Lumatone mapping for 63edo - Revision history

Lucius Chiaraviglio: /* Fog */ Insert Bryan Deister's Fog-Related Neutral Seconds Lumatone mapping before this

2026-08-10T06:15:41Z

Fog: Insert Bryan Deister's Fog-Related Neutral Seconds Lumatone mapping before this

← Older revision		Revision as of 06:15, 10 August 2026
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	As noted above, neither of these makes consonant chords particularly easy to play. The [[Misty_family#Fog\|Fog]] and [[Magic]] mappings have smaller ranges, but are more harmonically effective.		As noted above, neither of these makes consonant chords particularly easy to play. The [[Misty_family#Fog\|Fog]] and [[Magic]] mappings have smaller ranges, but are more harmonically effective.

			== Fog-Related Neutral Seconds ==
			In [[63edo]], it is possible to divide the octave into three parts, each 21\63 being a mildly sharp fwiwismic major third ~[[44/35]] (or more accurately but less practically, a near-just undetricesimal major third ~[[29/23]]), with a [[3L 3s]] scale (13:8 step ratio), similar to [[Misty_family#Fog\|fog]]. Unlike actual fog, the generator is a slightly flat undecimal neutral second ~[[12/11]], with the layout being designed for easy access to intervals that are close to common consonant intervals, but different (including the generator itself). The range is over five octaves, which is too much to include all of the notes in a standard-sized Lumatone. Despite the missing notes, [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/NwcS36rurOI ''63edo improv''] (2026-08-03), with the xenharmonic intervals forming a sound flavor that seems both Gaelic and Middle-Eastern.
			{{Lumatone EDO mapping\|n=63\|start=42\|xstep=8\|ystep=5}}

	== Fog ==		== Fog ==
	[[Misty_family#Fog\|~~Fog~~]] splits the octave into three parts with a [[3L 6s]] scale (11:5 step ratio), and uses a rightward generator 5\63, which functions as as sharp (and inconsistently mapped) septimal minor semitone ~[[21/20]] and a flat undecimal semitone ~[[35/33]]~~; two~~ of these make a near-just Quasi-meantone ~[[19/17]]; three of them make a somewhat flat classic major third ~[[5/4]], from which the fifth ~[[3/2]] is easily reachable by moving down-right. This mapping has the disadvantage of many notes in the bottom and top octaves being cut off by the left and right edges.		Actual [[Misty_family#Fog\|fog]] splits the octave into three parts with a [[3L 6s]] scale (11:5 step ratio), and uses a rightward generator 5\63, which functions as as sharp (and inconsistently mapped) septimal minor semitone ~[[21/20]] and a flat undecimal semitone ~[[35/33]], derived by 1/3-octave reduction of the fourth ~[[4/3]]. Two of these make a near-just Quasi-meantone ~[[19/17]]; three of them make a somewhat flat classic major third ~[[5/4]], from which the fifth ~[[3/2]] is easily reachable by moving down-right. This mapping has the disadvantage of many notes in the bottom and top octaves being cut off by the left and right edges, but at least no notes are missing out of the middle octaves (although this mapping offers only two of these).
	{{Lumatone EDO mapping\|n=63\|start=46\|xstep=5\|ystep=6}}		{{Lumatone EDO mapping\|n=63\|start=46\|xstep=5\|ystep=6}}

Lucius Chiaraviglio: /* Other Mappings */ Reorganize into separate mappings; fill in wording a bit; andand add Bryan Deister's Sevond-related mapping

2026-08-10T03:49:33Z

Other Mappings: Reorganize into separate mappings; fill in wording a bit; andand add Bryan Deister's Sevond-related mapping

← Older revision		Revision as of 03:49, 10 August 2026
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	{{Lumatone EDO mapping\|n=64\|start=56\|xstep=10\|ystep=-3}}		{{Lumatone EDO mapping\|n=64\|start=56\|xstep=10\|ystep=-3}}

	== ~~Other Mappings~~ ==		== Sevond-related ==
	Of the ~~mappings that cover all~~ the ~~notes~~, the [[~~7L 1s~~]] ~~scale~~ (of [[~~Sevond~~]] ~~temperament~~) ~~generated by 8~~/~~63 and the~~ [[~~3L 5s~~]] one ~~generated by 23/63 are highly efficient~~, with the ~~second of those keeping octaves closer to horizontal~~.		Since [[63edo]] is a multiple of 7edo, it can be used with a mapping that divides the octave into seven parts in the manner of [[whitewood]], but with more accuracy due to having a much better fifth; in this case, the actual temperament is related to [[sevond]], but unlike actual sevond, it uses a near-just septimal minor second ~[[7/6]] as its generator, which is 1/7-octave-reduced from 14\63 to 5\63. The 1/7-octave (9\63) is mapped most practically as a slightly flat undevicesimal submajor second ~[[21/19]], resulting in the reduced generator (5\63) being a slightly sharp large undevicesimal semitone ~[[19/18]]. [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/SQsDGSmEVQw ''63edo double improv''] (2026). The range is 4⅓ octaves (with only one repeated note in each octave), which slope upwards with the rows.
			{{Lumatone EDO mapping\|n=63\|start=59\|xstep=9\|ystep=-4}}

	=== Sevond ===		== Sevond ==
	In the [[~~Keemic temperaments#Sevond\|Sevond~~]] mapping, the octave is split into seven equal parts (9\63), and the rightward keyboard mapping generator 8\63 is one seventh part of the octave minus one minimal form Sevond generator (1\63). Unfortunately this does not lend itself to producing common intervals conveniently, unless by chance the intervals happen not to cross a vertical wraparound, the position of which shifts considerably when ascending in octaves.		In the [[7L 1s]] (8:7 step ratio) [[sevond]] mapping, the octave is split into seven equal parts (9\63), as above, but the period is reached by moving one key right plus one key up, and the rightward keyboard mapping generator 8\63 is one seventh part of the octave minus one minimal form Sevond generator (1\63, made by 1/7-octave-reducing the fifth ~[[3/2]]). Unfortunately this does not lend itself to producing common intervals conveniently, unless by chance the intervals happen not to cross a vertical wraparound, the position of which shifts considerably when ascending in octaves.
	{{Lumatone EDO mapping\|n=63\|start=38\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=63\|start=38\|xstep=8\|ystep=-1}}

	=== Sensi-related (non-Superleap) or Enneaportent ===		== Sensi-related (non-Superleap) or Enneaportent ==
	Like [[~~Sensi~~]], this mapping uses a slightly sharp septimal major third (~[[9/7]], as 23\63), and two of these stack to a classic major sixth (~[[5/3]]); however, unlike actual Sensi, this generator is not equated to the tridecimal semisixth (~[[13/10]] — instead of being tempered out, the superleap comma [[91/90]] is mapped very accurately to 1\63). As an alternative to 23\63, the actual keyboard rightward generator 6\63 (functioning as ~~[[15/14]] and ~[[16/15]]) can be used if the octave is divided into nine equal parts, making it one ninth part of the octave minus one minimal form generator, analogously to the Sevond mapping above, but in this case corresponding to the [[Marvel]] temperament [[Marvel_temperaments#Enneaportent\|Enneaportent]]. Unfortunately, the fourth ~[[4/3]] and the fifth ~[[3/2]] are inconveniently situated relative to the root note, and highly subject to the vagaries of vertical wraparound.		Like [[sensi]], this [[3L 5s]] (11:6 step ratio) mapping uses a slightly sharp septimal major third (~[[9/7]], as 23\63), and two of these stack to a classic major sixth (~[[5/3]]); however, unlike actual Sensi, this generator is not equated to the tridecimal semisixth (~[[13/10]] — instead of being tempered out, the superleap comma [[91/90]] is mapped very accurately to 1\63). As an alternative to 23\63, the actual keyboard rightward generator 6\63 (functioning as ~~[[15/14]] and ~[[16/15]]) can be used if the octave is divided into nine equal parts, making it one ninth part of the octave minus one minimal form generator, analogously to the Sevond mapping above, but in this case corresponding to the [[Marvel]] temperament [[Marvel_temperaments#Enneaportent\|Enneaportent]]. Unfortunately, the fourth ~[[4/3]] and the fifth ~[[3/2]] are inconveniently situated relative to the root note, and highly subject to the vagaries of vertical wraparound.
	{{Lumatone EDO mapping\|n=63\|start=47\|xstep=6\|ystep=5}}		{{Lumatone EDO mapping\|n=63\|start=47\|xstep=6\|ystep=5}}

	As noted above, neither of these makes consonant chords particularly easy to play. The [[Misty_family#Fog\|Fog]] and [[Magic]] mappings have smaller ranges, but are more harmonically effective.		As noted above, neither of these makes consonant chords particularly easy to play. The [[Misty_family#Fog\|Fog]] and [[Magic]] mappings have smaller ranges, but are more harmonically effective.

	=== Fog ===		== Fog ==
	Fog splits the octave into three parts, and uses a rightward generator 5\63, which functions as as sharp (and inconsistently mapped) septimal minor semitone ~[[21/20]] and a flat undecimal semitone ~[[35/33]]; two of these make a near-just Quasi-meantone ~[[19/17]]; three of them make a somewhat flat classic major third ~[[5/4]], from which the fifth ~[[3/2]] is easily reachable by moving down-right. This ~~gives it an advantage over~~ the ~~above two temperaments, although it shares their~~ disadvantage of many notes in the bottom and top octaves being cut off by the left and right edges.		[[Misty_family#Fog\|Fog]] splits the octave into three parts with a [[3L 6s]] scale (11:5 step ratio), and uses a rightward generator 5\63, which functions as as sharp (and inconsistently mapped) septimal minor semitone ~[[21/20]] and a flat undecimal semitone ~[[35/33]]; two of these make a near-just Quasi-meantone ~[[19/17]]; three of them make a somewhat flat classic major third ~[[5/4]], from which the fifth ~[[3/2]] is easily reachable by moving down-right. This mapping has the disadvantage of many notes in the bottom and top octaves being cut off by the left and right edges.
	{{Lumatone EDO mapping\|n=63\|start=46\|xstep=5\|ystep=6}}		{{Lumatone EDO mapping\|n=63\|start=46\|xstep=5\|ystep=6}}

	=== Magic ===		== Magic ==
	The generator for [[Magic_family\|Magic]] is a classic major third ~[[5/4]] as 20\63 (which is somewhat flat), and going down three of them and octave-reducing produces 3\63, the rightward generator of this mapping, whereas going up seven of these generators and octave-reducing yields 14\63, the down-right generator of this layout; stopping at the in-between point of five temperament generators up (octave-reduced) yields the fifth ~[[3/2]] at 37\63; of all of these intervals, the root note, major third, and fifth make a nearly horizontal and just slightly curved line segment, making at least the major triad easy to reach and not likely to be interrupted by a vertical wraparound. Again, this mapping does share the disadvantage with the previous mappings of having many notes of the bottom and top octaves being cut off by the left and right edges.		The generator for [[Magic_family\|Magic]] (with a [[3L 7s]] scale having a 14:3 stepratio) is a classic major third ~[[5/4]] as 20\63 (which is somewhat flat), and going down three of them and octave-reducing produces 3\63, the rightward generator of this mapping, whereas going up seven of these generators and octave-reducing yields 14\63, the down-right generator of this layout; stopping at the in-between point of five temperament generators up (octave-reduced) yields the fifth ~[[3/2]] at 37\63; of all of these intervals, the root note, major third, and fifth make a nearly horizontal and just slightly curved line segment, making at least the major triad easy to reach and not likely to be interrupted by a vertical wraparound. Again, this mapping does share the disadvantage with the previous mappings of having many notes of the bottom and top octaves being cut off by the left and right edges.
	{{Lumatone EDO mapping\|n=63\|start=13\|xstep=3\|ystep=11}}		{{Lumatone EDO mapping\|n=63\|start=13\|xstep=3\|ystep=11}}

Lucius Chiaraviglio: /* Pseudo-Isomorphic Pseudo-Diatonic */ Add more specific date to demo video Bryan Deister's ''63edo improv'' because another one is coming

2026-08-06T16:02:09Z

Pseudo-Isomorphic Pseudo-Diatonic: Add more specific date to demo video Bryan Deister's ''63edo improv'' because another one is coming

← Older revision		Revision as of 16:02, 6 August 2026
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	== Pseudo-Isomorphic Pseudo-Diatonic ==		== Pseudo-Isomorphic Pseudo-Diatonic ==
	[[Bryan Deister]] has used a pseudo-isomorphic pseudo-diatonic mapping laid out as for [[64edo]], but with note 63 actually being a duplicate of note 0 (but it is off the edge, so not visible unless this mapping would be used on a hypothetical XL-sized Lumatone). This is demonstrated in [https://www.youtube.com/shorts/EEAJ0AaWoJM ''63edo improv''] (2025), with a monochrome color scheme for additional challenge.		[[Bryan Deister]] has used a pseudo-isomorphic pseudo-diatonic mapping laid out as for [[64edo]], but with note 63 actually being a duplicate of note 0 (but it is off the edge, so not visible unless this mapping would be used on a hypothetical XL-sized Lumatone). This is demonstrated in [https://www.youtube.com/shorts/EEAJ0AaWoJM ''63edo improv''] (2025-10-19), with a monochrome color scheme for additional challenge.
	{{Lumatone EDO mapping\|n=64\|start=56\|xstep=10\|ystep=-3}}		{{Lumatone EDO mapping\|n=64\|start=56\|xstep=10\|ystep=-3}}

Lucius Chiaraviglio: /* Aureus Pseudo-Meantone */ Fix typo

2025-11-15T09:00:04Z

Aureus Pseudo-Meantone: Fix typo

← Older revision		Revision as of 09:00, 15 November 2025
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	== Aureus Pseudo-Meantone ==		== Aureus Pseudo-Meantone ==
	[[Bryan Deister]] has demonstrated a [[6L 1s]] (10:3 step ratio) mapping for [[63edo]] in [https://www.youtube.com/shorts/IYLzF4ogl_w ''microtonal improvisation in 63edo''] (2025). The generator 10\93 is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it just slightly flat; two of them make a somewhat flat classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 63edo represents ~19/17, ~[[10/9]], and ~[[9/8]] as distinct intervals — the syntonic comma [[81/80]] is not tempered out, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) Although 10\63 can reach all of the notes of 63edo without the need for a second generator, a second generator 7\63 (upward, as a tridecimal supraminor/neutral second that functions as both ~[[13/12]] and ~[[14/13]]) is convenient for quick access to additional common intervals — for instance, three rightward generators plus one upward generator reach the just slightly sharp fifth ~[[3/2]]; while five rightward generators minus one upwards generator reach a mildly sharp minor sixth ~[[8/5]]. The range is somewhat over four octaves (which slant up mildly) with no missed notes and no repeated notes.		[[Bryan Deister]] has demonstrated a [[6L 1s]] (10:3 step ratio) mapping for [[63edo]] in [https://www.youtube.com/shorts/IYLzF4ogl_w ''microtonal improvisation in 63edo''] (2025). The generator 10\63 is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it just slightly flat; two of them make a somewhat flat classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 63edo represents ~19/17, ~[[10/9]], and ~[[9/8]] as distinct intervals — the syntonic comma [[81/80]] is not tempered out, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) Although 10\63 can reach all of the notes of 63edo without the need for a second generator, a second generator 7\63 (upward, as a tridecimal supraminor/neutral second that functions as both ~[[13/12]] and ~[[14/13]]) is convenient for quick access to additional common intervals — for instance, three rightward generators plus one upward generator reach the just slightly sharp fifth ~[[3/2]]; while five rightward generators minus one upwards generator reach a mildly sharp minor sixth ~[[8/5]]. The range is somewhat over four octaves (which slant up mildly) with no missed notes and no repeated notes.

	{{Lumatone EDO mapping\|n=63\|start=6\|xstep=10\|ystep=-7}}		{{Lumatone EDO mapping\|n=63\|start=6\|xstep=10\|ystep=-7}}

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

Lucius Chiaraviglio: /* Pseudo-Meantone */ --> Aureus Pseudo-Meantone to be more specific about which kind of pseudo-meantone

2025-11-15T08:55:41Z

Pseudo-Meantone: --> Aureus Pseudo-Meantone to be more specific about which kind of pseudo-meantone

← Older revision		Revision as of 08:55, 15 November 2025
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	{{Lumatone EDO mapping\|n=63\|start=13\|xstep=3\|ystep=11}}		{{Lumatone EDO mapping\|n=63\|start=13\|xstep=3\|ystep=11}}

	== Pseudo-Meantone ==		== Aureus Pseudo-Meantone ==
	[[Bryan Deister]] has demonstrated a [[6L 1s]] (10:3 step ratio) mapping for [[63edo]] in [https://www.youtube.com/shorts/IYLzF4ogl_w ''microtonal improvisation in 63edo''] (2025). The generator 10\93 is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it just slightly flat; two of them make a somewhat flat classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 63edo represents ~19/17, ~[[10/9]], and ~[[9/8]] as distinct intervals — the syntonic comma [[81/80]] is not tempered out, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) Although 10\63 can reach all of the notes of 63edo without the need for a second generator, a second generator 7\63 (upward, as a tridecimal supraminor/neutral second that functions as both ~[[13/12]] and ~[[14/13]]) is convenient for quick access to additional common intervals — for instance, three rightward generators plus one upward generator reach the just slightly sharp fifth ~[[3/2]]; while five rightward generators minus one upwards generator reach a mildly sharp minor sixth ~[[8/5]]. The range is somewhat over four octaves (which slant up mildly) with no missed notes and no repeated notes.		[[Bryan Deister]] has demonstrated a [[6L 1s]] (10:3 step ratio) mapping for [[63edo]] in [https://www.youtube.com/shorts/IYLzF4ogl_w ''microtonal improvisation in 63edo''] (2025). The generator 10\93 is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it just slightly flat; two of them make a somewhat flat classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 63edo represents ~19/17, ~[[10/9]], and ~[[9/8]] as distinct intervals — the syntonic comma [[81/80]] is not tempered out, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) Although 10\63 can reach all of the notes of 63edo without the need for a second generator, a second generator 7\63 (upward, as a tridecimal supraminor/neutral second that functions as both ~[[13/12]] and ~[[14/13]]) is convenient for quick access to additional common intervals — for instance, three rightward generators plus one upward generator reach the just slightly sharp fifth ~[[3/2]]; while five rightward generators minus one upwards generator reach a mildly sharp minor sixth ~[[8/5]]. The range is somewhat over four octaves (which slant up mildly) with no missed notes and no repeated notes.

Lucius Chiaraviglio: /* Diatonic */ Add demo video

2025-11-02T20:58:56Z

Diatonic: Add demo video

← Older revision		Revision as of 20:58, 2 November 2025
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	== Diatonic ==		== Diatonic ==
	However, to the size of the edo, this mapping does not quite cover all the notes. In addition, the best approximation to [[5/4]] is the quadruply diminished or pentuply augmented 6th, which is extremely awkward to play with the root and 5th. The second best is shared with 12edo and is a triply augmented unison, which is slightly more ergonomic but still a tough stretch to play as a chord one-handed.		However, to the size of the edo, this mapping does not quite cover all the notes. In addition, the best approximation to [[5/4]] is the quadruply diminished or pentuply augmented 6th, which is extremely awkward to play with the root and 5th. The second best is shared with 12edo and is a triply augmented unison, which is slightly more ergonomic but still a tough stretch to play as a chord one-handed. Despite the missing notes, [[Bryan Deister]] has used this mapping, to make use of near-just ~[[14/11]] major thirds instead of ~5/4 major thirds, in [https://www.youtube.com/shorts/l-M2FZn2nC0 ''Venus as a Boy - Björk (microtonal cover in 63edo)''] (2025).
	{{Lumatone EDO mapping\|n=63\|start=6\|xstep=11\|ystep=-7}}		{{Lumatone EDO mapping\|n=63\|start=6\|xstep=11\|ystep=-7}}

Lucius Chiaraviglio: /* Diatonic */ Add Bryan Deister's pseudo-diatonic pseudo-isomorphic mapping

2025-10-11T21:20:45Z

Diatonic: Add Bryan Deister's pseudo-diatonic pseudo-isomorphic mapping

← Older revision		Revision as of 21:20, 11 October 2025
Line 4:		Line 4:
	However, to the size of the edo, this mapping does not quite cover all the notes. In addition, the best approximation to [[5/4]] is the quadruply diminished or pentuply augmented 6th, which is extremely awkward to play with the root and 5th. The second best is shared with 12edo and is a triply augmented unison, which is slightly more ergonomic but still a tough stretch to play as a chord one-handed.		However, to the size of the edo, this mapping does not quite cover all the notes. In addition, the best approximation to [[5/4]] is the quadruply diminished or pentuply augmented 6th, which is extremely awkward to play with the root and 5th. The second best is shared with 12edo and is a triply augmented unison, which is slightly more ergonomic but still a tough stretch to play as a chord one-handed.
	{{Lumatone EDO mapping\|n=63\|start=6\|xstep=11\|ystep=-7}}		{{Lumatone EDO mapping\|n=63\|start=6\|xstep=11\|ystep=-7}}

			== Pseudo-Isomorphic Pseudo-Diatonic ==
			[[Bryan Deister]] has used a pseudo-isomorphic pseudo-diatonic mapping laid out as for [[64edo]], but with note 63 actually being a duplicate of note 0 (but it is off the edge, so not visible unless this mapping would be used on a hypothetical XL-sized Lumatone). This is demonstrated in [https://www.youtube.com/shorts/EEAJ0AaWoJM ''63edo improv''] (2025), with a monochrome color scheme for additional challenge.
			{{Lumatone EDO mapping\|n=64\|start=56\|xstep=10\|ystep=-3}}

	== Other Mappings ==		== Other Mappings ==

Lucius Chiaraviglio: /* Other Mappings */ Identify the unnamed temperament, and add temperament text

2025-07-27T09:24:22Z

Other Mappings: Identify the unnamed temperament, and add temperament text

← Older revision		Revision as of 09:24, 27 July 2025
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	=== Sevond ===		=== Sevond ===
			In the [[Keemic temperaments#Sevond\|Sevond]] mapping, the octave is split into seven equal parts (9\63), and the rightward keyboard mapping generator 8\63 is one seventh part of the octave minus one minimal form Sevond generator (1\63). Unfortunately this does not lend itself to producing common intervals conveniently, unless by chance the intervals happen not to cross a vertical wraparound, the position of which shifts considerably when ascending in octaves.
	{{Lumatone EDO mapping\|n=63\|start=38\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=63\|start=38\|xstep=8\|ystep=-1}}

	=== ~~Unidentified temperament~~ ===		=== Sensi-related (non-Superleap) or Enneaportent ===
			Like [[Sensi]], this mapping uses a slightly sharp septimal major third (~[[9/7]], as 23\63), and two of these stack to a classic major sixth (~[[5/3]]); however, unlike actual Sensi, this generator is not equated to the tridecimal semisixth (~[[13/10]] — instead of being tempered out, the superleap comma [[91/90]] is mapped very accurately to 1\63). As an alternative to 23\63, the actual keyboard rightward generator 6\63 (functioning as ~~[[15/14]] and ~[[16/15]]) can be used if the octave is divided into nine equal parts, making it one ninth part of the octave minus one minimal form generator, analogously to the Sevond mapping above, but in this case corresponding to the [[Marvel]] temperament [[Marvel_temperaments#Enneaportent\|Enneaportent]]. Unfortunately, the fourth ~[[4/3]] and the fifth ~[[3/2]] are inconveniently situated relative to the root note, and highly subject to the vagaries of vertical wraparound.
	{{Lumatone EDO mapping\|n=63\|start=47\|xstep=6\|ystep=5}}		{{Lumatone EDO mapping\|n=63\|start=47\|xstep=6\|ystep=5}}

	~~However~~, neither of these makes consonant chords particularly easy to play. The [[~~fog~~]] and [[~~magic~~]] mappings have smaller ranges, but are more harmonically effective.		As noted above, neither of these makes consonant chords particularly easy to play. The [[Misty_family#Fog\|Fog]] and [[Magic]] mappings have smaller ranges, but are more harmonically effective.

	=== Fog ===		=== Fog ===
			Fog splits the octave into three parts, and uses a rightward generator 5\63, which functions as as sharp (and inconsistently mapped) septimal minor semitone ~[[21/20]] and a flat undecimal semitone ~[[35/33]]; two of these make a near-just Quasi-meantone ~[[19/17]]; three of them make a somewhat flat classic major third ~[[5/4]], from which the fifth ~[[3/2]] is easily reachable by moving down-right. This gives it an advantage over the above two temperaments, although it shares their disadvantage of many notes in the bottom and top octaves being cut off by the left and right edges.
	{{Lumatone EDO mapping\|n=63\|start=46\|xstep=5\|ystep=6}}		{{Lumatone EDO mapping\|n=63\|start=46\|xstep=5\|ystep=6}}

	=== Magic ===		=== Magic ===
			The generator for [[Magic_family\|Magic]] is a classic major third ~[[5/4]] as 20\63 (which is somewhat flat), and going down three of them and octave-reducing produces 3\63, the rightward generator of this mapping, whereas going up seven of these generators and octave-reducing yields 14\63, the down-right generator of this layout; stopping at the in-between point of five temperament generators up (octave-reduced) yields the fifth ~[[3/2]] at 37\63; of all of these intervals, the root note, major third, and fifth make a nearly horizontal and just slightly curved line segment, making at least the major triad easy to reach and not likely to be interrupted by a vertical wraparound. Again, this mapping does share the disadvantage with the previous mappings of having many notes of the bottom and top octaves being cut off by the left and right edges.
	{{Lumatone EDO mapping\|n=63\|start=13\|xstep=3\|ystep=11}}		{{Lumatone EDO mapping\|n=63\|start=13\|xstep=3\|ystep=11}}

Lucius Chiaraviglio: /* Pseudo-Meantone */ Add the aureusma as the quasi-meantone comma

2025-07-27T05:45:18Z

Pseudo-Meantone: Add the aureusma as the quasi-meantone comma

← Older revision		Revision as of 05:45, 27 July 2025
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	== Pseudo-Meantone ==		== Pseudo-Meantone ==
	[[Bryan Deister]] has demonstrated a [[6L 1s]] (10:3 step ratio) mapping for [[63edo]] in [https://www.youtube.com/shorts/IYLzF4ogl_w ''microtonal improvisation in 63edo''] (2025). The generator 10\93 is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it just slightly flat; two of them make a somewhat flat classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 63edo represents ~19/17, ~[[10/9]], and ~[[9/8]] as distinct intervals.) Although 10\63 can reach all of the notes of 63edo without the need for a second generator, a second generator 7\63 (upward, as a tridecimal supraminor/neutral second that functions as both ~[[13/12]] and ~[[14/13]]) is convenient for quick access to additional common intervals — for instance, three rightward generators plus one upward generator reach the just slightly sharp fifth ~[[3/2]]; while five rightward generators minus one upwards generator reach a mildly sharp minor sixth ~[[8/5]]. The range is somewhat over four octaves (which slant up mildly) with no missed notes and no repeated notes.		[[Bryan Deister]] has demonstrated a [[6L 1s]] (10:3 step ratio) mapping for [[63edo]] in [https://www.youtube.com/shorts/IYLzF4ogl_w ''microtonal improvisation in 63edo''] (2025). The generator 10\93 is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it just slightly flat; two of them make a somewhat flat classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 63edo represents ~19/17, ~[[10/9]], and ~[[9/8]] as distinct intervals — the syntonic comma [[81/80]] is not tempered out, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) Although 10\63 can reach all of the notes of 63edo without the need for a second generator, a second generator 7\63 (upward, as a tridecimal supraminor/neutral second that functions as both ~[[13/12]] and ~[[14/13]]) is convenient for quick access to additional common intervals — for instance, three rightward generators plus one upward generator reach the just slightly sharp fifth ~[[3/2]]; while five rightward generators minus one upwards generator reach a mildly sharp minor sixth ~[[8/5]]. The range is somewhat over four octaves (which slant up mildly) with no missed notes and no repeated notes.

	{{Lumatone EDO mapping\|n=63\|start=6\|xstep=10\|ystep=-7}}		{{Lumatone EDO mapping\|n=63\|start=6\|xstep=10\|ystep=-7}}

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

Lucius Chiaraviglio: Add names for the "Other" mappings when possible (need to reorganize and fill out this section but can't do it right now); add Bryan Deister's pseudo-meantone Lumatone mapping for 63edo

2025-07-24T08:25:46Z

Add names for the "Other" mappings when possible (need to reorganize and fill out this section but can't do it right now); add Bryan Deister's pseudo-meantone Lumatone mapping for 63edo

← Older revision		Revision as of 08:25, 24 July 2025
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	== Other Mappings ==		== Other Mappings ==
	Of the mappings that cover all the notes, the [[7L 1s]] scale generated by 8/63 and the [[3L 5s]] one generated by 23/63 are ~~the most~~ efficient, with the second of those keeping octaves closer to horizontal.		Of the mappings that cover all the notes, the [[7L 1s]] scale (of [[Sevond]] temperament) generated by 8/63 and the [[3L 5s]] one generated by 23/63 are highly efficient, with the second of those keeping octaves closer to horizontal.

			=== Sevond ===
	{{Lumatone EDO mapping\|n=63\|start=38\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=63\|start=38\|xstep=8\|ystep=-1}}

			=== Unidentified temperament ===
	{{Lumatone EDO mapping\|n=63\|start=47\|xstep=6\|ystep=5}}		{{Lumatone EDO mapping\|n=63\|start=47\|xstep=6\|ystep=5}}

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	=== Magic ===		=== Magic ===
	{{Lumatone EDO mapping\|n=63\|start=13\|xstep=3\|ystep=11}}		{{Lumatone EDO mapping\|n=63\|start=13\|xstep=3\|ystep=11}}

			== Pseudo-Meantone ==
			[[Bryan Deister]] has demonstrated a [[6L 1s]] (10:3 step ratio) mapping for [[63edo]] in [https://www.youtube.com/shorts/IYLzF4ogl_w ''microtonal improvisation in 63edo''] (2025). The generator 10\93 is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it just slightly flat; two of them make a somewhat flat classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 63edo represents ~19/17, ~[[10/9]], and ~[[9/8]] as distinct intervals.) Although 10\63 can reach all of the notes of 63edo without the need for a second generator, a second generator 7\63 (upward, as a tridecimal supraminor/neutral second that functions as both ~[[13/12]] and ~[[14/13]]) is convenient for quick access to additional common intervals — for instance, three rightward generators plus one upward generator reach the just slightly sharp fifth ~[[3/2]]; while five rightward generators minus one upwards generator reach a mildly sharp minor sixth ~[[8/5]]. The range is somewhat over four octaves (which slant up mildly) with no missed notes and no repeated notes.

			{{Lumatone EDO mapping\|n=63\|start=6\|xstep=10\|ystep=-7}}

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

← Older revision		Revision as of 06:15, 10 August 2026
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	As noted above, neither of these makes consonant chords particularly easy to play. The [[Misty_family#Fog\|Fog]] and [[Magic]] mappings have smaller ranges, but are more harmonically effective.		As noted above, neither of these makes consonant chords particularly easy to play. The [[Misty_family#Fog\|Fog]] and [[Magic]] mappings have smaller ranges, but are more harmonically effective.

			== Fog-Related Neutral Seconds ==
			In [[63edo]], it is possible to divide the octave into three parts, each 21\63 being a mildly sharp fwiwismic major third ~[[44/35]] (or more accurately but less practically, a near-just undetricesimal major third ~[[29/23]]), with a [[3L 3s]] scale (13:8 step ratio), similar to [[Misty_family#Fog\|fog]]. Unlike actual fog, the generator is a slightly flat undecimal neutral second ~[[12/11]], with the layout being designed for easy access to intervals that are close to common consonant intervals, but different (including the generator itself). The range is over five octaves, which is too much to include all of the notes in a standard-sized Lumatone. Despite the missing notes, [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/NwcS36rurOI ''63edo improv''] (2026-08-03), with the xenharmonic intervals forming a sound flavor that seems both Gaelic and Middle-Eastern.
			{{Lumatone EDO mapping\|n=63\|start=42\|xstep=8\|ystep=5}}

	== Fog ==		== Fog ==
	[[Misty_family#Fog\|~~Fog~~]] splits the octave into three parts with a [[3L 6s]] scale (11:5 step ratio), and uses a rightward generator 5\63, which functions as as sharp (and inconsistently mapped) septimal minor semitone ~[[21/20]] and a flat undecimal semitone ~[[35/33]]~~; two~~ of these make a near-just Quasi-meantone ~[[19/17]]; three of them make a somewhat flat classic major third ~[[5/4]], from which the fifth ~[[3/2]] is easily reachable by moving down-right. This mapping has the disadvantage of many notes in the bottom and top octaves being cut off by the left and right edges.		Actual [[Misty_family#Fog\|fog]] splits the octave into three parts with a [[3L 6s]] scale (11:5 step ratio), and uses a rightward generator 5\63, which functions as as sharp (and inconsistently mapped) septimal minor semitone ~[[21/20]] and a flat undecimal semitone ~[[35/33]], derived by 1/3-octave reduction of the fourth ~[[4/3]]. Two of these make a near-just Quasi-meantone ~[[19/17]]; three of them make a somewhat flat classic major third ~[[5/4]], from which the fifth ~[[3/2]] is easily reachable by moving down-right. This mapping has the disadvantage of many notes in the bottom and top octaves being cut off by the left and right edges, but at least no notes are missing out of the middle octaves (although this mapping offers only two of these).
	{{Lumatone EDO mapping\|n=63\|start=46\|xstep=5\|ystep=6}}		{{Lumatone EDO mapping\|n=63\|start=46\|xstep=5\|ystep=6}}

← Older revision		Revision as of 03:49, 10 August 2026
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	{{Lumatone EDO mapping\|n=64\|start=56\|xstep=10\|ystep=-3}}		{{Lumatone EDO mapping\|n=64\|start=56\|xstep=10\|ystep=-3}}

	== ~~Other Mappings~~ ==		== Sevond-related ==
	Of the ~~mappings that cover all~~ the ~~notes~~, the [[~~7L 1s~~]] ~~scale~~ (of [[~~Sevond~~]] ~~temperament~~) ~~generated by 8~~/~~63 and the~~ [[~~3L 5s~~]] one ~~generated by 23/63 are highly efficient~~, with the ~~second of those keeping octaves closer to horizontal~~.		Since [[63edo]] is a multiple of 7edo, it can be used with a mapping that divides the octave into seven parts in the manner of [[whitewood]], but with more accuracy due to having a much better fifth; in this case, the actual temperament is related to [[sevond]], but unlike actual sevond, it uses a near-just septimal minor second ~[[7/6]] as its generator, which is 1/7-octave-reduced from 14\63 to 5\63. The 1/7-octave (9\63) is mapped most practically as a slightly flat undevicesimal submajor second ~[[21/19]], resulting in the reduced generator (5\63) being a slightly sharp large undevicesimal semitone ~[[19/18]]. [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/SQsDGSmEVQw ''63edo double improv''] (2026). The range is 4⅓ octaves (with only one repeated note in each octave), which slope upwards with the rows.
			{{Lumatone EDO mapping\|n=63\|start=59\|xstep=9\|ystep=-4}}

	=== Sevond ===		== Sevond ==
	In the [[~~Keemic temperaments#Sevond\|Sevond~~]] mapping, the octave is split into seven equal parts (9\63), and the rightward keyboard mapping generator 8\63 is one seventh part of the octave minus one minimal form Sevond generator (1\63). Unfortunately this does not lend itself to producing common intervals conveniently, unless by chance the intervals happen not to cross a vertical wraparound, the position of which shifts considerably when ascending in octaves.		In the [[7L 1s]] (8:7 step ratio) [[sevond]] mapping, the octave is split into seven equal parts (9\63), as above, but the period is reached by moving one key right plus one key up, and the rightward keyboard mapping generator 8\63 is one seventh part of the octave minus one minimal form Sevond generator (1\63, made by 1/7-octave-reducing the fifth ~[[3/2]]). Unfortunately this does not lend itself to producing common intervals conveniently, unless by chance the intervals happen not to cross a vertical wraparound, the position of which shifts considerably when ascending in octaves.
	{{Lumatone EDO mapping\|n=63\|start=38\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=63\|start=38\|xstep=8\|ystep=-1}}

	=== Sensi-related (non-Superleap) or Enneaportent ===		== Sensi-related (non-Superleap) or Enneaportent ==
	Like [[~~Sensi~~]], this mapping uses a slightly sharp septimal major third (~[[9/7]], as 23\63), and two of these stack to a classic major sixth (~[[5/3]]); however, unlike actual Sensi, this generator is not equated to the tridecimal semisixth (~[[13/10]] — instead of being tempered out, the superleap comma [[91/90]] is mapped very accurately to 1\63). As an alternative to 23\63, the actual keyboard rightward generator 6\63 (functioning as ~~[[15/14]] and ~[[16/15]]) can be used if the octave is divided into nine equal parts, making it one ninth part of the octave minus one minimal form generator, analogously to the Sevond mapping above, but in this case corresponding to the [[Marvel]] temperament [[Marvel_temperaments#Enneaportent\|Enneaportent]]. Unfortunately, the fourth ~[[4/3]] and the fifth ~[[3/2]] are inconveniently situated relative to the root note, and highly subject to the vagaries of vertical wraparound.		Like [[sensi]], this [[3L 5s]] (11:6 step ratio) mapping uses a slightly sharp septimal major third (~[[9/7]], as 23\63), and two of these stack to a classic major sixth (~[[5/3]]); however, unlike actual Sensi, this generator is not equated to the tridecimal semisixth (~[[13/10]] — instead of being tempered out, the superleap comma [[91/90]] is mapped very accurately to 1\63). As an alternative to 23\63, the actual keyboard rightward generator 6\63 (functioning as ~~[[15/14]] and ~[[16/15]]) can be used if the octave is divided into nine equal parts, making it one ninth part of the octave minus one minimal form generator, analogously to the Sevond mapping above, but in this case corresponding to the [[Marvel]] temperament [[Marvel_temperaments#Enneaportent\|Enneaportent]]. Unfortunately, the fourth ~[[4/3]] and the fifth ~[[3/2]] are inconveniently situated relative to the root note, and highly subject to the vagaries of vertical wraparound.
	{{Lumatone EDO mapping\|n=63\|start=47\|xstep=6\|ystep=5}}		{{Lumatone EDO mapping\|n=63\|start=47\|xstep=6\|ystep=5}}

	As noted above, neither of these makes consonant chords particularly easy to play. The [[Misty_family#Fog\|Fog]] and [[Magic]] mappings have smaller ranges, but are more harmonically effective.		As noted above, neither of these makes consonant chords particularly easy to play. The [[Misty_family#Fog\|Fog]] and [[Magic]] mappings have smaller ranges, but are more harmonically effective.

	=== Fog ===		== Fog ==
	Fog splits the octave into three parts, and uses a rightward generator 5\63, which functions as as sharp (and inconsistently mapped) septimal minor semitone ~[[21/20]] and a flat undecimal semitone ~[[35/33]]; two of these make a near-just Quasi-meantone ~[[19/17]]; three of them make a somewhat flat classic major third ~[[5/4]], from which the fifth ~[[3/2]] is easily reachable by moving down-right. This ~~gives it an advantage over~~ the ~~above two temperaments, although it shares their~~ disadvantage of many notes in the bottom and top octaves being cut off by the left and right edges.		[[Misty_family#Fog\|Fog]] splits the octave into three parts with a [[3L 6s]] scale (11:5 step ratio), and uses a rightward generator 5\63, which functions as as sharp (and inconsistently mapped) septimal minor semitone ~[[21/20]] and a flat undecimal semitone ~[[35/33]]; two of these make a near-just Quasi-meantone ~[[19/17]]; three of them make a somewhat flat classic major third ~[[5/4]], from which the fifth ~[[3/2]] is easily reachable by moving down-right. This mapping has the disadvantage of many notes in the bottom and top octaves being cut off by the left and right edges.
	{{Lumatone EDO mapping\|n=63\|start=46\|xstep=5\|ystep=6}}		{{Lumatone EDO mapping\|n=63\|start=46\|xstep=5\|ystep=6}}

	=== Magic ===		== Magic ==
	The generator for [[Magic_family\|Magic]] is a classic major third ~[[5/4]] as 20\63 (which is somewhat flat), and going down three of them and octave-reducing produces 3\63, the rightward generator of this mapping, whereas going up seven of these generators and octave-reducing yields 14\63, the down-right generator of this layout; stopping at the in-between point of five temperament generators up (octave-reduced) yields the fifth ~[[3/2]] at 37\63; of all of these intervals, the root note, major third, and fifth make a nearly horizontal and just slightly curved line segment, making at least the major triad easy to reach and not likely to be interrupted by a vertical wraparound. Again, this mapping does share the disadvantage with the previous mappings of having many notes of the bottom and top octaves being cut off by the left and right edges.		The generator for [[Magic_family\|Magic]] (with a [[3L 7s]] scale having a 14:3 stepratio) is a classic major third ~[[5/4]] as 20\63 (which is somewhat flat), and going down three of them and octave-reducing produces 3\63, the rightward generator of this mapping, whereas going up seven of these generators and octave-reducing yields 14\63, the down-right generator of this layout; stopping at the in-between point of five temperament generators up (octave-reduced) yields the fifth ~[[3/2]] at 37\63; of all of these intervals, the root note, major third, and fifth make a nearly horizontal and just slightly curved line segment, making at least the major triad easy to reach and not likely to be interrupted by a vertical wraparound. Again, this mapping does share the disadvantage with the previous mappings of having many notes of the bottom and top octaves being cut off by the left and right edges.
	{{Lumatone EDO mapping\|n=63\|start=13\|xstep=3\|ystep=11}}		{{Lumatone EDO mapping\|n=63\|start=13\|xstep=3\|ystep=11}}