Lumatone mapping for 90edo: Difference between revisions

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== Diaschismic ==

== Undevicesimal Quasitonemic + Semitonismic + Archagallismic ==

On the other hand, the golden [[diaschismic]] mapping can cover the whole gamut, has better melodic properties than the diatonic mapping and makes harmonics easier to play together, although it needs to be expanded from [[2L 8s]] to [[10L 2s]] to hit every single note.

[[Bryan Deister]] has demonstrated a [[6L 6s]] (8:7 step ratio) [[6th-octave_temperaments|6th-octave temperament]] mapping for [[90edo]], in [https://www.youtube.com/shorts/LdxUD1taOqI ''<nowiki>Fantasy in 90edo [short clip]</nowiki>''] (2026). This temperament is similar to [[6th-octave_temperaments#Spoob|spoob]], but spoob itself (which equates the werckismic tone ~[[55/49]] to 1/6 of an octave) will not actually work in the [[patent val]] of 90edo, which maps 55/49 inconsistently. ("Undevicesimal quasitonemic" is a placeholder name, pending approval of an official name for this 6th-octave temperament.) Instead, it equates the near-just quasi-tempered whole tone ~[[64/57]] (one key right, as 15\90) to 1/6 of an octave — the [[undevicesimal quasitonema]] (34359738368/34296447249, name proposed by [[User:Xenllium|Xenllium]]) is tempered out. The down-right generator 8\90 is a near-just large septendecimal semitone ~[[17/16]]; two of them (passing a 6th-octave boundary) make a sharp (and inconsistently-mapped) Pythagorean whole tone ~[[9/8]] (the semitonisma [[289/288]] is tempered out); three of them make a somewhat sharp classic minor third ~[[6/5]] (the archagallisma [[24576/24565]] is tempered out). The range is slightly short of five octaves (which slope upwards with the rows), with many missing notes in each octave, but this is an interesting mapping nonetheless, and could shine on a hypothetical XL-sized Lumatone having at least 465 keys in a span of five octaves.

== Diaschismic + Charismic ==

On the other hand, the golden [[diaschismic]] mapping can cover the whole gamut, has better melodic properties than the diatonic mapping and makes harmonics easier to play together, although it needs to be expanded from [[2L 8s]] to [[10L 2s]] to hit every single note. The rightward generator 8\90 is a semitone that functions as both ~[[16/15]] and ~[[17/16]] (the charisma [[256/255]] is tempered out). Splitting the octave in half (the [[diaschisma]] 2048/2025 is tempered out) enables this generator to produce these mappings without [[contorsion]].

=== 2L 8s ===

With [[2L 8s]] (13:8 step ratio), the range is three octaves with a very mild upwards slope, but some notes are missing.

=== 10L 2s ===

[[Bryan Deister]] has demonstrated the [[Diaschismic]]-[[256/255|Charismic]] [[10L 2s]] mapping for [[90edo]] (with 8:5 step ratio), in [https://www.youtube.com/shorts/0j33e4F-4jY ''microtonal improvisation in 90edo''] (20025). The range is about 2⅔ octaves with no missed notes, with a mild upward slope.

@@ Line 5: / Line 5: @@
 {{Lumatone EDO mapping|n=90|start=12|xstep=16|ystep=-11}}
-== Diaschismic ==
+== Undevicesimal Quasitonemic + Semitonismic + Archagallismic ==
-On the other hand, the golden [[diaschismic]] mapping can cover the whole gamut, has better melodic properties than the diatonic mapping and makes harmonics easier to play together, although it needs to be expanded from [[2L&nbsp;8s]] to [[10L&nbsp;2s]] to hit every single note.
+[[Bryan Deister]] has demonstrated a [[6L&nbsp;6s]] (8:7 step ratio) [[6th-octave_temperaments|6th-octave temperament]] mapping for [[90edo]], in [https://www.youtube.com/shorts/LdxUD1taOqI ''<nowiki>Fantasy in 90edo [short clip]</nowiki>''] (2026). This temperament is similar to [[6th-octave_temperaments#Spoob|spoob]], but spoob itself (which equates the werckismic tone ~[[55/49]] to 1/6 of an octave) will not actually work in the [[patent val]] of 90edo, which maps 55/49 inconsistently. ("Undevicesimal quasitonemic" is a placeholder name, pending approval of an official name for this 6th-octave temperament.) Instead, it equates the near-just quasi-tempered whole tone ~[[64/57]] (one key right, as 15\90) to 1/6 of an octave &mdash; the [[undevicesimal quasitonema]] (34359738368/34296447249, name proposed by [[User:Xenllium|Xenllium]]) is tempered out. The down-right generator 8\90 is a near-just large septendecimal semitone ~[[17/16]]; two of them (passing a 6th-octave boundary) make a sharp (and inconsistently-mapped) Pythagorean whole tone ~[[9/8]] (the semitonisma [[289/288]] is tempered out); three of them make a somewhat sharp classic minor third ~[[6/5]] (the archagallisma [[24576/24565]] is tempered out). The range is slightly short of five octaves (which slope upwards with the rows), with many missing notes in each octave, but this is an interesting mapping nonetheless, and could shine on a hypothetical XL-sized Lumatone having at least 465 keys in a span of five octaves.
+{{Lumatone EDO mapping|n=90|start=86|xstep=15|ystep=-7}}
+== Diaschismic + Charismic ==
+On the other hand, the golden [[diaschismic]] mapping can cover the whole gamut, has better melodic properties than the diatonic mapping and makes harmonics easier to play together, although it needs to be expanded from [[2L&nbsp;8s]] to [[10L&nbsp;2s]] to hit every single note. The rightward generator 8\90 is a semitone that functions as both ~[[16/15]] and ~[[17/16]] (the charisma [[256/255]] is tempered out). Splitting the octave in half (the [[diaschisma]] 2048/2025 is tempered out) enables this generator to produce these mappings without [[contorsion]].
+=== 2L 8s ===
+With [[2L&nbsp;8s]] (13:8 step ratio), the range is three octaves with a very mild upwards slope, but some notes are missing.
 {{Lumatone EDO mapping|n=90|start=36|xstep=8|ystep=5}}
+=== 10L 2s ===
+[[Bryan Deister]] has demonstrated the [[Diaschismic]]-[[256/255|Charismic]] [[10L&nbsp;2s]] mapping for [[90edo]] (with 8:5 step ratio), in [https://www.youtube.com/shorts/0j33e4F-4jY ''microtonal improvisation in 90edo''] (20025). The range is about 2⅔ octaves with no missed notes, with a mild upward slope.
 {{Lumatone EDO mapping|n=90|start=84|xstep=8|ystep=-3}}
 {{Navbox Lumatone}}