263edo - 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"

2026-03-13T13:31:44Z

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 13:31, 13 March 2026
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	\| [[Würschmidt]]		\| [[Würschmidt]]
	\|}		\|}
	<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 19:29, 20 February 2025

2025-02-20T19:29:35Z

← Older revision		Revision as of 19:29, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:50, 15 January 2025

2025-01-15T16:50:21Z

← Older revision		Revision as of 16:50, 15 January 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro~~\|263~~}}		{{EDO intro}}

	== Theory ==		== Theory ==
Line 20:		Line 20:

	== Regular temperament properties ==		== Regular temperament properties ==
	\|}		{\| 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
	\| {{monzo\| 417 -263 }}		\| {{monzo\| 417 -263 }}
	\| {{val\| 263 417 }}		\| {{val\| 263 417 }}
	\| ~~−0~~.2229		\| −0.2229
	\| 0.2229		\| 0.2229
	\| 4.89		\| 4.89
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	\| 393216/390625, {{monzo\| 50 -33 1 }}		\| 393216/390625, {{monzo\| 50 -33 1 }}
	\| {{val\| 263 417 611 }}		\| {{val\| 263 417 611 }}
	\| ~~−0~~.3666		\| −0.3666
	\| 0.2728		\| 0.2728
	\| 5.98		\| 5.98
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	\| [[Würschmidt]]		\| [[Würschmidt]]
	\|}		\|}
	<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

ArrowHead294: Partial undo

2024-11-16T12:56:07Z

Partial undo

← Older revision		Revision as of 12:56, 16 November 2024
Line 20:		Line 20:

	== Regular temperament properties ==		== Regular temperament properties ==
	~~{{comma basis end}~~}		\|}
	\|-		\|-
	\| 2.3		\| 2.3
Line 35:		Line 35:
	\| 0.2728		\| 0.2728
	\| 5.98		\| 5.98
	~~{{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
Line 51:		Line 58:
	\| 5/4		\| 5/4
	\| [[Würschmidt]]		\| [[Würschmidt]]
	~~{{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

ArrowHead294 at 03:12, 16 November 2024

2024-11-16T03:12:24Z

← Older revision		Revision as of 03:12, 16 November 2024
Line 20:		Line 20:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis end}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|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
	\| {{monzo\| 417 -263 }}		\| {{monzo\| 417 -263 }}
	\| {{val\| 263 417 }}		\| {{val\| 263 417 }}
	\| -0.2229		\| −0.2229
	\| 0.2229		\| 0.2229
	\| 4.89		\| 4.89
Line 40:		Line 32:
	\| 393216/390625, {{monzo\| 50 -33 1 }}		\| 393216/390625, {{monzo\| 50 -33 1 }}
	\| {{val\| 263 417 611 }}		\| {{val\| 263 417 611 }}
	\| -0.3666		\| −0.3666
	\| 0.2728		\| 0.2728
	\| 5.98		\| 5.98
	\|}		{{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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	\| 5/4		\| 5/4
	\| [[Würschmidt]]		\| [[Würschmidt]]
	\|}		{{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}}

Lériendil at 21:56, 20 October 2024

2024-10-20T21:56:41Z

← Older revision		Revision as of 21:56, 20 October 2024
Line 15:		Line 15:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	263edo is the 56th [[prime edo]].		263edo is the 56th [[prime edo]].

			Notable supersets include [[789edo]], which triples it to achieve extreme accuracy in the [[2.5.7 subgroup]], and [[1578edo]], which sextuples it to be extremely strong in the [[11-limit]] add-17 and in higher limits.

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

FloraC: Cleanup

2024-03-11T04:58:32Z

Cleanup

← Older revision		Revision as of 04:58, 11 March 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|263}}		{{EDO intro\|263}}
	~~==Theory==~~
	263et tempers out 393216/390625 (Würschmidt comma) and \|50 -33 1> in the 5-limit. Using the patent val, it tempers out 4375/4374, 50421/50000, and 458752/455625 in the 7-limit; 441/440, 3388/3375, 16384/16335, and 26411/26244 in the 11-limit; 364/363, 2080/2079, 2197/2187, and 3584/3575 in the 13-limit; 595/594, 833/832, 936/935, and 1156/1155 in the 17-limit.

	Using the ~~263d~~ val, it tempers out ~~5120~~/~~5103~~, ~~16875~~/~~16807~~, and ~~1959552~~/~~1953125~~ in the 7-limit; ~~540~~/~~539~~, ~~1375~~/~~1372~~, 16384/16335, and ~~43923~~/~~43750~~ in the 11-limit; ~~351/350, 1001~~/~~1000~~, ~~1573~~/~~1568~~, 2197/2187, and ~~4225~~/~~4224~~ in the 13-limit.		== Theory ==
			263et [[tempering out\|tempers out]] 393216/390625 ([[würschmidt comma]]) and {{monzo\| 50 -33 1 }} in the 5-limit. Using the [[patent val]], it tempers out [[4375/4374]], [[50421/50000]], and 458752/455625 in the 7-limit; [[441/440]], [[3388/3375]], [[16384/16335]], and 26411/26244 in the 11-limit; [[364/363]], [[2080/2079]], [[2197/2187]], and 3584/3575 in the 13-limit; [[595/594]], [[833/832]], [[936/935]], and [[1156/1155]] in the 17-limit.

	Using the 263df val, it tempers out 352/351, 640/637, 729/728, and 3584/3575 in the 13-limit.		Using the 263d val, it tempers out [[5120/5103]], [[16875/16807]], and 1959552/1953125 in the 7-limit; [[540/539]], 1375/1372, 16384/16335, and 43923/43750 in the 11-limit; [[351/350]], [[1001/1000]], [[1573/1568]], 2197/2187, and [[4225/4224]] in the 13-limit.
	===Prime harmonics===
			Using the 263df val, it tempers out [[352/351]], [[640/637]], [[729/728]], and 3584/3575 in the 13-limit.

			Finally, it is accurate for the 17th harmonic, as the denominator of a convergent to log<sub>2</sub>17, after [[80edo\|80]] and before [[343edo\|343]].

			=== Prime harmonics ===
	{{Harmonics in equal\|263}}		{{Harmonics in equal\|263}}
	===Subsets and supersets===
	263edo is the 56th [[prime ~~EDO]]. It is accurate for the 17th harmonic, as the denominator of a convergent to log<sub>2</sub>17, after [[80edo\|80]] and before [[343edo\|343~~]].		=== Subsets and supersets ===
	==Regular temperament properties==		263edo is the 56th [[prime edo]].

			== 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
	\|{{monzo\|417 -263}}		\| {{monzo\| 417 -263 }}
	\|{{val\|263 417}}		\| {{val\| 263 417 }}
	\| -0.2229		\| -0.2229
	\| 0.2229		\| 0.2229
	\| 4.89		\| 4.89
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|393216/390625, {{monzo\|50 -33 1}}		\| 393216/390625, {{monzo\| 50 -33 1 }}
	\|{{val\|263 417 611}}		\| {{val\| 263 417 611 }}
	\| -0.3666		\| -0.3666
	\| 0.2728		\| 0.2728
	\| 5.98		\| 5.98
	\|}		\|}

	=== 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
	\|40\263		\| 40\263
	\|182.51		\| 182.51
	\|10/9		\| 10/9
	\|[[Minortone]]		\| [[Minortone]]
	\|-		\|-
	\|1		\| 1
	\|85\263		\| 85\263
	\|387.83		\| 387.83
	\|5/4		\| 5/4
	\|[[Würschmidt]]		\| [[Würschmidt]]
	\|}		\|}
	[[~~Category:Equal divisions of the~~ octave~~\|###~~]] <!-~~- 3-digit number -->~~		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct
	[[~~Category:Prime EDO~~]]

Francium: +regular temperament properties

2023-11-03T20:43:23Z

+regular temperament properties

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''263EDO''' is the [[EDO|equal division of the octave]] into 263 parts of 4.5627 [[cent]]s each. 263EDO is the 56th [[prime EDO]]. 263EDO is accurate for the 17th harmonic, as the denominator of a convergent to log<sub>2</sub>17, after [[80edo|80]] and before [[343edo|343]].
+{{EDO intro|263}}
+==Theory==
-It tempers out 393216/390625 (Würschmidt comma) and |50 -33 1&gt; in the 5-limit. Using the patent val, it tempers out 4375/4374, 50421/50000, and 458752/455625 in the 7-limit; 441/440, 3388/3375, 16384/16335, and 26411/26244 in the 11-limit; 364/363, 2080/2079, 2197/2187, and 3584/3575 in the 13-limit; 595/594, 833/832, 936/935, and 1156/1155 in the 17-limit.
+et tempers out 393216/390625 (Würschmidt comma) and |50 -33 1&gt; in the 5-limit. Using the patent val, it tempers out 4375/4374, 50421/50000, and 458752/455625 in the 7-limit; 441/440, 3388/3375, 16384/16335, and 26411/26244 in the 11-limit; 364/363, 2080/2079, 2197/2187, and 3584/3575 in the 13-limit; 595/594, 833/832, 936/935, and 1156/1155 in the 17-limit.
 Using the 263d val, it tempers out 5120/5103, 16875/16807, and 1959552/1953125 in the 7-limit; 540/539, 1375/1372, 16384/16335, and 43923/43750 in the 11-limit; 351/350, 1001/1000, 1573/1568, 2197/2187, and 4225/4224 in the 13-limit.
 Using the 263df val, it tempers out 352/351, 640/637, 729/728, and 3584/3575 in the 13-limit.
+===Prime harmonics===
 {{Harmonics in equal|263}}
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Prime EDO]]

BudjarnLambeth: Added "harmonics in equal" table and rearranged the order of sentences.

2023-06-24T03:28:02Z

Added "harmonics in equal" table and rearranged the order of sentences.

← Older revision		Revision as of 03:28, 24 June 2023
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	{{Infobox ET}}		{{Infobox ET}}
	'''263EDO''' is the [[EDO\|equal division of the octave]] into 263 parts of 4.5627 [[cent]]s each. ~~It tempers out 393216/390625 (Würschmidt comma) and \|50 -33 1> in~~ the 5-limit. Using the patent val, it tempers out 4375/4374, 50421/50000, and 458752/455625 in the 7-limit; 441/440, 3388/3375, 16384/16335, and 26411/26244 in the 11-limit; 364/363, 2080/2079, 2197/2187, and 3584/3575 in the 13-limit; 595/594, 833/832, 936/935, and 1156/1155 in the 17-limit. 263EDO is ~~acculate~~ for the 17th harmonic, as the denominator of a convergent to log<sub>2</sub>17, after [[80edo\|80]] and before [[343edo\|343]]. Using the 263d val, it tempers out 5120/5103, 16875/16807, and 1959552/1953125 in the 7-limit; 540/539, 1375/1372, 16384/16335, and 43923/43750 in the 11-limit; 351/350, 1001/1000, 1573/1568, 2197/2187, and 4225/4224 in the 13-limit. Using the 263df val, it tempers out 352/351, 640/637, 729/728, and 3584/3575 in the 13-limit.		'''263EDO''' is the [[EDO\|equal division of the octave]] into 263 parts of 4.5627 [[cent]]s each. 263EDO is the 56th [[prime EDO]]. 263EDO is accurate for the 17th harmonic, as the denominator of a convergent to log<sub>2</sub>17, after [[80edo\|80]] and before [[343edo\|343]].

	~~263EDO is~~ the ~~56th [[prime EDO]]~~.		It tempers out 393216/390625 (Würschmidt comma) and \|50 -33 1> in the 5-limit. Using the patent val, it tempers out 4375/4374, 50421/50000, and 458752/455625 in the 7-limit; 441/440, 3388/3375, 16384/16335, and 26411/26244 in the 11-limit; 364/363, 2080/2079, 2197/2187, and 3584/3575 in the 13-limit; 595/594, 833/832, 936/935, and 1156/1155 in the 17-limit.

			Using the 263d val, it tempers out 5120/5103, 16875/16807, and 1959552/1953125 in the 7-limit; 540/539, 1375/1372, 16384/16335, and 43923/43750 in the 11-limit; 351/350, 1001/1000, 1573/1568, 2197/2187, and 4225/4224 in the 13-limit.

			Using the 263df val, it tempers out 352/351, 640/637, 729/728, and 3584/3575 in the 13-limit.

			{{Harmonics in equal\|263}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
	[[Category:Prime EDO]]		[[Category:Prime EDO]]

Plumtree: Infobox ET added

2022-10-04T21:29:17Z

Infobox ET added

← Older revision		Revision as of 21:29, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''263EDO''' is the [[EDO\|equal division of the octave]] into 263 parts of 4.5627 [[cent]]s each. It tempers out 393216/390625 (Würschmidt comma) and \|50 -33 1> in the 5-limit. Using the patent val, it tempers out 4375/4374, 50421/50000, and 458752/455625 in the 7-limit; 441/440, 3388/3375, 16384/16335, and 26411/26244 in the 11-limit; 364/363, 2080/2079, 2197/2187, and 3584/3575 in the 13-limit; 595/594, 833/832, 936/935, and 1156/1155 in the 17-limit. 263EDO is acculate for the 17th harmonic, as the denominator of a convergent to log<sub>2</sub>17, after [[80edo\|80]] and before [[343edo\|343]]. Using the 263d val, it tempers out 5120/5103, 16875/16807, and 1959552/1953125 in the 7-limit; 540/539, 1375/1372, 16384/16335, and 43923/43750 in the 11-limit; 351/350, 1001/1000, 1573/1568, 2197/2187, and 4225/4224 in the 13-limit. Using the 263df val, it tempers out 352/351, 640/637, 729/728, and 3584/3575 in the 13-limit.		'''263EDO''' is the [[EDO\|equal division of the octave]] into 263 parts of 4.5627 [[cent]]s each. It tempers out 393216/390625 (Würschmidt comma) and \|50 -33 1> in the 5-limit. Using the patent val, it tempers out 4375/4374, 50421/50000, and 458752/455625 in the 7-limit; 441/440, 3388/3375, 16384/16335, and 26411/26244 in the 11-limit; 364/363, 2080/2079, 2197/2187, and 3584/3575 in the 13-limit; 595/594, 833/832, 936/935, and 1156/1155 in the 17-limit. 263EDO is acculate for the 17th harmonic, as the denominator of a convergent to log<sub>2</sub>17, after [[80edo\|80]] and before [[343edo\|343]]. Using the 263d val, it tempers out 5120/5103, 16875/16807, and 1959552/1953125 in the 7-limit; 540/539, 1375/1372, 16384/16335, and 43923/43750 in the 11-limit; 351/350, 1001/1000, 1573/1568, 2197/2187, and 4225/4224 in the 13-limit. Using the 263df val, it tempers out 352/351, 640/637, 729/728, and 3584/3575 in the 13-limit.