44edo - Revision history

Eliora: /* Subsets and supersets */

2026-10-07T22:01:13Z

Subsets and supersets

← Older revision		Revision as of 22:01, 7 October 2026
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	44edo has subsets {{EDOs\| 2, 4, 11, 22 }}.		44edo has subsets {{EDOs\| 2, 4, 11, 22 }}.

	One step of 44edo is very close (only 0.0086 cents sharp) to [[64/63]] (the septimal comma). [[Ruthenium]] temperament realizes this proximity through a regular temperament perspective, and it is supported by a large number of edos which are a multiple of 44 - for example [[1012edo]], [[1848edo]], and [[2684edo]]. The aforementioned 88edo, which doubles it, is a [[meantone]] tuning that corrects the 7th harmonic to near-just, although at the expense of increasing relative error of the 13th and 19th harmonics; alternatively, if it is treated as directly approximating the 9th harmonic, then it also corrects the 9th harmonic to near-just.		One step of 44edo is very close (only 0.0086 cents sharp) to [[64/63]] (the septimal comma). [[Ruthenium]] temperament realizes this proximity through a regular temperament perspective, and it is supported by a large number of edos which are a multiple of 44 - for example [[1012edo]], [[1848edo]], and [[2684edo]].

			The aforementioned 88edo, which doubles it, is a [[meantone]] tuning that corrects the 7th harmonic to near-just, although at the expense of increasing relative error of the 13th and 19th harmonics; alternatively, if it is treated as directly approximating the 9th harmonic, then it also corrects the 9th harmonic to near-just.

	== Intervals ==		== Intervals ==

Lucius Chiaraviglio: /* 21st century */ Bryan Deister's ''Prelude and Fugue in 44edo'' (2026): add full version

2026-10-06T03:42:42Z

21st century: Bryan Deister's ''Prelude and Fugue in 44edo'' (2026): add full version

← Older revision		Revision as of 03:42, 6 October 2026
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	** [https://www.youtube.com/watch?v=lclipVgCvf4 ''<nowiki>[complete song original release]</nowiki>'']		** [https://www.youtube.com/watch?v=lclipVgCvf4 ''<nowiki>[complete song original release]</nowiki>'']
	** [https://www.youtube.com/watch?v=JUVotVQwpiY ''<nowiki>[complete song Orpheum release]</nowiki>'']		** [https://www.youtube.com/watch?v=JUVotVQwpiY ''<nowiki>[complete song Orpheum release]</nowiki>'']
	* [https://www.youtube.com/shorts/xGLUmsK_W3o ''~~Prelude and Fugue in 44edo~~ <nowiki>[short clip]</nowiki>''] (~~2026~~)		* ''Prelude and Fugue in 44edo'' (2026)
			** [https://www.youtube.com/shorts/xGLUmsK_W3o ''<nowiki>[short clip]</nowiki>''] (Lumatone view)
			** [https://www.youtube.com/watch?v=93uKFjoaDag ''<nowiki>[full version]</nowiki>'']

	[[Category:44edo\| ]] <!-- main article -->		[[Category:44edo\| ]] <!-- main article -->
	{{todo\|add scales list}}		{{todo\|add scales list}}

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''Prelude and Fugue in 44edo [short clip]'' (2026); minor fixes to description of some previous videos; convert 1 microtonal cover by Bryan Deister to Modern Renderings format (had to add sub-sectipn for this)

2026-10-04T21:01:30Z

Music: Add Bryan Deister's ''Prelude and Fugue in 44edo <nowiki>[short clip]</nowiki>'' (2026); minor fixes to description of some previous videos; convert 1 microtonal cover by Bryan Deister to Modern Renderings format (had to add sub-sectipn for this)

← Older revision		Revision as of 21:01, 4 October 2026
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	== Music ==		== Music ==
			=== Modern renderings ===
			; ClascyJitto
			* [https://m.youtube.com/watch?v=U_7nziRy91g ''Leaning Dream''] via ''{{W\|Pizza Tower}}'' (2023) — adapted into 44edo with improvised counter-melodies by Bryan Deister (July 2024)

			=== 21st century ===
	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://m.youtube.com/watch?v=ljaSpsQP2qc ''~~Improvisation in 44edo~~''] (composed and played by Bryan Deister in May 2023, transcribed by [[Stephen Weigel]] in Sept ~~2024)~~		* [https://m.youtube.com/watch?v=ljaSpsQP2qc ''Bryan Deister microtonal improvisations transcribed (31edo to 50edo)''] (44edo section begins at 07:59; composed and played by Bryan Deister in May 2023, transcribed by [[Stephen Weigel]] in Sept 2024)
	* [https://m.youtube.com/watch?v=U_7nziRy91g ''Leaning Dream - Pizza Tower''] (adapted into 44edo by Bryan Deister in July 2024)		* [https://youtu.be/8iS_yIYYS9Q ''44edo improvisation''] (2024-10-19)
	* [https://youtu.be/8iS_yIYYS9Q ''44edo improvisation''] (~~Oct~~ 2024)		* [https://www.youtube.com/shorts/_GoQNEW24fQ ''44edo improv''] (2025-10-12)
	* [https://www.youtube.com/shorts/_GoQNEW24fQ ''44edo improv''] (~~Oct~~ 2025)
	* ''Buried Treasure - 44edo'' (2026)		* ''Buried Treasure - 44edo'' (2026)
	** [https://www.youtube.com/shorts/Oi3v0c7jbjM ''<nowiki>[short clip]</nowiki>'']		** [https://www.youtube.com/shorts/Oi3v0c7jbjM ''<nowiki>[short clip]</nowiki>''] (Lumatone view)
	** [https://www.youtube.com/shorts/ZOoiGuUA-9Y ''<nowiki>[short 2]</nowiki>'']		** [https://www.youtube.com/shorts/ZOoiGuUA-9Y ''<nowiki>[short 2]</nowiki>''] (Lumatone view)
	** [https://www.youtube.com/watch?v=lclipVgCvf4 ''<nowiki>[complete song original release]</nowiki>'']		** [https://www.youtube.com/watch?v=lclipVgCvf4 ''<nowiki>[complete song original release]</nowiki>'']
	** [https://www.youtube.com/watch?v=JUVotVQwpiY ''<nowiki>[complete song Orpheum release]</nowiki>'']		** [https://www.youtube.com/watch?v=JUVotVQwpiY ''<nowiki>[complete song Orpheum release]</nowiki>'']
			* [https://www.youtube.com/shorts/xGLUmsK_W3o ''Prelude and Fugue in 44edo <nowiki>[short clip]</nowiki>''] (2026)

	[[Category:44edo\| ]] <!-- main article -->		[[Category:44edo\| ]] <!-- main article -->
	{{todo\|add scales list}}		{{todo\|add scales list}}

BudjarnLambeth: {{todo|add scales list}}

2026-10-02T04:07:25Z

← Older revision		Revision as of 04:07, 2 October 2026
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	[[Category:44edo\| ]] <!-- main article -->		[[Category:44edo\| ]] <!-- main article -->
			{{todo\|add scales list}}

FloraC: /* Regular temperament properties */ + some missing temps

2026-05-14T18:58:39Z

Regular temperament properties: + some missing temps

@@ Line 421: / Line 421: @@
 | 22/21
 | [[Nautilus]] (44d)
 |-
 | 1
@@ Line 444: / Line 450: @@
 | 409.09
 | 5/4
-| [[Hocus]] (44)
+| [[Hocus]]
 |-
 | 2

Overthink: /* Intervals */ add 17/11 and complement; italicize inconsistent 9/8 and 16/9

2026-05-12T18:14:03Z

Intervals: add 17/11 and complement; italicize inconsistent 9/8 and 16/9

← Older revision		Revision as of 18:14, 12 May 2026
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	\| 6		\| 6
	\| 163.6		\| 163.6
	\| [[11/10]], [[12/11]], [[32/29]]~~, ''[[10/9]]''~~		\| ''[[10/9]]'', [[11/10]], [[12/11]], [[32/29]]
	\| Dudmajor 2nd, upmid 2nd		\| Dudmajor 2nd, upmid 2nd
	\| vvM2, ^~2		\| vvM2, ^~2
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	\| 8		\| 8
	\| 218.2		\| 218.2
	\| [[8/7]], [[9/8]], [[17/15]]		\| [[8/7]], ''[[9/8]]'', [[17/15]]
	\| Major 2nd		\| Major 2nd
	\| M2		\| M2
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	\| 16		\| 16
	\| 436.4		\| 436.4
	\| [[9/7]], ''[[14/11]]''		\| [[9/7]], ''[[14/11]]'', [[22/17]]
	\| Major 3rd		\| Major 3rd
	\| M3		\| M3
Line 226:		Line 226:
	\| 28		\| 28
	\| 763.6		\| 763.6
	\| [[14/9]], ''[[11/7]]''		\| [[14/9]], ''[[11/7]]'', [[17/11]]
	\| Minor 6th		\| Minor 6th
	\| m6		\| m6
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	\| 36		\| 36
	\| 981.8		\| 981.8
	\| [[7/4]], [[16/9]], [[30/17]]		\| [[7/4]], ''[[16/9]]'', [[30/17]]
	\| Minor 7th		\| Minor 7th
	\| m7		\| m7
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	\| 38		\| 38
	\| 1036.4		\| 1036.4
	\| [[11/6]], [[20/11]], [[29/16]]~~, ''[[9/5]]''~~		\| ''[[9/5]]'', [[11/6]], [[20/11]], [[29/16]]
	\| Dupminor 7th, downmid 7th		\| Dupminor 7th, downmid 7th
	\| ^^m7, v~7		\| ^^m7, v~7

FloraC: /* Notation */ improve description

2026-05-12T14:18:22Z

Notation: improve description

← Older revision		Revision as of 14:18, 12 May 2026
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	== Notation ==		== Notation ==
	=== Stein–Zimmermann–Gould notation ===		=== Stein–Zimmermann–Gould notation ===
	[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:		[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
	{{Sharpness-sharp6-szg}}		{{Sharpness-sharp6-szg}}

FloraC: /* Notation */ SZG notation

2026-05-12T13:22:03Z

Notation: SZG notation

← Older revision		Revision as of 13:22, 12 May 2026
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	== Notation ==		== Notation ==
	=== ~~Ups~~ and downs notation ===		=== Stein–Zimmermann–Gould notation ===
	44edo can be notated with ups and downs, spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc.		[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
			{{Sharpness-sharp6-szg}}

			If double arrows are not desirable, arrows can be attached to quarter-tone accidentals:
			{{Sharpness-sharp6-qt-szg}}

			=== Kite's ups and downs notation ===
			44edo can also be notated with [[Kite's ups and downs notation\|Kite's ups and downs]], spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc.
	{{Sharpness-sharp6a}}		{{Sharpness-sharp6a}}

	Half-sharps and half-flats can be used to avoid triple arrows:		Half-sharps and half-flats can be used to avoid triple arrows:
	{{Sharpness-sharp6b}}		{{Sharpness-sharp6b}}

	~~[[Alternative symbols for ups and downs notation#Sharp-6\| Alternative ups and downs]] have sharps and flats with arrows borrowed from extended [[Helmholtz–Ellis notation]]:~~
	~~{{Sharpness-sharp6}}~~

	~~If double arrows are not desirable, arrows can be attached to quarter-tone accidentals:~~
	~~{{Sharpness-sharp6-qt}}~~

	=== Sagittal notation ===		=== Sagittal notation ===

Overthink: /* Intervals */ add these accurate ones

2026-05-11T22:59:34Z

Intervals: add these accurate ones

← Older revision		Revision as of 22:59, 11 May 2026
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	\| 12		\| 12
	\| 327.3		\| 327.3
	\| [[6/5]], [[17/14]], ''[[11/9]]''		\| [[6/5]], ''[[11/9]]'', [[17/14]], [[29/24]]
	\| Dupminor 3rd, downmid 3rd		\| Dupminor 3rd, downmid 3rd
	\| ^^m3, v~3		\| ^^m3, v~3
Line 254:		Line 254:
	\| 32		\| 32
	\| 872.7		\| 872.7
	\| [[5/3]], [[28/17]], ''[[18/11]]''		\| [[5/3]], ''[[18/11]]'', [[28/17]], [[48/29]]
	\| Dudmajor 6th, upmid 6th		\| Dudmajor 6th, upmid 6th
	\| vvM6, ^~6		\| vvM6, ^~6

FloraC: + Approximation to JI section

2026-05-11T16:47:14Z

+ Approximation to JI section

← Older revision		Revision as of 16:47, 11 May 2026
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	\|}		\|}
	<nowiki/>* As a 19-limit temperament, with additional ratios of 23, 29, and 31		<nowiki/>* As a 19-limit temperament, with additional ratios of 23, 29, and 31

			== Approximation to JI ==
			=== Interval mappings ===
			{{Q-odd-limit intervals\|44}}

	== Notation ==		== Notation ==