Lumatone mapping for 72edo: Difference between revisions

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m →Guiron + Harry + Marvel + Marvolo + Mothra + Slendric: Make title correspond better to temperament support
→Guiron + Harry + Marvolo (Marvel) + Mothra + Slendric: Replace contorted Gamelismic clan temperaments with Miracle
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{{Lumatone EDO mapping|n=72|start=45|xstep=7|ystep=1}}
{{Lumatone EDO mapping|n=72|start=45|xstep=7|ystep=1}}


== Guiron + Harry + Marvolo (Marvel) + Mothra + Slendric ==
== Harry + Marvolo (Marvel) + Miracle ==


[[Bryan Deister]] has demonstrated a mapping of [[72edo]] as nine rings of [[8edo]] going right, offset so as to also produce the scale [[11L 9s (4/1-equivalent)]], in [https://www.youtube.com/shorts/VwVp3RVao_k ''microtonal improvisation in 72edo''] (2025). While this mapping works to get as many notes as possible of 72edo into 280 keys (yielding a range of over 3⅔ octaves, it was designed to work to support specific temperaments. The close approximations of ~[[6/5]] as 19\72 and ~[[5/4]] as 23\72 (if using note 0 as the root) are next to each other and not far from the root right and somewhat down. From note 0, moving right and somewhat down between the note 1 and note 6 keys to reach 14\72 yields a highly accurate ~[[8/7]], the generator of [[Gamelismic_clan#Guiron|Guiron]], [[Mothra]], and [[Slendric]]. Repeating this move twice more yields the highly accurate ~[[3/2]] as 42\72; repeating it once more after that to reach 56\72 yields an almost-just ~[[12/7]]; from there, moving one key to the right yields the primary generator of [[Marvel]] temperament, ~[[15/8]], as 65\72. The down-right generator 5\72 ([[20/19]] ~ [[21/20]] ~ [[22/21]]) matches [[Harry]] and [[Marvel_temperaments#Marvolo|Marvolo]].
[[Bryan Deister]] has demonstrated a mapping of [[72edo]] as nine rings of [[8edo]] going right, offset so as to also produce the scale [[11L 9s (4/1-equivalent)]], in [https://www.youtube.com/shorts/VwVp3RVao_k ''microtonal improvisation in 72edo''] (2025). While this mapping works to get as many notes as possible of 72edo into 280 keys (yielding a range of over 3⅔ octaves, it was designed to work to support specific temperaments. The close approximations of ~[[6/5]] as 19\72 and ~[[5/4]] as 23\72 (if using note 0 as the root) are next to each other and not far from the root right and somewhat down. From note 0, moving right and somewhat down between the note 1 and note 6 keys to reach 14\72 yields a highly accurate ~[[8/7]], which corresponds to two generators (~[[15/14]]) of [[Miracle]]. (It is also the generator of [[Gamelismic_clan#Guiron|Guiron]], [[Mothra]], and [[Slendric]], but 72edo is contorted in those temperaments). Repeating this move twice more yields the highly accurate ~[[3/2]] as 42\72; repeating it once more after that to reach 56\72 yields an almost-just ~[[12/7]]; from there, moving one key to the right yields the primary generator of [[Marvel]] temperament, ~[[15/8]], as 65\72. The down-right generator 5\72 ([[20/19]] ~ [[21/20]] ~ [[22/21]]) matches [[Harry]] and [[Marvel_temperaments#Marvolo|Marvolo]].


{{Lumatone EDO mapping|n=72|start=0|xstep=9|ystep=-4}}
{{Lumatone EDO mapping|n=72|start=0|xstep=9|ystep=-4}}


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

Revision as of 16:25, 30 May 2025

There are many conceivable ways to map 72edo onto the onto the Lumatone keyboard. However, it has 6 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them.

Diatonic

You can use either the second- best alternate fifth, but it is extremely sharp, so much so that "major seconds" become 8/7 instead of 9/8.

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or the third-best:

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but these do not cover the full gamut or make the best-tuned intervals easily accessible.

Miracle

Instead, the most efficient way to put the best-tuned intervals near each other while allowing access to all of them is the Miracle mapping, although this does reduce the range to a little over three octaves.

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Semimiracle

Slicing the period in half to produce semimiracle makes ratios of 13 and 17 just as easy to play as the 11-limit ones and also keeps octaves closer to horizontal.

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Harry + Marvolo (Marvel) + Miracle

Bryan Deister has demonstrated a mapping of 72edo as nine rings of 8edo going right, offset so as to also produce the scale 11L 9s (4/1-equivalent), in microtonal improvisation in 72edo (2025). While this mapping works to get as many notes as possible of 72edo into 280 keys (yielding a range of over 3⅔ octaves, it was designed to work to support specific temperaments. The close approximations of ~6/5 as 19\72 and ~5/4 as 23\72 (if using note 0 as the root) are next to each other and not far from the root right and somewhat down. From note 0, moving right and somewhat down between the note 1 and note 6 keys to reach 14\72 yields a highly accurate ~8/7, which corresponds to two generators (~15/14) of Miracle. (It is also the generator of Guiron, Mothra, and Slendric, but 72edo is contorted in those temperaments). Repeating this move twice more yields the highly accurate ~3/2 as 42\72; repeating it once more after that to reach 56\72 yields an almost-just ~12/7; from there, moving one key to the right yields the primary generator of Marvel temperament, ~15/8, as 65\72. The down-right generator 5\72 (20/19 ~ 21/20 ~ 22/21) matches Harry and Marvolo.

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