86edo - Revision history

BudjarnLambeth: /* See also */

2025-10-20T03:13:01Z

BudjarnLambeth: add see also

2025-10-20T03:05:03Z

add see also

← Older revision		Revision as of 03:05, 20 October 2025
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/5_W323Iea18 ''microtonal improvisation in 86edo''] (2025)		* [https://www.youtube.com/shorts/5_W323Iea18 ''microtonal improvisation in 86edo''] (2025)

			== See also ==
			* [[343edo#Scales\|343ed16]] (octave-stretched version of 86edo)

Fredg999: /* Theory */ Skip disambiguation page

2025-08-06T01:53:36Z

Theory: Skip disambiguation page

← Older revision		Revision as of 01:53, 6 August 2025
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	It is perhaps more interesting to consider the alternative 86e val, which tempers out [[121/120]] and [[243/242]] and [[support]]s 11-limit mohajira. The 86de val is a less good entry for 11-limit [[migration]]. In any case, this tuning is between [[31edo]] and [[55edo]], and replaces 43edo's lopsided placement of [[11/9]] and [[27/22]] with a true neutral third.		It is perhaps more interesting to consider the alternative 86e val, which tempers out [[121/120]] and [[243/242]] and [[support]]s 11-limit mohajira. The 86de val is a less good entry for 11-limit [[migration]]. In any case, this tuning is between [[31edo]] and [[55edo]], and replaces 43edo's lopsided placement of [[11/9]] and [[27/22]] with a true neutral third.

	86edo is closely related to the [[delta scale]], which is the equal division of the [[16/15\|classic diatonic semitone]] into eight parts of 13.9664{{c}} each.		86edo is closely related to the [[8ed16/15\|delta scale]], which is the equal division of the [[16/15\|classic diatonic semitone]] into eight parts of 13.9664{{c}} each.

	=== Odd harmonics ===		=== Odd harmonics ===

Lucius Chiaraviglio: /* Music */ Insert Instruments section before this, now that a Lumatone mapping for 86edo is now available

2025-07-21T09:05:16Z

Music: Insert Instruments section before this, now that a Lumatone mapping for 86edo is now available

← Older revision		Revision as of 09:05, 21 July 2025
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	== Interval table ==		== Interval table ==
	{{Interval table}}		{{Interval table}}

			== Instruments ==

			A [[Lumatone mapping for 86edo]] is available.

	== Music ==		== Music ==
	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/5_W323Iea18 ''microtonal improvisation in 86edo''] (2025)		* [https://www.youtube.com/shorts/5_W323Iea18 ''microtonal improvisation in 86edo''] (2025)

Lucius Chiaraviglio: /* Interval table */ Insert Music section after this, starting with Bryan Deister's ''microtonal improvisation in 86edo'' (2025)

2025-07-18T09:34:23Z

Interval table: Insert Music section after this, starting with Bryan Deister's ''microtonal improvisation in 86edo'' (2025)

← Older revision		Revision as of 09:34, 18 July 2025
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	== Interval table ==		== Interval table ==
	{{Interval table}}		{{Interval table}}

			== Music ==
			; [[Bryan Deister]]
			* [https://www.youtube.com/shorts/5_W323Iea18 ''microtonal improvisation in 86edo''] (2025)

ArrowHead294 at 16:31, 20 February 2025

2025-02-20T16:31:10Z

← Older revision		Revision as of 16:31, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|86~~}}		{{ED intro}}

	== Theory ==		== Theory ==
	86 = 2 × 43, and the [[patent val]] is a [[contorted]] [[43edo]] in the 5-limit. In the 7-limit the [[patent val]] [[tempering out\|tempers out]] 6144/6125, so that it [[support]]s the [[mohajira]] temperament. In the 11-limit it tempers out [[245/242]], [[540/539]] and [[4000/3993]], and in the 13-limit [[144/143]], [[196/195]] and [[676/675]]. It provides the optimal patent val for the 13-limit 9 & 86 temperament tempering out 144/143, 196/195, 245/242 and 676/675.		Since {{nowrap\|86 {{=}} 2 × 43}}, and the [[patent val]] is a [[contorted]] [[43edo]] in the 5-limit. In the 7-limit the [[patent val]] [[tempering out\|tempers out]] 6144/6125, so that it [[support]]s the [[mohajira]] temperament. In the 11-limit it tempers out [[245/242]], [[540/539]] and [[4000/3993]], and in the 13-limit [[144/143]], [[196/195]] and [[676/675]]. It provides the optimal patent val for the 13-limit 9 & 86 temperament tempering out 144/143, 196/195, 245/242 and 676/675.

	It is perhaps more interesting to consider the alternative 86e val, which tempers out [[121/120]] and [[243/242]] and [[support]]s 11-limit mohajira. The 86de val is a less good entry for 11-limit [[migration]]. In any case, this tuning is between [[31edo]] and [[55edo]], and replaces 43edo's lopsided placement of [[11/9]] and [[27/22]] with a true neutral third.		It is perhaps more interesting to consider the alternative 86e val, which tempers out [[121/120]] and [[243/242]] and [[support]]s 11-limit mohajira. The 86de val is a less good entry for 11-limit [[migration]]. In any case, this tuning is between [[31edo]] and [[55edo]], and replaces 43edo's lopsided placement of [[11/9]] and [[27/22]] with a true neutral third.

	86edo is closely related to the [[delta scale]], which is the equal division of the [[16/15\|classic diatonic semitone]] into eight parts of 13.9664 ~~cents~~ each.		86edo is closely related to the [[delta scale]], which is the equal division of the [[16/15\|classic diatonic semitone]] into eight parts of 13.9664{{c}} each.

	=== Odd harmonics ===		=== Odd harmonics ===

FloraC: /* Theory */ expand

2024-06-21T08:29:01Z

Theory: expand

← Older revision		Revision as of 08:29, 21 June 2024
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	== Theory ==		== Theory ==
	86 = 2 × 43, and the [[patent val]] is a [[contorted]] [[43edo]] in the 5-limit. In the 7-limit the patent val tempers out 6144/6125, so that it [[support]]s mohajira temperament. In the 11-limit it tempers out [[245/242]], [[540/539]] and [[4000/3993]], and in the 13-limit [[144/143]], [[196/195]] and [[676/675]]. It provides the optimal patent val for the 13-limit 9 & 86 temperament tempering out 144/143, 196/195, 245/242 and 676/675.		86 = 2 × 43, and the [[patent val]] is a [[contorted]] [[43edo]] in the 5-limit. In the 7-limit the [[patent val]] [[tempering out\|tempers out]] 6144/6125, so that it [[support]]s the [[mohajira]] temperament. In the 11-limit it tempers out [[245/242]], [[540/539]] and [[4000/3993]], and in the 13-limit [[144/143]], [[196/195]] and [[676/675]]. It provides the optimal patent val for the 13-limit 9 & 86 temperament tempering out 144/143, 196/195, 245/242 and 676/675.

			It is perhaps more interesting to consider the alternative 86e val, which tempers out [[121/120]] and [[243/242]] and [[support]]s 11-limit mohajira. The 86de val is a less good entry for 11-limit [[migration]]. In any case, this tuning is between [[31edo]] and [[55edo]], and replaces 43edo's lopsided placement of [[11/9]] and [[27/22]] with a true neutral third.

	86edo is closely related to the [[delta scale]], which is the equal division of the [[16/15\|classic diatonic semitone]] into eight parts of 13.9664 cents each.		86edo is closely related to the [[delta scale]], which is the equal division of the [[16/15\|classic diatonic semitone]] into eight parts of 13.9664 cents each.
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	86edo contains [[2edo]] and [[43edo]] as subsets. [[258edo]], which triples it, is a notable tuning.		86edo contains [[2edo]] and [[43edo]] as subsets. [[258edo]], which triples it, is a notable tuning.

	== Interval table ==		== Interval table ==
	{{Interval table}}		{{Interval table}}

FloraC: +subsets and supersets

2024-06-21T08:18:55Z

+subsets and supersets

← Older revision		Revision as of 08:18, 21 June 2024
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	{{EDO intro\|86}}		{{EDO intro\|86}}

	86 = 2 × 43, and the [[patent val]] is a [[contorted]] [[43edo~~\|43~~]] in the 5-limit. In the 7-limit the patent val tempers out 6144/6125, so that it [[support]]s mohajira temperament. In the 11-limit it tempers out [[245/242]], [[540/539]] and [[4000/3993]], and in the 13-limit [[144/143]], [[196/195]] and [[676/675]]. It provides the optimal patent val for the 13-limit 9 & 86 temperament tempering out 144/143, 196/195, 245/242 and 676/675.		== Theory ==
			86 = 2 × 43, and the [[patent val]] is a [[contorted]] [[43edo]] in the 5-limit. In the 7-limit the patent val tempers out 6144/6125, so that it [[support]]s mohajira temperament. In the 11-limit it tempers out [[245/242]], [[540/539]] and [[4000/3993]], and in the 13-limit [[144/143]], [[196/195]] and [[676/675]]. It provides the optimal patent val for the 13-limit 9 & 86 temperament tempering out 144/143, 196/195, 245/242 and 676/675.

	86edo is closely related to the [[delta scale]], which is the equal division of the [[16/15\|classic diatonic semitone]] into eight parts of 13.9664 cents each.		86edo is closely related to the [[delta scale]], which is the equal division of the [[16/15\|classic diatonic semitone]] into eight parts of 13.9664 cents each.
Line 8:		Line 9:
	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|86}}		{{Harmonics in equal\|86}}

			=== Subsets and supersets ===
			86edo contains [[2edo]] and [[43edo]] as subsets. [[258edo]], which triples it, is a notable tuning.

	== Interval table ==		== Interval table ==
	{{Interval table}}		{{Interval table}}

FloraC: Fix intro; style; -redundant category

2023-08-18T02:52:32Z

Fix intro; style; -redundant category

← Older revision		Revision as of 02:52, 18 August 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro}}. 86 = 2 * 43, and the [[patent val]] is a [[contorted]] [[43edo\|43]] in the 5-limit. In the 7-limit the patent val tempers out 6144/6125, so that it [[support]]s mohajira temperament. In the 11-limit it tempers out 245/242, 540/539 and 4000/3993, and in the 13-limit 144/143, 196/195 and 676/675. It provides the optimal patent val for the 13-limit 9&86 temperament tempering out 144/143, 196/195, 245/242 and 676/675.		{{EDO intro\|86}}

	86edo is closely related to the [[delta scale]], which is the equal division of the [[16/15\|classic diatonic semitone]] into eight parts of 13.9664 cents each.		86 = 2 × 43, and the [[patent val]] is a [[contorted]] [[43edo\|43]] in the 5-limit. In the 7-limit the patent val tempers out 6144/6125, so that it [[support]]s mohajira temperament. In the 11-limit it tempers out [[245/242]], [[540/539]] and [[4000/3993]], and in the 13-limit [[144/143]], [[196/195]] and [[676/675]]. It provides the optimal patent val for the 13-limit 9 & 86 temperament tempering out 144/143, 196/195, 245/242 and 676/675.
	{{~~harmonics~~ in equal\|86}}
			86edo is closely related to the [[delta scale]], which is the equal division of the [[16/15\|classic diatonic semitone]] into eight parts of 13.9664 cents each.

			=== Odd harmonics ===
			{{Harmonics in equal\|86}}

	== Interval table ==		== Interval table ==
	{{Interval table}}		{{Interval table}}
	~~[[Category:Equal divisions of the octave\|##]] <!-- 2-digit number -->~~

CompactStar at 03:14, 5 July 2023

2023-07-05T03:14:36Z

← Older revision		Revision as of 03:14, 5 July 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''86edo''' is the [[~~EDO~~\|equal division of the octave]] into 86 parts of 13.9535 cents each~~. 86 = 2 * 43, and the [[patent val]] is a [[contorted]] [[43edo\|43]] in the 5-limit. In the 7-limit the patent val tempers out 6144/6125, so that it [[support]]s mohajira temperament. In the 11-limit it tempers out 245/242, 540/539 and 4000/3993, and in the 13-limit 144/143, 196/195 and 676/675. It provides the optimal patent val for the 13-limit 9&86 temperament tempering out 144/143, 196/195, 245/242 and 676/675.		{{EDO intro}}. 86 = 2 * 43, and the [[patent val]] is a [[contorted]] [[43edo\|43]] in the 5-limit. In the 7-limit the patent val tempers out 6144/6125, so that it [[support]]s mohajira temperament. In the 11-limit it tempers out 245/242, 540/539 and 4000/3993, and in the 13-limit 144/143, 196/195 and 676/675. It provides the optimal patent val for the 13-limit 9&86 temperament tempering out 144/143, 196/195, 245/242 and 676/675.

	86edo is closely related to the [[delta scale]], which is the equal division of the [[16/15\|classic diatonic semitone]] into eight parts of 13.9664 cents each.		86edo is closely related to the [[delta scale]], which is the equal division of the [[16/15\|classic diatonic semitone]] into eight parts of 13.9664 cents each.
	{{harmonics in equal\|86}}		{{harmonics in equal\|86}}

			== Interval table ==
			{{Interval table}}
	[[Category:Equal divisions of the octave\|##]] <!-- 2-digit number -->		[[Category:Equal divisions of the octave\|##]] <!-- 2-digit number -->

← Older revision		Revision as of 03:13, 20 October 2025
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	== See also ==		== See also ==
	* [[343edo#~~Scales~~\|343ed16]] (octave-stretched version of 86edo)		* [[343edo#343ed16\|343ed16]] (octave-stretched version of 86edo)