7ed5/2 - Revision history

FloraC at 14:27, 27 May 2026

2026-05-27T14:27:56Z

← Older revision		Revision as of 14:27, 27 May 2026
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	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|7\|5\|2\|columns=11}}		{{Harmonics in equal\|7\|5\|2\|columns=11}}
	{{Harmonics in equal\|7\|5\|2\|columns=12\|start=12\|collapsed=true\|Approximation of harmonics in 7ed5/2 (continued)}}		{{Harmonics in equal\|7\|5\|2\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 7ed5/2 (continued)}}

	== Intervals ==		== Intervals ==

FloraC: Llywelyn, not necessarily semaja

2026-05-27T14:27:38Z

Llywelyn, not necessarily semaja

← Older revision		Revision as of 14:27, 27 May 2026
Line 3:		Line 3:

	== Theory ==		== Theory ==
	7ed5/2 corresponds to 5.2953…[[edo]]. It ~~is related to~~ the [[~~semaja~~]] temperament. Its [[patent val]] tempers out the same 5-limit commas as [[5edo]], but the mapping of 7 and higher prime harmonics differs.		7ed5/2 corresponds to 5.2953…[[edo]]. It can function as a generator chain for the [[llywelyn]] temperament. Its [[patent val]] tempers out the same 5-limit commas as [[5edo]], but the mapping of 7 and higher prime harmonics differs.

	=== Harmonics ===		=== Harmonics ===
Line 18:		Line 18:
	\| 1		\| 1
	\| 227		\| 227
	\| 17/15		\| 8/7, 25/22
	\|-		\|-
	\| 2		\| 2
Line 26:		Line 26:
	\| 3		\| 3
	\| 680		\| 680
	\| 34/23		\| 65/44
	\|-		\|-
	\| 4		\| 4
	\| 906		\| 906
	\| 11/7		\| 22/13
	\|-		\|-
	\| 5		\| 5
	\| 1133		\| 1133
	\| 23/12		\| 25/13
	\|-		\|-
	\| 6		\| 6
	\| 1360		\| 1360
	\| 11/5		\| 11/5, 35/16
	\|-		\|-
	\| 7		\| 7

FloraC: Standardize the layout

2026-05-27T13:54:59Z

Standardize the layout

← Older revision		Revision as of 13:54, 27 May 2026
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''7ED5~~/2~~''' is the equal division of the [[5/2]] interval into 7 parts of 226.6162 [[cent]]s each, corresponding~~ to 5.~~2953~~ [[~~EDO~~]]. It is related to the [[~~Porwell temperaments #Semaja\|~~semaja ~~temperament~~]]. Its patent val tempers out the same 5-limit commas as [[5edo~~\|5EDO~~]], but mapping of 7 and higher prime harmonics differs ~~to 5EDO~~.		{{ED intro}}

			== Theory ==
			7ed5/2 corresponds to 5.2953…[[edo]]. It is related to the [[semaja]] temperament. Its [[patent val]] tempers out the same 5-limit commas as [[5edo]], but the mapping of 7 and higher prime harmonics differs.

			=== Harmonics ===
			{{Harmonics in equal\|7\|5\|2\|columns=11}}
			{{Harmonics in equal\|7\|5\|2\|columns=12\|start=12\|collapsed=true\|Approximation of harmonics in 7ed5/2 (continued)}}

	== Intervals ==		== Intervals ==
	{\| class="wikitable mw-~~collapsible~~"		{\| class="wikitable center-1 right-2"
	\|+		\|+
	!~~Step~~		! #
	!~~Interval (¢)~~		! Cents
	!~~JI approximated~~		! Approximated ratio
	~~!Simplified~~ ratio
	\|-		\|-
	\|1		\| 1
	\|~~226.62~~		\| 227
	~~\|34/30~~		\| 17/15
	\|17/15
	\|-		\|-
	\|2		\| 2
	\|453~~.23~~		\| 453
	~~\|39/30~~		\| 13/10
	\|13/10
	\|-		\|-
	\|3		\| 3
	\|~~679.85~~		\| 680
	\|34/23		\| 34/23
	\|
	\|-		\|-
	\|4		\| 4
	\|906~~.47~~		\| 906
	\|66/39		\| 11/7
	~~\|22/14~~
	\|-		\|-
	\|5		\| 5
	\|1133~~.08~~		\| 1133
	\|23/12		\| 23/12
	\|
	\|-		\|-
	\|6		\| 6
	\|~~1359.70~~		\| 1360
	~~\|66/30~~		\| 11/5
	\|11/5
	\|-		\|-
	\|7		\| 7
	\|1586~~.31~~		\| 1586
	\|5/2		\| 5/2
	\|
	\|}		\|}
	~~The subgroup interpretation used is 5/2.12.23.34.39.51.58.66. Other interpretations are possible. Don't forget that fractions can multiply, e.g. 12*5/2=30.~~

	~~== Harmonics ==~~
	~~{{Harmonics in equal~~
	~~\| steps = 7~~
	~~\| num = 5~~
	~~\| denom = 2~~
	}}
	~~{{Harmonics in equal~~
	~~\| steps = 7~~
	~~\| num = 5~~
	~~\| denom = 2~~
	~~\| start = 12~~
	~~\| collapsed = 1~~
	}}


	~~{{todo\|expand}}~~
	~~[[Category:Nonoctave]]~~

Fredg999 category edits: Removing from Category:Ed5/2 using Cat-a-lot

2025-08-01T18:40:40Z

Removing from Category:Ed5/2 using Cat-a-lot

← Older revision		Revision as of 18:40, 1 August 2025
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	{{todo\|expand}}		{{todo\|expand}}
	~~[[Category:Ed5/2]]~~
	[[Category:Nonoctave]]		[[Category:Nonoctave]]

BudjarnLambeth at 07:10, 17 December 2024

2024-12-17T07:10:40Z

← Older revision		Revision as of 07:10, 17 December 2024
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	}}		}}


			{{todo\|expand}}
	[[Category:Ed5/2]]		[[Category:Ed5/2]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]

BudjarnLambeth: /* Intervals */ Add manual table of intervals

2024-12-17T06:57:36Z

Intervals: Add manual table of intervals

@@ Line 3: / Line 3: @@
 == Intervals ==
-{{Interval table}}
+{| class="wikitable mw-collapsible"
 == Harmonics ==

BudjarnLambeth: Intro inter harm

2024-10-04T08:45:22Z

Intro inter harm

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 '''7ED5/2''' is the equal division of the [[5/2]] interval into 7 parts of 226.6162 [[cent]]s each, corresponding to 5.2953 [[EDO]]. It is related to the [[Porwell temperaments #Semaja|semaja temperament]]. Its patent val tempers out the same 5-limit commas as [[5edo|5EDO]], but mapping of 7 and higher prime harmonics differs to 5EDO.
 [[Category:Ed5/2]]
 [[Category:Nonoctave]]

Plumtree: Infobox ET added

2022-10-05T20:36:51Z

Infobox ET added

← Older revision		Revision as of 20:36, 5 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''7ED5/2''' is the equal division of the [[5/2]] interval into 7 parts of 226.6162 [[cent]]s each, corresponding to 5.2953 [[EDO]]. It is related to the [[Porwell temperaments #Semaja\|semaja temperament]]. Its patent val tempers out the same 5-limit commas as [[5edo\|5EDO]], but mapping of 7 and higher prime harmonics differs to 5EDO.		'''7ED5/2''' is the equal division of the [[5/2]] interval into 7 parts of 226.6162 [[cent]]s each, corresponding to 5.2953 [[EDO]]. It is related to the [[Porwell temperaments #Semaja\|semaja temperament]]. Its patent val tempers out the same 5-limit commas as [[5edo\|5EDO]], but mapping of 7 and higher prime harmonics differs to 5EDO.

	[[Category:Ed5/2]]		[[Category:Ed5/2]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]

Xenllium: Created page with "'''7ED5/2''' is the equal division of the 5/2 interval into 7 parts of 226.6162 cents each, corresponding to 5.2953 EDO. It is related to the Porwell temperament..."

2022-01-18T12:11:55Z

Created page with "'''7ED5/2''' is the equal division of the 5/2 interval into 7 parts of 226.6162 cents each, corresponding to 5.2953 EDO. It is related to the Porwell temperament..."

New page

'''7ED5/2''' is the equal division of the [[5/2]] interval into 7 parts of 226.6162 [[cent]]s each, corresponding to 5.2953 [[EDO]]. It is related to the [[Porwell temperaments #Semaja|semaja temperament]]. Its patent val tempers out the same 5-limit commas as [[5edo|5EDO]], but mapping of 7 and higher prime harmonics differs to 5EDO.

[[Category:Ed5/2]]
[[Category:Nonoctave]]