253edo - 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"

2026-03-13T13:32:45Z

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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	\| [[Cotritone]]		\| [[Cotritone]]
	\|}		\|}
	<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

	== Scales ==		== Scales ==

FloraC: + category

2025-07-12T12:47:05Z

+ category

← Older revision		Revision as of 12:47, 12 July 2025
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	* 20 20 20 11 20 20 20 20 11 20 20 20 20 11: [[11L 3s\|Ketradektriatoh scale]]		* 20 20 20 11 20 20 20 20 11 20 20 20 20 11: [[11L 3s\|Ketradektriatoh scale]]

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

Lériendil: Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"

2025-04-17T02:28:53Z

Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"

← Older revision		Revision as of 02:28, 17 April 2025
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	\| 498.02		\| 498.02
	\| 4/3		\| 4/3
	\| [[Helmholtz temperament\|Helmholtz]]		\| [[Helmholtz (temperament)\|Helmholtz]]
	\|-		\|-
	\| 1		\| 1
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	== Scales ==		== Scales ==
	* 63 32 63 63 32: One of many [[3L 2s\|pentic]] scales available		* 63 32 63 63 32: One of many [[3L 2s\|pentic]] scales available
	* 43 43 19 43 43 43 19: [[Helmholtz temperament\|Helmholtz]][7]		* 43 43 19 43 43 43 19: [[Helmholtz (temperament)\|Helmholtz]][7]
	* 41 41 24 41 41 41 24: [[Meantone]][7]		* 41 41 24 41 41 41 24: [[Meantone]][7]
	* 35 35 35 35 35 35 35 8: [[Porcupine]][8]		* 35 35 35 35 35 35 35 8: [[Porcupine]][8]

Nick Vuci: Edited Helmholtz redirect

2025-04-16T15:39:39Z

Edited Helmholtz redirect

← Older revision		Revision as of 15:39, 16 April 2025
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	\| 498.02		\| 498.02
	\| 4/3		\| 4/3
	\| [[Helmholtz]]		\| [[Helmholtz temperament\|Helmholtz]]
	\|-		\|-
	\| 1		\| 1
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	== Scales ==		== Scales ==
	* 63 32 63 63 32: One of many [[3L 2s\|pentic]] scales available		* 63 32 63 63 32: One of many [[3L 2s\|pentic]] scales available
	* 43 43 19 43 43 43 19: [[Helmholtz]][7]		* 43 43 19 43 43 43 19: [[Helmholtz temperament\|Helmholtz]][7]
	* 41 41 24 41 41 41 24: [[Meantone]][7]		* 41 41 24 41 41 41 24: [[Meantone]][7]
	* 35 35 35 35 35 35 35 8: [[Porcupine]][8]		* 35 35 35 35 35 35 35 8: [[Porcupine]][8]

Tristanbay: /* Subsets and supersets */Added brief mention of 1012edo as a superset

2025-02-28T20:23:34Z

Subsets and supersets: Added brief mention of 1012edo as a superset

← Older revision		Revision as of 20:23, 28 February 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 253 factors into 11 × 23, and has subset edos [[11edo]] and [[23edo]].		Since 253 factors into 11 × 23, and has subset edos [[11edo]] and [[23edo]]. [[1012edo]] divides 253edo's step size into 4 equal parts and provides a good approximation of the 13-limit.

	== Regular temperament properties ==		== Regular temperament properties ==

ArrowHead294 at 14:25, 20 February 2025

2025-02-20T14:25:50Z

← Older revision		Revision as of 14:25, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|253~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T15:44:37Z

Theory: cleanup

← Older revision		Revision as of 15:44, 17 January 2025
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	== Theory ==		== Theory ==
	253edo is [[consistent]] to the [[17-odd-limit]], approximating the fifth by 148\253 (0.021284 cents sharper than the just 3/2), and the [[prime harmonic]]s from 5 to 17 are all slightly flat. It [[tempers out]] [[32805/32768]] in the 5-limit; [[2401/2400]] in the 7-limit; [[385/384]], 1375/1372 and [[4000/3993]] in the 11-limit; [[325/324]], [[1575/1573]] and [[2200/2197]] in the 13-limit; [[375/374]] and [[595/594]] in the 17-limit. It provides the [[optimal patent val]] for the [[tertiaschis]] temperament, and a good tuning for the [[sesquiquartififths]] temperament in the higher limits.		253edo is [[consistent]] to the [[17-odd-limit]], approximating the fifth by 148\253 (0.021284 cents sharper than the just 3/2), and the [[prime harmonic]]s from 5 to 17 are all slightly flat. As an equal temperament, it [[tempering out\|tempers out]] [[32805/32768]] in the [[5-limit]]; [[2401/2400]] in the [[7-limit]]; [[385/384]], [[1375/1372]] and [[4000/3993]] in the [[11-limit]]; [[325/324]], [[1575/1573]] and [[2200/2197]] in the [[13-limit]]; [[375/374]] and [[595/594]] in the [[17-limit]]. It provides the [[optimal patent val]] for the [[tertiaschis]] temperament, and a good tuning for the [[sesquiquartififths]] temperament in the higher limits.

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 253 factors into ~~{{factorisation\|253}}~~, and has subset edos [[11edo]] and [[23edo]].		Since 253 factors into 11 × 23, and has subset edos [[11edo]] and [[23edo]].

	== Regular temperament properties ==		== Regular temperament properties ==

ArrowHead294 at 14:21, 16 January 2025

2025-01-16T14:21:22Z

← Older revision		Revision as of 14:21, 16 January 2025
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	== Theory ==		== Theory ==
	253edo is [[consistent]] to the [[17-odd-limit]], approximating the fifth by 148\253 (0.021284 cents sharper than the just 3/2), and the [[prime harmonic]]s from 5 to 17 are all slightly flat. ~~The equal temperament~~ [[~~tempering out\|~~tempers out]] [[32805/32768]] in the 5-limit; [[2401/2400]] in the 7-limit; [[385/384]], 1375/1372 and [[4000/3993]] in the 11-limit; [[325/324]], [[1575/1573]] and [[2200/2197]] in the 13-limit; [[375/374]] and [[595/594]] in the 17-limit. It provides the [[optimal patent val]] for the [[tertiaschis]] temperament, and a good tuning for the [[sesquiquartififths]] temperament in the higher limits.		253edo is [[consistent]] to the [[17-odd-limit]], approximating the fifth by 148\253 (0.021284 cents sharper than the just 3/2), and the [[prime harmonic]]s from 5 to 17 are all slightly flat. It [[tempers out]] [[32805/32768]] in the 5-limit; [[2401/2400]] in the 7-limit; [[385/384]], 1375/1372 and [[4000/3993]] in the 11-limit; [[325/324]], [[1575/1573]] and [[2200/2197]] in the 13-limit; [[375/374]] and [[595/594]] in the 17-limit. It provides the [[optimal patent val]] for the [[tertiaschis]] temperament, and a good tuning for the [[sesquiquartififths]] temperament in the higher limits.

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	253 ~~= 11 × 23~~, and has subset edos [[11edo]] and [[23edo]].		Since 253 factors into {{factorisation\|253}}, and has subset edos [[11edo]] and [[23edo]].

	== Regular temperament properties ==		== Regular temperament properties ==
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	\| {{monzo\| 401 -253 }}		\| {{monzo\| 401 -253 }}
	\| {{mapping\| 253 401 }}		\| {{mapping\| 253 401 }}
	\| ~~−0~~.007		\| −0.007
	\| 0.007		\| 0.007
	\| 0.14		\| 0.14
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	\| [[Cotritone]]		\| [[Cotritone]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==

ArrowHead294: Partial undo

2024-11-16T12:23:36Z

Partial undo

← Older revision		Revision as of 12:23, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
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	\| 0.295		\| 0.295
	\| 6.22		\| 6.22
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
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	\| 7/5		\| 7/5
	\| [[Cotritone]]		\| [[Cotritone]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Scales ==		== Scales ==

ArrowHead294 at 04:49, 16 November 2024

2024-11-16T04:49:25Z

← Older revision		Revision as of 04:49, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal 8ve <br>Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{monzo\| 401 -253 }}		\| {{monzo\| 401 -253 }}
	\| {{mapping\| 253 401 }}		\| {{mapping\| 253 401 }}
	\| -0.007		\| −0.007
	\| 0.007		\| 0.007
	\| 0.14		\| 0.14
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	\| 0.295		\| 0.295
	\| 6.22		\| 6.22
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
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	\| 7/5		\| 7/5
	\| [[Cotritone]]		\| [[Cotritone]]
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	== Scales ==		== Scales ==