Lumatone mapping for 72edo: Difference between revisions

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{{Lumatone mapping intro}} You can use either the second ~~or third~~ best alternate ~~fifths~~, but ~~they will not cover the full gamut or make the best-tuned intervals easily accessible~~.

== 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.

or the third-best:

~~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~~.

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.

=== 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.

== Harry + Marvolo (Marvel) + Miracle ==

~~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~~.

[[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]].

== Ennealimmal (currently untested) ==

This mapping uses [[ennealimmal]] temperament; it maps one axis to 1\9 and one axis to ~21/20, an ennealimmal generator.

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-{{Lumatone mapping intro}} You can use either the second or third best alternate fifths, but they will not cover the full gamut or make the best-tuned intervals easily accessible.
+{{Lumatone mapping intro}}
+== 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.
 {{Lumatone EDO mapping|n=72|start=24|xstep=14|ystep=-13}}
+or the third-best:
 {{Lumatone EDO mapping|n=72|start=48|xstep=10|ystep=1}}
-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.
+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.
 {{Lumatone EDO mapping|n=72|start=30|xstep=7|ystep=2}}
+=== 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.
+{{Lumatone EDO mapping|n=72|start=45|xstep=7|ystep=1}}
+== Harry + Marvolo (Marvel) + Miracle ==
-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.
+[[Bryan Deister]] has demonstrated a mapping of [[72edo]] as nine rings of [[8edo]] going right, offset so as to also produce the scale [[11L&nbsp;9s&nbsp;(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=45|xstep=7|ystep=1}}
+== Ennealimmal (currently untested) ==
+This mapping uses [[ennealimmal]] temperament; it maps one axis to 1\9 and one axis to ~21/20, an ennealimmal generator.
+{{Lumatone EDO mapping|n=72|start=0|xstep=8|ystep=-5}}
 {{Navbox Lumatone}}