Lumatone mapping for 90edo: Difference between revisions

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== Undevicesimal Quasitonemic + Semitonismic + Archagallismic ==

[[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 ''90edo ~~improv~~''] (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.

[[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.

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 == Undevicesimal Quasitonemic + Semitonismic + Archagallismic ==
-[[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 ''90edo improv''] (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.
+[[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}}