226edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:32:08Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:32, 13 March 2026
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	\| [[Lagaca]]		\| [[Lagaca]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

ArrowHead294 at 22:48, 20 February 2025

2025-02-20T22:48:02Z

← Older revision		Revision as of 22:48, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|226~~}}		{{ED intro}}

	== Theory ==		== Theory ==
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	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
			\|-
	! rowspan="2" \| [[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \| [[Comma list~~\|Comma List~~]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br>8ve ~~Stretch~~ (¢)		! rowspan="2" \| Optimal<br />8ve stretch (¢)
	! colspan="2" \| Tuning ~~Error~~		! colspan="2" \| Tuning error
	\|-		\|-
	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	! [[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
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	\| {{monzo\| 17 1 -8 }}, {{monzo\| -32 29 -6 }}		\| {{monzo\| 17 1 -8 }}, {{monzo\| -32 29 -6 }}
	\| {{mapping\| 226 358 525 }}		\| {{mapping\| 226 358 525 }}
	\| 0.0386		\| +0.0386
	\| 0.5044		\| 0.5044
	\| 9.50		\| 9.50
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	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		\|-
			! Periods<br />per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>~~Ratio~~*		! Associated<br />ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\| [[Lagaca]]		\| [[Lagaca]]
	\|}		\|}
			<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

FloraC: /* Regular temperament properties */ +hemiseven

2024-04-02T06:23:35Z

Regular temperament properties: +hemiseven

← Older revision		Revision as of 06:23, 2 April 2024
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	\| 5/4		\| 5/4
	\| [[Würschmidt]] (5-limit)		\| [[Würschmidt]] (5-limit)
			\|-
			\| 1
			\| 91\226
			\| 483.19
			\| 320/243
			\| [[Hemiseven]] (7-limit)
	\|-		\|-
	\| 2		\| 2

FloraC: Cleanup; note its relation to 113edo

2024-04-02T06:20:44Z

Cleanup; note its relation to 113edo

← Older revision		Revision as of 06:20, 2 April 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|226}}		{{EDO intro\|226}}

	== Theory ==		== Theory ==
	~~226et~~ [[~~tempering_out~~\|tempers out]] ~~2029~~/~~2024~~ in the [[7-limit]]; 243/242 and [[~~Quartisma\|117440512/117406179~~]] in the [[11-limit]]; ~~as well as~~ 364/363 and 729/728, in the [[13-limit]].		226edo is closely related to [[113edo]], but its mapping of [[harmonic]] [[5/1\|5]] is sharp instead of flat. Unlike 113, 226 is only [[consistent]] to the [[5-odd-limit]]. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[1029/1024]] and [[19683/19600]] in the [[7-limit]]; [[243/242]], [[9801/9800]] and notably the [[quartisma]] in the [[11-limit]]; and [[364/363]] and [[729/728]] in the [[13-limit]].

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|226}}		{{Harmonics in equal\|226}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	226 factors into 2 × 113, with [[2edo]] and [[113edo]] as its subset edos. [[904edo]], which quadruples it, gives a good correction to the harmonic 7.		226 factors into 2 × 113, with [[2edo]] and [[113edo]] as its subset edos. [[904edo]], which quadruples it, gives a good correction to the harmonic 7.
	==Regular temperament properties==
			== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \|[[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal<br>8ve Stretch (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	! colspan="2" \|Tuning Error		! colspan="2" \| Tuning Error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	~~\|2.3~~		\| 2.3.5
	~~\|{{monzo\|-179 113}}~~		\| {{monzo\| 17 1 -8 }}, {{monzo\| -32 29 -6 }}
	~~\|{{val\|226 358}}~~		\| {{mapping\| 226 358 525 }}
	~~\| 0.3376~~
	~~\| 0.3377~~
	~~\| 6.36~~
	\|-
	\|2.3.5
	\|{{monzo\|17 1 -8}}, {{monzo\|-32 29 -6}}
	\|{{~~val~~\|226 358 525}}
	\| 0.0386		\| 0.0386
	\| 0.5044		\| 0.5044
	\| 9.50		\| 9.50
	\|}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(reduced)~~		! Generator*
	! Cents~~<br>(reduced)~~		! Cents*
	! Associated<br>~~ratio~~		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|73\226		\| 73\226
	\|387.61		\| 387.61
	\|5/4		\| 5/4
	\|[[Würschmidt]]		\| [[Würschmidt]] (5-limit)
	\|-		\|-
	\|2		\| 2
	\|23\226		\| 23\226
	\|122.12		\| 122.12
	\|15/14		\| 15/14
	\|[[Lagaca]]		\| [[Lagaca]]
	\|}		\|}

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

Francium: /* Regular temperament properties */

2023-10-29T10:01:59Z

Regular temperament properties

← Older revision		Revision as of 10:01, 29 October 2023
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	\|2.3.5		\|2.3.5
	\|{{monzo\|17 1 -8}}, {{monzo\|-32 29 -6}}		\|{{monzo\|17 1 -8}}, {{monzo\|-32 29 -6}}
			\|{{val\|226 358 525}}
	\| 0.0386		\| 0.0386
	\| 0.5044		\| 0.5044

Francium at 10:01, 29 October 2023

2023-10-29T10:01:14Z

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''226edo''' is the [[EDO|equal division of the octave]] into 226 parts of 5.3097 [[cent]]s each.  It [[tempering_out|tempers out]] 2029/2024 in the [[7-limit]]; 243/242 and [[Quartisma|117440512/117406179]] in the [[11-limit]]; as well as 364/363 and 729/728, in the [[13-limit]].
+{{EDO intro|226}}
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->

BudjarnLambeth: Added "harmonics in equal" table

2023-06-24T03:37:51Z

Added "harmonics in equal" table

← Older revision		Revision as of 03:37, 24 June 2023
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	'''226edo''' is the [[EDO\|equal division of the octave]] into 226 parts of 5.3097 [[cent]]s each. It [[tempering_out\|tempers out]] 2029/2024 in the [[7-limit]]; 243/242 and [[Quartisma\|117440512/117406179]] in the [[11-limit]]; as well as 364/363 and 729/728, in the [[13-limit]].		'''226edo''' is the [[EDO\|equal division of the octave]] into 226 parts of 5.3097 [[cent]]s each. It [[tempering_out\|tempers out]] 2029/2024 in the [[7-limit]]; 243/242 and [[Quartisma\|117440512/117406179]] in the [[11-limit]]; as well as 364/363 and 729/728, in the [[13-limit]].

			{{Harmonics in equal\|226}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Plumtree: Infobox ET added

2022-10-04T21:25:10Z

Infobox ET added

← Older revision		Revision as of 21:25, 4 October 2022
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			{{Infobox ET}}
	'''226edo''' is the [[EDO\|equal division of the octave]] into 226 parts of 5.3097 [[cent]]s each. It [[tempering_out\|tempers out]] 2029/2024 in the [[7-limit]]; 243/242 and [[Quartisma\|117440512/117406179]] in the [[11-limit]]; as well as 364/363 and 729/728, in the [[13-limit]].		'''226edo''' is the [[EDO\|equal division of the octave]] into 226 parts of 5.3097 [[cent]]s each. It [[tempering_out\|tempers out]] 2029/2024 in the [[7-limit]]; 243/242 and [[Quartisma\|117440512/117406179]] in the [[11-limit]]; as well as 364/363 and 729/728, in the [[13-limit]].

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

Fredg999 category edits: Sort key

2022-07-03T18:44:22Z

Sort key

← Older revision		Revision as of 18:44, 3 July 2022
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	'''226edo''' is the [[EDO\|equal division of the octave]] into 226 parts of 5.3097 [[cent]]s each. It [[tempering_out\|tempers out]] 2029/2024 in the [[7-limit]]; 243/242 and [[Quartisma\|117440512/117406179]] in the [[11-limit]]; as well as 364/363 and 729/728, in the [[13-limit]].		'''226edo''' is the [[EDO\|equal division of the octave]] into 226 parts of 5.3097 [[cent]]s each. It [[tempering_out\|tempers out]] 2029/2024 in the [[7-limit]]; 243/242 and [[Quartisma\|117440512/117406179]] in the [[11-limit]]; as well as 364/363 and 729/728, in the [[13-limit]].

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

Keenan Pepper category edits: Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

2020-12-04T23:13:19Z

Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

← Older revision		Revision as of 23:13, 4 December 2020
Line 1:		Line 1:
	'''226edo''' is the [[EDO\|equal division of the octave]] into 226 parts of 5.3097 [[cent]]s each. It [[tempering_out\|tempers out]] 2029/2024 in the [[7-limit]]; 243/242 and [[Quartisma\|117440512/117406179]] in the [[11-limit]]; as well as 364/363 and 729/728, in the [[13-limit]].		'''226edo''' is the [[EDO\|equal division of the octave]] into 226 parts of 5.3097 [[cent]]s each. It [[tempering_out\|tempers out]] 2029/2024 in the [[7-limit]]; 243/242 and [[Quartisma\|117440512/117406179]] in the [[11-limit]]; as well as 364/363 and 729/728, in the [[13-limit]].

	[[Category:~~Edo~~]]		[[Category:Equal divisions of the octave]]