228edo - Revision history

ArrowHead294 at 14:20, 20 February 2025

2025-02-20T14:20:15Z

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

	It is the first merger of [[12edo]] and [[19edo]], and its step size is the difference between 12edo's and 19edo's fifths. The equal temperament [[tempering out\|tempers out]] the [[Pythagorean comma]], 531441/524288, in the 3-limit, and [[225/224]] and [[250047/250000]] in the 7-limit, so that it [[support]]s 7-limit [[compton]] temperament and in fact provides the [[optimal patent val]]. In the 11-limit it tempers out 225/224, [[441/440]], 1375/1372 and 4375/4356, so that it supports 11-limit compton. Aside from the Pythagorean comma, the 12-comma, it tempers out the [[enneadeca]] or 19-tone-comma, and this is reflected in the fact that 228 = 12 × 19.		It is the first merger of [[12edo]] and [[19edo]], and its step size is the difference between 12edo's and 19edo's fifths. The equal temperament [[tempering out\|tempers out]] the [[Pythagorean comma]], 531441/524288, in the 3-limit, and [[225/224]] and [[250047/250000]] in the 7-limit, so that it [[support]]s 7-limit [[compton]] temperament and in fact provides the [[optimal patent val]]. In the 11-limit it tempers out 225/224, [[441/440]], 1375/1372 and 4375/4356, so that it supports 11-limit compton. Aside from the Pythagorean comma, the 12-comma, it tempers out the [[enneadeca]] or 19-tone-comma, and this is reflected in the fact that 228 = 12 × 19.

FloraC: Cleanup

2024-04-02T05:49:37Z

Cleanup

← Older revision		Revision as of 05:49, 2 April 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~The ''228 equal division'' divides the octave into 228 equal parts of 5.263 cents each.~~ It is the first merger of [[12edo]] and [[19edo]], and its step size is the difference between 12edo's and 19edo's fifths. It tempers out the [[Pythagorean comma]], 531441/524288, in the 3-limit, and [[225/224]] and [[250047/250000]] in the 7-limit, so that it [[support]]s 7-limit [[compton]] temperament and in fact provides the [[optimal patent val]]. In the 11-limit it tempers out 225/224, 441/440, 1375/1372 and 4375/4356, so that it supports 11-limit compton. Aside from the Pythagorean comma, the 12-comma, it tempers out the [[enneadeca]] or 19-tone-comma, and this is reflected in the fact that 228 = 12 × 19.		{{EDO intro}}

			It is the first merger of [[12edo]] and [[19edo]], and its step size is the difference between 12edo's and 19edo's fifths. The equal temperament [[tempering out\|tempers out]] the [[Pythagorean comma]], 531441/524288, in the 3-limit, and [[225/224]] and [[250047/250000]] in the 7-limit, so that it [[support]]s 7-limit [[compton]] temperament and in fact provides the [[optimal patent val]]. In the 11-limit it tempers out 225/224, [[441/440]], 1375/1372 and 4375/4356, so that it supports 11-limit compton. Aside from the Pythagorean comma, the 12-comma, it tempers out the [[enneadeca]] or 19-tone-comma, and this is reflected in the fact that 228 = 12 × 19.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|228}}		{{Harmonics in equal\|228}}

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

CompactStar at 00:37, 12 June 2023

2023-06-12T00:37:30Z

← Older revision		Revision as of 00:37, 12 June 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	The ''228 equal division'' divides the octave into 228 equal parts of 5.263 cents each. It tempers out the [[Pythagorean comma]], 531441/524288, in the 3-limit, and [[225/224]] and [[250047/250000]] in the 7-limit, so that it [[support]]s 7-limit [[compton]] temperament and in fact provides the [[optimal patent val]]. In the 11-limit it tempers out 225/224, 441/440, 1375/1372 and 4375/4356, so that it supports 11-limit compton. Aside from the Pythagorean comma, the 12-comma, it tempers out the [[enneadeca]] or 19-tone-comma, and this is reflected in the fact that 228 = 12 × 19.		The ''228 equal division'' divides the octave into 228 equal parts of 5.263 cents each. It is the first merger of [[12edo]] and [[19edo]], and its step size is the difference between 12edo's and 19edo's fifths. It tempers out the [[Pythagorean comma]], 531441/524288, in the 3-limit, and [[225/224]] and [[250047/250000]] in the 7-limit, so that it [[support]]s 7-limit [[compton]] temperament and in fact provides the [[optimal patent val]]. In the 11-limit it tempers out 225/224, 441/440, 1375/1372 and 4375/4356, so that it supports 11-limit compton. Aside from the Pythagorean comma, the 12-comma, it tempers out the [[enneadeca]] or 19-tone-comma, and this is reflected in the fact that 228 = 12 × 19.

	=== Odd harmonics ===		=== Odd harmonics ===

Plumtree: Infobox ET now computes most parameters automatically

2022-10-04T16:15:59Z

Infobox ET now computes most parameters automatically

← Older revision		Revision as of 16:15, 4 October 2022
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	{{Infobox ET		{{Infobox ET}}
	~~\| Prime factorization = 2<sup>2</sup> × 3 × 19~~
	~~\| Step size = 5.26316¢~~
	~~\| Sharp fifth = 134\228 (705.26¢)~~
	~~\| Flat fifth = 133\228 (700.00¢) (→ [[12edo\|7\12]])~~
	~~\| Major 2nd = 39\228 (205.26¢)~~
	~~\| Consistency = 7~~
	}}
	The ''228 equal division'' divides the octave into 228 equal parts of 5.263 cents each. It tempers out the [[Pythagorean comma]], 531441/524288, in the 3-limit, and [[225/224]] and [[250047/250000]] in the 7-limit, so that it [[support]]s 7-limit [[compton]] temperament and in fact provides the [[optimal patent val]]. In the 11-limit it tempers out 225/224, 441/440, 1375/1372 and 4375/4356, so that it supports 11-limit compton. Aside from the Pythagorean comma, the 12-comma, it tempers out the [[enneadeca]] or 19-tone-comma, and this is reflected in the fact that 228 = 12 × 19.		The ''228 equal division'' divides the octave into 228 equal parts of 5.263 cents each. It tempers out the [[Pythagorean comma]], 531441/524288, in the 3-limit, and [[225/224]] and [[250047/250000]] in the 7-limit, so that it [[support]]s 7-limit [[compton]] temperament and in fact provides the [[optimal patent val]]. In the 11-limit it tempers out 225/224, 441/440, 1375/1372 and 4375/4356, so that it supports 11-limit compton. Aside from the Pythagorean comma, the 12-comma, it tempers out the [[enneadeca]] or 19-tone-comma, and this is reflected in the fact that 228 = 12 × 19.

FloraC: Rework the infobox as a dual-fifth system

2022-09-12T17:57:27Z

Rework the infobox as a dual-fifth system

← Older revision		Revision as of 17:57, 12 September 2022
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	{{Infobox ET		{{Infobox ET
	\| Prime factorization = ~~19 × 3 ×~~ 2<sup>2</sup>		\| Prime factorization = 2<sup>2</sup> × 3 × 19
	\| Step size = 5.26316¢		\| Step size = 5.26316¢
	\| ~~Fifth~~ = 133\228 (~~700¢~~) (→7\12)		\| Sharp fifth = 134\228 (705.26¢)
	\| Major 2nd = 38\228 (~~200¢)~~		\| Flat fifth = 133\228 (700.00¢) (→ [[12edo\|7\12]])
	~~\| Semitones = 38:38 (100¢:100¢~~)		\| Major 2nd = 39\228 (205.26¢)
	\| Consistency = 7		\| Consistency = 7
	}}		}}
	The ''228 equal division'' divides the octave into 228 equal parts of 5.263 cents each. It tempers out the Pythagorean comma, 531441/524288, in the 3-limit, and 225/224 and 250047/250000 in the 7-limit, so that it [[support]]s 7-limit [[~~Pythagorean_family\|~~compton ~~temperament~~]] and in fact provides the [[optimal patent val]]. In the 11-limit it tempers out 225/224, 441/440, 1375/1372 and 4375/4356, so that it supports 11-limit compton. Aside from the Pythagorean comma, the 12-comma, it tempers out the [[enneadeca]] or 19-tone-comma, and this is reflected in the fact that 228 = 12 × 19.		The ''228 equal division'' divides the octave into 228 equal parts of 5.263 cents each. It tempers out the [[Pythagorean comma]], 531441/524288, in the 3-limit, and [[225/224]] and [[250047/250000]] in the 7-limit, so that it [[support]]s 7-limit [[compton]] temperament and in fact provides the [[optimal patent val]]. In the 11-limit it tempers out 225/224, 441/440, 1375/1372 and 4375/4356, so that it supports 11-limit compton. Aside from the Pythagorean comma, the 12-comma, it tempers out the [[enneadeca]] or 19-tone-comma, and this is reflected in the fact that 228 = 12 × 19.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 13:		Line 13:

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

FloraC: Relocate the infobox; +odd harmonics table

2022-09-12T17:52:39Z

Relocate the infobox; +odd harmonics table

← Older revision		Revision as of 17:52, 12 September 2022
Line 1:		Line 1:
	The ''228 equal division'' divides the octave into 228 equal parts of 5.263 cents each. It tempers out the Pythagorean comma, 531441/524288, in the 3-limit, and 225/224 and 250047/250000 in the 7-limit, so that it [[support]]s 7-limit [[Pythagorean_family\|compton temperament]] and in fact provides the [[Optimal_patent_val\|optimal patent val]]. In the 11-limit it tempers out 225/224, 441/440, 1375/1372 and 4375/4356, so that it supports 11-limit compton. Aside from the Pythagorean comma, the 12-comma, it tempers out the [[enneadeca]] or 19-tone-comma, and this is reflected in the fact that 228 = 12 * 19.
	{{Infobox ET		{{Infobox ET
	\| Prime factorization = 19 × 3 × 2<sup>2</sup>		\| Prime factorization = 19 × 3 × 2<sup>2</sup>
Line 8:		Line 7:
	\| Consistency = 7		\| Consistency = 7
	}}		}}
			The ''228 equal division'' divides the octave into 228 equal parts of 5.263 cents each. It tempers out the Pythagorean comma, 531441/524288, in the 3-limit, and 225/224 and 250047/250000 in the 7-limit, so that it [[support]]s 7-limit [[Pythagorean_family\|compton temperament]] and in fact provides the [[optimal patent val]]. In the 11-limit it tempers out 225/224, 441/440, 1375/1372 and 4375/4356, so that it supports 11-limit compton. Aside from the Pythagorean comma, the 12-comma, it tempers out the [[enneadeca]] or 19-tone-comma, and this is reflected in the fact that 228 = 12 × 19.

			=== Odd harmonics ===
			{{Harmonics in equal\|228}}

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

Gud2228 at 15:43, 12 September 2022

2022-09-12T15:43:40Z

← Older revision		Revision as of 15:43, 12 September 2022
Line 6:		Line 6:
	\| Major 2nd = 38\228 (200¢)		\| Major 2nd = 38\228 (200¢)
	\| Semitones = 38:38 (100¢:100¢)		\| Semitones = 38:38 (100¢:100¢)
	\| Consistency = 5		\| Consistency = 7
	}}		}}

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

Gud2228 at 15:41, 12 September 2022

2022-09-12T15:41:36Z

← Older revision		Revision as of 15:41, 12 September 2022
Line 3:		Line 3:
	\| Prime factorization = 19 × 3 × 2<sup>2</sup>		\| Prime factorization = 19 × 3 × 2<sup>2</sup>
	\| Step size = 5.26316¢		\| Step size = 5.26316¢
	\| Fifth = 133\228 (700¢)		\| Fifth = 133\228 (700¢) (→7\12)
	\| Major 2nd = 38\228 (200¢)		\| Major 2nd = 38\228 (200¢)
	\| Semitones = 38:38 (100¢:100¢)		\| Semitones = 38:38 (100¢:100¢)

Gud2228 at 15:40, 12 September 2022

2022-09-12T15:40:54Z

← Older revision		Revision as of 15:40, 12 September 2022
Line 5:		Line 5:
	\| Fifth = 133\228 (700¢)		\| Fifth = 133\228 (700¢)
	\| Major 2nd = 38\228 (200¢)		\| Major 2nd = 38\228 (200¢)
	\| Semitones = (100¢:100¢)		\| Semitones = 38:38 (100¢:100¢)
	\| Consistency = 5		\| Consistency = 5
	}}		}}

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

Gud2228 at 15:40, 12 September 2022

2022-09-12T15:40:22Z

← Older revision		Revision as of 15:40, 12 September 2022
Line 1:		Line 1:
	The ''228 equal division'' divides the octave into 228 equal parts of 5.263 cents each. It tempers out the Pythagorean comma, 531441/524288, in the 3-limit, and 225/224 and 250047/250000 in the 7-limit, so that it [[support]]s 7-limit [[Pythagorean_family\|compton temperament]] and in fact provides the [[Optimal_patent_val\|optimal patent val]]. In the 11-limit it tempers out 225/224, 441/440, 1375/1372 and 4375/4356, so that it supports 11-limit compton. Aside from the Pythagorean comma, the 12-comma, it tempers out the [[enneadeca]] or 19-tone-comma, and this is reflected in the fact that 228 = 12 * 19.		The ''228 equal division'' divides the octave into 228 equal parts of 5.263 cents each. It tempers out the Pythagorean comma, 531441/524288, in the 3-limit, and 225/224 and 250047/250000 in the 7-limit, so that it [[support]]s 7-limit [[Pythagorean_family\|compton temperament]] and in fact provides the [[Optimal_patent_val\|optimal patent val]]. In the 11-limit it tempers out 225/224, 441/440, 1375/1372 and 4375/4356, so that it supports 11-limit compton. Aside from the Pythagorean comma, the 12-comma, it tempers out the [[enneadeca]] or 19-tone-comma, and this is reflected in the fact that 228 = 12 * 19.
			{{Infobox ET
			\| Prime factorization = 19 × 3 × 2<sup>2</sup>
			\| Step size = 5.26316¢
			\| Fifth = 133\228 (700¢)
			\| Major 2nd = 38\228 (200¢)
			\| Semitones = (100¢:100¢)
			\| Consistency = 5
			}}

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