80ed6 - Revision history

ArrowHead294 at 15:01, 16 July 2025

2025-07-16T15:01:10Z

← Older revision		Revision as of 15:01, 16 July 2025
Line 20:		Line 20:
	* [[72ed5]] – relative ed5		* [[72ed5]] – relative ed5
	* [[87ed7]] – relative ed7		* [[87ed7]] – relative ed7
			* [[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]]

ArrowHead294: /* See also */

2025-06-10T13:32:04Z

FloraC: /* Theory */ expand on its tuning characteristics

2025-03-30T17:24:44Z

Theory: expand on its tuning characteristics

← Older revision		Revision as of 17:24, 30 March 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	80ed6 is related to [[31edo]], but with the 6/1 rather than the [[2/1]] being just. This stretches the octave by about 2 cents. Like 31edo, 80ed6 is [[consistent]] to the [[integer limit\|12-integer-limit]].		80ed6 is related to [[31edo]], but with the 6/1 rather than the [[2/1]] being just. This stretches the octave by about 2 cents. Like 31edo, 80ed6 is [[consistent]] to the [[integer limit\|12-integer-limit]]. It is pretty well optimized for the [[11-limit]], trading the accuracy of the [[5/1\|5th]] and [[7/1\|7th]] [[harmonic]]s for an improved [[3/1\|3rd harmonic]] and a massively improved [[11/1\|11th harmonic]], which is only 2.5 cents flat of just (in comparison, 31edo's 11th harmonic is 9.4 cents flat). Also improved is the [[23/1\|23rd harmonic]], which is now only 0.1 cents sharp of just.

			The [[13/1\|13th]], [[17/1\|17th]], and [[19/1\|19th harmonics]] are now about halfway between the steps, suggesting the use of [[160ed6]].

	=== Harmonics ===		=== Harmonics ===
Line 10:		Line 12:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 80 factors into primes as {{nowrap\| 2<sup>4</sup> × 5 }}, 80ed6 has subset ed6's {{EDs\|equave=6\| 2, 4, 5, 8, 10, 16, 20, and 40 }}.		Since 80 factors into primes as {{nowrap\| 2<sup>4</sup> × 5 }}, 80ed6 has subset ed6's {{EDs\|equave=6\| 2, 4, 5, 8, 10, 16, 20, and 40 }}. 160ed6, which doubles it, much corrects its 13th, 17th, and 19th harmonics.

	== See also ==		== See also ==

FloraC: /* Theory */ note consistency. Fix harmonics table

2025-03-24T11:59:31Z

Theory: note consistency. Fix harmonics table

← Older revision		Revision as of 11:59, 24 March 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	80ed6 is related to [[31edo]], but with the 6/1 rather than the [[2/1]] being just. This stretches the octave by about 2 cents.		80ed6 is related to [[31edo]], but with the 6/1 rather than the [[2/1]] being just. This stretches the octave by about 2 cents. Like 31edo, 80ed6 is [[consistent]] to the [[integer limit\|12-integer-limit]].

	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|80\|6\|1\|intervals=~~prime~~\|columns=11}}		{{Harmonics in equal\|80\|6\|1\|intervals=integer\|columns=11}}
	{{Harmonics in equal\|80\|6\|1\|intervals=~~prime~~\|columns=12\|start=12\|collapsed=true\|Approximation of harmonics in 80ed6 (continued)}}		{{Harmonics in equal\|80\|6\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|Approximation of harmonics in 80ed6 (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

FloraC: /* Theory */ +subsets and supersets

2025-03-24T11:58:22Z

Theory: +subsets and supersets

← Older revision		Revision as of 11:58, 24 March 2025
Line 8:		Line 8:
	{{Harmonics in equal\|80\|6\|1\|intervals=prime\|columns=11}}		{{Harmonics in equal\|80\|6\|1\|intervals=prime\|columns=11}}
	{{Harmonics in equal\|80\|6\|1\|intervals=prime\|columns=12\|start=12\|collapsed=true\|Approximation of harmonics in 80ed6 (continued)}}		{{Harmonics in equal\|80\|6\|1\|intervals=prime\|columns=12\|start=12\|collapsed=true\|Approximation of harmonics in 80ed6 (continued)}}

			=== Subsets and supersets ===
			Since 80 factors into primes as {{nowrap\| 2<sup>4</sup> × 5 }}, 80ed6 has subset ed6's {{EDs\|equave=6\| 2, 4, 5, 8, 10, 16, 20, and 40 }}.

	== See also ==		== See also ==

FloraC: Cleanup

2025-03-24T11:57:13Z

Cleanup

← Older revision		Revision as of 11:57, 24 March 2025
Line 2:		Line 2:
	{{ED intro}}		{{ED intro}}

	~~80ED6~~ is related to [[31edo]], but with the 6/1 rather than the 2/1 being just. This stretches the octave by about 2 cents.		== Theory ==
			80ed6 is related to [[31edo]], but with the 6/1 rather than the [[2/1]] being just. This stretches the octave by about 2 cents.

	~~Lookalikes: [[18edf]], [[31edo]], [[39cET]], [[49edt]], [[72ed5]]~~		=== Harmonics ===
			{{Harmonics in equal\|80\|6\|1\|intervals=prime\|columns=11}}
			{{Harmonics in equal\|80\|6\|1\|intervals=prime\|columns=12\|start=12\|collapsed=true\|Approximation of harmonics in 80ed6 (continued)}}

	== ~~Harmonics~~ ==		== See also ==
	~~{{Harmonics in equal\|80\|6\|1\|prec=2\|columns=8}}~~		* [[18edf]] – relative edf
	~~{{Harmonics in equal\|80\|6\|1\|prec=2\|columns=8\|start=9}}~~		* [[31edo]] – relative edo
			* [[49edt]] – relative edt
			* [[72ed5]] – relative ed5
	~~{{stub}}~~		* [[87ed7]] – relative ed7
	[[~~Category:Edonoi~~]]		* [[111ed12]] – relative ed12
			* [[39cET]]

ArrowHead294 at 16:47, 21 January 2025

2025-01-21T16:47:55Z

← Older revision		Revision as of 16:47, 21 January 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''[[Ed6\|Division of the sixth harmonic]] into 80 equal parts''' (80ED6) is related to [[31edo\|31 edo]], but with the 6/1 rather than the 2/1 being just. The octave is about 2 cents stretched and the step size is 38.77 cents.		{{ED intro}}

	~~Lookalikes:~~ [[31edo]], ~~[[49edt]], [[72ed5]], [[18edf]]~~		80ED6 is related to [[31edo]], but with the 6/1 rather than the 2/1 being just. This stretches the octave by about 2 cents.

	==Harmonics==		Lookalikes: [[18edf]], [[31edo]], [[39cET]], [[49edt]], [[72ed5]]

			== Harmonics ==
	{{Harmonics in equal\|80\|6\|1\|prec=2\|columns=8}}		{{Harmonics in equal\|80\|6\|1\|prec=2\|columns=8}}
	{{Harmonics in equal\|80\|6\|1\|prec=2\|columns=8\|start=9}}		{{Harmonics in equal\|80\|6\|1\|prec=2\|columns=8\|start=9}}

BudjarnLambeth: Stub, wide table

2024-12-22T04:33:33Z

Stub, wide table

← Older revision		Revision as of 04:33, 22 December 2024
Line 5:		Line 5:

	==Harmonics==		==Harmonics==
	{{Harmonics in equal\|80\|6\|1\|prec=2\|columns=15}}		{{Harmonics in equal\|80\|6\|1\|prec=2\|columns=8}}
			{{Harmonics in equal\|80\|6\|1\|prec=2\|columns=8\|start=9}}


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

ArrowHead294 at 17:20, 13 May 2024

2024-05-13T17:20:39Z

← Older revision		Revision as of 17:20, 13 May 2024
Line 3:		Line 3:

	Lookalikes: [[31edo]], [[49edt]], [[72ed5]], [[18edf]]		Lookalikes: [[31edo]], [[49edt]], [[72ed5]], [[18edf]]

			==Harmonics==
			{{Harmonics in equal\|80\|6\|1\|prec=2\|columns=15}}

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

ArrowHead294: Created page with "{{Infobox ET}} '''Division of the sixth harmonic into 80 equal parts''' (80ED6) is related to 31 edo, but with the 6/1 rather than the 2/1 being just. The oc..."

2024-05-09T14:41:37Z

Created page with "{{Infobox ET}} '''Division of the sixth harmonic into 80 equal parts''' (80ED6) is related to 31 edo, but with the 6/1 rather than the 2/1 being just. The oc..."

New page

{{Infobox ET}}
'''[[Ed6|Division of the sixth harmonic]] into 80 equal parts''' (80ED6) is related to [[31edo|31 edo]], but with the 6/1 rather than the 2/1 being just. The octave is about 2 cents stretched and the step size is 38.77 cents.

Lookalikes: [[31edo]], [[49edt]], [[72ed5]], [[18edf]]

[[Category:Edonoi]]

← Older revision		Revision as of 13:32, 10 June 2025
Line 21:		Line 21:
	* [[87ed7]] – relative ed7		* [[87ed7]] – relative ed7
	* [[111ed12]] – relative ed12		* [[111ed12]] – relative ed12
			* [[204ed96]] – close to the zeta-optimized tuning for 31edo
	* [[39cET]]		* [[39cET]]

			[[Category:31edo]]