26edo - Revision history

Lucius Chiaraviglio: /* 21st century */ Bryan Deister's ''Caprice in 26edo'' (2026): Add full version

2026-08-26T08:54:12Z

21st century: Bryan Deister's ''Caprice in 26edo'' (2026): Add full version

← Older revision		Revision as of 08:54, 26 August 2026
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	** [https://www.youtube.com/watch?v=XplpKE_Tc38 <nowiki>[full version[</nowiki>] (with animation by WIRED0006)		** [https://www.youtube.com/watch?v=XplpKE_Tc38 <nowiki>[full version[</nowiki>] (with animation by WIRED0006)
	* [https://www.youtube.com/shorts/wHGLOaeAkt8 ''26edo groove''] (2026)		* [https://www.youtube.com/shorts/wHGLOaeAkt8 ''26edo groove''] (2026)
	* [https://www.youtube.com/shorts/WvnJb5VNGj4 ''<nowiki>~~Caprice in 26edo~~ [short clip]</nowiki>''] (~~2026~~)		* ''Caprice in 26edo'' (2026)
			** [https://www.youtube.com/shorts/WvnJb5VNGj4 <nowiki>[short clip]</nowiki>] (Lumatone view)
			** [https://www.youtube.com/watch?v=mMQADmxJkFc <nowiki>[full version]</nowiki>]

	; [[User:Eboone\|Ebooone]]		; [[User:Eboone\|Ebooone]]

Lucius Chiaraviglio: /* 21st century */ Add Bryan Deister's ''Caprice in 26edo [short clip]'' (2026)

2026-08-24T02:32:03Z

21st century: Add Bryan Deister's ''Caprice in 26edo [short clip]'' (2026)

← Older revision		Revision as of 02:32, 24 August 2026
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	** [https://www.youtube.com/watch?v=XplpKE_Tc38 <nowiki>[full version[</nowiki>] (with animation by WIRED0006)		** [https://www.youtube.com/watch?v=XplpKE_Tc38 <nowiki>[full version[</nowiki>] (with animation by WIRED0006)
	* [https://www.youtube.com/shorts/wHGLOaeAkt8 ''26edo groove''] (2026)		* [https://www.youtube.com/shorts/wHGLOaeAkt8 ''26edo groove''] (2026)
			* [https://www.youtube.com/shorts/WvnJb5VNGj4 ''<nowiki>Caprice in 26edo [short clip]</nowiki>''] (2026)

	; [[User:Eboone\|Ebooone]]		; [[User:Eboone\|Ebooone]]

Lucius Chiaraviglio: /* Instruments */ Add ''A rough introduction to 26edo on the Lumatone'' by YoVariable (2026)

2026-07-05T01:51:53Z

Instruments: Add ''A rough introduction to 26edo on the Lumatone'' by YoVariable (2026)

← Older revision		Revision as of 01:51, 5 July 2026
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	* [[Lumatone mapping for 26edo]]		* [[Lumatone mapping for 26edo]]

			* [https://www.youtube.com/watch?v=HrZ-PoUXGTg ''A rough introduction to 26edo on the Lumatone''] by [[YoVariable]] (2026)

	== Literature ==		== Literature ==
	[http://www.ronsword.com Sword, Ron. Icosihexaphonic Scales for Guitar. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.]		[http://www.ronsword.com Sword, Ron. Icosihexaphonic Scales for Guitar. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.]

Lucius Chiaraviglio: /* 21st century */ Bryan Deister's''My Violet - 26edo'' (2026): Add full version

2026-06-06T02:58:51Z

21st century: Bryan Deister's''My Violet - 26edo'' (2026): Add full version

← Older revision		Revision as of 02:58, 6 June 2026
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	* [https://www.youtube.com/shorts/1aCl6tuVS0c ''Happy Together - The Turtles (microtonal cover in 26edo)''] (2026)		* [https://www.youtube.com/shorts/1aCl6tuVS0c ''Happy Together - The Turtles (microtonal cover in 26edo)''] (2026)
	* ''My Violet - 26edo'' (2026)		* ''My Violet - 26edo'' (2026)
	** [https://www.youtube.com/shorts/m76bQWxg_CA <nowiki>[short 1]</nowiki>'']		** [https://www.youtube.com/shorts/m76bQWxg_CA <nowiki>[short 1]</nowiki>] (Lumatone view)
	** [https://www.youtube.com/shorts/L2JzCNj6jak <nowiki>[short 2]</nowiki>'']		** [https://www.youtube.com/shorts/L2JzCNj6jak <nowiki>[short 2]</nowiki>] (Lumatone view)
			** [https://www.youtube.com/watch?v=XplpKE_Tc38 <nowiki>[full version[</nowiki>] (with animation by WIRED0006)
	* [https://www.youtube.com/shorts/wHGLOaeAkt8 ''26edo groove''] (2026)		* [https://www.youtube.com/shorts/wHGLOaeAkt8 ''26edo groove''] (2026)

FloraC: Move Fynn's comma to subsets and supersets section

2026-04-11T07:44:13Z

Move Fynn's comma to subsets and supersets section

← Older revision		Revision as of 07:44, 11 April 2026
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	{{~~interwiki~~		{{Interwiki
			\| en = 26edo
	\| de = 26-EDO		\| de = 26-EDO
	~~\| en = 26edo~~
	\| es =		\| es =
	\| ja =		\| ja =
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	26edo has a [[3/2\|perfect fifth]] of about 692 cents and [[tempering out\|tempers out]] [[81/80]] in the [[5-limit]], making it a very flat [[meantone]] tuning (0.088957{{c}} flat of the [[4/9-comma meantone]] fifth) with a very soft [[5L 2s\|diatonic scale]].		26edo has a [[3/2\|perfect fifth]] of about 692 cents and [[tempering out\|tempers out]] [[81/80]] in the [[5-limit]], making it a very flat [[meantone]] tuning (0.088957{{c}} flat of the [[4/9-comma meantone]] fifth) with a very soft [[5L 2s\|diatonic scale]].

	In the [[7-limit]], it tempers out [[50/49]], [[525/512]], [[875/864~~]], and [[Fynn's comma~~]], and [[support]]s temperaments like [[injera]], [[flattone]], [[lemba]], and [[doublewide]]. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13-odd-limit]] [[consistent]]ly. 26edo has a very good approximation of the harmonic seventh ([[7/4]]), as it is the denominator of a convergent to log<sub>2</sub>7.		In the [[7-limit]], it tempers out [[50/49]], [[525/512]], and [[875/864]], and [[support]]s temperaments like [[injera]], [[flattone]], [[lemba]], and [[doublewide]]. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13-odd-limit]] [[consistent]]ly. 26edo has a very good approximation of the harmonic seventh ([[7/4]]), as it is the denominator of a convergent to log<sub>2</sub>7.

	26edo's minor sixth (1.6158) is very close to {{nowrap\|''φ'' ≈ 1.6180}} (i.e. the golden ratio).		26edo's minor sixth (1.6158) is very close to {{nowrap\|''φ'' ≈ 1.6180}} (i.e. the golden ratio).
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	26edo has [[2edo]] and [[13edo]] as subsets, of which 13edo is non-trivial, sharing the 2.9.5.21.11.13.17.19-subgroup with 26edo. Multiplying 26edo by 3 yields [[78edo]], which corrects several harmonics. [[104edo]] is a notable dual-5s system. [[130edo]], [[364edo]], [[494edo]], and [[624edo]] do well in approximating JI, though they are more complex.		26edo has [[2edo]] and [[13edo]] as subsets, of which 13edo is non-trivial, sharing the 2.9.5.21.11.13.17.19-subgroup with 26edo.

			26edo tempers out [[Fynn's comma]], which sets ~7/4 to 21\26. This is shared by several notable superset edos. Multiplying 26edo by 3 yields [[78edo]], which corrects several harmonics. [[104edo]] is a notable dual-5's system. [[130edo]], [[364edo]], [[494edo]], and [[624edo]] do well in approximating JI, though they are more complex.

	== Intervals ==		== Intervals ==

Fynn Cerulean: Added note that 26EDO tempers out Fynn's comma

2026-04-11T03:24:56Z

Added note that 26EDO tempers out Fynn's comma

← Older revision		Revision as of 03:24, 11 April 2026
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	26edo has a [[3/2\|perfect fifth]] of about 692 cents and [[tempering out\|tempers out]] [[81/80]] in the [[5-limit]], making it a very flat [[meantone]] tuning (0.088957{{c}} flat of the [[4/9-comma meantone]] fifth) with a very soft [[5L 2s\|diatonic scale]].		26edo has a [[3/2\|perfect fifth]] of about 692 cents and [[tempering out\|tempers out]] [[81/80]] in the [[5-limit]], making it a very flat [[meantone]] tuning (0.088957{{c}} flat of the [[4/9-comma meantone]] fifth) with a very soft [[5L 2s\|diatonic scale]].

	In the [[7-limit]], it tempers out [[50/49]], [[525/512]], ~~and~~ [[875/864]], and [[support]]s temperaments like [[injera]], [[flattone]], [[lemba]], and [[doublewide]]. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13-odd-limit]] [[consistent]]ly. 26edo has a very good approximation of the harmonic seventh ([[7/4]]), as it is the denominator of a convergent to log<sub>2</sub>7.		In the [[7-limit]], it tempers out [[50/49]], [[525/512]], [[875/864]], and [[Fynn's comma]], and [[support]]s temperaments like [[injera]], [[flattone]], [[lemba]], and [[doublewide]]. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13-odd-limit]] [[consistent]]ly. 26edo has a very good approximation of the harmonic seventh ([[7/4]]), as it is the denominator of a convergent to log<sub>2</sub>7.

	26edo's minor sixth (1.6158) is very close to {{nowrap\|''φ'' ≈ 1.6180}} (i.e. the golden ratio).		26edo's minor sixth (1.6158) is very close to {{nowrap\|''φ'' ≈ 1.6180}} (i.e. the golden ratio).

Overthink: /* Approximation to irrational intervals */ clarify

2026-03-27T22:06:34Z

Approximation to irrational intervals: clarify

← Older revision		Revision as of 22:06, 27 March 2026
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	== Approximation to irrational intervals ==		== Approximation to irrational intervals ==
	26edo approximates both [[acoustic phi]] (the [[golden ratio]]) and [[pi]] quite accurately. Not until 1076edo do we find a better edo in terms of relative error on these intervals.		26edo approximates both [[acoustic phi]] (the [[golden ratio]]) and [[pi]] quite accurately. Not until 1076edo do we find a better edo in terms of relative error on these intervals{{Clarify}}.

	{\| class="wikitable center-all"		{\| class="wikitable center-all"

Overthink: /* Intervals */ add 26/21, 64/49, and complements

2026-03-27T22:05:56Z

Intervals: add 26/21, 64/49, and complements

← Older revision		Revision as of 22:05, 27 March 2026
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	\| 8		\| 8
	\| 369.23		\| 369.23
	\| [[5/4]], [[11/9]], [[16/13]]		\| [[5/4]], [[11/9]], [[16/13]], [[26/21]]
	\| M3		\| M3
	\| F#		\| F#
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	\| 10		\| 10
	\| 461.54		\| 461.54
	\| [[21/16]], [[13/10]]		\| [[21/16]], [[13/10]], [[64/49]]
	\| d4		\| d4
	\| Gb		\| Gb
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	\| 16		\| 16
	\| 738.46		\| 738.46
	\| [[32/21]], [[20/13]]		\| [[32/21]], [[20/13]], [[49/32]]
	\| A5		\| A5
	\| A#		\| A#
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	\| 18		\| 18
	\| 830.77		\| 830.77
	\| [[13/8]], [[8/5]]		\| [[8/5]], [[13/8]], [[21/13]]
	\| m6		\| m6
	\| Bb		\| Bb

Lucius Chiaraviglio: /* 21st century */ Add Bryan Deister's ''26edo groove'' (2026)

2026-03-27T06:37:36Z

21st century: Add Bryan Deister's ''26edo groove'' (2026)

← Older revision		Revision as of 06:37, 27 March 2026
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	** [https://www.youtube.com/shorts/m76bQWxg_CA <nowiki>[short 1]</nowiki>'']		** [https://www.youtube.com/shorts/m76bQWxg_CA <nowiki>[short 1]</nowiki>'']
	** [https://www.youtube.com/shorts/L2JzCNj6jak <nowiki>[short 2]</nowiki>'']		** [https://www.youtube.com/shorts/L2JzCNj6jak <nowiki>[short 2]</nowiki>'']
			* [https://www.youtube.com/shorts/wHGLOaeAkt8 ''26edo groove''] (2026)

	; [[User:Eboone\|Ebooone]]		; [[User:Eboone\|Ebooone]]

Lucius Chiaraviglio: /* Music */ Split into 26edo proper and unequal derivatives of 26edo, starting with Bryan Deister's Daisy Bell - Harry Dacre (microtonal cover in unequal 26ish tone [displaced from 26edo in dozens]) (2026)

2026-02-25T08:36:57Z

Music: Split into 26edo proper and unequal derivatives of 26edo, starting with Bryan Deister's Daisy Bell - Harry Dacre (microtonal cover in unequal 26ish tone [displaced from 26edo in dozens]) (2026)

← Older revision		Revision as of 08:36, 25 February 2026
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	{{Catrel\|26edo tracks}}		{{Catrel\|26edo tracks}}

	=== Modern renderings ===		=== 26 equal divisions of the octave (26edo proper) ===
			==== Modern renderings ====
	; {{W\|Johann Sebastian Bach}}		; {{W\|Johann Sebastian Bach}}
	* [https://www.youtube.com/watch?v=LUNOFjiyZ0Y ''Contrapunctus 4'' from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)		* [https://www.youtube.com/watch?v=LUNOFjiyZ0Y ''Contrapunctus 4'' from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
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	* [https://www.youtube.com/watch?v=-EVO5ntuoSM ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024)		* [https://www.youtube.com/watch?v=-EVO5ntuoSM ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024)

	=== 21st century ===		==== 21st century ====
	; [[Abnormality]]		; [[Abnormality]]
	* [https://www.youtube.com/watch?v=Tl-AN2zQeAI ''Break''] (2024)		* [https://www.youtube.com/watch?v=Tl-AN2zQeAI ''Break''] (2024)
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	; [[YoVariable]]		; [[YoVariable]]
	* [https://www.youtube.com/watch?v=01w70PbbT3o ''Jingle Bells (26edo microtonal Lumatone cover + Mystery Song)''] (2025)		* [https://www.youtube.com/watch?v=01w70PbbT3o ''Jingle Bells (26edo microtonal Lumatone cover + Mystery Song)''] (2025)

			=== Unequal Derivatives of 26edo ===
			; [[Bryan Deister]]
			* [https://www.youtube.com/shorts/mzUGcki6H0Y ''<nowiki>Daisy Bell - Harry Dacre (microtonal cover in unequal 26ish tone [displaced from 26edo in dozens])</nowiki>''] (2026) — from Bryan Deister's video comments, "displacement in cents roughly: 0, -8, -3, -12, 14, 5, 18, 3, -12, 13, -15, 10" (these repeat every 12 notes, NOT every 13 note semi-octave, thus causing each octave to be different)

	[[Category:Listen]]		[[Category:Listen]]