Lumatone mapping for 89edo - Revision history

Lucius Chiaraviglio: /* Diatonic */ The diatonic mapping can be used for playing in a very good quasi-meantone — added demo video

2026-04-16T23:14:04Z

Diatonic: The diatonic mapping can be used for playing in a very good quasi-meantone — added demo video

← Older revision		Revision as of 23:14, 16 April 2026
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	== Diatonic ==		== Diatonic ==
	Note that since 89edo is a [[schismatic]] tuning, the best approximation to 5/4 is the diminished fourth.		Note that since 89edo is a [[schismatic]] tuning, the best approximation to ~[[5/4]] is the diminished fourth. That said, since the fifth ~[3/2] is flattened by almost exactly one quarer of Boethius' comma [[513/512]], the meantone major third is almost exactly Boethius' major third ~[[24/19]], and since one third of such a small comma is not very far off from one fourth, the corresponding minor third ~[[19/16]] is also not too far from just. Using 89edo as a quasi-meantone tuning with the extremely accurate ~[[24/19]] substituting for the less accurate ~5/4 will enable many chords to be played despite the missing notes, as demonstrated in [https://www.youtube.com/shorts/mU4KcJd6E7U ''89edo improv''] (2026), and it would be possible to switch between presets for different subsets of 89edo to enable modulation to remote keys.
	{{Lumatone EDO mapping\|n=89\|start=2\|xstep=15\|ystep=-8}}		{{Lumatone EDO mapping\|n=89\|start=2\|xstep=15\|ystep=-8}}

Lucius Chiaraviglio: /* Char-based + Sesquart rank-3 temperament */ Add step ratio

2025-08-03T18:10:09Z

Char-based + Sesquart rank-3 temperament: Add step ratio

← Older revision		Revision as of 18:10, 3 August 2025
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	== Char-based + Sesquart rank-3 temperament ==		== Char-based + Sesquart rank-3 temperament ==
	[[Bryan Deister]] has demonstrated a [[10L 3s]] mapping for [[89edo]] in [https://www.youtube.com/watch?v=2JNIeqvXKlM ''microtonal improvisation in 89edo''] (2025). The rightward generator 8\89 functions as both the [[16/15]] (the classical diatonic semitone) and [[17/16]] (the large septendecimal semitone), meaning that the charisma [[256/255]] is tempered out, although 89edo is not listed as a tuning of any of the temperaments on the page for 256/255. Eight of these generators make a near-just Axirabian paraminor fifth ~[[16/11]]. Although being prime, 89edo technically needs no second generator, a second generator helps with reaching consonant intervals other than ~16/11; one obvious choice is the scale chroma (upwards generator) 5\89 which functions as a somewhat sharp small tridecimal third tone ~[[27/26]]; three of these make a near-just Pythagorean whole tone ~[[9/8]]; four of them make a near-just septimal minor third ~[[7/6]]. It is also possible to combine both generators to get 13\89, a slightly sharp undevicesimal supraneutral second ~[[21/19]]; four of these generator combinations make a near-just fifth ~[[3/2]], as in [[Schismatic_family#Sesquiquartififths\|Sesquiquartififths]] temperament and its higher-limit [[Schismatic_family#Sesquart\|Sesquart]] extension. The range is slightly over 2⅓ octaves with no missed notes and a few repeated notes, and the octaves slope up mildly.		[[Bryan Deister]] has demonstrated a [[10L 3s]] (8:3 step ratio) mapping for [[89edo]] in [https://www.youtube.com/watch?v=2JNIeqvXKlM ''microtonal improvisation in 89edo''] (2025). The rightward generator 8\89 functions as both the [[16/15]] (the classical diatonic semitone) and [[17/16]] (the large septendecimal semitone), meaning that the charisma [[256/255]] is tempered out, although 89edo is not listed as a tuning of any of the temperaments on the page for 256/255. Eight of these generators make a near-just Axirabian paraminor fifth ~[[16/11]]. Although being prime, 89edo technically needs no second generator, a second generator helps with reaching consonant intervals other than ~16/11; one obvious choice is the scale chroma (upwards generator) 5\89 which functions as a somewhat sharp small tridecimal third tone ~[[27/26]]; three of these make a near-just Pythagorean whole tone ~[[9/8]]; four of them make a near-just septimal minor third ~[[7/6]]. It is also possible to combine both generators to get 13\89, a slightly sharp undevicesimal supraneutral second ~[[21/19]]; four of these generator combinations make a near-just fifth ~[[3/2]], as in [[Schismatic_family#Sesquiquartififths\|Sesquiquartififths]] temperament and its higher-limit [[Schismatic_family#Sesquart\|Sesquart]] extension. The range is slightly over 2⅓ octaves with no missed notes and a few repeated notes, and the octaves slope up mildly.
	{{Lumatone EDO mapping\|n=89\|start=4\|xstep=8\|ystep=-5}}		{{Lumatone EDO mapping\|n=89\|start=4\|xstep=8\|ystep=-5}}

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

Lucius Chiaraviglio: Add Bryan Deister's Char-based + Sesquart rank-3 temperament mapping

2025-08-01T07:30:00Z

Add Bryan Deister's Char-based + Sesquart rank-3 temperament mapping

← Older revision		Revision as of 07:30, 1 August 2025
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	The [[Orgone]] mapping focusses on making the 2.7.11 subgroup easy to play, but is extremely efficient at covering that and only a tenth of a cent off the minimax tuning, plus it skips or repeats fewer notes at the edges.		The [[Orgone]] mapping focusses on making the 2.7.11 subgroup easy to play, but is extremely efficient at covering that and only a tenth of a cent off the minimax tuning, plus it skips or repeats fewer notes at the edges.
	{{Lumatone EDO mapping\|n=89\|start=76\|xstep=7\|ystep=3}}		{{Lumatone EDO mapping\|n=89\|start=76\|xstep=7\|ystep=3}}

			== Char-based + Sesquart rank-3 temperament ==
			[[Bryan Deister]] has demonstrated a [[10L 3s]] mapping for [[89edo]] in [https://www.youtube.com/watch?v=2JNIeqvXKlM ''microtonal improvisation in 89edo''] (2025). The rightward generator 8\89 functions as both the [[16/15]] (the classical diatonic semitone) and [[17/16]] (the large septendecimal semitone), meaning that the charisma [[256/255]] is tempered out, although 89edo is not listed as a tuning of any of the temperaments on the page for 256/255. Eight of these generators make a near-just Axirabian paraminor fifth ~[[16/11]]. Although being prime, 89edo technically needs no second generator, a second generator helps with reaching consonant intervals other than ~16/11; one obvious choice is the scale chroma (upwards generator) 5\89 which functions as a somewhat sharp small tridecimal third tone ~[[27/26]]; three of these make a near-just Pythagorean whole tone ~[[9/8]]; four of them make a near-just septimal minor third ~[[7/6]]. It is also possible to combine both generators to get 13\89, a slightly sharp undevicesimal supraneutral second ~[[21/19]]; four of these generator combinations make a near-just fifth ~[[3/2]], as in [[Schismatic_family#Sesquiquartififths\|Sesquiquartififths]] temperament and its higher-limit [[Schismatic_family#Sesquart\|Sesquart]] extension. The range is slightly over 2⅓ octaves with no missed notes and a few repeated notes, and the octaves slope up mildly.
			{{Lumatone EDO mapping\|n=89\|start=4\|xstep=8\|ystep=-5}}

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

Yourmusic Productions: Create Page.

2025-03-26T22:04:48Z

Create Page.

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{{Lumatone mapping intro}} Due to the size of the edo, this mapping covers less than 2/3rds of the notes.

== Diatonic ==
Note that since 89edo is a [[schismatic]] tuning, the best approximation to 5/4 is the diminished fourth.
{{Lumatone EDO mapping|n=89|start=2|xstep=15|ystep=-8}}

== Other Mappings ==
The smallest mapping that covers the whole gamut is the [[4L 7s]] one. Interestingly, there are two different mappings that fit that criteria, both good.
=== Myna ===
The [[myna]] mapping is quite lopsided, but is the optimal patent val for the temperament and efficiently gives access to the full 11-limit.
{{Lumatone EDO mapping|n=89|start=58|xstep=3|ystep=14}}

=== Orgone ===
The [[Orgone]] mapping focusses on making the 2.7.11 subgroup easy to play, but is extremely efficient at covering that and only a tenth of a cent off the minimax tuning, plus it skips or repeats fewer notes at the edges.
{{Lumatone EDO mapping|n=89|start=76|xstep=7|ystep=3}}

{{Navbox Lumatone}}