ~~demonstrates~~ this mapping in [https://www.youtube.com/shorts/3la1W-_-ceA ''36edo cowbell''] (2025).		If you want an evenly distributed heptatonic scale that gives easy access to the perfect fifth, you instead need to use the [[Squirrel]] mapping. [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/shorts/3la1W-_-ceA ''36edo cowbell''] (2025).
	{{Lumatone EDO mapping\|n=36\|start=15\|xstep=5\|ystep=1}}		{{Lumatone EDO mapping\|n=36\|start=15\|xstep=5\|ystep=1}}

Lucius Chiaraviglio: /* Squirrel */ Added demo video

2025-11-09T22:44:37Z

Squirrel: Added demo video

← Older revision		Revision as of 22:44, 9 November 2025
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	== Squirrel ==		== Squirrel ==
	If you want an evenly distributed heptatonic scale that gives easy access to the perfect fifth, you instead need to use the [[Squirrel]] mapping.		If you want an evenly distributed heptatonic scale that gives easy access to the perfect fifth, you instead need to use the [[Squirrel]] mapping. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/3la1W-_-ceA ''36edo cowbell''] (2025).
	{{Lumatone EDO mapping\|n=36\|start=15\|xstep=5\|ystep=1}}		{{Lumatone EDO mapping\|n=36\|start=15\|xstep=5\|ystep=1}}

Yourmusic Productions: Fix math error, expansion on what baladic is good at.

2025-08-19T11:25:02Z

Fix math error, expansion on what baladic is good at.

← Older revision		Revision as of 11:25, 19 August 2025
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	{{Lumatone EDO mapping\|n=36\|start=9\|xstep=7\|ystep=-6}}		{{Lumatone EDO mapping\|n=36\|start=9\|xstep=7\|ystep=-6}}

	== ~~Echidnic~~ ==		== Baladic ==
	Another option is the [[6L 4s]] [[~~Echidnic~~]] mapping:		Another good option is the [[4L 2s]] [[Baladic]] mapping, which divides the octave in two to add easily accessible ratios of 13 & 17 to slendrics 2.3.7 subgroup and keeps octaves near horizontal, while keeping the less well tuned ratios of 5 and 11 distant from one-another.
	{{Lumatone EDO mapping\|n=36\|start=34\|xstep=7\|ystep=-3}}		{{Lumatone EDO mapping\|n=36\|start=34\|xstep=7\|ystep=-3}}

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

Lucius Chiaraviglio: /* Slendric */ Put link to 5L 1s scale in the right place

2025-08-10T21:55:01Z

Slendric: Put link to 5L 1s scale in the right place

← Older revision		Revision as of 21:55, 10 August 2025
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	=== 5L 1s (7:1 step ratio, large reverse chroma, down-right-divided octave) ===		=== 5L 1s (7:1 step ratio, large reverse chroma, down-right-divided octave) ===
	The 5L 1s (7:1 step ratio, upside-down scale) large reverse chroma mapping uses a slightly larger but very hard scale to compact the standard diatonic scale into two strings of single-step movements (although still rotated from the custmoary orientation), while also making offset strings of [[6edo]] into compact down-right key sequences, thereby dividing each octave into six parts, which may be useful for playing divided-octave temperaments. However, this makes fingerings for many chords somewhat awkward while putting octaves all over the place.		The [[5L 1s]] (7:1 step ratio, upside-down scale) large reverse chroma mapping uses a slightly larger but very hard scale to compact the standard diatonic scale into two strings of single-step movements (although still rotated from the custmoary orientation), while also making offset strings of [[6edo]] into compact down-right key sequences, thereby dividing each octave into six parts, which may be useful for playing divided-octave temperaments. However, this makes fingerings for many chords somewhat awkward while putting octaves all over the place.
	{{Lumatone EDO mapping\|n=36\|start=21\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=36\|start=21\|xstep=7\|ystep=-1}}

	=== 5L 1s (7:1 step ratio, large forward chroma, up-divided octave) ===		=== 5L 1s (7:1 step ratio, large forward chroma, up-divided octave) ===
	A [[5L 1s]] (7:1 step ratio, large forward chroma) version of the Slendric mapping uses a large chroma (thus making a very hard version of this scale), and achieves octaves that only slope up moderately (but more than in the 1L 4s mapping) while still having the notes of the standard diatonic scale still easily accessible, although still rotated from their customary orientation. Offset strings of 6edo are now compact upwards key sequences, which may still be useful for playing divided-octave temperaments, although more likely to pass through a vertical wrapround than in the reverse-chroma 5L 1s mapping. [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/watch?v=psvrsa10-Wo ''36edo jam''] (2025)].		A 5L 1s (7:1 step ratio, large forward chroma) version of the Slendric mapping uses a large chroma (thus making a very hard version of this scale), and achieves octaves that only slope up moderately (but more than in the 1L 4s mapping) while still having the notes of the standard diatonic scale still easily accessible, although still rotated from their customary orientation. Offset strings of 6edo are now compact upwards key sequences, which may still be useful for playing divided-octave temperaments, although more likely to pass through a vertical wrapround than in the reverse-chroma 5L 1s mapping. [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/watch?v=psvrsa10-Wo ''36edo jam''] (2025)].
	{{Lumatone EDO mapping\|n=36\|start=9\|xstep=7\|ystep=-6}}		{{Lumatone EDO mapping\|n=36\|start=9\|xstep=7\|ystep=-6}}

Lucius Chiaraviglio: /* Slendric */ Reorganize; add temperament and ergonomics description; add Bryan Deister's version (including link to demo video)

2025-08-10T21:53:21Z

Slendric: Reorganize; add temperament and ergonomics description; add Bryan Deister's version (including link to demo video)

← Older revision		Revision as of 21:53, 10 August 2025
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	== Slendric ==		== Slendric ==
	However, since 36edo works best as a 7-limit system, ~~the~~ [[Slendric]] ~~mapping is~~ probably preferable, since it most efficiently takes advantage of the very accurate 3 and 7 while also spanning the widest range that allows access to the full gamut at the same time.		However, since 36edo works best as a 7-limit system, [[Slendric]] mappings are probably preferable, since it most efficiently takes advantage of the very accurate 3 and 7 while also spanning the widest range that allows access to the full gamut at the same time. Slendric mappings use the very accurate (just slightly sharp) septimal whole tone ~[[8/7]] as the generator, and three of these make the very accurate (just slightly flat) fifth ~[[3/2]] (the gamelisma [[1029/1024]] being tempered out). This achieves a range a bit over six octaves with no missing notes and some repeated notes to mitigate vertical wraparounds.

			=== 1L 4s (8:7 step ratio, small reverse chroma) ===
			The [[1L 4s]] (8:7 step ratio) small reverse chroma mapping uses a small soft scale to get the most level (just slightly rising) octaves, but spreads out the notes of the standard diatonic scale (although accessing them is still intuitive although rotated), although the reverse chroma may be counterintuitive for many users.
	{{Lumatone EDO mapping\|n=36\|start=9\|xstep=7\|ystep=1}}		{{Lumatone EDO mapping\|n=36\|start=9\|xstep=7\|ystep=1}}

			=== 5L 1s (7:1 step ratio, large reverse chroma, down-right-divided octave) ===
			The 5L 1s (7:1 step ratio, upside-down scale) large reverse chroma mapping uses a slightly larger but very hard scale to compact the standard diatonic scale into two strings of single-step movements (although still rotated from the custmoary orientation), while also making offset strings of [[6edo]] into compact down-right key sequences, thereby dividing each octave into six parts, which may be useful for playing divided-octave temperaments. However, this makes fingerings for many chords somewhat awkward while putting octaves all over the place.
			{{Lumatone EDO mapping\|n=36\|start=21\|xstep=7\|ystep=-1}}

	~~Reversing~~ the ~~direction~~ of the ~~chroma makes~~ the diatonic scale ~~easier to play~~, ~~but makes fingerings~~ for ~~many chords somewhat awkward while putting octaves all over~~ the ~~place~~.		=== 5L 1s (7:1 step ratio, large forward chroma, up-divided octave) ===
	{{Lumatone EDO mapping\|n=36\|start=21\|xstep=7\|ystep=-1}}		A [[5L 1s]] (7:1 step ratio, large forward chroma) version of the Slendric mapping uses a large chroma (thus making a very hard version of this scale), and achieves octaves that only slope up moderately (but more than in the 1L 4s mapping) while still having the notes of the standard diatonic scale still easily accessible, although still rotated from their customary orientation. Offset strings of 6edo are now compact upwards key sequences, which may still be useful for playing divided-octave temperaments, although more likely to pass through a vertical wrapround than in the reverse-chroma 5L 1s mapping. [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/watch?v=psvrsa10-Wo ''36edo jam''] (2025)].
			{{Lumatone EDO mapping\|n=36\|start=9\|xstep=7\|ystep=-6}}

	== Echidnic ==		== Echidnic ==

ArrowHead294 at 15:05, 23 March 2025

2025-03-23T15:05:02Z

← Older revision		Revision as of 15:05, 23 March 2025
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	{{Lumatone mapping intro}} (This includes both the second and third best alternative fifths.)		{{Lumatone mapping intro}} (This includes both the second and third best alternative fifths.)

	If you want an evenly distributed heptatonic scale that gives easy access to the perfect fifth, you instead need to use the [[~~squirrel~~]] mapping.		== Squirrel ==
			If you want an evenly distributed heptatonic scale that gives easy access to the perfect fifth, you instead need to use the [[Squirrel]] mapping.
	{{Lumatone EDO mapping\|n=36\|start=15\|xstep=5\|ystep=1}}		{{Lumatone EDO mapping\|n=36\|start=15\|xstep=5\|ystep=1}}

			== Liese (Triton) ==
	The [[Liese]] mapping also provides a heptatonic scale which reaches the fifth in three steps, and keeps octaves horizontal, but is very lopsided.		The [[Liese]] mapping also provides a heptatonic scale which reaches the fifth in three steps, and keeps octaves horizontal, but is very lopsided.
	{{Lumatone EDO mapping\|n=36\|start=24\|xstep=2\|ystep=11}}		{{Lumatone EDO mapping\|n=36\|start=24\|xstep=2\|ystep=11}}

			== Slendric ==
	However, since 36edo works best as a 7-limit system, the [[~~slendric~~]] mapping is probably preferable, since it most efficiently takes advantage of the very accurate 3 and 7 while also spanning the widest range that allows access to the full gamut at the same time.		However, since 36edo works best as a 7-limit system, the [[Slendric]] mapping is probably preferable, since it most efficiently takes advantage of the very accurate 3 and 7 while also spanning the widest range that allows access to the full gamut at the same time.
	{{Lumatone EDO mapping\|n=36\|start=9\|xstep=7\|ystep=1}}		{{Lumatone EDO mapping\|n=36\|start=9\|xstep=7\|ystep=1}}

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	{{Lumatone EDO mapping\|n=36\|start=21\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=36\|start=21\|xstep=7\|ystep=-1}}

			== Echidnic ==
	Another option is the [[6L 4s]] [[Echidnic]] mapping:		Another option is the [[6L 4s]] [[Echidnic]] mapping:
	{{Lumatone EDO mapping\|n=36\|start=34\|xstep=7\|ystep=-3}}		{{Lumatone EDO mapping\|n=36\|start=34\|xstep=7\|ystep=-3}}

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

ArrowHead294 at 17:33, 14 March 2025

2025-03-14T17:33:40Z

← Older revision		Revision as of 17:33, 14 March 2025
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	~~There are many conceivable ways to map [[36edo]] 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, including~~ both the second and third best alternative ~~5ths~~. If you want an evenly distributed heptatonic scale that gives easy access to the perfect fifth, you instead need to use the [[squirrel]] mapping.		{{Lumatone mapping intro}} (This includes both the second and third best alternative fifths.)

			If you want an evenly distributed heptatonic scale that gives easy access to the perfect fifth, you instead need to use the [[squirrel]] mapping.
	{{Lumatone EDO mapping\|n=36\|start=15\|xstep=5\|ystep=1}}		{{Lumatone EDO mapping\|n=36\|start=15\|xstep=5\|ystep=1}}

ArrowHead294 at 19:09, 23 January 2025

2025-01-23T19:09:06Z

← Older revision		Revision as of 19:09, 23 January 2025
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	{{Lumatone EDO mapping\|n=36\|start=21\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=36\|start=21\|xstep=7\|ystep=-1}}

	{{Lumatone mapping ~~navigation~~}}
			Another option is the [[6L 4s]] [[Echidnic]] mapping:
			{{Lumatone EDO mapping\|n=36\|start=34\|xstep=7\|ystep=-3}}

			{{Navbox Lumatone}}