87ed7 - Revision history

ArrowHead294: /* See also */

2025-07-16T15:01:22Z

2025-06-18T13:26:02Z

← Older revision		Revision as of 13:26, 18 June 2025
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	== Theory ==		== Theory ==
	87ed7 is related to [[31edo]], but with the 7/1 rather than the [[2/1]] being just. The octave is slightly stretched (about 0.3862 ~~cents~~). Like 31edo, 87ed7 is [[consistent]] through the [[integer limit\|12-integer-limit]].		87ed7 is related to [[31edo]], but with the 7/1 rather than the [[2/1]] being just. The octave is slightly stretched (about 0.3862{{c}}). Like 31edo, 87ed7 is [[consistent]] through the [[integer limit\|12-integer-limit]].

	=== Harmonics ===		=== Harmonics ===

2025-06-10T13:32:15Z

2025-04-20T20:17:08Z

2025-03-24T12:41:06Z

Theory

← Older revision		Revision as of 12:41, 24 March 2025
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	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|87\|7\|1\|intervals=integer\|columns=12}}		{{Harmonics in equal\|87\|7\|1\|intervals=integer\|columns=11}}
	{{Harmonics in equal\|87\|7\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 87ed7 (continued)}}		{{Harmonics in equal\|87\|7\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 87ed7 (continued)}}

2025-03-24T12:39:07Z

Theory: note consistency and +subsets and supersets

← Older revision		Revision as of 12:39, 24 March 2025
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	== Theory ==		== Theory ==
	87ed7 is related to [[31edo]], but with the 7/1 rather than the [[2/1]] being just. The octave is slightly stretched (about 0.3862 cents).		87ed7 is related to [[31edo]], but with the 7/1 rather than the [[2/1]] being just. The octave is slightly stretched (about 0.3862 cents). Like 31edo, 87ed7 is [[consistent]] through the [[integer limit\|12-integer-limit]].

	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|87\|7\|1\|intervals=integer\|columns=12}}		{{Harmonics in equal\|87\|7\|1\|intervals=integer\|columns=12}}
	{{Harmonics in equal\|87\|7\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 87ed7 (continued)}}		{{Harmonics in equal\|87\|7\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 87ed7 (continued)}}

			=== Subsets and supersets ===
			Since 87 factors into primes as {{nowrap\| 3 × 29 }}, 87ed7 contains [[3ed7]] and [[29ed7]] as subset ed7's.

	== Intervals ==		== Intervals ==

2025-03-24T12:35:56Z

Cleanup (2/2, replacing the incomplete interval table with the machine-generated one)

2025-03-24T12:34:38Z

Cleanup (1/)

← Older revision		Revision as of 12:34, 24 March 2025
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''[[Ed7\|Division of the 7th harmonic]] into 87 equal parts''' (~~87ed7) is related to [[31edo~~\|31 edo~~]], but with the 7/1 rather than the 2/1 being just. The octave is slightly stretched (about 0.3862 cents) ~~and the step size is about 38.7221 cents~~.		{{ED intro}}

			== Theory ==
			87ed7 is related to [[31edo]], but with the 7/1 rather than the [[2/1]] being just. The octave is slightly stretched (about 0.3862 cents).

			=== Harmonics ===
			{{Harmonics in equal\|87\|7\|1\|intervals=integer\|columns=12}}
			{{Harmonics in equal\|87\|7\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 87ed7 (continued)}}

	== Intervals ==		== Intervals ==
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	\|}		\|}

	== ~~Harmonics~~ ==		== See also ==
	~~{{Harmonics in equal\|87\|7\|1\|intervals=prime}}~~		* [[18edf]] – relative edf
	~~{{Harmonics in equal\|87\|7\|1\|intervals=prime\|collapsed=1\|start=12}}~~		* [[31edo]] – relative edo
			* [[49edt]] – relative edt
			* [[72ed5]] – relative ed5
	~~{{stub}}~~		* [[80ed6]] – relative ed6
	[[~~Category:Ed7~~]]		* [[111ed12]] – relative ed12
	[[~~Category:Edonoi~~]]		* [[39cET]]

2024-12-23T00:41:49Z

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 00:41, 23 December 2024
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	'''[[Ed7\|Division of the 7th harmonic]] into 87 equal parts''' (87ed7) is related to [[31edo\|31 edo]], but with the 7/1 rather than the 2/1 being just. The octave is slightly stretched (about 0.3862 cents) and the step size is about 38.7221 cents.		'''[[Ed7\|Division of the 7th harmonic]] into 87 equal parts''' (87ed7) is related to [[31edo\|31 edo]], but with the 7/1 rather than the 2/1 being just. The octave is slightly stretched (about 0.3862 cents) and the step size is about 38.7221 cents.

	{\| class="wikitable"		== Intervals ==
			{\| class="wikitable mw-collapsible"
			\|+ Intervals of 87ed7
	\|-		\|-
	! \| degree		! \| degree
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	\|}		\|}

			== Harmonics ==
			{{Harmonics in equal\|87\|7\|1\|intervals=prime}}
			{{Harmonics in equal\|87\|7\|1\|intervals=prime\|collapsed=1\|start=12}}


			{{stub}}
	[[Category:Ed7]]		[[Category:Ed7]]
	[[Category:Edonoi]]		[[Category:Edonoi]]

2022-10-05T20:33:41Z

Infobox ET added

← Older revision		Revision as of 20:33, 5 October 2022
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			{{Infobox ET}}
	'''[[Ed7\|Division of the 7th harmonic]] into 87 equal parts''' (87ed7) is related to [[31edo\|31 edo]], but with the 7/1 rather than the 2/1 being just. The octave is slightly stretched (about 0.3862 cents) and the step size is about 38.7221 cents.		'''[[Ed7\|Division of the 7th harmonic]] into 87 equal parts''' (87ed7) is related to [[31edo\|31 edo]], but with the 7/1 rather than the 2/1 being just. The octave is slightly stretched (about 0.3862 cents) and the step size is about 38.7221 cents.

← Older revision		Revision as of 15:01, 16 July 2025
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	* [[72ed5]] – relative ed5		* [[72ed5]] – relative ed5
	* [[80ed6]] – relative ed6		* [[80ed6]] – relative ed6
			* [[107ed11]] – relative ed11
	* [[111ed12]] – relative ed12		* [[111ed12]] – relative ed12
			* [[138ed22]] – relative ed22
	* [[204ed96]] – close to the zeta-optimized tuning for 31edo		* [[204ed96]] – close to the zeta-optimized tuning for 31edo
	* [[39cET]]		* [[39cET]]

	[[Category:31edo]]		[[Category:31edo]]

← Older revision		Revision as of 13:32, 10 June 2025
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	* [[72ed5]] – relative ed5		* [[72ed5]] – relative ed5
	* [[80ed6]] – relative ed6		* [[80ed6]] – relative ed6
	* [[107ed11]] – relative ed11
	* [[111ed12]] – relative ed12		* [[111ed12]] – relative ed12
			* [[204ed96]] – close to the zeta-optimized tuning for 31edo
	* [[39cET]]		* [[39cET]]

			[[Category:31edo]]