Lumatone mapping for 78edo - Revision history

Lucius Chiaraviglio: /* Unnamed rank-3 temperament mapping */ Fix typo

2025-07-10T17:32:15Z

Unnamed rank-3 temperament mapping: Fix typo

← Older revision		Revision as of 17:32, 10 July 2025
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	== Unnamed rank-3 temperament mapping ==		== Unnamed rank-3 temperament mapping ==

	[[Bryan Deister]]] has demonsrated a Lumatone mapping for [[78edo]] that lays out scales [[11L 1s]] (7:1 step ratio) and [[6L 6s]] (7:6 step ratio), in [https://www.youtube.com/shorts/jxYRAo6jHaE ''microtonal improvisation in 78edo''] (2025). The rightward generator 7\78 is slightly sharp large septendecimal semitone ~[[17/16]]; two of them make a slightly flat biyatismic whole tone ~[[17/15]]; and six of them readh a slightly flat undecimal minor fifth ~[[16/11]]. The down-right generator 6\78 is a somewhat sharp small undevicesimal semitone ~[[20/19]]; stacking these can yield both a slightly sharp undecimal major fourth ~[[11/8]] (as 36\78, six generators) and slightly flat undecimal minor fifth ~16/11 (as 42\78, seven down-right generators, same as six rightward generators). The range is somewhat under three octaves, with all notes represented; octaves alternate between far and near, with an overall upwards slant.		[[Bryan Deister]] has demonsrated a Lumatone mapping for [[78edo]] that lays out scales [[11L 1s]] (7:1 step ratio) and [[6L 6s]] (7:6 step ratio), in [https://www.youtube.com/shorts/jxYRAo6jHaE ''microtonal improvisation in 78edo''] (2025). The rightward generator 7\78 is slightly sharp large septendecimal semitone ~[[17/16]]; two of them make a slightly flat biyatismic whole tone ~[[17/15]]; and six of them readh a slightly flat undecimal minor fifth ~[[16/11]]. The down-right generator 6\78 is a somewhat sharp small undevicesimal semitone ~[[20/19]]; stacking these can yield both a slightly sharp undecimal major fourth ~[[11/8]] (as 36\78, six generators) and slightly flat undecimal minor fifth ~16/11 (as 42\78, seven down-right generators, same as six rightward generators). The range is somewhat under three octaves, with all notes represented; octaves alternate between far and near, with an overall upwards slant.
	{{Lumatone EDO mapping\|n=78\|start=61\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=78\|start=61\|xstep=7\|ystep=-1}}

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

Lucius Chiaraviglio: Add Bryan Deister's Lumatone mapping for 78edo

2025-07-03T07:56:46Z

Add Bryan Deister's Lumatone mapping for 78edo

← Older revision		Revision as of 07:56, 3 July 2025
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	The [[7L 3s]] neutral thirds mapping also covers the whole gamut about as efficiently as possible and keeps octaves closer to horizontal.		The [[7L 3s]] neutral thirds mapping also covers the whole gamut about as efficiently as possible and keeps octaves closer to horizontal.
	{{Lumatone EDO mapping\|n=78\|start=76\|xstep=9\|ystep=-4}}		{{Lumatone EDO mapping\|n=78\|start=76\|xstep=9\|ystep=-4}}

			== Unnamed rank-3 temperament mapping ==

			[[Bryan Deister]]] has demonsrated a Lumatone mapping for [[78edo]] that lays out scales [[11L 1s]] (7:1 step ratio) and [[6L 6s]] (7:6 step ratio), in [https://www.youtube.com/shorts/jxYRAo6jHaE ''microtonal improvisation in 78edo''] (2025). The rightward generator 7\78 is slightly sharp large septendecimal semitone ~[[17/16]]; two of them make a slightly flat biyatismic whole tone ~[[17/15]]; and six of them readh a slightly flat undecimal minor fifth ~[[16/11]]. The down-right generator 6\78 is a somewhat sharp small undevicesimal semitone ~[[20/19]]; stacking these can yield both a slightly sharp undecimal major fourth ~[[11/8]] (as 36\78, six generators) and slightly flat undecimal minor fifth ~16/11 (as 42\78, seven down-right generators, same as six rightward generators). The range is somewhat under three octaves, with all notes represented; octaves alternate between far and near, with an overall upwards slant.
			{{Lumatone EDO mapping\|n=78\|start=61\|xstep=7\|ystep=-1}}

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

ArrowHead294 at 15:30, 23 March 2025

2025-03-23T15:30:58Z

← Older revision		Revision as of 15:30, 23 March 2025
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	There are many conceivable ways to map [[78edo]] onto the onto the Lumatone keyboard. However, since it has 2 mutually-exclusive rings of [[39edo]] fifths, the [[Standard Lumatone mapping for Pythagorean]] is not one of them. The second best 5th produces three mutually-exclusive rings of [[26edo]] 5ths, so that doesn't work either, and the third ~~& 4th~~ best are out of the diatonic tuning range. On the other hand, the [[keen]] mapping can cover the whole gamut and make harmonics easy to play together, although it needs to be expanded from [[2L 8s]] to [[10L 2s]] to hit every ~~single~~ note.		There are many conceivable ways to map [[78edo]] onto the onto the Lumatone keyboard. However, since it has 2 mutually-exclusive rings of [[39edo]] fifths, the [[Standard Lumatone mapping for Pythagorean]] is not one of them. The second best 5th produces three mutually-exclusive rings of [[26edo]] 5ths, so that doesn't work either, and the third and fourth best are out of the diatonic tuning range.

			== Keen ==
			On the other hand, the [[keen]] mapping can cover the whole gamut and make harmonics easy to play together, although it needs to be expanded from [[2L 8s]] to [[10L 2s]] to hit every note.
	{{Lumatone EDO mapping\|n=78\|start=33\|xstep=7\|ystep=4}}		{{Lumatone EDO mapping\|n=78\|start=33\|xstep=7\|ystep=4}}


	{{Lumatone EDO mapping\|n=78\|start=71\|xstep=7\|ystep=-3}}		{{Lumatone EDO mapping\|n=78\|start=71\|xstep=7\|ystep=-3}}

	The [[7L 3s]] neutral thirds mapping also covers the whole gamut about as efficiently as possible and keeps octaves closer to horizontal.		== Neutral thirds ==
			The [[7L 3s]] neutral thirds mapping also covers the whole gamut about as efficiently as possible and keeps octaves closer to horizontal.
	{{Lumatone EDO mapping\|n=78\|start=76\|xstep=9\|ystep=-4}}		{{Lumatone EDO mapping\|n=78\|start=76\|xstep=9\|ystep=-4}}

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

Yourmusic Productions: Create Page.

2025-03-23T11:55:23Z

Create Page.

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There are many conceivable ways to map [[78edo]] onto the onto the Lumatone keyboard. However, since it has 2 mutually-exclusive rings of [[39edo]] fifths, the [[Standard Lumatone mapping for Pythagorean]] is not one of them. The second best 5th produces three mutually-exclusive rings of [[26edo]] 5ths, so that doesn't work either, and the third & 4th best are out of the diatonic tuning range. On the other hand, the [[keen]] mapping can cover the whole gamut and make harmonics easy to play together, although it needs to be expanded from [[2L 8s]] to [[10L 2s]] to hit every single note.
{{Lumatone EDO mapping|n=78|start=33|xstep=7|ystep=4}}
{{Lumatone EDO mapping|n=78|start=71|xstep=7|ystep=-3}}

The [[7L 3s]] neutral thirds mapping also covers the whole gamut about as efficiently as possible and keeps octaves closer to horizontal.
{{Lumatone EDO mapping|n=78|start=76|xstep=9|ystep=-4}}

{{Navbox Lumatone}}