186ed6 - Revision history

FloraC: /* See also */ +258ed12

2025-05-22T11:31:40Z

FloraC: /* Theory */ rework to address more primes

2025-04-10T20:15:36Z

Theory: rework to address more primes

← Older revision		Revision as of 20:15, 10 April 2025
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	== Theory ==		== Theory ==
	186ed6 is closely related to [[72edo]], but with the 6th harmonic rather than the [[2/1\|octave]] being just, which results in the octaves being stretched by about 0.757{{c}}. Like 72edo, 186ed6 is [[consistent]] to the [[integer limit\|18-integer-limit]], and significantly ~~improves on~~ 72edo~~'s approximation to 13~~.		186ed6 is closely related to [[72edo]], but with the 6th harmonic rather than the [[2/1\|octave]] being just, which results in the octaves being stretched by about 0.757{{c}}. Like 72edo, 186ed6 is [[consistent]] to the [[integer limit\|18-integer-limit]]. While it tunes 2 and [[11/1\|11]] sharp, the [[3/1\|3]] and [[5/1\|5]] remain flat as in 72edo but less so, and the [[7/1\|7]] is practically pure. Moreover, the [[13/1\|13]] and [[17/1\|17]] are significantly improved compared to 72edo, although the [[19/1\|19]] becomes worse.

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

FloraC: /* Theory */ +subsets and supersets

2025-04-10T19:57:56Z

Theory: +subsets and supersets

← Older revision		Revision as of 19:57, 10 April 2025
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	{{Harmonics in equal\|186\|6\|1\|intervals=integer\|columns=11}}		{{Harmonics in equal\|186\|6\|1\|intervals=integer\|columns=11}}
	{{Harmonics in equal\|186\|6\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 186ed6 (continued)}}		{{Harmonics in equal\|186\|6\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 186ed6 (continued)}}

			=== Subsets and supersets ===
			Since 186 factors into primes as {{nowrap\| 2 × 3 × 31 }}, 186ed6 contains subset ed6's {{EDs\|equave=6\| 2, 3, 6, 31, 62, and 93 }}.

	== See also ==		== See also ==
	* [[72edo]] – relative edo		* [[72edo]] – relative edo
	* [[114edt]] – relative edt		* [[114edt]] – relative edt

FloraC: Cleanup

2025-04-10T19:56:20Z

Cleanup

← Older revision		Revision as of 19:56, 10 April 2025
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	{{ED intro}}		{{ED intro}}

	~~186ED6~~ is related to [[72edo~~\|72 edo~~]], but with the ~~6/1~~ rather than the 2/1 being just, which results in the octaves being stretched by about 1.~~2347~~{{c}}. It is consistent to the 18-[[integer-limit]], and significantly improves on 72edo's approximation to 13.		== Theory ==
			186ed6 is closely related to [[72edo]], but with the 6th harmonic rather than the [[2/1\|octave]] being just, which results in the octaves being stretched by about 0.757{{c}}. Like 72edo, 186ed6 is [[consistent]] to the [[integer limit\|18-integer-limit]], and significantly improves on 72edo's approximation to 13.

	~~Lookalikes: [[72edo]], [[114edt]]~~		=== Harmonics ===
			{{Harmonics in equal\|186\|6\|1\|intervals=integer\|columns=11}}
			{{Harmonics in equal\|186\|6\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 186ed6 (continued)}}

	== ~~Harmonics~~ ==		== See also ==
	~~{{Harmonics in equal\|186\|6\|1\|intervals=prime}}~~		* [[72edo]] – relative edo
	~~{{Harmonics in equal\|186\|6\|1\|intervals=prime\|collapsed=1\|start=12}}~~		* [[114edt]] – relative edt


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

ArrowHead294: Adopt &lt;nowiki&gt;{{ED intro}}&lt;/nowiki&gt; template

2025-02-07T19:08:27Z

Adopt &lt;nowiki&gt;{{ED intro}}&lt;/nowiki&gt; template

← Older revision		Revision as of 19:08, 7 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''[[Ed6\|Division of the sixth harmonic]] into 186 equal parts''' (~~186ED6) is related to [[72edo\|72 edo]], but with the 6/1 rather than the 2/1 being just~~. The octave is~~ about 1.2347 ~~cents stretched and the step size is about 16.6838 cents~~. It is consistent to the 18-[[integer-limit]], and significantly improves on 72edo's approximation to 13.		{{ED intro}}

			186ED6 is related to [[72edo\|72 edo]], but with the 6/1 rather than the 2/1 being just, which results in the octaves being stretched by about 1.2347{{c}}. It is consistent to the 18-[[integer-limit]], and significantly improves on 72edo's approximation to 13.

	Lookalikes: [[72edo]], [[114edt]]		Lookalikes: [[72edo]], [[114edt]]

	==Harmonics==		== Harmonics ==
	{{Harmonics in equal\|186\|6\|1\|intervals=prime}}		{{Harmonics in equal\|186\|6\|1\|intervals=prime}}
	{{Harmonics in equal\|186\|6\|1\|intervals=prime\|collapsed=1\|start=12}}		{{Harmonics in equal\|186\|6\|1\|intervals=prime\|collapsed=1\|start=12}}

BudjarnLambeth: Misleading link

2024-12-22T04:45:58Z

Misleading link

← Older revision		Revision as of 04:45, 22 December 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[Ed6\|Division of the sixth harmonic]] into 186 equal parts''' (186ED6) is related to [[72edo\|72 edo]], but with the 6/1 rather than the 2/1 being just. The octave is about 1.2347 cents stretched and the step size is about 16.6838 cents. It is consistent to the [[~~17-odd-limit\|18-~~integer-limit]], and significantly improves on 72edo's approximation to 13.		'''[[Ed6\|Division of the sixth harmonic]] into 186 equal parts''' (186ED6) is related to [[72edo\|72 edo]], but with the 6/1 rather than the 2/1 being just. The octave is about 1.2347 cents stretched and the step size is about 16.6838 cents. It is consistent to the 18-[[integer-limit]], and significantly improves on 72edo's approximation to 13.

	Lookalikes: [[72edo]], [[114edt]]		Lookalikes: [[72edo]], [[114edt]]

BudjarnLambeth: Wide table

2024-12-22T04:45:39Z

Wide table

← Older revision		Revision as of 04:45, 22 December 2024
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	~~{{Stub}}~~
	{{Infobox ET}}		{{Infobox ET}}
	'''[[Ed6\|Division of the sixth harmonic]] into 186 equal parts''' (186ED6) is related to [[72edo\|72 edo]], but with the 6/1 rather than the 2/1 being just. The octave is about 1.2347 cents stretched and the step size is about 16.6838 cents. It is consistent to the [[17-odd-limit\|18-integer-limit]], and significantly improves on 72edo's approximation to 13.		'''[[Ed6\|Division of the sixth harmonic]] into 186 equal parts''' (186ED6) is related to [[72edo\|72 edo]], but with the 6/1 rather than the 2/1 being just. The octave is about 1.2347 cents stretched and the step size is about 16.6838 cents. It is consistent to the [[17-odd-limit\|18-integer-limit]], and significantly improves on 72edo's approximation to 13.
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	==Harmonics==		==Harmonics==
	{{Harmonics in equal\|186\|6\|1\|~~prec~~=2\|~~columns~~=17}}		{{Harmonics in equal\|186\|6\|1\|intervals=prime}}
			{{Harmonics in equal\|186\|6\|1\|intervals=prime\|collapsed=1\|start=12}}


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

BudjarnLambeth at 10:30, 5 October 2024

2024-10-05T10:30:11Z

← Older revision		Revision as of 10:30, 5 October 2024
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	==Harmonics==		==Harmonics==
	{{Harmonics in equal\|186\|6\|1\|prec=2\|columns=17}}		{{Harmonics in equal\|186\|6\|1\|prec=2\|columns=17}}

	~~==Intervals==~~
	~~{{Interval table}}~~

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

BudjarnLambeth: Intervals

2024-10-03T20:00:50Z

Intervals

← Older revision		Revision as of 20:00, 3 October 2024
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	==Harmonics==		==Harmonics==
	{{Harmonics in equal\|186\|6\|1\|prec=2\|columns=17}}		{{Harmonics in equal\|186\|6\|1\|prec=2\|columns=17}}

			==Intervals==
			{{Interval table}}

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

ArrowHead294: Created page with

2024-05-09T14:50:53Z

Created page with

New page

{{Stub}}
{{Infobox ET}}
'''[[Ed6|Division of the sixth harmonic]] into 186 equal parts''' (186ED6) is related to [[72edo|72 edo]], but with the 6/1 rather than the 2/1 being just. The octave is about 1.2347 cents stretched and the step size is about 16.6838 cents. It is consistent to the [[17-odd-limit|18-integer-limit]], and significantly improves on 72edo's approximation to 13.

Lookalikes: [[72edo]], [[114edt]]

==Harmonics==
{{Harmonics in equal|186|6|1|prec=2|columns=17}}

[[Category:Edonoi]]

← Older revision		Revision as of 11:31, 22 May 2025
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	* [[72edo]] – relative edo		* [[72edo]] – relative edo
	* [[114edt]] – relative edt		* [[114edt]] – relative edt
			* [[258ed12]] – relative ed12