Lumatone mapping for 13edo - Revision history

Lucius Chiaraviglio: /* Father + Aurora + Variant Orwell */ Insert Bryan Deister's Sephiroth + Variant Orwell + Meansquared mapping after this

2026-03-04T10:16:40Z

Father + Aurora + Variant Orwell: Insert Bryan Deister's Sephiroth + Variant Orwell + Meansquared mapping after this

← Older revision		Revision as of 10:16, 4 March 2026
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	[[Bryan Deister]] has demonstrated a [[3L 2s]] (3:2 step ratio) [[aurora]]/[[father]] mapping for [[13edo]], in [https://www.youtube.com/shorts/YiIr9l0M67w ''Holding Back My Endless Sigh - 13edo''] (2026). The generator 8\13 (three keys right and one key down-right from the root note) can be taken as a very sharp fifth (~[[3/2]], for father temperament) or a moderately sharp septimal superfifth (~[[32/21]], for aurora temperament). Even more simply, this mapping also functions for a [[4L 5s]] (2:1 step ratio) scale for a variant of [[Orwell]] temperament, with the one key right generator being 3\13, which functions as (among other things) a rather sharp septimal minor third ~[[7/6]] (requires the 13d val) or a flat tridecimal minor third ~[[13/11]], of which two make a slightly sharp undecimal major fourth ~[[11/8]]; three of them make a sharp classic minor sixth ~[[8/5]]; four of them make a very flat classic major seventh ~[[15/8]]; and after octave-reduction, seven of them make the super-sharp fifth ~[[3/2]] (better constituted as a near-just vicesimotertial inframinor sixth ~[[23/15]], or a slightly sharp septendecimal superfifth ~[[26/17]], or a moderately sharp septimal superfifth ~32/21 as in aurora above); and eight of them make a very sharp septimal minor seventh ~[[7/4]] (if using the 13d val) or a near-just classic minor seventh ~[[9/5]] (requires constitution of the 9 as 3♯ × 3♭). The range is over seven octaves, with notes repeated multiple times, but unfortunately the downwards slope of the octaves, although mild, would make mapping to multiple manuals tricky.		[[Bryan Deister]] has demonstrated a [[3L 2s]] (3:2 step ratio) [[aurora]]/[[father]] mapping for [[13edo]], in [https://www.youtube.com/shorts/YiIr9l0M67w ''Holding Back My Endless Sigh - 13edo''] (2026). The generator 8\13 (three keys right and one key down-right from the root note) can be taken as a very sharp fifth (~[[3/2]], for father temperament) or a moderately sharp septimal superfifth (~[[32/21]], for aurora temperament). Even more simply, this mapping also functions for a [[4L 5s]] (2:1 step ratio) scale for a variant of [[Orwell]] temperament, with the one key right generator being 3\13, which functions as (among other things) a rather sharp septimal minor third ~[[7/6]] (requires the 13d val) or a flat tridecimal minor third ~[[13/11]], of which two make a slightly sharp undecimal major fourth ~[[11/8]]; three of them make a sharp classic minor sixth ~[[8/5]]; four of them make a very flat classic major seventh ~[[15/8]]; and after octave-reduction, seven of them make the super-sharp fifth ~[[3/2]] (better constituted as a near-just vicesimotertial inframinor sixth ~[[23/15]], or a slightly sharp septendecimal superfifth ~[[26/17]], or a moderately sharp septimal superfifth ~32/21 as in aurora above); and eight of them make a very sharp septimal minor seventh ~[[7/4]] (if using the 13d val) or a near-just classic minor seventh ~[[9/5]] (requires constitution of the 9 as 3♯ × 3♭). The range is over seven octaves, with notes repeated multiple times, but unfortunately the downwards slope of the octaves, although mild, would make mapping to multiple manuals tricky.
	{{Lumatone EDO mapping\|n=13\|start=0\|xstep=3\|ystep=-1}}		{{Lumatone EDO mapping\|n=13\|start=0\|xstep=3\|ystep=-1}}

			== Sephiroth + Variant Orwell + Meansquared ==
			It is possible to follow in the footsteps of [[magic]]/[[muggles]] temperament for [[13edo]], but using a much flatter classic major third ~[[5/4]] (as 4\13) as the generator, as [[sephiroth]], producing a [[3L 1s]] scale (4:1 step ratio) going right and up, as used by [[Bryan Deister]] in [https://www.youtube.com/shorts/LOgt_in9SD0 ''a microtonal totentanz in 13edo''] (2023). This also supports scales [[1L 3s]] (4:3 step ratio, going down-right, as in variant [[orwell]], although it would be awkward to play the more familiar [[4L 5s]] scale) and [[5L 2s (4/1-equivalent)]] (4:3 step ratio, going overall straight right through the octave zig-zag, as in [[meansquared]]). Octaves alternate between near/mid/far and mid-near/mid-far, with double octaves being perfectly level (thus enabling dual manuals); the range is 10¼ octaves.
			{{Lumatone EDO mapping\|n=13\|start=11\|xstep=4\|ystep=-1}}

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

Lucius Chiaraviglio: /* Father + Aurora + Variant Orwell */ Further adjustment of description

2026-02-18T09:18:09Z

Father + Aurora + Variant Orwell: Further adjustment of description

← Older revision		Revision as of 09:18, 18 February 2026
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	== Father + Aurora + Variant Orwell ==		== Father + Aurora + Variant Orwell ==
	[[Bryan Deister]] has demonstrated a [[3L 2s]] (3:2 step ratio) [[~~Aurora~~]]/[[~~Father~~]] mapping for [[13edo]], in [https://www.youtube.com/shorts/YiIr9l0M67w ''Holding Back My Endless Sigh - 13edo''] (2026). The generator 8\13 (three keys right and one key down-right from the root note) can be taken as a very sharp fifth (~[[3/2]], for ~~Father~~ temperament) or a moderately sharp septimal superfifth (~[[32/21]], for ~~Aurora~~ temperament). Even more simply, this mapping also functions for a [[4L 5s]] (2:1 step ratio) scale for a variant of [[Orwell]] temperament, with the one key right generator being 3\13, which functions as (among other things) a rather sharp septimal minor third ~[[7/6]] (requires the 13d val) or a flat tridecimal minor third ~[[13/11]], of which two make a slightly sharp undecimal major fourth ~[[11/8]]; three of them make a sharp classic minor sixth ~[[8/5]]; four of them make a very flat classic major seventh ~[[15/8]]; and after octave-reduction, seven of them make the super-sharp fifth ~[[3/2]] (better constituted as a near-just vicesimotertial inframinor sixth ~[[23/15]] or a slightly sharp septendecimal superfifth ~[[26/17]]); and eight of them make a very sharp septimal minor seventh ~[[7/4]] (if using the 13d val) or a near-just classic minor seventh ~[[9/5]] (requires constitution of the 9 as 3♯ × 3♭). The range is over seven octaves, with notes repeated multiple times, but unfortunately the downwards slope of the octaves, although mild, would make mapping to multiple manuals tricky.		[[Bryan Deister]] has demonstrated a [[3L 2s]] (3:2 step ratio) [[aurora]]/[[father]] mapping for [[13edo]], in [https://www.youtube.com/shorts/YiIr9l0M67w ''Holding Back My Endless Sigh - 13edo''] (2026). The generator 8\13 (three keys right and one key down-right from the root note) can be taken as a very sharp fifth (~[[3/2]], for father temperament) or a moderately sharp septimal superfifth (~[[32/21]], for aurora temperament). Even more simply, this mapping also functions for a [[4L 5s]] (2:1 step ratio) scale for a variant of [[Orwell]] temperament, with the one key right generator being 3\13, which functions as (among other things) a rather sharp septimal minor third ~[[7/6]] (requires the 13d val) or a flat tridecimal minor third ~[[13/11]], of which two make a slightly sharp undecimal major fourth ~[[11/8]]; three of them make a sharp classic minor sixth ~[[8/5]]; four of them make a very flat classic major seventh ~[[15/8]]; and after octave-reduction, seven of them make the super-sharp fifth ~[[3/2]] (better constituted as a near-just vicesimotertial inframinor sixth ~[[23/15]], or a slightly sharp septendecimal superfifth ~[[26/17]], or a moderately sharp septimal superfifth ~32/21 as in aurora above); and eight of them make a very sharp septimal minor seventh ~[[7/4]] (if using the 13d val) or a near-just classic minor seventh ~[[9/5]] (requires constitution of the 9 as 3♯ × 3♭). The range is over seven octaves, with notes repeated multiple times, but unfortunately the downwards slope of the octaves, although mild, would make mapping to multiple manuals tricky.
	{{Lumatone EDO mapping\|n=13\|start=0\|xstep=3\|ystep=-1}}		{{Lumatone EDO mapping\|n=13\|start=0\|xstep=3\|ystep=-1}}

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

Lucius Chiaraviglio: /* Father + Aurora + Variant Orwell */ Add better constitution of the fifth

2026-02-18T08:26:18Z

Father + Aurora + Variant Orwell: Add better constitution of the fifth

← Older revision		Revision as of 08:26, 18 February 2026
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	== Father + Aurora + Variant Orwell ==		== Father + Aurora + Variant Orwell ==
	[[Bryan Deister]] has demonstrated a [[3L 2s]] (3:2 step ratio) [[Aurora]]/[[Father]] mapping for [[13edo]], in [https://www.youtube.com/shorts/YiIr9l0M67w ''Holding Back My Endless Sigh - 13edo''] (2026). The generator 8\13 (three keys right and one key down-right from the root note) can be taken as a very sharp fifth (~[[3/2]], for Father temperament) or a moderately sharp septimal superfifth (~[[32/21]], for Aurora temperament). Even more simply, this mapping also functions for a [[4L 5s]] (2:1 step ratio) scale for a variant of [[Orwell]] temperament, with the one key right generator being 3\13, which functions as (among other things) a rather sharp septimal minor third ~[[7/6]] (requires the 13d val) or a flat tridecimal minor third ~[[13/11]], of which two make a slightly sharp undecimal major fourth ~[[11/8]]; three of them make a sharp classic minor sixth ~[[8/5]]; four of them make a very flat classic major seventh ~[[15/8]]; and after octave-reduction, seven of them make the super-sharp fifth ~[[3/2]]; and eight of them make a very sharp septimal minor seventh ~[[7/4]] (if using the 13d val) or a near-just classic minor seventh ~[[9/5]] (requires constitution of the 9 as 3♯ × 3♭). The range is over seven octaves, with notes repeated multiple times, but unfortunately the downwards slope of the octaves, although mild, would make mapping to multiple manuals tricky.		[[Bryan Deister]] has demonstrated a [[3L 2s]] (3:2 step ratio) [[Aurora]]/[[Father]] mapping for [[13edo]], in [https://www.youtube.com/shorts/YiIr9l0M67w ''Holding Back My Endless Sigh - 13edo''] (2026). The generator 8\13 (three keys right and one key down-right from the root note) can be taken as a very sharp fifth (~[[3/2]], for Father temperament) or a moderately sharp septimal superfifth (~[[32/21]], for Aurora temperament). Even more simply, this mapping also functions for a [[4L 5s]] (2:1 step ratio) scale for a variant of [[Orwell]] temperament, with the one key right generator being 3\13, which functions as (among other things) a rather sharp septimal minor third ~[[7/6]] (requires the 13d val) or a flat tridecimal minor third ~[[13/11]], of which two make a slightly sharp undecimal major fourth ~[[11/8]]; three of them make a sharp classic minor sixth ~[[8/5]]; four of them make a very flat classic major seventh ~[[15/8]]; and after octave-reduction, seven of them make the super-sharp fifth ~[[3/2]] (better constituted as a near-just vicesimotertial inframinor sixth ~[[23/15]] or a slightly sharp septendecimal superfifth ~[[26/17]]); and eight of them make a very sharp septimal minor seventh ~[[7/4]] (if using the 13d val) or a near-just classic minor seventh ~[[9/5]] (requires constitution of the 9 as 3♯ × 3♭). The range is over seven octaves, with notes repeated multiple times, but unfortunately the downwards slope of the octaves, although mild, would make mapping to multiple manuals tricky.
	{{Lumatone EDO mapping\|n=13\|start=0\|xstep=3\|ystep=-1}}		{{Lumatone EDO mapping\|n=13\|start=0\|xstep=3\|ystep=-1}}

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

Lucius Chiaraviglio: /* Father + Aurora */ Add Variant Orwell temperament

2026-02-18T08:10:06Z

Father + Aurora: Add Variant Orwell temperament

← Older revision		Revision as of 08:10, 18 February 2026
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	{{Lumatone EDO mapping\|n=13\|start=12\|xstep=5\|ystep=-2}}		{{Lumatone EDO mapping\|n=13\|start=12\|xstep=5\|ystep=-2}}

	== Father + Aurora ==		== Father + Aurora + Variant Orwell ==
	[[Bryan Deister]] has demonstrated a [[3L 2s]] (3:2 step ratio) [[Aurora]]/[[Father]] mapping for [[13edo]], in [https://www.youtube.com/shorts/YiIr9l0M67w ''Holding Back My Endless Sigh - 13edo''] (2026). The generator 8\13 (three keys right and one key down-right from the root note) can be taken as a very sharp fifth (~[[3/2]], for Father temperament) or a moderately sharp septimal superfifth (~[[32/21]], for Aurora temperament). The range is over seven octaves, with notes repeated multiple times, but unfortunately the downwards slope of the octaves, although mild, would make mapping to multiple manuals tricky.		[[Bryan Deister]] has demonstrated a [[3L 2s]] (3:2 step ratio) [[Aurora]]/[[Father]] mapping for [[13edo]], in [https://www.youtube.com/shorts/YiIr9l0M67w ''Holding Back My Endless Sigh - 13edo''] (2026). The generator 8\13 (three keys right and one key down-right from the root note) can be taken as a very sharp fifth (~[[3/2]], for Father temperament) or a moderately sharp septimal superfifth (~[[32/21]], for Aurora temperament). Even more simply, this mapping also functions for a [[4L 5s]] (2:1 step ratio) scale for a variant of [[Orwell]] temperament, with the one key right generator being 3\13, which functions as (among other things) a rather sharp septimal minor third ~[[7/6]] (requires the 13d val) or a flat tridecimal minor third ~[[13/11]], of which two make a slightly sharp undecimal major fourth ~[[11/8]]; three of them make a sharp classic minor sixth ~[[8/5]]; four of them make a very flat classic major seventh ~[[15/8]]; and after octave-reduction, seven of them make the super-sharp fifth ~[[3/2]]; and eight of them make a very sharp septimal minor seventh ~[[7/4]] (if using the 13d val) or a near-just classic minor seventh ~[[9/5]] (requires constitution of the 9 as 3♯ × 3♭). The range is over seven octaves, with notes repeated multiple times, but unfortunately the downwards slope of the octaves, although mild, would make mapping to multiple manuals tricky.
	{{Lumatone EDO mapping\|n=13\|start=0\|xstep=3\|ystep=-1}}		{{Lumatone EDO mapping\|n=13\|start=0\|xstep=3\|ystep=-1}}

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

Lucius Chiaraviglio: Add Bryan Deister's Father + Aurora mapping; add headings

2026-01-11T08:53:58Z

Add Bryan Deister's Father + Aurora mapping; add headings

← Older revision		Revision as of 08:53, 11 January 2026
Line 1:		Line 1:
	There are several possible ways to map [[13edo]] onto the onto the Lumatone keyboard. However, none of them even remotely approximate the [[Standard Lumatone mapping for Pythagorean]]. The following mapping for [[13edo]] can be used for every [[MOS]] scale in 13edo with {{nowrap\|L {{=}} 2\13}} and {{nowrap\|s {{=}} 1\13}}, such as [[5L 3s]] and [[6L 1s]].		There are several possible ways to map [[13edo]] onto the onto the Lumatone keyboard. However, none of them even remotely approximate the [[Standard Lumatone mapping for Pythagorean]].

			== Archaeotonic (exo-Tetracot) ==
			The following mapping for [[13edo]] can be used for every [[MOS]] scale in 13edo with {{nowrap\|L {{=}} 2\13}} and {{nowrap\|s {{=}} 1\13}}, such as [[5L 3s]] and [[6L 1s]].
	{{Lumatone EDO mapping\|n=13\|start=0\|xstep=2\|ystep=-1}}		{{Lumatone EDO mapping\|n=13\|start=0\|xstep=2\|ystep=-1}}

			== Fibotonic (compressed) ==
	Since 13edo is a small edo, you can compress this down to a [[2L 1s]] scale that extends range past human hearing (or more practically, enables division into multiple zones for different instruments) and puts all kinds of intervals within easy reach in different directions while still having a moderate number of repeated notes.		Since 13edo is a small edo, you can compress this down to a [[2L 1s]] scale that extends range past human hearing (or more practically, enables division into multiple zones for different instruments) and puts all kinds of intervals within easy reach in different directions while still having a moderate number of repeated notes.
	{{Lumatone EDO mapping\|n=13\|start=12\|xstep=5\|ystep=-2}}		{{Lumatone EDO mapping\|n=13\|start=12\|xstep=5\|ystep=-2}}

			== Father + Aurora ==
			[[Bryan Deister]] has demonstrated a [[3L 2s]] (3:2 step ratio) [[Aurora]]/[[Father]] mapping for [[13edo]], in [https://www.youtube.com/shorts/YiIr9l0M67w ''Holding Back My Endless Sigh - 13edo''] (2026). The generator 8\13 (three keys right and one key down-right from the root note) can be taken as a very sharp fifth (~[[3/2]], for Father temperament) or a moderately sharp septimal superfifth (~[[32/21]], for Aurora temperament). The range is over seven octaves, with notes repeated multiple times, but unfortunately the downwards slope of the octaves, although mild, would make mapping to multiple manuals tricky.
			{{Lumatone EDO mapping\|n=13\|start=0\|xstep=3\|ystep=-1}}

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

Lucius Chiaraviglio: Add another use for the extreme range

2026-01-10T11:11:35Z

Add another use for the extreme range

← Older revision		Revision as of 11:11, 10 January 2026
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	{{Lumatone EDO mapping\|n=13\|start=0\|xstep=2\|ystep=-1}}		{{Lumatone EDO mapping\|n=13\|start=0\|xstep=2\|ystep=-1}}

	Since 13edo is a small edo, you can compress this down to a [[2L 1s]] scale that extends range past human hearing and puts all kinds of intervals within easy reach in different directions while still having a moderate number of repeated notes.		Since 13edo is a small edo, you can compress this down to a [[2L 1s]] scale that extends range past human hearing (or more practically, enables division into multiple zones for different instruments) and puts all kinds of intervals within easy reach in different directions while still having a moderate number of repeated notes.
	{{Lumatone EDO mapping\|n=13\|start=12\|xstep=5\|ystep=-2}}		{{Lumatone EDO mapping\|n=13\|start=12\|xstep=5\|ystep=-2}}

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

Yourmusic Productions: Expansion.

2025-07-26T08:04:04Z

Expansion.

← Older revision		Revision as of 08:04, 26 July 2025
Line 1:		Line 1:
	The following mapping for [[13edo]] can be used for every [[MOS]] scale in 13edo with {{nowrap\|L {{=}} 2\13}} and {{nowrap\|s {{=}} 1\13}}, such as [[5L 3s]] and [[6L 1s]].		There are several possible ways to map [[13edo]] onto the onto the Lumatone keyboard. However, none of them even remotely approximate the [[Standard Lumatone mapping for Pythagorean]]. The following mapping for [[13edo]] can be used for every [[MOS]] scale in 13edo with {{nowrap\|L {{=}} 2\13}} and {{nowrap\|s {{=}} 1\13}}, such as [[5L 3s]] and [[6L 1s]].
	{{Lumatone EDO mapping\|n=13\|start=0\|xstep=2\|ystep=-1}}		{{Lumatone EDO mapping\|n=13\|start=0\|xstep=2\|ystep=-1}}

			Since 13edo is a small edo, you can compress this down to a [[2L 1s]] scale that extends range past human hearing and puts all kinds of intervals within easy reach in different directions while still having a moderate number of repeated notes.
			{{Lumatone EDO mapping\|n=13\|start=12\|xstep=5\|ystep=-2}}

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

ArrowHead294 at 14:34, 23 March 2025

2025-03-23T14:34:50Z

← Older revision		Revision as of 14:34, 23 March 2025
Line 1:		Line 1:
	The following mapping for [[13edo]] can be used for every [[MOS]] scale in 13edo with {{nowrap\|L {{=}} 2\13}} and {{nowrap\|s {{=}} 1\13}}, such as [[5L 3s]] and [[6L 1s]].		The following mapping for [[13edo]] can be used for every [[MOS]] scale in 13edo with {{nowrap\|L {{=}} 2\13}} and {{nowrap\|s {{=}} 1\13}}, such as [[5L 3s]] and [[6L 1s]].

	{{Lumatone EDO mapping\|n=13\|start=0\|xstep=2\|ystep=-1}}		{{Lumatone EDO mapping\|n=13\|start=0\|xstep=2\|ystep=-1}}

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

ArrowHead294 at 16:49, 11 February 2025

2025-02-11T16:49:13Z

← Older revision		Revision as of 16:49, 11 February 2025
Line 1:		Line 1:
	The following mapping for [[13edo]] can be used for every [[MOS]] scale in 13edo with L = 2\13 and s = 1\13, such as [[5L 3s]] and [[6L 1s]].		The following mapping for [[13edo]] can be used for every [[MOS]] scale in 13edo with {{nowrap\|L {{=}} 2\13}} and {{nowrap\|s {{=}} 1\13}}, such as [[5L 3s]] and [[6L 1s]].

	{{Lumatone EDO mapping\|n=13\|start=0\|xstep=2\|ystep=-1}}		{{Lumatone EDO mapping\|n=13\|start=0\|xstep=2\|ystep=-1}}

	{{Lumatone ~~mapping navigation~~}}		{{Navbox Lumatone}}

ArrowHead294: Category is added automatically now

2024-11-17T01:22:31Z

Category is added automatically now

← Older revision		Revision as of 01:22, 17 November 2024
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	{{Lumatone mapping navigation}}		{{Lumatone mapping navigation}}

	~~[[Category:Lumatone mappings]]~~