21ed5/2 - Revision history

BudjarnLambeth: /* Harmonics */

2024-10-04T08:36:39Z

Harmonics

← Older revision		Revision as of 08:36, 4 October 2024
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	From a no-threes point of view, 21ed5/2 tempers out [[50/49]] in the 7-limit (being a jubilic system similar to [[13ed5/2]]), [[625/616]] and [[176/175]] in the 11-limit, and 143/140, 715/686 and [[847/845]] in the 13-limit. It is not particularly excellent as a no-threes system with the 5/4 and 7/4 being noticeably off, but can work for 5/2-equivalent jubilic.		From a no-threes point of view, 21ed5/2 tempers out [[50/49]] in the 7-limit (being a jubilic system similar to [[13ed5/2]]), [[625/616]] and [[176/175]] in the 11-limit, and 143/140, 715/686 and [[847/845]] in the 13-limit. It is not particularly excellent as a no-threes system with the 5/4 and 7/4 being noticeably off, but can work for 5/2-equivalent jubilic.

	=== Harmonics ===		== Harmonics ==
	{{Harmonics in equal\|21\|5\|2}}		{{Harmonics in equal
			\| steps = 21
			\| num = 5
			\| denom = 2
			}}
			{{Harmonics in equal
			\| steps = 21
			\| num = 5
			\| denom = 2
			\| start = 12
			\| collapsed = 1
			}}

	== Interval table ==		== Interval table ==

2023-07-13T03:17:13Z

← Older revision		Revision as of 03:17, 13 July 2023
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	\|-		\|-
	\|16		\|16
	\|		\|1208.620
	\|		\|P
	\|[[2/1]]		\|[[2/1]]
	\|-		\|-
	\|17		\|17
	\|		\|1284.159
	\|		\|P&, Q@
	\|[[52/25]]		\|[[52/25]]
	\|-		\|-
	\|18		\|18
	\|		\|1359.698
	\|		\|Q
	\|[[11/5]]		\|[[11/5]]
	\|-		\|-
	\|19		\|19
	\|		\|1435.236
	\|		\|Q&
	\|[[16/7]]		\|[[16/7]]
	\|-		\|-
	\|20		\|20
	\|		\|1510.775
	\|		\|J@
	\|[[26/11]]		\|[[26/11]]
	\|-		\|-
	\|21		\|21
	\|		\|1586.314
	\|		\|J
	\|[[5/2]]		\|[[5/2]]
	\|}		\|}

	<nowiki>*</nowiki> Based on treating 21ed5/2 as a no-threes 13-limit temperament		<nowiki>*</nowiki> Based on treating 21ed5/2 as a no-threes 13-limit temperament

2023-07-13T03:14:32Z

2023-07-13T03:10:32Z

← Older revision		Revision as of 03:10, 13 July 2023
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	<nowiki>*</nowiki> Based on treating 21ed5/2 as a no-threes 13-limit temperament		<nowiki>*</nowiki> Based on treating 21ed5/2 as a no-threes 13-limit temperament

	~~{{Interval table}}~~

2023-07-13T03:10:22Z

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 |}

2023-07-13T03:08:01Z

2023-07-13T03:07:47Z

← Older revision		Revision as of 03:07, 13 July 2023
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	\|		\|
	\|		\|
	}		\|}

	<nowiki>*</nowiki> Based on treating 21ed5/2 as a no-threes 13-limit temperament		<nowiki>*</nowiki> Based on treating 21ed5/2 as a no-threes 13-limit temperament

	{{Interval table}}		{{Interval table}}

2023-07-13T03:07:37Z

← Older revision		Revision as of 03:07, 13 July 2023
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	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|21\|5\|2}}		{{Harmonics in equal\|21\|5\|2}}

			== Interval table ==
			{\|class="wikitable"
			\|-
			!Steps
			!Cents
			![[5L 3s (5/2-equivalent)\|Jubilic[8]]] notation
			!Approximate ratios*
			\|-
			\|0
			\|0.000
			\|J
			\|[[1/1]]
			\|-
			\|1
			\|75.539
			\|J&
			\|[[26/25]]
			\|-
			\|2
			\|151.078
			\|K@
			\|[[35/32]]
			\|-
			\|3
			\|
			\|
			\|[[8/7]], [[28/25]]
			\|-
			\|4
			\|
			\|
			\|[[13/11]], [[77/64]]
			\|-
			\|5
			\|
			\|
			\|[[5/4]], [[11/9]], [[16/13]], [[49/40]]
			\|-
			\|6
			\|
			\|
			\|
			\|[[13/10]], [[32/25]]
			\|-
			\|7
			\|
			\|
			\|
			\|[[11/8]], [[35/26]]
			\|-
			\|8
			\|
			\|
			\|
			\|[[7/5]], [[10/7]]
			\|-
			\|9
			\|
			\|
			\|
			\|[[16/11]], [[52/35]]
			\|-
			\|10
			\|
			\|
			\|
			\|[[11/7]], [[20/13]], [[25/16]], [[49/32]]
			\|-
			\|11
			\|
			\|
			\|
			\|[[8/5]], [[13/8]]
			\|-
			\|12
			\|
			\|
			\|
			\|[[22/13]], [[55/32]]
			\|-
			\|13
			\|
			\|
			\|
			\|
			}
			<nowiki>*</nowiki> Based on treating 21ed5/2 as a no-threes 13-limit temperament

			{{Interval table}}

2023-07-12T01:15:10Z

← Older revision		Revision as of 01:15, 12 July 2023
Line 2:		Line 2:
	'''21ed5/2''' is the equal division of the [[5/2]] interval into 21 parts of approximately 75.539 [[cent]]s each. It roughly corresponds to [[16edo]].		'''21ed5/2''' is the equal division of the [[5/2]] interval into 21 parts of approximately 75.539 [[cent]]s each. It roughly corresponds to [[16edo]].
	== Theory ==		== Theory ==
	From a no-threes point of view, 21ed5/2 tempers out [[50/49]] in the 7-limit (being a jubilic system similar to [[13ed5/2]]), [[625/616]] and [[176/175]] in the 11-limit, and 143/140, 715/686 and [[847/845]] in the 13-limit.		From a no-threes point of view, 21ed5/2 tempers out [[50/49]] in the 7-limit (being a jubilic system similar to [[13ed5/2]]), [[625/616]] and [[176/175]] in the 11-limit, and 143/140, 715/686 and [[847/845]] in the 13-limit. It is not particularly excellent as a no-threes system with the 5/4 and 7/4 being noticeably off, but can work for 5/2-equivalent jubilic.

	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|21\|5\|2}}		{{Harmonics in equal\|21\|5\|2}}

2023-07-12T01:13:11Z

← Older revision		Revision as of 01:13, 12 July 2023
Line 4:		Line 4:
	From a no-threes point of view, 21ed5/2 tempers out [[50/49]] in the 7-limit (being a jubilic system similar to [[13ed5/2]]), [[625/616]] and [[176/175]] in the 11-limit, and 143/140, 715/686 and [[847/845]] in the 13-limit.		From a no-threes point of view, 21ed5/2 tempers out [[50/49]] in the 7-limit (being a jubilic system similar to [[13ed5/2]]), [[625/616]] and [[176/175]] in the 11-limit, and 143/140, 715/686 and [[847/845]] in the 13-limit.

	=== ~~Odd harmonics~~ ===		=== Harmonics ===
	{{Harmonics in equal\|21\|5\|2}}		{{Harmonics in equal\|21\|5\|2}}