34ed7 - Revision history

ArrowHead294: /* See also */

2025-06-10T13:27:27Z

ArrowHead294: /* See also */

2025-06-10T13:27:17Z

ArrowHead294 at 13:16, 10 June 2025

2025-06-10T13:16:58Z

← Older revision		Revision as of 13:16, 10 June 2025
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	== Theory ==		== Theory ==
	34ed7 is related to [[12edo]], but with the 7/1 rather than the 2/1 being just. ~~The~~ octave ~~is about~~ 11.0026 ~~cents compressed and the step size is about 99.0831 cents~~. It is consistent to the [[integer limit\|11-integer-limit]], but not to the 12-integer-limit. In comparison, 12edo is only consistent up to the 10-integer-limit.		34ed7 is related to [[12edo]], but with the 7/1 rather than the 2/1 being just. This compresses the octave by 11.0026{{c}}, a small but significant deviation. It is consistent to the [[integer limit\|11-integer-limit]], but not to the 12-integer-limit. In comparison, 12edo is only consistent up to the 10-integer-limit.

	=== Harmonics ===		=== Harmonics ===
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	== Intervals ==		== Intervals ==
	{\| class="wikitable center-1 right-2"		{\| class="wikitable center-1 right-2"
	\|+ Intervals of 34ed7		\|+ style="font-size: 105%;" \| Intervals of 34ed7
	\|-		\|-
	! #		! #

Lériendil: removed deletion notice; is sufficiently different from 12edo to not count as an octave stretch

2025-04-11T01:09:53Z

removed deletion notice; is sufficiently different from 12edo to not count as an octave stretch

← Older revision		Revision as of 01:09, 11 April 2025
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	~~{{delete\|reason=12edo octave stretching is addressed and should be addressed in "octave stretch" section of the 12edo page. Neighboring ed7s do not have articles}}~~
	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}

Hkm at 23:35, 10 April 2025

2025-04-10T23:35:19Z

← Older revision		Revision as of 23:35, 10 April 2025
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			{{delete\|reason=12edo octave stretching is addressed and should be addressed in "octave stretch" section of the 12edo page. Neighboring ed7s do not have articles}}
	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}

FloraC: /* Theory */ +subsets and supersets

2025-01-15T15:12:19Z

Theory: +subsets and supersets

← Older revision		Revision as of 15:12, 15 January 2025
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	{{Harmonics in equal\|34\|7\|1\|intervals=integer}}		{{Harmonics in equal\|34\|7\|1\|intervals=integer}}
	{{Harmonics in equal\|34\|7\|1\|intervals=integer\|start=12\|columns=12\|collapsed=true\|title=Approximation of harmonics in 34ed7 (continued)}}		{{Harmonics in equal\|34\|7\|1\|intervals=integer\|start=12\|columns=12\|collapsed=true\|title=Approximation of harmonics in 34ed7 (continued)}}

			=== Subsets and supersets ===
			Since 34 factors into 2 × 17, 34ed7 contains [[2ed7]] and [[17ed7]] as subsets.

	== Intervals ==		== Intervals ==

FloraC: Cleanup

2025-01-15T15:08:37Z

Cleanup

Show changes

BudjarnLambeth: stub or Todo:expand • add table or make collapsible if needed • add harmonics if missing • improve linking if needed • add subheadings if needed

2024-12-23T00:07:26Z

stub or Todo:expand • add table or make collapsible if needed • add harmonics if missing • improve linking if needed • add subheadings if needed

← Older revision		Revision as of 00:07, 23 December 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[Ed7\|Division of the 7th harmonic]] into 34 equal parts''' (34ED7) is related to [[12edo\|12 EDO]], but with the 7/1 rather than the 2/1 being just. The octave is about 11.0026 cents compressed and the step size is about 99.0831 cents~~. It is consistent to the [[11-odd-limit\|11-integer-limit]], but not to the 12-integer-limit. In comparison, 12EDO is only consistent up to the [[9-odd-limit\|10-integer-limit]]~~.		'''[[Ed7\|Division of the 7th harmonic]] into 34 equal parts''' (34ED7) is related to [[12edo\|12 EDO]], but with the 7/1 rather than the 2/1 being just. The octave is about 11.0026 cents compressed and the step size is about 99.0831 cents.

	{\| class="wikitable"		34ED7 is consistent to the 11-[[integer-limit]], but not to the 12-integer-limit. In comparison, 12EDO is only consistent up to the 10-[[integer-limit]].

			== Intervals ==
			{\| class="wikitable mw-collapsible"
			\|+ Intervals of 34ed7
	\|-		\|-
	! \| degree		! \| degree
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	\| \| [[7/4\|harmonic seventh]] plus two octaves		\| \| [[7/4\|harmonic seventh]] plus two octaves
	\|}		\|}

			== Harmonics ==
			{{Harmonics in equal\|34\|7\|1\|intervals=prime}}
			{{Harmonics in equal\|34\|7\|1\|intervals=prime\|collapsed=1\|start=12}}

	== Regular temperaments ==		== Regular temperaments ==
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	* [[18/17s equal temperament\|AS18/17]] - relative [[AS\|ambitonal sequence]]		* [[18/17s equal temperament\|AS18/17]] - relative [[AS\|ambitonal sequence]]


			{{todo\|expand}}
	[[Category:Ed7]]		[[Category:Ed7]]
	[[Category:Edonoi]]		[[Category:Edonoi]]

Plumtree: Infobox ET added

2022-10-05T20:31:52Z

Infobox ET added

← Older revision		Revision as of 20:31, 5 October 2022
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			{{Infobox ET}}
	'''[[Ed7\|Division of the 7th harmonic]] into 34 equal parts''' (34ED7) is related to [[12edo\|12 EDO]], but with the 7/1 rather than the 2/1 being just. The octave is about 11.0026 cents compressed and the step size is about 99.0831 cents. It is consistent to the [[11-odd-limit\|11-integer-limit]], but not to the 12-integer-limit. In comparison, 12EDO is only consistent up to the [[9-odd-limit\|10-integer-limit]].		'''[[Ed7\|Division of the 7th harmonic]] into 34 equal parts''' (34ED7) is related to [[12edo\|12 EDO]], but with the 7/1 rather than the 2/1 being just. The octave is about 11.0026 cents compressed and the step size is about 99.0831 cents. It is consistent to the [[11-odd-limit\|11-integer-limit]], but not to the 12-integer-limit. In comparison, 12EDO is only consistent up to the [[9-odd-limit\|10-integer-limit]].

Xenllium at 11:25, 27 November 2021

2021-11-27T11:25:53Z

@@ Line 185: / Line 185: @@
 == Regular temperaments ==
-{{See also|16ed5/2 #Regular temperaments}}
+{{See also| Quintaleap family }}
-ED7 can also be thought of as a [[generator]] of the 11-limit temperament which tempers out 896/891, 1375/1372, and 4375/4356, which is a [[cluster temperament]] with 12 clusters of notes in an octave (''quintupole'' temperament). This temperament is supported by [[12edo|12EDO]], [[109edo|109EDO]], and [[121edo|121EDO]] among others.
+ED7 can also be thought of as a [[generator]] of the 11-limit temperament which tempers out 896/891, 1375/1372, and 4375/4356, which is a [[cluster temperament]] with 12 clusters of notes in an octave (''[[Quintaleap family #Quintupole|quintupole]]'' temperament). This temperament is supported by [[12edo|12EDO]], [[109edo|109EDO]], and [[121edo|121EDO]] among others.
 == See also ==

← Older revision		Revision as of 13:27, 10 June 2025
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	* [[76ed80]] – close to the zeta-optimized tuning for 12edo		* [[76ed80]] – close to the zeta-optimized tuning for 12edo
	* [[1ed18/17\|AS18/17]] – relative [[AS\|ambitonal sequence]]		* [[1ed18/17\|AS18/17]] – relative [[AS\|ambitonal sequence]]

			[[Category:12edo]]

← Older revision		Revision as of 13:27, 10 June 2025
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	* [[40ed10]] – relative ed10		* [[40ed10]] – relative ed10
	* [[42ed11]] – relative ed11		* [[42ed11]] – relative ed11
			* [[76ed80]] – close to the zeta-optimized tuning for 12edo
	* [[1ed18/17\|AS18/17]] – relative [[AS\|ambitonal sequence]]		* [[1ed18/17\|AS18/17]] – relative [[AS\|ambitonal sequence]]