Lumatone mapping for 89edo: Difference between revisions

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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.

== Char-based + Sesquart rank-3 temperament ==

[[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.

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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.
 {{Lumatone EDO mapping|n=89|start=76|xstep=7|ystep=3}}
+== Char-based + Sesquart rank-3 temperament ==
+[[Bryan Deister]] has demonstrated a [[10L&nbsp;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}}
 {{Navbox Lumatone}}