306edo - Revision history

Lucius Chiaraviglio: /* Subsets and supersets */ Add superset 612edo

2025-11-29T07:09:01Z

Subsets and supersets: Add superset 612edo

← Older revision		Revision as of 07:09, 29 November 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 306 factors into {{factorization\|306}}, 306edo has subset edos {{EDOs\| 2, 3, 6, 9, 17, 18, 34, 51, 102, and 153 }}.		Since 306 factors into {{factorization\|306}}, 306edo has subset edos {{EDOs\| 2, 3, 6, 9, 17, 18, 34, 51, 102, and 153 }}. [[612edo]], which doubles it, provides corrections for the 5th, 11th, and 29th harmonics.

	[[Category:3-limit record edos\|###]] <!-- 3-digit number -->		[[Category:3-limit record edos\|###]] <!-- 3-digit number -->

FloraC: + category

2025-07-12T12:47:26Z

+ category

← Older revision		Revision as of 12:47, 12 July 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 306 factors into {{factorization\|306}}, 306edo has subset edos {{EDOs\| 2, 3, 6, 9, 17, 18, 34, 51, 102, and 153 }}.		Since 306 factors into {{factorization\|306}}, 306edo has subset edos {{EDOs\| 2, 3, 6, 9, 17, 18, 34, 51, 102, and 153 }}.

			[[Category:3-limit record edos\|###]] <!-- 3-digit number -->

ArrowHead294 at 14:33, 20 February 2025

2025-02-20T14:33:59Z

← Older revision		Revision as of 14:33, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	306edo provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[patent val]] [[tempering out\|tempers out]] 78732/78125 ([[sensipent comma]]), whereas the alternative 306c val tempers out 32805/32768 ([[schisma]]). In the 7-limit the patent val tempers out [[6144/6125]], whereas 306c tempers out [[16875/16807]]. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].		306edo provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[patent val]] [[tempering out\|tempers out]] 78732/78125 ([[sensipent comma]]), whereas the alternative 306c val tempers out 32805/32768 ([[schisma]]). In the 7-limit the patent val tempers out [[6144/6125]], whereas 306c tempers out [[16875/16807]]. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].

Tristanbay: Added mention of 306edo's association with Valotti temperament

2024-10-20T18:14:08Z

Added mention of 306edo's association with Valotti temperament

← Older revision		Revision as of 18:14, 20 October 2024
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	306edo provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[patent val]] [[tempering out\|tempers out]] 78732/78125 ([[sensipent comma]]), whereas the alternative 306c val tempers out 32805/32768 ([[schisma]]). In the 7-limit the patent val tempers out [[6144/6125]], whereas 306c tempers out [[16875/16807]]. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].		306edo provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[patent val]] [[tempering out\|tempers out]] 78732/78125 ([[sensipent comma]]), whereas the alternative 306c val tempers out 32805/32768 ([[schisma]]). In the 7-limit the patent val tempers out [[6144/6125]], whereas 306c tempers out [[16875/16807]]. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].

			306edo provides an excellent approximation of [[Well temperament#Historical well temperaments\|Valotti temperament]] due to its representation of the [[Pythagorean comma]] as 6 steps.

	=== Prime harmonics ===		=== Prime harmonics ===

FloraC: Cleanup and +subsets and supersets

2024-02-21T11:07:30Z

Cleanup and +subsets and supersets

← Older revision		Revision as of 11:07, 21 February 2024
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	{{EDO intro}}		{{EDO intro}}

	It provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[~~Patent_val\|~~patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].		306edo provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[patent val]] [[tempering out\|tempers out]] 78732/78125 ([[sensipent comma]]), whereas the alternative 306c val tempers out 32805/32768 ([[schisma]]). In the 7-limit the patent val tempers out [[6144/6125]], whereas 306c tempers out [[16875/16807]]. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].

	==~~Harmonics~~==		=== Prime harmonics ===
	{{~~harmonics~~ in equal\|306~~\|start=2~~\|prec=3~~\|intervals=prime~~}}		{{Harmonics in equal\|306\|prec=3}}

	~~[[Category:Equal divisions of the octave~~\|~~###]] <!--~~ 3~~-digit number -->~~		=== Subsets and supersets ===
			Since 306 factors into {{factorization\|306}}, 306edo has subset edos {{EDOs\| 2, 3, 6, 9, 17, 18, 34, 51, 102, and 153 }}.

BudjarnLambeth: EDO intro & subheading

2024-02-05T01:55:27Z

EDO intro & subheading

← Older revision		Revision as of 01:55, 5 February 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~The '''306 equal division''' divides the octave into 306 equal parts of 3.9216 cents each, and thereby~~ provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val\|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].		{{EDO intro}}

			It provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val\|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].

			==Harmonics==
	{{harmonics in equal\|306\|start=2\|prec=3\|intervals=prime}}		{{harmonics in equal\|306\|start=2\|prec=3\|intervals=prime}}

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Plumtree: Infobox ET added

2022-10-04T21:49:16Z

Infobox ET added

← Older revision		Revision as of 21:49, 4 October 2022
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			{{Infobox ET}}
	The '''306 equal division''' divides the octave into 306 equal parts of 3.9216 cents each, and thereby provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val\|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].		The '''306 equal division''' divides the octave into 306 equal parts of 3.9216 cents each, and thereby provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val\|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].
	{{harmonics in equal\|306\|start=2\|prec=3\|intervals=prime}}		{{harmonics in equal\|306\|start=2\|prec=3\|intervals=prime}}

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Royalmilktea: harmonics precision

2022-10-03T03:20:32Z

harmonics precision

← Older revision		Revision as of 03:20, 3 October 2022
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	The '''306 equal division''' divides the octave into 306 equal parts of 3.9216 cents each, and thereby provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val\|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].		The '''306 equal division''' divides the octave into 306 equal parts of 3.9216 cents each, and thereby provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val\|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].
	{{harmonics in equal\|306\|start=2\|intervals=prime}}		{{harmonics in equal\|306\|start=2\|prec=3\|intervals=prime}}

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Royalmilktea at 03:19, 3 October 2022

2022-10-03T03:19:53Z

← Older revision		Revision as of 03:19, 3 October 2022
Line 1:		Line 1:
	The '''306 equal division''' divides the octave into 306 equal parts of 3.9216 cents each, and thereby provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val\|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].		The '''306 equal division''' divides the octave into 306 equal parts of 3.9216 cents each, and thereby provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val\|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].
			{{harmonics in equal\|306\|start=2\|intervals=prime}}

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Fredg999 category edits: Sort key

2022-07-03T19:14:41Z

Sort key

← Older revision		Revision as of 19:14, 3 July 2022
Line 1:		Line 1:
	The '''306 equal division''' divides the octave into 306 equal parts of 3.9216 cents each, and thereby provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val\|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].		The '''306 equal division''' divides the octave into 306 equal parts of 3.9216 cents each, and thereby provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val\|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].

			[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

← Older revision		Revision as of 21:49, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	The '''306 equal division''' divides the octave into 306 equal parts of 3.9216 cents each, and thereby provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val\|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].		The '''306 equal division''' divides the octave into 306 equal parts of 3.9216 cents each, and thereby provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val\|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].
	{{harmonics in equal\|306\|start=2\|prec=3\|intervals=prime}}		{{harmonics in equal\|306\|start=2\|prec=3\|intervals=prime}}

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

← Older revision		Revision as of 03:20, 3 October 2022
Line 1:		Line 1:
	The '''306 equal division''' divides the octave into 306 equal parts of 3.9216 cents each, and thereby provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val\|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].		The '''306 equal division''' divides the octave into 306 equal parts of 3.9216 cents each, and thereby provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val\|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].
	{{harmonics in equal\|306\|start=2\|intervals=prime}}		{{harmonics in equal\|306\|start=2\|prec=3\|intervals=prime}}

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

← Older revision		Revision as of 03:19, 3 October 2022
Line 1:		Line 1:
	The '''306 equal division''' divides the octave into 306 equal parts of 3.9216 cents each, and thereby provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val\|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].		The '''306 equal division''' divides the octave into 306 equal parts of 3.9216 cents each, and thereby provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val\|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo\|31\53]] and before [[665edo\|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].
			{{harmonics in equal\|306\|start=2\|intervals=prime}}

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->