9ed5/3 - Revision history

Xenllium at 06:57, 22 February 2026

2026-02-22T06:57:16Z

← Older revision		Revision as of 06:57, 22 February 2026
Line 2:		Line 2:
	'''9ed5/3''' is the [[Ed5/3\|equal division of the just major sixth]] into nine parts of 98.2621 [[cent]]s each, corresponding to 12.2122[[edo]]. It is very closely related to the [[Passion family#Passion\|passion temperament]].		'''9ed5/3''' is the [[Ed5/3\|equal division of the just major sixth]] into nine parts of 98.2621 [[cent]]s each, corresponding to 12.2122[[edo]]. It is very closely related to the [[Passion family#Passion\|passion temperament]].

	==Intervals==		== Intervals ==
	{\| class="wikitable right-2 center-3"		{\| class="wikitable right-2 center-3"
	\|+		\|+
	!Degrees		! Degrees
	!Cents		! Cents
	!5/3.4/3.7/3 interpretation		! 5/3.4/3.7/3 interpretation
	\|-		\|-
	\|1		\| 1
	\|98.2621		\| 98.2621
	\|[[16/15]], [[21/20]]		\| [[16/15]], [[21/20]]
	\|-		\|-
	\|2		\| 2
	\|196.~~5241~~		\| 196.5242
	\|[[28/25]]		\| [[28/25]]
	\|-		\|-
	\|3		\| 3
	\|294.7862		\| 294.7862
	\|[[25/21]]		\| [[25/21]]
	\|-		\|-
	\|4		\| 4
	\|393.0483		\| 393.0483
	\|[[5/4]]		\| [[5/4]]
	\|-		\|-
	\|5		\| 5
	\|491.3104		\| 491.3104
	\|[[4/3]]		\| [[4/3]]
	\|-		\|-
	\|6		\| 6
	\|589.5725		\| 589.5725
	\|[[7/5]]		\| [[7/5]]
	\|-		\|-
	\|7		\| 7
	\|687.~~83455~~		\| 687.8346
	\|[[112/75]]		\| [[112/75]]
	\|-		\|-
	\|8		\| 8
	\|786.0966		\| 786.0966
	\|[[25/16]], [[80/63]]		\| [[25/16]], [[80/63]]
	\|-		\|-
	\|'''9'''		\| '''9'''
	\|'''884.3587'''		\| '''884.3587'''
	\|'''[[5/3]] (just)'''		\| '''[[5/3]] (just)'''
	\|-		\|-
	\|10		\| 10
	\|982.~~6207~~		\| 982.6208
	\|[[7/4]], [[16/9]]		\| [[7/4]], [[16/9]]
	\|-		\|-
	\|11		\| 11
	\|1080.~~8828~~		\| 1080.8829
	\|[[28/15]]		\| [[28/15]]
	\|-		\|-
	\|12		\| 12
	\|1179.~~14495~~		\| 1179.1450
	\|[[49/25]]		\| [[49/25]]
	\|-		\|-
	\|13		\| 13
	\|1277.~~407~~		\| 1277.4070
	\|[[25/12]]		\| [[25/12]]
	\|-		\|-
	\|14		\| 14
	\|1375.6691		\| 1375.6691
	\|[[20/9]]		\| [[20/9]]
	\|-		\|-
	\|15		\| 15
	\|1473.9312		\| 1473.9312
	\|[[7/3]]		\| [[7/3]]
	\|}		\|}

Line 77:		Line 77:

	== See also ==		== See also ==
	* [~~https://en.xen.wiki/w/Equal-step_tuning#~~Alpha-beta~~-gamma_family_of_equal_divisions Alpha-beta-gamma_family_of_equal_divisions~~]		* [[Alpha, beta, and gamma family of equal divisions]]

	~~{{todo\|inline=1\|improve synopsis\|expand}}~~
	[[Category:Nonoctave]]		[[Category:Nonoctave]]

Contribution at 01:46, 28 October 2025

2025-10-28T01:46:29Z

← Older revision		Revision as of 01:46, 28 October 2025
Line 76:		Line 76:
	{{Harmonics in equal\|9\|5\|3\|collapsed=1\|start=12}}		{{Harmonics in equal\|9\|5\|3\|collapsed=1\|start=12}}

			== See also ==
			* [https://en.xen.wiki/w/Equal-step_tuning#Alpha-beta-gamma_family_of_equal_divisions Alpha-beta-gamma_family_of_equal_divisions]

	{{todo\|inline=1\|improve synopsis\|expand}}		{{todo\|inline=1\|improve synopsis\|expand}}
	[[Category:Nonoctave]]		[[Category:Nonoctave]]

Lériendil at 14:20, 24 April 2025

2025-04-24T14:20:35Z

← Older revision		Revision as of 14:20, 24 April 2025
Line 43:		Line 43:
	\|'''9'''		\|'''9'''
	\|'''884.3587'''		\|'''884.3587'''
	\|[[5/3]] (just)		\|'''[[5/3]] (just)'''
	\|-		\|-
	\|10		\|10

Lériendil at 14:19, 24 April 2025

2025-04-24T14:19:44Z

← Older revision		Revision as of 14:19, 24 April 2025
Line 3:		Line 3:

	==Intervals==		==Intervals==
	{\| class="wikitable"		{\| class="wikitable right-2 center-3"
	\|+		\|+
	!Degrees		!Degrees
	!~~9ed(~~5/3)		!Cents
			!5/3.4/3.7/3 interpretation
	\|-		\|-
	\|1		\|1
	\|98.2621		\|98.2621
			\|[[16/15]], [[21/20]]
	\|-		\|-
	\|2		\|2
	\|196.5241		\|196.5241
			\|[[28/25]]
	\|-		\|-
	\|3		\|3
	\|294.7862		\|294.7862
			\|[[25/21]]
	\|-		\|-
	\|4		\|4
	\|393.0483		\|393.0483
			\|[[5/4]]
	\|-		\|-
	\|5		\|5
	\|491.3104		\|491.3104
			\|[[4/3]]
	\|-		\|-
	\|6		\|6
	\|589.5725		\|589.5725
			\|[[7/5]]
	\|-		\|-
	\|7		\|7
	\|687.83455		\|687.83455
			\|[[112/75]]
	\|-		\|-
	\|8		\|8
	\|786.0966		\|786.0966
			\|[[25/16]], [[80/63]]
	\|-		\|-
	\|'''9'''		\|'''9'''
	\|'''884.3587'''		\|'''884.3587'''
			\|[[5/3]] (just)
	\|-		\|-
	\|10		\|10
	\|982.6207		\|982.6207
			\|[[7/4]], [[16/9]]
	\|-		\|-
	\|11		\|11
	\|1080.8828		\|1080.8828
			\|[[28/15]]
	\|-		\|-
	\|12		\|12
	\|1179.14495		\|1179.14495
			\|[[49/25]]
	\|-		\|-
	\|13		\|13
	\|1277.407		\|1277.407
			\|[[25/12]]
	\|-		\|-
	\|14		\|14
	\|1375.6691		\|1375.6691
			\|[[20/9]]
	\|-		\|-
	\|15		\|15
	\|1473.9312		\|1473.9312
			\|[[7/3]]
	\|}		\|}
	~~{{todo\|inline=1\|complete section\|clarify\|text=Explain what this table is used for~~.}}
			The interval interpretations listed belong to the generator chain of [[septimal passion]] without octaves.

	== Harmonics ==		== Harmonics ==

Lériendil: removed the weird phi thing

2025-04-24T14:09:54Z

removed the weird phi thing

← Older revision		Revision as of 14:09, 24 April 2025
Line 6:		Line 6:
	\|+		\|+
	!Degrees		!Degrees
	~~!15ed(11φ+5\9φ+4)~~
	!9ed(5/3)		!9ed(5/3)
	\|-		\|-
	\|1		\|1
	~~\|98.25665~~
	\|98.2621		\|98.2621
	\|-		\|-
	\|2		\|2
	~~\|196.5133~~
	\|196.5241		\|196.5241
	\|-		\|-
	\|3		\|3
	~~\|294.7699~~
	\|294.7862		\|294.7862
	\|-		\|-
	\|4		\|4
	~~\|393.0266~~
	\|393.0483		\|393.0483
	\|-		\|-
	\|5		\|5
	~~\|491.2832~~
	\|491.3104		\|491.3104
	\|-		\|-
	\|6		\|6
	~~\|589.5399~~
	\|589.5725		\|589.5725
	\|-		\|-
	\|7		\|7
	~~\|687.7965~~
	\|687.83455		\|687.83455
	\|-		\|-
	\|8		\|8
	~~\|786.0532~~
	\|786.0966		\|786.0966
	\|-		\|-
	\|9		\|'''9'''
	\|~~884.3098~~		\|'''884.3587'''
	\|884.3587
	\|-		\|-
	\|10		\|10
	~~\|982.56645~~
	\|982.6207		\|982.6207
	\|-		\|-
	\|11		\|11
	~~\|1080.8231~~
	\|1080.8828		\|1080.8828
	\|-		\|-
	\|12		\|12
	~~\|1179.07976~~
	\|1179.14495		\|1179.14495
	\|-		\|-
	\|13		\|13
	~~\|1277.3364~~
	\|1277.407		\|1277.407
	\|-		\|-
	\|14		\|14
	~~\|1375.593~~
	\|1375.6691		\|1375.6691
	\|-		\|-
	\|15		\|15
	~~\|1473.8497~~
	\|1473.9312		\|1473.9312
	\|}		\|}

BudjarnLambeth at 22:30, 21 December 2024

2024-12-21T22:30:17Z

← Older revision		Revision as of 22:30, 21 December 2024
Line 69:		Line 69:
	\|1473.9312		\|1473.9312
	\|}		\|}
	{{todo\|inline=1\|complete section\|clarify\|Explain what this table is used for.}}		{{todo\|inline=1\|complete section\|clarify\|text=Explain what this table is used for.}}

	== Harmonics ==		== Harmonics ==

BudjarnLambeth: Harmonics

2024-12-21T22:30:00Z

Harmonics

← Older revision		Revision as of 22:30, 21 December 2024
Line 3:		Line 3:

	==Intervals==		==Intervals==
	~~{{todo\|inline=1\|complete section\|clarify\|Explain what this table is used for.}}~~
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
Line 70:		Line 69:
	\|1473.9312		\|1473.9312
	\|}		\|}
			{{todo\|inline=1\|complete section\|clarify\|Explain what this table is used for.}}

			== Harmonics ==
			{{Harmonics in equal\|9\|5\|3}}
			{{Harmonics in equal\|9\|5\|3\|collapsed=1\|start=12}}


	{{todo\|inline=1\|improve synopsis\|expand}}		{{todo\|inline=1\|improve synopsis\|expand}}
	[[Category:Nonoctave]]		[[Category:Nonoctave]]

BudjarnLambeth: Todos

2024-12-21T22:24:24Z

Todos

← Older revision		Revision as of 22:24, 21 December 2024
Line 2:		Line 2:
	'''9ed5/3''' is the [[Ed5/3\|equal division of the just major sixth]] into nine parts of 98.2621 [[cent]]s each, corresponding to 12.2122[[edo]]. It is very closely related to the [[Passion family#Passion\|passion temperament]].		'''9ed5/3''' is the [[Ed5/3\|equal division of the just major sixth]] into nine parts of 98.2621 [[cent]]s each, corresponding to 12.2122[[edo]]. It is very closely related to the [[Passion family#Passion\|passion temperament]].

			==Intervals==
			{{todo\|inline=1\|complete section\|clarify\|Explain what this table is used for.}}
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
	!Degrees		!Degrees
	!15ed(11φ+5\9φ+4)~9ed(5/3)		!15ed(11φ+5\9φ+4)
			!9ed(5/3)
	\|-		\|-
	\|1		\|1
	\|98.25665		\|98.25665
	98.2621		\|98.2621
	\|-		\|-
	\|2		\|2
	\|196.5133		\|196.5133
	196.5241		\|196.5241
	\|-		\|-
	\|3		\|3
	\|294.7699		\|294.7699
	294.7862		\|294.7862
	\|-		\|-
	\|4		\|4
	\|393.0266		\|393.0266
	393.0483		\|393.0483
	\|-		\|-
	\|5		\|5
	\|491.2832		\|491.2832
	491.3104		\|491.3104
	\|-		\|-
	\|6		\|6
	\|589.5399		\|589.5399
	589.5725		\|589.5725
	\|-		\|-
	\|7		\|7
	\|687.7965		\|687.7965
	687.83455		\|687.83455
	\|-		\|-
	\|8		\|8
	\|786.0532		\|786.0532
	786.0966		\|786.0966
	\|-		\|-
	\|9		\|9
	\|884.3098		\|884.3098
	884.3587		\|884.3587
	\|-		\|-
	\|10		\|10
	\|982.56645		\|982.56645
	982.6207		\|982.6207
	\|-		\|-
	\|11		\|11
	\|1080.8231		\|1080.8231
	1080.8828		\|1080.8828
	\|-		\|-
	\|12		\|12
	\|1179.07976		\|1179.07976
	1179.14495		\|1179.14495
	\|-		\|-
	\|13		\|13
	\|1277.3364		\|1277.3364
	1277.407		\|1277.407
	\|-		\|-
	\|14		\|14
	\|1375.593		\|1375.593
	1375.6691		\|1375.6691
	\|-		\|-
	\|15		\|15
	\|1473.8497		\|1473.8497
	1473.9312		\|1473.9312
	\|}		\|}


			{{todo\|inline=1\|improve synopsis\|expand}}
	[[Category:Nonoctave]]		[[Category:Nonoctave]]

Lériendil at 02:19, 11 December 2024

2024-12-11T02:19:37Z

← Older revision		Revision as of 02:19, 11 December 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''9ed5/3''' is the [[Ed5/3\|equal division of the just major sixth]] into ~~sixteen~~ parts of 98.2621 [[cent]]s each, corresponding to 12.2122[[edo]]. It is very closely related to the [[Passion family#Passion\|passion temperament]].		'''9ed5/3''' is the [[Ed5/3\|equal division of the just major sixth]] into nine parts of 98.2621 [[cent]]s each, corresponding to 12.2122[[edo]]. It is very closely related to the [[Passion family#Passion\|passion temperament]].

	{\| class="wikitable"		{\| class="wikitable"

Lériendil at 23:40, 10 December 2024

2024-12-10T23:40:53Z

← Older revision		Revision as of 23:40, 10 December 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''9ed5/3''' is the [[Ed5/3\|equal division of the just major sixth]] into sixteen parts of 98.2621 [[cent]]s each, corresponding to 12.2122[[edo]]. It is very closely related to the [[~~Archytas clan~~ #Passion\|passion temperament]].		'''9ed5/3''' is the [[Ed5/3\|equal division of the just major sixth]] into sixteen parts of 98.2621 [[cent]]s each, corresponding to 12.2122[[edo]]. It is very closely related to the [[Passion family#Passion\|passion temperament]].

	{\| class="wikitable"		{\| class="wikitable"