56edo - Revision history

Lucius Chiaraviglio: /* Modern renderings */ Add Aiobahn's ''I'm Here'' (2019) — microtonal cover in 56edo by Bryan Deister

2026-10-27T15:59:28Z

Modern renderings: Add Aiobahn's ''I'm Here'' (2019) — microtonal cover in 56edo by Bryan Deister

← Older revision		Revision as of 15:59, 27 October 2026
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	== Music ==		== Music ==
	=== Modern renderings ===		=== Modern renderings ===
			; Aiobahn
			* [https://www.youtube.com/shorts/MduoLpDFG4Y ''I'm Here''] (2019) — microtonal cover in 56edo by [[Bryan Deister]]

	; {{W\|The Beatles}}		; {{W\|The Beatles}}
	* [https://www.youtube.com/shorts/WsvSVp3xyr8 "I Will" from ''The Beatles''] (1968) – covered by [[Bryan Deister]] (2026)		* [https://www.youtube.com/shorts/WsvSVp3xyr8 "I Will" from ''The Beatles''] (1968) – covered by Bryan Deister (2026)

	; {{W\|Susumu Hirasawa}}		; {{W\|Susumu Hirasawa}}

Lucius Chiaraviglio: /* 21st century */ Add Claudi Meneghin's ''CANON in F, 2-in-1: First Part, RECTUS'' (2026)

2026-09-06T05:38:50Z

21st century: Add Claudi Meneghin's ''CANON in F, 2-in-1: First Part, RECTUS'' (2026)

← Older revision		Revision as of 05:38, 6 September 2026
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	* [https://www.youtube.com/watch?v=3oO1SIVWBgI ''Mirror Canon in F''] (2020)		* [https://www.youtube.com/watch?v=3oO1SIVWBgI ''Mirror Canon in F''] (2020)
	* [https://www.youtube.com/watch?v=s1h083BRWXU ''Canon 3-in-1 on a Ground''] (2020)		* [https://www.youtube.com/watch?v=s1h083BRWXU ''Canon 3-in-1 on a Ground''] (2020)
			* [https://www.youtube.com/shorts/eyuifKaRCrY ''CANON in F, 2-in-1: First Part, RECTUS''] (2026)

	[[Category:Hemithirds]]		[[Category:Hemithirds]]

Lucius Chiaraviglio: /* 21st century */ Add Bryan Deister's ''56edo groove'' (2026)

2026-07-01T01:41:26Z

21st century: Add Bryan Deister's ''56edo groove'' (2026)

← Older revision		Revision as of 01:41, 1 July 2026
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	* [https://www.youtube.com/shorts/o0imqFPDh9k ''56edo''] (2023)		* [https://www.youtube.com/shorts/o0imqFPDh9k ''56edo''] (2023)
	* [https://www.youtube.com/watch?v=qzMOnS-lgWs ''Waltz in 56edo''] (2025)		* [https://www.youtube.com/watch?v=qzMOnS-lgWs ''Waltz in 56edo''] (2025)
			* [https://www.youtube.com/shorts/5j-TAkmdWqc ''56edo groove''] (2026)

	; [[Budjarn Lambeth]]		; [[Budjarn Lambeth]]

FloraC: /* Music */ identify the original works of Bryan Deister's arrangements

2026-05-09T16:15:31Z

Music: identify the original works of Bryan Deister's arrangements

@@ Line 349: / Line 349: @@
 == Music ==
 ; [[Bryan Deister]]
 * [https://www.youtube.com/shorts/o0imqFPDh9k ''56edo''] (2023)
 * [https://www.youtube.com/watch?v=qzMOnS-lgWs ''Waltz in 56edo''] (2025)
 ; [[Budjarn Lambeth]]

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''I Will - The Beatles (microtonal cover in 56edo)'' (2026)

2026-05-09T10:32:36Z

Music: Add Bryan Deister's ''I Will - The Beatles (microtonal cover in 56edo)'' (2026)

← Older revision		Revision as of 10:32, 9 May 2026
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	** [https://www.youtube.com/shorts/M1HitTFYVu0 <nowiki>[Short]</nowiki>] (with Lumatone view)		** [https://www.youtube.com/shorts/M1HitTFYVu0 <nowiki>[Short]</nowiki>] (with Lumatone view)
	** [https://www.youtube.com/watch?v=mGcPxb-ESAQ <nowiki>[Full version]</nowiki>]		** [https://www.youtube.com/watch?v=mGcPxb-ESAQ <nowiki>[Full version]</nowiki>]
			* [https://www.youtube.com/shorts/WsvSVp3xyr8 ''I Will - The Beatles (microtonal cover in 56edo)''] (2026)

	; [[Budjarn Lambeth]]		; [[Budjarn Lambeth]]

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"

2026-03-13T13:32:35Z

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 13:32, 13 March 2026
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	\| [[Sevond]]		\| [[Sevond]]
	\|}		\|}
	<nowiki/>* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|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

	== Scales ==		== Scales ==

Overthink: /* Theory */ a few minor changes

2026-02-05T03:58:21Z

Theory: a few minor changes

← Older revision		Revision as of 03:58, 5 February 2026
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	== Theory ==		== Theory ==
	56edo shares its near perfect quality of the [[5/4\|classical major third]] with [[28edo]], which it doubles, while also adding a superpythagorean 5th in the "shrub region" between those of [[17edo]] and [[22edo]]. It has decent approximations to [[prime harmonic]]s up to [[19/1\|19]], but due to the sharpness of its harmonic [[3/1\|3]], several intervals of [[9/1\|9]] are [[consistency\|inconsistent]]. Therefore, 56edo is not very popular compared to edos like [[53edo]] or [[58edo]].		56edo shares its near perfect quality of the [[5/4\|classical major third]] with [[28edo]], which it doubles, while also adding a superpythagorean 5th in the "shrub region" between those of [[17edo]] and [[22edo]]. It has decent approximations of [[prime harmonic]]s up to [[19/1\|19]], but due to the sharpness of its harmonic [[3/1\|3]], several intervals of [[9/1\|9]] are [[consistency\|inconsistent]]. Therefore, 56edo is not very popular compared to edos like [[53edo]] or [[58edo]].

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== As a tuning of other temperaments ===		=== As a tuning of other temperaments ===
	In the 5-limit, 56et most notably tempers out the [[diaschisma]], as well as the [[shibboleth comma]]. Using the [[patent val]], it tempers out [[686/675]], [[875/864]], and [[1029/1024]] in the [[7-limit]], [[100/99]], [[245/242]], and [[385/384]] in the [[11-limit]], and [[91/90]] and [[169/168]] in the 13-limit. It supports the diaschismic extension [[keen]] in the 7- and 11-limit, and its 13- and 17-limit extension [[keenic]]. It also supports [[hemithirds]], [[superkleismic]], and [[sycamore]] in various limits, being an especially optimal tuning for sycamore in the 11-, and 13-limits. It is also a very sharp tuning of [[slendric]], mapping 7/6 to an [[Ultramajor and inframinor\|inframinor]] third of 257.1[[Cent\|{{c}}]], and mapping 9/7 inconsistently to an ultramajor third of 450{{c}}.		In the 5-limit, 56et most notably tempers out the [[diaschisma]], as well as the [[shibboleth comma]]. Using the [[patent val]], it tempers out [[686/675]], [[875/864]], and [[1029/1024]] in the [[7-limit]], [[100/99]], [[245/242]], and [[385/384]] in the [[11-limit]], and [[91/90]] and [[169/168]] in the 13-limit. It supports the diaschismic extension [[keen]] in the 7- and 11-limit, and its 13- and 17-limit extension [[keenic]]. It also supports [[hemithirds]], [[superkleismic]], and [[sycamore]] in various limits, being an especially optimal tuning for sycamore in the 11- and 13-limits. It also supports a very sharp tuning of [[slendric]], mapping 7/6 to an [[Ultramajor and inframinor\|inframinor]] third of 257.1[[Cent\|{{c}}]], and mapping 9/7 inconsistently to an ultramajor third of 450{{c}}.

	Another interesting val to consider is 56d ({{Val\|56 89 130 '''158'''}}), which maps 7/4 sharply to around 986{{c}}. This mapping tempers out [[50/49]] and [[64/63]] in the 7-limit, providing an alternative to [[22edo]] for [[pajara]]. It improves accuracy of the 3rd harmonic and makes the 5th harmonic basically just, especially improving [[6/5]] and [[10/9]], which are quite out of tune in 22edo. Its approximated 7th harmonic is sharper than 22edo's, and combined with the fact that the 3rd harmonic is sharp, one may ~~want~~ to [[Octave stretch\|compress the octave]], using tunings such as [[145ed6]] or [[201ed12]]. It is also an excellent tuning for the 11-limit version of pajara, which additionally tempers out [[99/98]], [[100/99]], ~~and~~ [[176/175]]. Finally, it gives an excellent tuning for the no-~~fives~~ [[supra]] temperament tempering out [[64/63]] and [[99/98]].		Another interesting val to consider is 56d ({{Val\|56 89 130 '''158''' 194}}), which maps 7/4 sharply to around 986{{c}}. This mapping tempers out [[50/49]] and [[64/63]] in the 7-limit, providing an alternative to [[22edo]] for [[pajara]]. It improves accuracy of the 3rd harmonic and makes the 5th harmonic basically just, especially improving [[6/5]] and [[10/9]], which are quite out of tune in 22edo. Its approximated 7th harmonic is sharper than 22edo's, and combined with the fact that the 3rd harmonic is sharp, one may wish to [[Octave stretch\|compress the octave]], using tunings such as [[145ed6]] or [[201ed12]]. It is also an excellent tuning for the 11-limit version of pajara, which additionally tempers out [[99/98]], [[100/99]], [[176/175]], and [[896/891]]. Finally, it gives an excellent tuning for the [[2.3.7.11 subgroup\|2.3.7.11-subgroup]] [[supra]] temperament tempering out [[64/63]] and [[99/98]].

	=== Miscellaneous properties ===		=== Miscellaneous properties ===

Lucius Chiaraviglio: /* Music */ Bryan Deister's ''Parade - Susumu Hirasawa (microtonal cover in 56edo)'' (2026): Add full version

2026-02-04T07:57:56Z

Music: Bryan Deister's ''Parade - Susumu Hirasawa (microtonal cover in 56edo)'' (2026): Add full version

← Older revision		Revision as of 07:57, 4 February 2026
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	* [https://www.youtube.com/watch?v=xkfao6yGKGE ''Curious Light - DOORS (microtonal cover in 56edo)''] (2025)		* [https://www.youtube.com/watch?v=xkfao6yGKGE ''Curious Light - DOORS (microtonal cover in 56edo)''] (2025)
	* [https://www.youtube.com/watch?v=qzMOnS-lgWs ''Waltz in 56edo''] (2025)		* [https://www.youtube.com/watch?v=qzMOnS-lgWs ''Waltz in 56edo''] (2025)
	* [https://www.youtube.com/shorts/M1HitTFYVu0 ~~''Parade - Susumu Hirasawa~~ (~~microtonal cover in 56edo~~)''] ~~(2026)~~		* ''Parade - Susumu Hirasawa (microtonal cover in 56edo)'' (2026)
			** [https://www.youtube.com/shorts/M1HitTFYVu0 <nowiki>[Short]</nowiki>] (with Lumatone view)
			** [https://www.youtube.com/watch?v=mGcPxb-ESAQ <nowiki>[Full version]</nowiki>]

	; [[Budjarn Lambeth]]		; [[Budjarn Lambeth]]

Lucius Chiaraviglio: /* Music */ ''Parade - Susumu Hirasawa (microtonal cover in 56edo)'' (2026)

2026-02-03T09:02:17Z

Music: ''Parade - Susumu Hirasawa (microtonal cover in 56edo)'' (2026)

← Older revision		Revision as of 09:02, 3 February 2026
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	* [https://www.youtube.com/watch?v=xkfao6yGKGE ''Curious Light - DOORS (microtonal cover in 56edo)''] (2025)		* [https://www.youtube.com/watch?v=xkfao6yGKGE ''Curious Light - DOORS (microtonal cover in 56edo)''] (2025)
	* [https://www.youtube.com/watch?v=qzMOnS-lgWs ''Waltz in 56edo''] (2025)		* [https://www.youtube.com/watch?v=qzMOnS-lgWs ''Waltz in 56edo''] (2025)
			* [https://www.youtube.com/shorts/M1HitTFYVu0 ''Parade - Susumu Hirasawa (microtonal cover in 56edo)''] (2026)

	; [[Budjarn Lambeth]]		; [[Budjarn Lambeth]]

Overthink: oops

2026-01-19T03:28:37Z

oops

← Older revision		Revision as of 03:28, 19 January 2026
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	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}

	~~== Theory ==~~
	== Theory ==		== Theory ==
	56edo shares its near perfect quality of the [[5/4\|classical major third]] with [[28edo]], which it doubles, while also adding a superpythagorean 5th in the "shrub region" between those of [[17edo]] and [[22edo]]. It has decent approximations to [[prime harmonic]]s up to [[19/1\|19]], but due to the sharpness of its harmonic [[3/1\|3]], several intervals of [[9/1\|9]] are [[consistency\|inconsistent]]. Therefore, 56edo is not very popular compared to edos like [[53edo]] or [[58edo]].		56edo shares its near perfect quality of the [[5/4\|classical major third]] with [[28edo]], which it doubles, while also adding a superpythagorean 5th in the "shrub region" between those of [[17edo]] and [[22edo]]. It has decent approximations to [[prime harmonic]]s up to [[19/1\|19]], but due to the sharpness of its harmonic [[3/1\|3]], several intervals of [[9/1\|9]] are [[consistency\|inconsistent]]. Therefore, 56edo is not very popular compared to edos like [[53edo]] or [[58edo]].