669edo - Revision history

Francium: changed EDO intro to ED intro

2025-02-21T05:41:26Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:41, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|669~~}}		{{ED intro}}

	669edo is [[consistent]] in the [[7-odd-limit]], although it has significant errors on the [[3/1\|3rd]] and the [[5/1\|5th]] [[harmonic]]s. Besides that, 669c [[val]] is a tuning for the [[sensipent]] temperament in the 5-limit.		669edo is [[consistent]] in the [[7-odd-limit]], although it has significant errors on the [[3/1\|3rd]] and the [[5/1\|5th]] [[harmonic]]s. Besides that, 669c [[val]] is a tuning for the [[sensipent]] temperament in the 5-limit.

Eliora: /* Odd harmonics */ declutter

2024-02-03T11:51:28Z

Odd harmonics: declutter

← Older revision		Revision as of 11:51, 3 February 2024
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|669}}		{{Harmonics in equal\|669}}
	{{Harmonics in equal\|669\|start=12}}		{{Harmonics in equal\|669\|start=12\|collapsed=1}}
	{{Harmonics in equal\|669\|start=23}}		{{Harmonics in equal\|669\|start=23\|collapsed=1}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 669 factors into {{factorization\|669}}, 669edo contains [[3edo]] and [[223edo]] as subsets.		Since 669 factors into {{factorization\|669}}, 669edo contains [[3edo]] and [[223edo]] as subsets.

BudjarnLambeth: /* Odd harmonics */ Added tables to illustrate text

2024-02-03T11:34:16Z

Odd harmonics: Added tables to illustrate text

← Older revision		Revision as of 11:34, 3 February 2024
Line 8:		Line 8:
	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|669}}		{{Harmonics in equal\|669}}
			{{Harmonics in equal\|669\|start=12}}
			{{Harmonics in equal\|669\|start=23}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 669 factors into {{factorization\|669}}, 669edo contains [[3edo]] and [[223edo]] as subsets.		Since 669 factors into {{factorization\|669}}, 669edo contains [[3edo]] and [[223edo]] as subsets.

FloraC: +subsets and supersets

2023-11-02T12:39:57Z

+subsets and supersets

← Older revision		Revision as of 12:39, 2 November 2023
Line 8:		Line 8:
	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|669}}		{{Harmonics in equal\|669}}

			=== Subsets and supersets ===
			Since 669 factors into {{factorization\|669}}, 669edo contains [[3edo]] and [[223edo]] as subsets.

FloraC: Cleanup

2023-10-22T08:31:06Z

Cleanup

← Older revision		Revision as of 08:31, 22 October 2023
Line 2:		Line 2:
	{{EDO intro\|669}}		{{EDO intro\|669}}

	669edo is consistent in the 7-odd-limit, although it has significant errors on the 3rd and the 5th ~~harmonics~~. Besides that, 669c val is a tuning for the [[sensipent]] temperament in the 5-limit.		669edo is [[consistent]] in the [[7-odd-limit]], although it has significant errors on the [[3/1\|3rd]] and the [[5/1\|5th]] [[harmonic]]s. Besides that, 669c [[val]] is a tuning for the [[sensipent]] temperament in the 5-limit.

	669edo appears ~~much more useful as a~~ higher~~-limit system~~, with harmonics 37 through 53 all having an error of 20% or less, with a comma basis for the 2.37.41.43.47.53 subgroup being {75809/75776, 1874161/1873232, 151124317/151101728, 9033613312/9032089499, 9795995841727/9788230467584}.		669edo appears better at approximating higher harmonics, with harmonics 37 through 53 all having an error of 20% or less, with a [[comma basis]] for the 2.37.41.43.47.53 [[subgroup]] being {75809/75776, 1874161/1873232, 151124317/151101728, 9033613312/9032089499, 9795995841727/9788230467584}. Overall, the subgroup which provides satisfactory results for 669edo is 2.7.19.29.37.41.43.47.53.

	~~Overall, the subgroup which provides satisfactory results for 669edo is 2.7.19.29.37.41.43.47.53.~~		=== Odd harmonics ===
			{{Harmonics in equal\|669}}
	===~~Harmonics~~===
	{{~~harmonics~~ in equal\|669}}

BudjarnLambeth at 06:43, 9 July 2023

2023-07-09T06:43:39Z

← Older revision		Revision as of 06:43, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|669}}		{{EDO intro\|669}}

BudjarnLambeth at 05:34, 9 July 2023

2023-07-09T05:34:17Z

← Older revision		Revision as of 05:34, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|669}}		{{EDO intro\|669}}

Eliora: Created page with "{{Infobox ET}} {{EDO intro|669}} 669edo is consistent in the 7-odd-limit, although it has significant errors on the 3rd and the 5th harmonics. Besides that, 669c val is a tun..."

2023-02-18T17:20:28Z

Created page with "{{Infobox ET}} {{EDO intro|669}} 669edo is consistent in the 7-odd-limit, although it has significant errors on the 3rd and the 5th harmonics. Besides that, 669c val is a tun..."

New page

{{Infobox ET}}
{{EDO intro|669}}

669edo is consistent in the 7-odd-limit, although it has significant errors on the 3rd and the 5th harmonics. Besides that, 669c val is a tuning for the [[sensipent]] temperament in the 5-limit.

669edo appears much more useful as a higher-limit system, with harmonics 37 through 53 all having an error of 20% or less, with a comma basis for the 2.37.41.43.47.53 subgroup being {75809/75776, 1874161/1873232, 151124317/151101728, 9033613312/9032089499, 9795995841727/9788230467584}.

Overall, the subgroup which provides satisfactory results for 669edo is 2.7.19.29.37.41.43.47.53.

===Harmonics===
{{harmonics in equal|669}}