91edo - Revision history

Lucius Chiaraviglio: /* Music */ Add Modern Renderings section, starting with Maretu's ''Aishite ita no ni'' (2023) – microtonal cover in 91edo by Bryan Deister (2026)

2026-05-14T08:01:43Z

Music: Add Modern Renderings section, starting with Maretu's ''Aishite ita no ni'' (2023) – microtonal cover in 91edo by Bryan Deister (2026)

← Older revision		Revision as of 08:01, 14 May 2026
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	== Music ==		== Music ==
			=== Modern renderings ===
			; {{W\|Maretu}}
			* [https://www.youtube.com/shorts/7RDvArkSJrk ''Aishite ita no ni''] (2023) – microtonal cover in 91edo by [[Bryan Deister]] (2026)

			=== 21st century ===
	; [[Mercury Amalgam]]		; [[Mercury Amalgam]]
	* ''Sadness - Nope'' (2022) – [https://mercuryamalgam.bandcamp.com/track/sadness-nope-the-molecular-agoge-pt-2 Bandcamp] \| [https://www.youtube.com/watch?v=_5WS7AGZxm4 YouTube]		* ''Sadness - Nope'' (2022) – [https://mercuryamalgam.bandcamp.com/track/sadness-nope-the-molecular-agoge-pt-2 Bandcamp] \| [https://www.youtube.com/watch?v=_5WS7AGZxm4 YouTube]

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:30:09Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:30, 13 March 2026
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	\| [[Trideci]] (91)<br>[[Aluminium]] (91c)		\| [[Trideci]] (91)<br>[[Aluminium]] (91c)
	\|}		\|}
	<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	<nowiki/>** Derived from scales in the Scales section, official name not decided upon yet.		<nowiki/>** Derived from scales in the Scales section, official name not decided upon yet.

FloraC: Cleanup

2025-10-27T13:31:09Z

Cleanup

← Older revision		Revision as of 13:31, 27 October 2025
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	\| 435.16		\| 435.16
	\| 9/7		\| 9/7
	\| [[Supermajor]]		\| [[Supermajor (temperament)\|Supermajor]]
	\|-		\|-
	\| 1		\| 1
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	\| [[Trideci]] (91)<br>[[Aluminium]] (91c)		\| [[Trideci]] (91)<br>[[Aluminium]] (91c)
	\|}		\|}
	<nowiki/>* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[normal ~~lists~~\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms\|minimal form]] in parentheses if distinct

	<nowiki/>** Derived from scales in the Scales section, official name not decided upon yet.		<nowiki/>** Derived from scales in the Scales section, official name not decided upon yet.
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	== Instruments ==		== Instruments ==

	A [[Lumatone mapping for 91edo]] is available.		A [[Lumatone mapping for 91edo]] is available.

Lériendil: Text replacement - "(unchanged-interval)" to "(unchanged interval)"

2025-06-21T06:59:34Z

Text replacement - "(unchanged-interval)" to "(unchanged interval)"

← Older revision		Revision as of 06:59, 21 June 2025
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	The [[harmonic]]s [[3/1\|3]], [[5/1\|5]] and [[7/1\|7]] for 91edo are on the flat side, making this a mostly flat system. It [[tempering out\|tempers out]] [[15625/15552]] in the 5-limit, [[225/224]] and [[4375/4374]] in the 7-limit, [[245/242]], [[385/384]] in the 11-limit, and [[105/104]], [[144/143]], [[196/195]] in the 13-limit. It provides the [[optimal patent val]] for 11- and 13-limit [[septimin]] temperament, and the 13-limit rank-3 [[tripod]] temperament, as well as the 11-limit rank-4 temperament tempering out 245/242 and the 13-limit rank-5 temperament tempering out 105/104, or rank-4 tempering out 105/104 and 144/143, or else 105/104 and 196/195 and hence 225/224 also.		The [[harmonic]]s [[3/1\|3]], [[5/1\|5]] and [[7/1\|7]] for 91edo are on the flat side, making this a mostly flat system. It [[tempering out\|tempers out]] [[15625/15552]] in the 5-limit, [[225/224]] and [[4375/4374]] in the 7-limit, [[245/242]], [[385/384]] in the 11-limit, and [[105/104]], [[144/143]], [[196/195]] in the 13-limit. It provides the [[optimal patent val]] for 11- and 13-limit [[septimin]] temperament, and the 13-limit rank-3 [[tripod]] temperament, as well as the 11-limit rank-4 temperament tempering out 245/242 and the 13-limit rank-5 temperament tempering out 105/104, or rank-4 tempering out 105/104 and 144/143, or else 105/104 and 196/195 and hence 225/224 also.

	Using the 91c val, it is audibly indistinguishable from a closed system of [[1/7-comma meantone]], with a 5th only 0.018 cents sharper. The chromatic semitone in this scale corresponds to 135/128, the [[eigenmonzo]] (unchanged-interval) of [[1/7-comma meantone]]. Being 7 steps, what is also remarkable is that in this instance the chromatic semitone is equal to one step of [[13edo]]. Since 135/128 is also equal to 1/13 of the octave, the 91c [[val]] tempers out the [[aluminium comma]] in the 5-limit.		Using the 91c val, it is audibly indistinguishable from a closed system of [[1/7-comma meantone]], with a 5th only 0.018 cents sharper. The chromatic semitone in this scale corresponds to 135/128, the [[eigenmonzo]] (unchanged interval) of [[1/7-comma meantone]]. Being 7 steps, what is also remarkable is that in this instance the chromatic semitone is equal to one step of [[13edo]]. Since 135/128 is also equal to 1/13 of the octave, the 91c [[val]] tempers out the [[aluminium comma]] in the 5-limit.

	It also tempers out the {{monzo\| -11 26 -13 }}, the tridecatonic comma, which assigns [[10/9]] to 2/13 of the octave, and it supports [[trideci]] in the 7-limit, tempering out 4375/4374 and 83349/81920. It supports a variant of [[semaphore]] temperament which tempers out the {{monzo\| -42 23 2 }} comma in the 2.3.7 [[subgroup]], and is generated by a 19\91 generator. It is the second highest in a series of four consecutive edos that temper out [[quartisma]] ({{monzo\| 24 -6 0 1 -5 }}), and as a corollary it is a tuning for the [[quartkeenlig]] temperament, which can also act as a [[23edo and octave stretching\|stretched]] [[23edo]]. In the 13-limit, it supports [[vidar]] and gives a reasonable tuning for its size.		It also tempers out the {{monzo\| -11 26 -13 }}, the tridecatonic comma, which assigns [[10/9]] to 2/13 of the octave, and it supports [[trideci]] in the 7-limit, tempering out 4375/4374 and 83349/81920. It supports a variant of [[semaphore]] temperament which tempers out the {{monzo\| -42 23 2 }} comma in the 2.3.7 [[subgroup]], and is generated by a 19\91 generator. It is the second highest in a series of four consecutive edos that temper out [[quartisma]] ({{monzo\| 24 -6 0 1 -5 }}), and as a corollary it is a tuning for the [[quartkeenlig]] temperament, which can also act as a [[23edo and octave stretching\|stretched]] [[23edo]]. In the 13-limit, it supports [[vidar]] and gives a reasonable tuning for its size.

Lucius Chiaraviglio: /* Music */ Insert Instruments section before this, now that a Lumatone mapping for 91edo is now available

2025-06-08T07:54:09Z

Music: Insert Instruments section before this, now that a Lumatone mapping for 91edo is now available

← Older revision		Revision as of 07:54, 8 June 2025
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	* ConcocticSubset[7]: 17 10 17 10 17 10 17		* ConcocticSubset[7]: 17 10 17 10 17 10 17
	* ConcocticMaqamSikah: 10 17 17 10 10 17 10		* ConcocticMaqamSikah: 10 17 17 10 10 17 10

			== Instruments ==

			A [[Lumatone mapping for 91edo]] is available.

	== Music ==		== Music ==

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''improv 91edo'' (2025)

2025-06-08T06:32:01Z

Music: Add Bryan Deister's ''improv 91edo'' (2025)

← Older revision		Revision as of 06:32, 8 June 2025
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/HaYUAg30298 ''microtonal improvisation in 91edo''] (2025)		* [https://www.youtube.com/shorts/HaYUAg30298 ''microtonal improvisation in 91edo''] (2025)
			* [https://www.youtube.com/shorts/z6PeEocYMV8 ''improv 91edo''] (2025)

	; [[Chris Vaisvil]]		; [[Chris Vaisvil]]

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''microtonal improvisation in 91edo'' (2025)

2025-06-02T20:55:10Z

Music: Add Bryan Deister's ''microtonal improvisation in 91edo'' (2025)

← Older revision		Revision as of 20:55, 2 June 2025
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	; [[Mercury Amalgam]]		; [[Mercury Amalgam]]
	* ''Sadness - Nope'' (2022) – [https://mercuryamalgam.bandcamp.com/track/sadness-nope-the-molecular-agoge-pt-2 Bandcamp] \| [https://www.youtube.com/watch?v=_5WS7AGZxm4 YouTube]		* ''Sadness - Nope'' (2022) – [https://mercuryamalgam.bandcamp.com/track/sadness-nope-the-molecular-agoge-pt-2 Bandcamp] \| [https://www.youtube.com/watch?v=_5WS7AGZxm4 YouTube]

			; [[Bryan Deister]]
			* [https://www.youtube.com/shorts/HaYUAg30298 ''microtonal improvisation in 91edo''] (2025)

	; [[Chris Vaisvil]]		; [[Chris Vaisvil]]

FloraC: Move the intervals and notation section to the expected place

2025-04-03T15:08:27Z

Move the intervals and notation section to the expected place

Show changes

FloraC: /* Notation */ fix the broken table and make it collapsed by default

2025-04-03T15:05:42Z

Notation: fix the broken table and make it collapsed by default

← Older revision		Revision as of 15:05, 3 April 2025
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	== Notation ==		== Notation ==

	=== Ups and downs notation ===		=== Ups and downs notation ===

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	[[User:Eliora\|Eliora]], who believes the diatonic way of naming intervals in 91edo is not useful due to the fact that other temperaments and techniques for 91edo are more prominent, proposes a way of naming that merges the factors 7 and 13—7 equidistant notes are named do, re, mi, and 13 are named by some other virtue. The proposition is to use Old Slavic letter names, since no one uses them for naming or in mathematics. The {{nowrap\|7 + 13}} naming convention can be called a duality notation. Intervals can be named through Latin ones for the 7-note scale, and Greek ones for the 13-note.		[[User:Eliora\|Eliora]], who believes the diatonic way of naming intervals in 91edo is not useful due to the fact that other temperaments and techniques for 91edo are more prominent, proposes a way of naming that merges the factors 7 and 13—7 equidistant notes are named do, re, mi, and 13 are named by some other virtue. The proposition is to use Old Slavic letter names, since no one uses them for naming or in mathematics. The {{nowrap\|7 + 13}} naming convention can be called a duality notation. Intervals can be named through Latin ones for the 7-note scale, and Greek ones for the 13-note.

	{\| class="wikitable mw-collapsible"		{\| class="wikitable center-1 mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| Table of intervals in 91edo		\|+ style="font-size: 105%; white-space: nowrap;" \| Table of intervals in 91edo
	\|-		\|-
	!		! #
	~~! &~~#~~35;~~		! Eliora's naming system
	! Eliora's ~~Naming System~~		! Eliora's notation
	! Eliora's ~~Notation~~		! Associated ratio
	! Associated ~~Ratio~~
	\|-		\|-
	\| 0		\| 0
	\| unison<br />perfect prime <br />perfect prota		\| unison<br>perfect prime <br>perfect prota
	\| A <br />Az (А)		\| A <br />Az (А)
	\| [[1/1]]		\| [[1/1]]
	\|-		\|-
	\| 1		\| 1
	\| major prime <br />major prota		\| major prime <br>major prota
	\| A# <br />Az#		\| A# <br>Az#
	\| [[1728/1715]]		\| [[1728/1715]]
	\|-		\|-
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	\|-		\|-
	\| 13		\| 13
	\| neutral secunde <br />minor tritia		\| neutral secunde <br>minor tritia
	\| B<br />Vedi♭		\| B<br>Vedi♭
	\| [[11/10]]		\| [[11/10]]
	\|-		\|-
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	\|-		\|-
	\| 26		\| 26
	\| neutral tertie <br />diminished pemptia		\| neutral tertie <br>diminished pemptia
	\| C <br />Dobro♭♭		\| C <br>Dobro♭♭
	\| [[11/9]]		\| [[11/9]]
	\|-		\|-
	\| 27		\| 27
	\| major tertie <br />minor pemptia		\| major tertie <br>minor pemptia
	\| C# <br />Dobro♭		\| C# <br />Dobro♭
	\| [[16/13]], 27/22		\| [[16/13]], 27/22
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	\|-		\|-
	\| 39		\| 39
	\| neutral quarte <br />bidiminished hebdomia		\| neutral quarte <br>bidiminished hebdomia
	\| D<br />Zhivete♭♭♭		\| D<br>Zhivete♭♭♭
	\|		\|
	\|-		\|-
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	\|-		\|-
	\| 54		\| 54
	\| augmented quinte <br />diminished ennatia		\| augmented quinte <br>diminished ennatia
	\| E## <br />Zemle♭♭		\| E## <br>Zemle♭♭
	\| [[256/169]]		\| [[256/169]]
	\|-		\|-
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	\|-		\|-
	\| 64		\| 64
	\| major decatia <br />minor sexte		\| major decatia <br>minor sexte
	\| Izhe# <br />F♭		\| Izhe# <br>F♭
	\|		\|
	\|-		\|-
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	\|-		\|-
	\| 91		\| 91
	\| perfect octave <br />perfect decatotetartia		\| perfect octave <br>perfect decatotetartia
	\| A<br />Az (А)		\| A<br>Az (А)
	\| [[2/1]] exact		\| [[2/1]] exact
	\|}		\|}

FloraC: -obviously unreasonable mapping

2025-04-03T15:03:28Z

-obviously unreasonable mapping

← Older revision		Revision as of 15:03, 3 April 2025
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	\| 0.860		\| 0.860
	\| 6.51		\| 6.51
	~~\|- style="border-top: double;"~~
	~~\| 2.3.5~~
	~~\| 81/80, {{vector\|52, 1, -23}}~~
	~~\| {{mapping\| 91 144 212 }} (91c)~~
	~~\| −0.696~~
	~~\| 2.468~~
	~~\| 18.713~~
	\|}		\|}