Lumatone mapping for 72edo - Revision history

Lucius Chiaraviglio: /* Catakleismic-related rank-3 (Harmonic table) */ Remove incorrect scale; a MOS scale does not really make sense for this type of mapping

2026-08-21T18:09:07Z

Catakleismic-related rank-3 (Harmonic table): Remove incorrect scale; a MOS scale does not really make sense for this type of mapping

← Older revision		Revision as of 18:09, 21 August 2026
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	== Catakleismic-related rank-3 (Harmonic table) ==		== Catakleismic-related rank-3 (Harmonic table) ==
	[[Bryan Deister]] has demonstrated ~~a [[1L 1s]] (42:23 step ratio)~~ mapping for [[72edo]] in [https://www.youtube.com/shorts/a07Q_zQHe9M ''72edo groove''] (2026). The rightward generator 42\72 is the near-just perfect fifth ~[[3/2]]; the upward generator 19\72 is the near-just classic minor third ~[[6/5]] (as in [[catakleismic]] temperament); this makes the down-right generator 23/72 the near-just classic major third ~[[5/4]] (being derived from the other generators, this does not expand the temperament beyond rank-3). That makes this mapping sort of a harmonic table mapping, although different from that for [[12edo]] since neither the classic major third nor the classic minor third divide 72edo evenly, thus causing comma pumping if either of these is stacked with itself. With such a compressed layout, most notes are not present in any one octave, but all notes are present in some octave, even within the limited part of the Lumatone that was actually mapped in the demonstration video; the synthesized sound used in the demonstration video also ensures that all of the notes are audible, even pushing the brain to do automatic octave-reduction.		[[Bryan Deister]] has demonstrated an ultra-compressed mapping for [[72edo]] in [https://www.youtube.com/shorts/a07Q_zQHe9M ''72edo groove''] (2026). The rightward generator 42\72 is the near-just perfect fifth ~[[3/2]]; the upward generator 19\72 is the near-just classic minor third ~[[6/5]] (as in [[catakleismic]] temperament); this makes the down-right generator 23/72 the near-just classic major third ~[[5/4]] (being derived from the other generators, this does not expand the temperament beyond rank-3). That makes this mapping sort of a harmonic table mapping, although different from that for [[12edo]] since neither the classic major third nor the classic minor third divide 72edo evenly, thus causing comma pumping if either of these is stacked with itself. With such a compressed layout, most notes are not present in any one octave, but all notes are present in some octave, even within the limited part of the Lumatone that was actually mapped in the demonstration video; the synthesized sound used in the demonstration video also ensures that all of the notes are audible, even pushing the brain to do automatic octave-reduction.
	{{Lumatone EDO mapping\|n=72\|start=64\|xstep=42\|ystep=-19}}		{{Lumatone EDO mapping\|n=72\|start=64\|xstep=42\|ystep=-19}}

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

Lucius Chiaraviglio: /* Catakleismic-related rank-3 (Harmonic table) Lumatone mappings */ Fix section heading

2026-08-21T06:04:29Z

Catakleismic-related rank-3 (Harmonic table) Lumatone mappings: Fix section heading

← Older revision		Revision as of 06:04, 21 August 2026
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	{{Lumatone EDO mapping\|n=72\|start=0\|xstep=8\|ystep=-5}}		{{Lumatone EDO mapping\|n=72\|start=0\|xstep=8\|ystep=-5}}

	== Catakleismic-related rank-3 (Harmonic table) ~~Lumatone mappings~~ ==		== Catakleismic-related rank-3 (Harmonic table) ==
	[[Bryan Deister]] has demonstrated a [[1L 1s]] (42:23 step ratio) mapping for [[72edo]] in [https://www.youtube.com/shorts/a07Q_zQHe9M ''72edo groove''] (2026). The rightward generator 42\72 is the near-just perfect fifth ~[[3/2]]; the upward generator 19\72 is the near-just classic minor third ~[[6/5]] (as in [[catakleismic]] temperament); this makes the down-right generator 23/72 the near-just classic major third ~[[5/4]] (being derived from the other generators, this does not expand the temperament beyond rank-3). That makes this mapping sort of a harmonic table mapping, although different from that for [[12edo]] since neither the classic major third nor the classic minor third divide 72edo evenly, thus causing comma pumping if either of these is stacked with itself. With such a compressed layout, most notes are not present in any one octave, but all notes are present in some octave, even within the limited part of the Lumatone that was actually mapped in the demonstration video; the synthesized sound used in the demonstration video also ensures that all of the notes are audible, even pushing the brain to do automatic octave-reduction.		[[Bryan Deister]] has demonstrated a [[1L 1s]] (42:23 step ratio) mapping for [[72edo]] in [https://www.youtube.com/shorts/a07Q_zQHe9M ''72edo groove''] (2026). The rightward generator 42\72 is the near-just perfect fifth ~[[3/2]]; the upward generator 19\72 is the near-just classic minor third ~[[6/5]] (as in [[catakleismic]] temperament); this makes the down-right generator 23/72 the near-just classic major third ~[[5/4]] (being derived from the other generators, this does not expand the temperament beyond rank-3). That makes this mapping sort of a harmonic table mapping, although different from that for [[12edo]] since neither the classic major third nor the classic minor third divide 72edo evenly, thus causing comma pumping if either of these is stacked with itself. With such a compressed layout, most notes are not present in any one octave, but all notes are present in some octave, even within the limited part of the Lumatone that was actually mapped in the demonstration video; the synthesized sound used in the demonstration video also ensures that all of the notes are audible, even pushing the brain to do automatic octave-reduction.
	{{Lumatone EDO mapping\|n=72\|start=64\|xstep=42\|ystep=-19}}		{{Lumatone EDO mapping\|n=72\|start=64\|xstep=42\|ystep=-19}}

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

Lucius Chiaraviglio: /* Ennealimmal (currently untested) */ Add Bryan Deister's Catakleismic-related rank-3 (Harmonic table) Lumatone mapping

2026-08-21T06:04:06Z

Ennealimmal (currently untested): Add Bryan Deister's Catakleismic-related rank-3 (Harmonic table) Lumatone mapping

← Older revision		Revision as of 06:04, 21 August 2026
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	This mapping uses [[ennealimmal]] temperament; it maps one axis to 1\9 and one axis to ~21/20, an ennealimmal generator.		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}}		{{Lumatone EDO mapping\|n=72\|start=0\|xstep=8\|ystep=-5}}

			== Catakleismic-related rank-3 (Harmonic table) Lumatone mappings ==
			[[Bryan Deister]] has demonstrated a [[1L 1s]] (42:23 step ratio) mapping for [[72edo]] in [https://www.youtube.com/shorts/a07Q_zQHe9M ''72edo groove''] (2026). The rightward generator 42\72 is the near-just perfect fifth ~[[3/2]]; the upward generator 19\72 is the near-just classic minor third ~[[6/5]] (as in [[catakleismic]] temperament); this makes the down-right generator 23/72 the near-just classic major third ~[[5/4]] (being derived from the other generators, this does not expand the temperament beyond rank-3). That makes this mapping sort of a harmonic table mapping, although different from that for [[12edo]] since neither the classic major third nor the classic minor third divide 72edo evenly, thus causing comma pumping if either of these is stacked with itself. With such a compressed layout, most notes are not present in any one octave, but all notes are present in some octave, even within the limited part of the Lumatone that was actually mapped in the demonstration video; the synthesized sound used in the demonstration video also ensures that all of the notes are audible, even pushing the brain to do automatic octave-reduction.
			{{Lumatone EDO mapping\|n=72\|start=64\|xstep=42\|ystep=-19}}

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

Inthar: /* Ennealimmal (currently untested) */

2026-04-08T23:43:06Z

Ennealimmal (currently untested)

← Older revision		Revision as of 23:43, 8 April 2026
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	== Ennealimmal (currently untested) ==		== Ennealimmal (currently untested) ==
	This mapping uses [[ennealimmal]] temperament; it maps one axis to 1\9 and one axis to ~21/20, an ennealimmal generator.		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=-13}}		{{Lumatone EDO mapping\|n=72\|start=0\|xstep=8\|ystep=-5}}

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

Inthar: /* Ennealimmal */

2026-04-08T23:18:00Z

Ennealimmal

← Older revision		Revision as of 23:18, 8 April 2026
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	{{Lumatone EDO mapping\|n=72\|start=0\|xstep=9\|ystep=-4}}		{{Lumatone EDO mapping\|n=72\|start=0\|xstep=9\|ystep=-4}}

	== Ennealimmal ==		== Ennealimmal (currently untested) ==
	This mapping uses [[ennealimmal]] temperament; it maps one axis to 1\9 and one axis to ~21/20, an ennealimmal generator.		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=-13}}		{{Lumatone EDO mapping\|n=72\|start=0\|xstep=8\|ystep=-13}}

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

Inthar at 23:14, 8 April 2026

2026-04-08T23:14:49Z

← Older revision		Revision as of 23:14, 8 April 2026
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	{{Lumatone EDO mapping\|n=72\|start=0\|xstep=9\|ystep=-4}}		{{Lumatone EDO mapping\|n=72\|start=0\|xstep=9\|ystep=-4}}

			== Ennealimmal ==
			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=-13}}

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

Lucius Chiaraviglio: /* Guiron + Harry + Marvolo (Marvel) + Mothra + Slendric */ Replace contorted Gamelismic clan temperaments with Miracle

2025-05-30T16:25:42Z

Guiron + Harry + Marvolo (Marvel) + Mothra + Slendric: Replace contorted Gamelismic clan temperaments with Miracle

← Older revision		Revision as of 16:25, 30 May 2025
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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}}

Lucius Chiaraviglio: /* Guiron + Harry + Marvel + Marvolo + Mothra + Slendric */ Make title correspond better to temperament support

2025-05-30T07:17:50Z

Guiron + Harry + Marvel + Marvolo + Mothra + Slendric: Make title correspond better to temperament support

← Older revision		Revision as of 07:17, 30 May 2025
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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 + Marvel ~~+ Marvolo~~ + Mothra + Slendric ==		== Guiron + Harry + Marvolo (Marvel) + Mothra + Slendric ==

	[[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]], 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]].

Lucius Chiaraviglio: Add Bryan Deister's 72edo Lumatone mapping

2025-05-30T06:29:15Z

Add Bryan Deister's 72edo Lumatone mapping

← Older revision		Revision as of 06:29, 30 May 2025
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	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.		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}}		{{Lumatone EDO mapping\|n=72\|start=45\|xstep=7\|ystep=1}}

			== Guiron + Harry + Marvel + Marvolo + Mothra + Slendric ==

			[[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]].

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

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

ArrowHead294: /* Diatonic */

2025-05-22T18:59:32Z

Diatonic

← Older revision		Revision as of 18:59, 22 May 2025
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	== Diatonic ==		== Diatonic ==
	You can use either the second- best alternate fifth:		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}}		{{Lumatone EDO mapping\|n=72\|start=24\|xstep=14\|ystep=-13}}

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

	== Miracle ==		== Miracle ==