71edo - Revision history

Overthink: /* Theory */ vals

2026-06-19T20:51:52Z

Theory: vals

← Older revision		Revision as of 20:51, 19 June 2026
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	== Theory ==		== Theory ==
	71edo is a [[dual-fifth]] system, with the flat fifth (which is near the fifths of [[26edo]] and [[45edo]]) [[support]]ing [[flattone]] temperament, and the sharp fifth (which is near [[22edo]]'s fifth) supporting [[superpyth]]. Unlike small dual-fifth systems such as [[18edo]], both fifths are close approximations of 3/2.		71edo is a [[dual-fifth]] system, with the flat fifth (which is near the fifths of [[26edo]] and [[45edo]]) [[support]]ing [[flattone]] temperament with the 71c [[val]], and the sharp fifth (which is near [[22edo]]'s fifth) supporting [[superpyth]] with 71d. Unlike small dual-fifth systems such as [[18edo]], both fifths are close approximations of 3/2.

	Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] 20480/19683 and [[393216/390625]] in the [[5-limit]], [[875/864]], [[1029/1024]] and [[4000/3969]] in the [[7-limit]], [[100/99]] and [[245/242]] in the [[11-limit]], and [[91/90]] in the [[13-limit]]. In the 13-limit it supplies the optimal [[patent val]] for the 29 & 71 and 34 & 37 temperaments.		Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] 20480/19683 and [[393216/390625]] in the [[5-limit]], [[875/864]], [[1029/1024]] and [[4000/3969]] in the [[7-limit]], [[100/99]] and [[245/242]] in the [[11-limit]], and [[91/90]] in the [[13-limit]]. In the 13-limit it supplies the optimal [[patent val]] for the 29 & 71 and 34 & 37 temperaments.
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	71edo is the 20th [[prime edo]], following [[67edo]] and before [[73edo]]. [[142edo]], which doubles it, provides correction for the harmonic 3.		71edo is the 20th [[prime edo]], following [[67edo]] and before [[73edo]]. [[142edo]], which doubles it, provides correction for the harmonic 3.

	== Intervals ==		== Intervals ==

Lucius Chiaraviglio: /* Music */ Bryan Deister's ''Waltz in 71edo'' (2026): Add full version

2026-03-13T00:34:52Z

Music: Bryan Deister's ''Waltz in 71edo'' (2026): Add full version

← Older revision		Revision as of 00:34, 13 March 2026
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	* [https://www.youtube.com/shorts/qeYTgpddpw0 ''Glaceir - Deltarune (microtonal cover in 71edo)''] (2026)		* [https://www.youtube.com/shorts/qeYTgpddpw0 ''Glaceir - Deltarune (microtonal cover in 71edo)''] (2026)
	* [https://www.youtube.com/shorts/QMvxgs2UBDM ''The Time - Dancing Line (microtonal cover in 71edo)''] (2026)		* [https://www.youtube.com/shorts/QMvxgs2UBDM ''The Time - Dancing Line (microtonal cover in 71edo)''] (2026)
	* [https://www.youtube.com/shorts/vj2v8NFlrNo ~~''Waltz in 71edo''~~] (~~2026~~)		* ''Waltz in 71edo'' (2026)
			** [https://www.youtube.com/shorts/vj2v8NFlrNo <nowiki>[short]</nowiki>] (with Lumatone view)
			** [https://www.youtube.com/watch?v=fT-3gSfxLX8 <nowiki>[full version]</nowiki>]

	; [[Francium]]		; [[Francium]]

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''Waltz in 71edo'' (2026)

2026-03-09T02:38:31Z

Music: Add Bryan Deister's ''Waltz in 71edo'' (2026)

← Older revision		Revision as of 02:38, 9 March 2026
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	* [https://www.youtube.com/shorts/qeYTgpddpw0 ''Glaceir - Deltarune (microtonal cover in 71edo)''] (2026)		* [https://www.youtube.com/shorts/qeYTgpddpw0 ''Glaceir - Deltarune (microtonal cover in 71edo)''] (2026)
	* [https://www.youtube.com/shorts/QMvxgs2UBDM ''The Time - Dancing Line (microtonal cover in 71edo)''] (2026)		* [https://www.youtube.com/shorts/QMvxgs2UBDM ''The Time - Dancing Line (microtonal cover in 71edo)''] (2026)
			* [https://www.youtube.com/shorts/vj2v8NFlrNo ''Waltz in 71edo''] (2026)

	; [[Francium]]		; [[Francium]]

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''The Time - Dancing Line (microtonal cover in 71edo)'' (2026)

2026-03-07T08:54:13Z

Music: Add Bryan Deister's ''The Time - Dancing Line (microtonal cover in 71edo)'' (2026)

← Older revision		Revision as of 08:54, 7 March 2026
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	* [https://www.youtube.com/shorts/nMMSQdIV30I ''71edo improv''] (2025)		* [https://www.youtube.com/shorts/nMMSQdIV30I ''71edo improv''] (2025)
	* [https://www.youtube.com/shorts/qeYTgpddpw0 ''Glaceir - Deltarune (microtonal cover in 71edo)''] (2026)		* [https://www.youtube.com/shorts/qeYTgpddpw0 ''Glaceir - Deltarune (microtonal cover in 71edo)''] (2026)
			* [https://www.youtube.com/shorts/QMvxgs2UBDM ''The Time - Dancing Line (microtonal cover in 71edo)''] (2026)

	; [[Francium]]		; [[Francium]]

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''Glaceir - Deltarune (microtonal cover in 71edo)'' (2026)

2026-02-06T16:09:16Z

Music: Add Bryan Deister's ''Glaceir - Deltarune (microtonal cover in 71edo)'' (2026)

← Older revision		Revision as of 16:09, 6 February 2026
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/nMMSQdIV30I ''71edo improv''] (2025)		* [https://www.youtube.com/shorts/nMMSQdIV30I ''71edo improv''] (2025)
			* [https://www.youtube.com/shorts/qeYTgpddpw0 ''Glaceir - Deltarune (microtonal cover in 71edo)''] (2026)

	; [[Francium]]		; [[Francium]]

ArrowHead294 at 12:08, 30 June 2025

2025-06-30T12:08:00Z

@@ Line 87: / Line 87: @@
 In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.
 == Instruments ==
 A [[Lumatone mapping for 71edo]] is available.

Lucius Chiaraviglio: /* Music */ Insert Instruments section before this, now that a Lumatone mapping for 71edo is now available

2025-05-08T20:16:09Z

Music: Insert Instruments section before this, now that a Lumatone mapping for 71edo is now available

← Older revision		Revision as of 20:16, 8 May 2025
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	In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma\|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.		In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma\|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.

			== Instruments ==

			A [[Lumatone mapping for 71edo]] is available.

	== Music ==		== Music ==

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''71edo improv'' (2025)

2025-05-06T09:11:35Z

Music: Add Bryan Deister's ''71edo improv'' (2025)

← Older revision		Revision as of 09:11, 6 May 2025
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	== Music ==		== Music ==
			; [[Bryan Deister]]
			* [https://www.youtube.com/shorts/nMMSQdIV30I ''71edo improv''] (2025)

	; [[Francium]]		; [[Francium]]
	* [https://www.youtube.com/watch?v=_FPTUlO6jNI ''Dancing in the Mosh Pit''] (2023)		* [https://www.youtube.com/watch?v=_FPTUlO6jNI ''Dancing in the Mosh Pit''] (2023)

ArrowHead294 at 18:16, 20 February 2025

2025-02-20T18:16:07Z

← Older revision		Revision as of 18:16, 20 February 2025
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	== Notation ==		== Notation ==
			=== Sagittal notation ===
	===Sagittal notation===		==== Best fifth notation ====
	====Best fifth notation====		===== Evo flavor =====
	=====Evo flavor=====

	<imagemap>		<imagemap>
	File:71-EDO_Evo_Sagittal.svg		File:71-EDO_Evo_Sagittal.svg
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	</imagemap>		</imagemap>

	=====Revo flavor=====		===== Revo flavor =====

	<imagemap>		<imagemap>
	File:71-EDO_Revo_Sagittal.svg		File:71-EDO_Revo_Sagittal.svg
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	</imagemap>		</imagemap>

	=====Evo-SZ flavor=====		===== Evo-SZ flavor =====

	<imagemap>		<imagemap>
	File:71-EDO_Evo-SZ_Sagittal.svg		File:71-EDO_Evo-SZ_Sagittal.svg
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	In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma\|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.		In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma\|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.

	====Second-best fifth notation====		==== Second-best fifth notation ====
	This notation uses the same sagittal sequence as EDOs [[50edo#Sagittal notation\|50]], [[57edo#Sagittal notation\|57]], and [[64edo#Sagittal notation\|64]].		This notation uses the same sagittal sequence as EDOs [[50edo#Sagittal notation\|50]], [[57edo#Sagittal notation\|57]], and [[64edo#Sagittal notation\|64]].
	~~=====Evo flavor=====~~

			===== Evo flavor =====
	<imagemap>		<imagemap>
	File:71b_Evo_Sagittal.svg		File:71b_Evo_Sagittal.svg
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	</imagemap>		</imagemap>

	=====Revo flavor=====		===== Revo flavor =====

	<imagemap>		<imagemap>
	File:71b_Revo_Sagittal.svg		File:71b_Revo_Sagittal.svg

Francium: changed EDO intro to ED intro

2025-02-19T18:19:56Z

changed EDO intro to ED intro

← Older revision		Revision as of 18:19, 19 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|71~~}}		{{ED intro}}

	== Theory ==		== Theory ==