7ed5 - Revision history

FloraC: Undo

2026-05-27T13:46:57Z

Undo

← Older revision		Revision as of 13:46, 27 May 2026
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	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}

	~~== Harmonics ==~~
	~~{{Harmonics in equal~~
	~~\| num = 5~~
	~~\| denom = 1~~
	~~\| steps = 7~~
	~~\| columns = 13}}~~

	== Theory ==		== Theory ==

MisterShafXen: /* Harmonics */

2025-06-22T21:58:40Z

Harmonics

← Older revision		Revision as of 21:58, 22 June 2025
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	== Harmonics ==		== Harmonics ==
			{{Harmonics in equal
			\| num = 5
			\| denom = 1
			\| steps = 7
			\| columns = 13}}

	== Theory ==		== Theory ==

MisterShafXen at 21:57, 22 June 2025

2025-06-22T21:57:11Z

← Older revision		Revision as of 21:57, 22 June 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}

			== Harmonics ==

	== Theory ==		== Theory ==

FloraC: +subsets and supersets

2025-01-23T08:30:19Z

+subsets and supersets

← Older revision		Revision as of 08:30, 23 January 2025
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	{{Harmonics in equal\|7\|5\|1}}		{{Harmonics in equal\|7\|5\|1}}
	{{Harmonics in equal\|7\|5\|1\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 7ed5 (contined)}}		{{Harmonics in equal\|7\|5\|1\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 7ed5 (contined)}}

			=== Subsets and supersets ===
			7ed5 is the 4th [[prime equal division\|prime ed5]], past [[5ed5]] and before [[11ed5]].

	== Intervals ==		== Intervals ==

FloraC: Cleanup. Request explanation

2025-01-23T08:28:44Z

Cleanup. Request explanation

← Older revision		Revision as of 08:28, 23 January 2025
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[Ed5\|Division of the 5th harmonic]] into 7 equal parts''' (7ed5) is related to [[3edo\|3 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656 cents compressed and the step size is about 398.0448 cents. It is present (though possibly tempered) in any [[regular temperament]] which tempers out [[441/440]] and 244515348/244140625 in the [[11-limit]], such as [[equal temperament]]s [[3edo\|3]], [[12edo\|12]], [[15edo\|15]], [[175edo\|175]], [[190edo\|190]], [[202edo\|202]], and [[217edo]].		{{ED intro}}

	~~Due~~ to [[~~Kirnberger's atom~~]], ~~its~~ step is ~~100~~.~~0002¢ flat of~~ [[4/3]].		== Theory ==
			7ed5 is related to [[3edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 6 cents compressed and the step size is about 398 cents. It is present (though possibly tempered) in any [[regular temperament]] which [[tempering out\|tempers out]] [[441/440]] and 244515348/244140625 in the [[11-limit]], such as [[equal temperament]]s [[3edo\|3]], [[12edo\|12]], [[15edo\|15]], [[175edo\|175]], [[190edo\|190]], [[202edo\|202]], and [[217edo]].

	== Harmonics ==		Due to [[Kirnberger's atom]], its step is 100.0002¢ flat of [[4/3]]{{clarify}}.
	{{Harmonics in equal
	\| ~~steps =~~ 7		=== Harmonics ===
	\| ~~num =~~ 5		{{Harmonics in equal\|7\|5\|1}}
	\| ~~denom =~~ 1		{{Harmonics in equal\|7\|5\|1\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 7ed5 (contined)}}
	}}
	{{Harmonics in equal
	\| ~~steps =~~ 7
	\| ~~num =~~ 5
	\| ~~denom~~ = 1
	\| start = 12
	\| collapsed = 1
	}}

	== Intervals ==		== Intervals ==
			{\| class="wikitable center-1 right-2"
	{\| class="wikitable"
	\|-		\|-
	! ~~\| degree~~		! #
	! ~~\| cents value~~		! Cents
	! ~~\| corresponding <br>JI intervals~~		! Approximate ratios
	~~! \| comments~~
	\|-		\|-
	\| \| 0		\| 0
	\| \| 0.0000		\| 0
	\| ~~\| '''exact~~ [[1/1]]~~'''~~		\| [[1/1]]
	~~\| \|~~
	\|-		\|-
	\| \| 1		\| 1
	\| \| 398~~.0448~~		\| 398
	~~\| \| 34/27~~		\| [[5/4]], 34/27
	\| ~~\| pseudo-~~[[5/4]]
	\|-		\|-
	\| \| 2		\| 2
	\| \| 796~~.0896~~		\| 796
	\| \| [[19/12]]		\| [[19/12]]
	~~\| \|~~
	\|-		\|-
	\| \| 3		\| 3
	\| \| 1194~~.1344~~		\| 1194
	\| ~~\| 255/128~~		\| [[2/1]], 255/128
	~~\| \| pseudo-~~[[~~octave~~]]
	\|-		\|-
	\| \| 4		\| 4
	\| \| 1592~~.1793~~		\| 1592
	~~\| \| 128/51~~		\| [[5/2]], 128/51
	\| ~~\| pseudo-~~[[5/2]]
	\|-		\|-
	\| \| 5		\| 5
	\| \| 1990~~.2241~~		\| 1990
	~~\| \| [[30/19~~\|60/19]]		\| 60/19
	~~\| \|~~
	\|-		\|-
	\| \| 6		\| 6
	\| \| 2388~~.2689~~		\| 2388
	~~\| \| 135/34~~		\| [[4/1]], 135/34
	\| ~~\| pseudo-~~[[4/1]]
	\|-		\|-
	\| \| 7		\| 7
	\| \| 2786~~.3137~~		\| 2786
	\| ~~\| '''exact~~ [[5/1]]~~'''~~		\| [[5/1]]
	~~\| \| just major third plus two octaves~~
	\|}		\|}

	~~[[Category:Ed5]]~~
	~~[[Category:Edonoi]]~~

Recentlymaterialized at 04:38, 23 January 2025

2025-01-23T04:38:55Z

← Older revision		Revision as of 04:38, 23 January 2025
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[Ed5\|Division of the 5th harmonic]] into 7 equal parts''' (7ed5) is related to [[3edo\|3 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656 cents compressed and the step size is about 398.0448 cents. It is ~~related to the~~ regular ~~temperaments~~ which ~~temper~~ out 441/440 and 244515348/244140625 in the 11-limit, ~~which is supported by~~ [[3edo\|3]], [[12edo\|12]], [[15edo\|15]], [[175edo\|175]], [[190edo\|190]], [[202edo\|202]], and~~/or~~ [[217edo~~\|217~~]] ~~EDOs~~.		'''[[Ed5\|Division of the 5th harmonic]] into 7 equal parts''' (7ed5) is related to [[3edo\|3 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656 cents compressed and the step size is about 398.0448 cents. It is present (though possibly tempered) in any [[regular temperament]] which tempers out [[441/440]] and 244515348/244140625 in the [[11-limit]], such as [[equal temperament]]s [[3edo\|3]], [[12edo\|12]], [[15edo\|15]], [[175edo\|175]], [[190edo\|190]], [[202edo\|202]], and [[217edo]].

			Due to [[Kirnberger's atom]], its step is 100.0002¢ flat of [[4/3]].

	== Harmonics ==		== Harmonics ==

BudjarnLambeth: Harnonics

2024-10-05T03:49:28Z

Harnonics

← Older revision		Revision as of 03:49, 5 October 2024
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	== Harmonics ==		== Harmonics ==
	{{Harmonics in equal\|7\|5\|1}}		{{Harmonics in equal
			\| steps = 7
			\| num = 5
			\| denom = 1
			}}
			{{Harmonics in equal
			\| steps = 7
			\| num = 5
			\| denom = 1
			\| start = 12
			\| collapsed = 1
			}}

	== Intervals ==		== Intervals ==

BudjarnLambeth: Added subheadings and table of harmonics

2024-01-16T01:30:44Z

Added subheadings and table of harmonics

← Older revision		Revision as of 01:30, 16 January 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[Ed5\|Division of the 5th harmonic]] into 7 equal parts''' (7ed5) is related to [[3edo\|3 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656 cents compressed and the step size is about 398.0448 cents. It is related to the regular temperaments which temper out 441/440 and 244515348/244140625 in the 11-limit, which is supported by [[3edo\|3]], [[12edo\|12]], [[15edo\|15]], [[175edo\|175]], [[190edo\|190]], [[202edo\|202]], and/or [[217edo\|217]] EDOs.		'''[[Ed5\|Division of the 5th harmonic]] into 7 equal parts''' (7ed5) is related to [[3edo\|3 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656 cents compressed and the step size is about 398.0448 cents. It is related to the regular temperaments which temper out 441/440 and 244515348/244140625 in the 11-limit, which is supported by [[3edo\|3]], [[12edo\|12]], [[15edo\|15]], [[175edo\|175]], [[190edo\|190]], [[202edo\|202]], and/or [[217edo\|217]] EDOs.

			== Harmonics ==
			{{Harmonics in equal\|7\|5\|1}}

			== Intervals ==

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

Plumtree: Infobox ET added

2022-10-05T20:43:13Z

Infobox ET added

← Older revision		Revision as of 20:43, 5 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''[[Ed5\|Division of the 5th harmonic]] into 7 equal parts''' (7ed5) is related to [[3edo\|3 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656 cents compressed and the step size is about 398.0448 cents. It is related to the regular temperaments which temper out 441/440 and 244515348/244140625 in the 11-limit, which is supported by [[3edo\|3]], [[12edo\|12]], [[15edo\|15]], [[175edo\|175]], [[190edo\|190]], [[202edo\|202]], and/or [[217edo\|217]] EDOs.		'''[[Ed5\|Division of the 5th harmonic]] into 7 equal parts''' (7ed5) is related to [[3edo\|3 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656 cents compressed and the step size is about 398.0448 cents. It is related to the regular temperaments which temper out 441/440 and 244515348/244140625 in the 11-limit, which is supported by [[3edo\|3]], [[12edo\|12]], [[15edo\|15]], [[175edo\|175]], [[190edo\|190]], [[202edo\|202]], and/or [[217edo\|217]] EDOs.

Xenllium: Created page with "'''Division of the 5th harmonic into 7 equal parts''' (7ed5) is related to 3 edo, but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656..."

2019-02-22T08:25:35Z

Created page with "'''Division of the 5th harmonic into 7 equal parts''' (7ed5) is related to 3 edo, but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656..."

New page

'''[[Ed5|Division of the 5th harmonic]] into 7 equal parts''' (7ed5) is related to [[3edo|3 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656 cents compressed and the step size is about 398.0448 cents. It is related to the regular temperaments which temper out 441/440 and 244515348/244140625 in the 11-limit, which is supported by [[3edo|3]], [[12edo|12]], [[15edo|15]], [[175edo|175]], [[190edo|190]], [[202edo|202]], and/or [[217edo|217]] EDOs.

{| class="wikitable"
|-
! | degree
! | cents value
! | corresponding <br>JI intervals
! | comments
|-
| | 0
| | 0.0000
| | '''exact [[1/1]]'''
| |
|-
| | 1
| | 398.0448
| | 34/27
| | pseudo-[[5/4]]
|-
| | 2
| | 796.0896
| | [[19/12]]
| |
|-
| | 3
| | 1194.1344
| | 255/128
| | pseudo-[[octave]]
|-
| | 4
| | 1592.1793
| | 128/51
| | pseudo-[[5/2]]
|-
| | 5
| | 1990.2241
| | [[30/19|60/19]]
| |
|-
| | 6
| | 2388.2689
| | 135/34
| | pseudo-[[4/1]]
|-
| | 7
| | 2786.3137
| | '''exact [[5/1]]'''
| | just major third plus two octaves
|}

[[Category:Ed5]]
[[Category:Edonoi]]