81edo - Revision history

FloraC: /* Notation */ SZG notation

2026-05-12T14:09:45Z

Notation: SZG notation

← Older revision		Revision as of 14:09, 12 May 2026
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	== Notation ==		== Notation ==
	===~~Ups~~ and downs notation===		=== Stein–Zimmermann–Gould notation ===
	81edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).		[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
			{{Sharpness-sharp5-szg}}

			=== Kite's ups and downs notation ===
			81edo can also be notated with [[Kite's ups and downs notation\|Kite's ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
	{{Sharpness-sharp5a}}		{{Sharpness-sharp5a}}
	Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5\|alternative ups and downs]]. Here, this can be done using sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
	~~{{Sharpness-sharp5}}~~
	=== Tom Winspear's notation ===		=== Tom Winspear's notation ===
	[[File:81 EDO Accidentals.png\|alt=\|959x959px]]		[[File:81 EDO Accidentals.png\|alt=\|959x959px]]

Lucius Chiaraviglio: /* Regular temperament properties */ Insert Approximation to JI before this

2026-01-19T22:15:01Z

Regular temperament properties: Insert Approximation to JI before this

← Older revision		Revision as of 22:15, 19 January 2026
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	81edo accidentals created and used by [[Tom Winspear]], based on those provided in [[Scala]] though with a logic correction. The innermost accidentals represent one edostep, followed by two, then the bracket representing three. What appears to be a half-sharp is actually a fifth-sharp. Conventional sharp/doublesharp/flat/doubleflat accidentals are reached in steps of five and the pattern repeats itself on them. The chromatic scale can be notated utilizing only six accidentals in either direction—the rest are for enharmonics.		81edo accidentals created and used by [[Tom Winspear]], based on those provided in [[Scala]] though with a logic correction. The innermost accidentals represent one edostep, followed by two, then the bracket representing three. What appears to be a half-sharp is actually a fifth-sharp. Conventional sharp/doublesharp/flat/doubleflat accidentals are reached in steps of five and the pattern repeats itself on them. The chromatic scale can be notated utilizing only six accidentals in either direction—the rest are for enharmonics.

			== Approximation to JI ==
			=== 15-odd-limit interval mappings ===
			{{Q-odd-limit intervals\|81\|15}}

	== Regular temperament properties ==		== Regular temperament properties ==

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''81edo improv'' (2025)

2025-12-03T15:18:02Z

Music: Add Bryan Deister's ''81edo improv'' (2025)

← Older revision		Revision as of 15:18, 3 December 2025
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/5O6Cyawjkd8 ''''microtonal improvisation in 81edo''] (2025)		* [https://www.youtube.com/shorts/5O6Cyawjkd8 ''''microtonal improvisation in 81edo''] (2025)
			* [https://www.youtube.com/shorts/yY0TzTiNeB8 ''81edo improv''] (2025)

	== Notes ==		== Notes ==

BudjarnLambeth: /* Scales */ add 1

2025-11-17T07:29:13Z

Scales: add 1

← Older revision		Revision as of 07:29, 17 November 2025
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	* [[Leantone7]]		* [[Leantone7]]
	* [[Leantone13]]		* [[Leantone13]]
			* [[User:BudjarnLambeth/Antechinus\|Antechinus]]

	== Instruments ==		== Instruments ==

Lucius Chiaraviglio: /* Instruments */ Add Lumatone mapping for 81edo

2025-07-14T07:43:44Z

Instruments: Add Lumatone mapping for 81edo

← Older revision		Revision as of 07:43, 14 July 2025
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	Dominant 7th: 10113xx		Dominant 7th: 10113xx

			=== Keyboards ===
			A [[Lumatone mapping for 81edo]] is available.

	== Music ==		== Music ==

Lucius Chiaraviglio: /* Instruments */ Insert music section after this, starting with Bryan Deister's ''microtonal improvisation in 81edo'' (2025)

2025-07-13T12:54:26Z

Instruments: Insert music section after this, starting with Bryan Deister's ''microtonal improvisation in 81edo'' (2025)

← Older revision		Revision as of 12:54, 13 July 2025
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	Dominant 7th: 10113xx		Dominant 7th: 10113xx

			== Music ==

			; [[Bryan Deister]]
			* [https://www.youtube.com/shorts/5O6Cyawjkd8 ''''microtonal improvisation in 81edo''] (2025)

	== Notes ==		== Notes ==

MisterShafXen at 09:26, 1 July 2025

2025-07-01T09:26:19Z

← Older revision		Revision as of 09:26, 1 July 2025
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	== Notation ==		== Notation ==
	===Ups and downs notation===		===Ups and downs notation===
	~~32edo~~ can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).		81edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
	{{Sharpness-sharp5a}}		{{Sharpness-sharp5a}}
	Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5\|alternative ups and downs]]. Here, this can be done using sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:		Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5\|alternative ups and downs]]. Here, this can be done using sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:

BudjarnLambeth: /* Instruments */ merged

2025-04-27T03:29:47Z

Instruments: merged

@@ Line 46: / Line 46: @@
 == Instruments ==
-[[Skip fretting system 81 7 20]]
+=== Skip fretting ===
 == Notes ==

FloraC: No need to remind readers of what a regular temperament is everywhere

2025-04-11T11:01:31Z

No need to remind readers of what a regular temperament is everywhere

← Older revision		Revision as of 11:01, 11 April 2025
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	81edo is notable as a tuning for [[meantone family\|meantone]] and related temperaments and is the [[optimal patent val]] for a number of them. In particular it is the optimal patent val for 5-limit meantone, 7-limit meantone, 11-limit meanpop, 13-limit meanpop, and the rank-3 temperament [[erato]]. The electronic music pioneer {{w\|Daphne Oram}} was interested in 81edo<ref>[https://web.archive.org/web/20120211182601/http://daphneoram.org/2012/01/13/letter-from-yehudi-menuhin/ Letter from Yehudi Menuhin to Daphne Oram]</ref>. As a step in the [[Golden meantone]] series of edos, 81edo marks the point at which the series ceases to display audible changes to meantone temperament, and is also the edo with the lowest average and most evenly spread Just-error across the scale (though 31edo does have the best [[7/4\|harmonic 7th]]). However, it is no longer [[consistent]] in the [[9-odd-limit]], as the best direct approximations of [[9/8]] and [[10/9]] are one step above and below the patent val mapping.		81edo is notable as a tuning for [[meantone family\|meantone]] and related temperaments and is the [[optimal patent val]] for a number of them. In particular it is the optimal patent val for 5-limit meantone, 7-limit meantone, 11-limit meanpop, 13-limit meanpop, and the rank-3 temperament [[erato]]. The electronic music pioneer {{w\|Daphne Oram}} was interested in 81edo<ref>[https://web.archive.org/web/20120211182601/http://daphneoram.org/2012/01/13/letter-from-yehudi-menuhin/ Letter from Yehudi Menuhin to Daphne Oram]</ref>. As a step in the [[Golden meantone]] series of edos, 81edo marks the point at which the series ceases to display audible changes to meantone temperament, and is also the edo with the lowest average and most evenly spread Just-error across the scale (though 31edo does have the best [[7/4\|harmonic 7th]]). However, it is no longer [[consistent]] in the [[9-odd-limit]], as the best direct approximations of [[9/8]] and [[10/9]] are one step above and below the patent val mapping.

	Besides meantone, 81edo is a tuning for the [[cobalt]] temperament, since 81 contains 27 as a divisor. It also tunes the unnamed 15 & 51 temperament which divides the octave into 3 equal parts, and is a member of the [[augmented-cloudy equivalence continuum]]. The 81bd val is a tuning for the [[Porcupine family#Septimal porcupine\|septimal porcupine]] temperament. ~~(''See [[regular temperament]] for more about what all this means and how to use it.'')~~		Besides meantone, 81edo is a tuning for the [[cobalt]] temperament, since 81 contains 27 as a divisor. It also tunes the unnamed 15 & 51 temperament which divides the octave into 3 equal parts, and is a member of the [[augmented-cloudy equivalence continuum]]. The 81bd val is a tuning for the [[Porcupine family#Septimal porcupine\|septimal porcupine]] temperament.

	In the higher limits, it is a strong tuning for the 2.5.17.19 subgroup, and also can be used to map [[19/17]] to the meantone major second resulting from stacking of two patent val fifths (13\81).		In the higher limits, it is a strong tuning for the 2.5.17.19 subgroup, and also can be used to map [[19/17]] to the meantone major second resulting from stacking of two patent val fifths (13\81).

BudjarnLambeth: /* Theory */ (''See regular temperament for more about what all this means and how to use it.'')

2025-04-11T07:21:56Z

Theory: (''See regular temperament for more about what all this means and how to use it.'')

← Older revision		Revision as of 07:21, 11 April 2025
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	81edo is notable as a tuning for [[meantone family\|meantone]] and related temperaments and is the [[optimal patent val]] for a number of them. In particular it is the optimal patent val for 5-limit meantone, 7-limit meantone, 11-limit meanpop, 13-limit meanpop, and the rank-3 temperament [[erato]]. The electronic music pioneer {{w\|Daphne Oram}} was interested in 81edo<ref>[https://web.archive.org/web/20120211182601/http://daphneoram.org/2012/01/13/letter-from-yehudi-menuhin/ Letter from Yehudi Menuhin to Daphne Oram]</ref>. As a step in the [[Golden meantone]] series of edos, 81edo marks the point at which the series ceases to display audible changes to meantone temperament, and is also the edo with the lowest average and most evenly spread Just-error across the scale (though 31edo does have the best [[7/4\|harmonic 7th]]). However, it is no longer [[consistent]] in the [[9-odd-limit]], as the best direct approximations of [[9/8]] and [[10/9]] are one step above and below the patent val mapping.		81edo is notable as a tuning for [[meantone family\|meantone]] and related temperaments and is the [[optimal patent val]] for a number of them. In particular it is the optimal patent val for 5-limit meantone, 7-limit meantone, 11-limit meanpop, 13-limit meanpop, and the rank-3 temperament [[erato]]. The electronic music pioneer {{w\|Daphne Oram}} was interested in 81edo<ref>[https://web.archive.org/web/20120211182601/http://daphneoram.org/2012/01/13/letter-from-yehudi-menuhin/ Letter from Yehudi Menuhin to Daphne Oram]</ref>. As a step in the [[Golden meantone]] series of edos, 81edo marks the point at which the series ceases to display audible changes to meantone temperament, and is also the edo with the lowest average and most evenly spread Just-error across the scale (though 31edo does have the best [[7/4\|harmonic 7th]]). However, it is no longer [[consistent]] in the [[9-odd-limit]], as the best direct approximations of [[9/8]] and [[10/9]] are one step above and below the patent val mapping.

	Besides meantone, 81edo is a tuning for the [[cobalt]] temperament, since 81 contains 27 as a divisor. It also tunes the unnamed 15 & 51 temperament which divides the octave into 3 equal parts, and is a member of the [[augmented-cloudy equivalence continuum]]. The 81bd val is a tuning for the [[Porcupine family#Septimal porcupine\|septimal porcupine]] temperament.		Besides meantone, 81edo is a tuning for the [[cobalt]] temperament, since 81 contains 27 as a divisor. It also tunes the unnamed 15 & 51 temperament which divides the octave into 3 equal parts, and is a member of the [[augmented-cloudy equivalence continuum]]. The 81bd val is a tuning for the [[Porcupine family#Septimal porcupine\|septimal porcupine]] temperament. (''See [[regular temperament]] for more about what all this means and how to use it.'')

	In the higher limits, it is a strong tuning for the 2.5.17.19 subgroup, and also can be used to map [[19/17]] to the meantone major second resulting from stacking of two patent val fifths (13\81).		In the higher limits, it is a strong tuning for the 2.5.17.19 subgroup, and also can be used to map [[19/17]] to the meantone major second resulting from stacking of two patent val fifths (13\81).