525edo - 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"

2026-03-13T13:32:00Z

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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	\| [[Vasca]]		\| [[Vasca]]
	\|}		\|}
	<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

	[[Category:Akjayland]]		[[Category:Akjayland]]

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

2025-04-17T02:28:58Z

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

← Older revision		Revision as of 02:28, 17 April 2025
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	\| 498.29		\| 498.29
	\| 4/3		\| 4/3
	\| [[Helmholtz temperament\|Helmholtz]]		\| [[Helmholtz (temperament)\|Helmholtz]]
	\|-		\|-
	\| 3		\| 3

Sintel: fix helmholtz link

2025-04-16T15:39:38Z

fix helmholtz link

← Older revision		Revision as of 15:39, 16 April 2025
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	\| 498.29		\| 498.29
	\| 4/3		\| 4/3
	\| [[Helmholtz]]		\| [[Helmholtz temperament\|Helmholtz]]
	\|-		\|-
	\| 3		\| 3

ArrowHead294 at 22:45, 20 February 2025

2025-02-20T22:45:05Z

← Older revision		Revision as of 22:45, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|525~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T16:24:10Z

Theory: cleanup

← Older revision		Revision as of 16:24, 17 January 2025
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	== Theory ==		== Theory ==
	525edo is [[distinctly consistent]] through the [[25-odd-limit]]. It [[tempers out]] the [[schisma]], 32805/32768, and {{monzo\| 8 77 -56 }} in the 5-limit; [[250047/250000]], [[703125/702464]] and {{monzo\| 21 3 1 -10 }} in the 7-limit; [[3025/3024]], 24057/24010, 102487/102400 and 180224/180075 in the 11-limit; [[729/728]], [[1716/1715]], [[2200/2197]], [[4096/4095]] and 14641/14625 in the 13-limit; [[1089/1088]], [[1275/1274]], and [[2025/2023]] in the 17-limit; [[2376/2375]] in the 19-limit; and [[1197/1196]], [[1496/1495]], [[2024/2023]], and [[2025/2024]] in the 23-limit.		525edo is [[distinctly consistent]] through the [[25-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] the [[schisma]], 32805/32768, and {{monzo\| 8 77 -56 }} in the 5-limit; [[250047/250000]], [[703125/702464]] and {{monzo\| 21 3 1 -10 }} in the 7-limit; [[3025/3024]], 24057/24010, 102487/102400 and 180224/180075 in the 11-limit; [[729/728]], [[1716/1715]], [[2200/2197]], [[4096/4095]] and 14641/14625 in the 13-limit; [[1089/1088]], [[1275/1274]], and [[2025/2023]] in the 17-limit; [[2376/2375]] in the 19-limit; and [[1197/1196]], [[1496/1495]], [[2024/2023]], and [[2025/2024]] in the 23-limit.

	It allows [[essentially tempered chord]]s of [[squbemic chords]] and [[petrmic chords]] in the 13-odd-limit.		It allows [[essentially tempered chord]]s of [[squbemic chords]] and [[petrmic chords]] in the 13-odd-limit.
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|525~~\|columns=11~~}}		{{Harmonics in equal\|525}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 525 factors into ~~{{factorization\|525}}~~, 525edo has subset edos {{EDOs\| 3, 5, 7, 15, 21, 25, 35, 75, 105, 175 }}.		Since 525 factors into 3 × 5<sup>2</sup> × 7, 525edo has subset edos {{EDOs\| 3, 5, 7, 15, 21, 25, 35, 75, 105, 175 }}.

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

ArrowHead294 at 14:16, 16 January 2025

2025-01-16T14:16:29Z

← Older revision		Revision as of 14:16, 16 January 2025
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	== Theory ==		== Theory ==
	525edo is [[~~consistency\|~~distinctly consistent]] through the [[25-odd-limit]]. ~~The equal temperament~~ [[~~tempering out\|~~tempers out]] the [[schisma]], 32805/32768, and {{monzo\| 8 77 -56 }} in the 5-limit; [[250047/250000]], [[703125/702464]] and {{monzo\| 21 3 1 -10 }} in the 7-limit; [[3025/3024]], 24057/24010, 102487/102400 and 180224/180075 in the 11-limit; [[729/728]], [[1716/1715]], [[2200/2197]], [[4096/4095]] and 14641/14625 in the 13-limit; [[1089/1088]], [[1275/1274]], and [[2025/2023]] in the 17-limit; [[2376/2375]] in the 19-limit; and [[1197/1196]], [[1496/1495]], [[2024/2023]], and [[2025/2024]] in the 23-limit.		525edo is [[distinctly consistent]] through the [[25-odd-limit]]. It [[tempers out]] the [[schisma]], 32805/32768, and {{monzo\| 8 77 -56 }} in the 5-limit; [[250047/250000]], [[703125/702464]] and {{monzo\| 21 3 1 -10 }} in the 7-limit; [[3025/3024]], 24057/24010, 102487/102400 and 180224/180075 in the 11-limit; [[729/728]], [[1716/1715]], [[2200/2197]], [[4096/4095]] and 14641/14625 in the 13-limit; [[1089/1088]], [[1275/1274]], and [[2025/2023]] in the 17-limit; [[2376/2375]] in the 19-limit; and [[1197/1196]], [[1496/1495]], [[2024/2023]], and [[2025/2024]] in the 23-limit.

	It allows [[essentially tempered chord]]s of [[squbemic chords]] and [[petrmic chords]] in the 13-odd-limit.		It allows [[essentially tempered chord]]s of [[squbemic chords]] and [[petrmic chords]] in the 13-odd-limit.
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	It supports the 35th-octave temperament [[35th-octave temperaments#Tritonopodismic\|tritonopodismic]].		It supports the 35th-octave temperament [[35th-octave temperaments#Tritonopodismic\|tritonopodismic]].

	525edo supports 21st-octave temperament called [[akjayland]], and the 23-limit extension of akjayland called [[21st-octave temperaments\|vasca]], described as 357 & 525. It is more suitable to view this temperament as vasca in 525edo as opposed to simply akjayland, since 525edo is consistent in the 23-odd-limit, while other edos which support akjayland are not. As a corollary of supporting vasca, 525edo also supports the relationship that sets 11\21 to [[23/16]].		525edo supports 21st-octave temperament called [[akjayland]], and the 23-limit extension of akjayland called [[21st-octave temperaments\|vasca]], described as {{nowrap\|357 & 525}}. It is more suitable to view this temperament as vasca in 525edo as opposed to simply akjayland, since 525edo is consistent in the 23-odd-limit, while other edos which support akjayland are not. As a corollary of supporting vasca, 525edo also supports the relationship that sets 11\21 to [[23/16]].

	=== Prime harmonics ===		=== Prime harmonics ===
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	\| 729/728, 1089/1088, 1275/1274, 1716/1715, 2025/2023, 2200/2197		\| 729/728, 1089/1088, 1275/1274, 1716/1715, 2025/2023, 2200/2197
	\| {{mapping\| 525 832 1219 1474 1816 1943 2146 }}		\| {{mapping\| 525 832 1219 1474 1816 1943 2146 }}
	\| ~~−0~~.0040		\| −0.0040
	\| 0.1091		\| 0.1091
	\| 4.77		\| 4.77
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	\| 729/728, 1089/1088, 1197/1196, 1275/1274, 1496/1495, 1716/1715, 2024/2023, 2025/2023		\| 729/728, 1089/1088, 1197/1196, 1275/1274, 1496/1495, 1716/1715, 2024/2023, 2025/2023
	\| {{mapping\| 525 832 1219 1474 1816 1943 2146 2230 2375 }}		\| {{mapping\| 525 832 1219 1474 1816 1943 2146 2230 2375 }}
	\| ~~−0~~.0007		\| −0.0007
	\| 0.1029		\| 0.1029
	\| 4.50		\| 4.50
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	\| [[Vasca]]		\| [[Vasca]]
	\|}		\|}
	<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

	[[Category:Akjayland]]		[[Category:Akjayland]]

ArrowHead294: Partial undo

2024-11-16T12:23:56Z

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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	\| 0.1029		\| 0.1029
	\| 4.50		\| 4.50
	~~{{comma basis end}~~}		\|}
	* 525et has lower absolute errors than any previous equal temperaments in the 19- and 23-limit. In the 19-limit it beats [[460edo\|460]] and is bettered by [[566edo\|566g]]. In the 23-limit it beats [[422edo\|422]] and is bettered by [[581edo\|581]].		* 525et has lower absolute errors than any previous equal temperaments in the 19- and 23-limit. In the 19-limit it beats [[460edo\|460]] and is bettered by [[566edo\|566g]]. In the 23-limit it beats [[422edo\|422]] and is bettered by [[581edo\|581]].

	=== 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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	\| 168/143<br />(?)		\| 168/143<br />(?)
	\| [[Vasca]]		\| [[Vasca]]
	~~{{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

	[[Category:Akjayland]]		[[Category:Akjayland]]

ArrowHead294 at 04:48, 16 November 2024

2024-11-16T04:48:39Z

← Older revision		Revision as of 04:48, 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
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	\| 729/728, 1089/1088, 1275/1274, 1716/1715, 2025/2023, 2200/2197		\| 729/728, 1089/1088, 1275/1274, 1716/1715, 2025/2023, 2200/2197
	\| {{mapping\| 525 832 1219 1474 1816 1943 2146 }}		\| {{mapping\| 525 832 1219 1474 1816 1943 2146 }}
	\| -0.0040		\| −0.0040
	\| 0.1091		\| 0.1091
	\| 4.77		\| 4.77
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	\| 729/728, 1089/1088, 1197/1196, 1275/1274, 1496/1495, 1716/1715, 2024/2023, 2025/2023		\| 729/728, 1089/1088, 1197/1196, 1275/1274, 1496/1495, 1716/1715, 2024/2023, 2025/2023
	\| {{mapping\| 525 832 1219 1474 1816 1943 2146 2230 2375 }}		\| {{mapping\| 525 832 1219 1474 1816 1943 2146 2230 2375 }}
	\| -0.0007		\| −0.0007
	\| 0.1029		\| 0.1029
	\| 4.50		\| 4.50
	\|}		{{comma basis end}}
	* 525et has lower absolute errors than any previous equal temperaments in the 19- and 23-limit. In the 19-limit it beats [[460edo\|460]] and is bettered by [[566edo\|566g]]. In the 23-limit it beats [[422edo\|422]] and is bettered by [[581edo\|581]].		* 525et has lower absolute errors than any previous equal temperaments in the 19- and 23-limit. In the 19-limit it beats [[460edo\|460]] and is bettered by [[566edo\|566g]]. In the 23-limit it beats [[422edo\|422]] and is bettered by [[581edo\|581]].

	=== 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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	\|-		\|-
	\| 3		\| 3
	\| 218\525<br>(43\525)		\| 218\525<br />(43\525)
	\| 498.29<br>(98.29)		\| 498.29<br />(98.29)
	\| 4/3<br>(18/17)		\| 4/3<br />(18/17)
	\| [[Term]]		\| [[Term]]
	\|-		\|-
	\| 3		\| 3
	\| 109\525<br>(66\525)		\| 109\525<br />(66\525)
	\| 249.14<br>(150.86)		\| 249.14<br />(150.86)
	\| 15/13<br>(12/11)		\| 15/13<br />(12/11)
	\| [[Hemiterm]] (525f)		\| [[Hemiterm]] (525f)
	\|-		\|-
	\| 7		\| 7
	\| 218\525<br>(7\525)		\| 218\525<br />(7\525)
	\| 498.29<br>(16.00)		\| 498.29<br />(16.00)
	\| 4/3<br>(99/98)		\| 4/3<br />(99/98)
	\| [[Septant]]		\| [[Septant]]
	\|-		\|-
	\| 21		\| 21
	\| 256\525<br>(6\525)		\| 256\525<br />(6\525)
	\| 585.14<br>(13.71)		\| 585.14<br />(13.71)
	\| 91875/65536<br>(126/125)		\| 91875/65536<br />(126/125)
	\| [[Akjayland]]		\| [[Akjayland]]
	\|-		\|-
	\| 21		\| 21
	\| 122\525<br>(22\525)		\| 122\525<br />(22\525)
	\| 278.85<br>(50.29)		\| 278.85<br />(50.29)
	\| 168/143<br>(?)		\| 168/143<br />(?)
	\| [[Vasca]]		\| [[Vasca]]
	\|}		{{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}}

	[[Category:Akjayland]]		[[Category:Akjayland]]

FloraC: +23-limit data

2024-10-12T13:48:22Z

+23-limit data

← Older revision		Revision as of 13:48, 12 October 2024
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	== Theory ==		== Theory ==
	525edo is [[consistency\|distinctly consistent]] through the [[25-odd-limit]]. The equal temperament [[tempering out\|tempers out]] the [[schisma]], 32805/32768, and {{monzo\| 8 77 -56 }} in the 5-limit; [[250047/250000]], [[703125/702464]] and {{monzo\| 21 3 1 -10 }} in the 7-limit; [[3025/3024]], 24057/24010, 102487/102400 and 180224/180075 in the 11-limit; [[729/728]], [[1716/1715]], [[2200/2197]], [[4096/4095]] and 14641/14625 in the 13-limit; [[1089/1088]], [[1275/1274]], and [[2025/2023]] in the 17-limit; 2376/2375 in the 19-limit.		525edo is [[consistency\|distinctly consistent]] through the [[25-odd-limit]]. The equal temperament [[tempering out\|tempers out]] the [[schisma]], 32805/32768, and {{monzo\| 8 77 -56 }} in the 5-limit; [[250047/250000]], [[703125/702464]] and {{monzo\| 21 3 1 -10 }} in the 7-limit; [[3025/3024]], 24057/24010, 102487/102400 and 180224/180075 in the 11-limit; [[729/728]], [[1716/1715]], [[2200/2197]], [[4096/4095]] and 14641/14625 in the 13-limit; [[1089/1088]], [[1275/1274]], and [[2025/2023]] in the 17-limit; [[2376/2375]] in the 19-limit; and [[1197/1196]], [[1496/1495]], [[2024/2023]], and [[2025/2024]] in the 23-limit.

	It allows [[essentially tempered chord]]s of [[squbemic chords]] and [[petrmic chords]] in the 13-odd-limit.		It allows [[essentially tempered chord]]s of [[squbemic chords]] and [[petrmic chords]] in the 13-odd-limit.
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	\| 0.1064		\| 0.1064
	\| 4.66		\| 4.66
			\|-
			\| 2.3.5.7.11.13.17.19.23
			\| 729/728, 1089/1088, 1197/1196, 1275/1274, 1496/1495, 1716/1715, 2024/2023, 2025/2023
			\| {{mapping\| 525 832 1219 1474 1816 1943 2146 2230 2375 }}
			\| -0.0007
			\| 0.1029
			\| 4.50
	\|}		\|}
	* 525et has lower absolute errors than any previous equal temperaments in the 19- and 23-limit. In the 19-limit it beats [[460edo\|460]] and is bettered by [[566edo\|566g]]. In the 23-limit it beats [[422edo\|422]] and is bettered by [[581edo\|581]].		* 525et has lower absolute errors than any previous equal temperaments in the 19- and 23-limit. In the 19-limit it beats [[460edo\|460]] and is bettered by [[566edo\|566g]]. In the 23-limit it beats [[422edo\|422]] and is bettered by [[581edo\|581]].

FloraC: Adopt template: Factorization

2023-11-02T13:47:39Z

Adopt template: Factorization

← Older revision		Revision as of 13:47, 2 November 2023
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 525 factors into ~~3 × 5<sup>2</sup> × 7~~, 525edo has subset edos {{EDOs\| 3, 5, 7, 15, 21, 25, 35, 75, 105, 175 }}.		Since 525 factors into {{factorization\|525}}, 525edo has subset edos {{EDOs\| 3, 5, 7, 15, 21, 25, 35, 75, 105, 175 }}.

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