638edo - 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"

2026-03-13T13:32:26Z

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
Line 87:		Line 87:
	\| [[Quatracot]]		\| [[Quatracot]]
	\|}		\|}
	<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:Quatracot]]		[[Category:Quatracot]]

ArrowHead294 at 15:42, 20 February 2025

2025-02-20T15:42:29Z

← Older revision		Revision as of 15:42, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:51, 15 January 2025

2025-01-15T18:51:28Z

← Older revision		Revision as of 18:51, 15 January 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro~~\|638~~}}		{{EDO intro}}

	== Theory ==		== Theory ==
	The equal temperament [[tempering out\|tempers out]] the minortone comma, {{monzo\| -16 35 -17 }}, in the 5-limit, [[4375/4374]] in the 7-limit, [[3025/3024]], [[9801/9800]], and 43923/43904, in the 11-limit; and [[625/624]], [[729/728]], [[1575/1573]], [[2200/2197]] and [[4225/4224]] in the 13-limit. It supplies the [[optimal patent val]] for [[quatracot]], the 224 & 414 temperament.		The equal temperament [[tempering out\|tempers out]] the minortone comma, {{monzo\| -16 35 -17 }}, in the 5-limit, [[4375/4374]] in the 7-limit, [[3025/3024]], [[9801/9800]], and 43923/43904, in the 11-limit; and [[625/624]], [[729/728]], [[1575/1573]], [[2200/2197]] and [[4225/4224]] in the 13-limit. It supplies the [[optimal patent val]] for [[quatracot]], the {{nowrap\|224 & 414}} temperament.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 638 factors as ~~2 × 11 × 29~~, 638edo has subset edos {{EDOs\| 2, 11, 22, 29, 58, and 319 }}.		Since 638 factors as {{factorisation\|638}}, 638edo has subset edos {{EDOs\| 2, 11, 22, 29, 58, and 319 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 87:		Line 87:
	\| [[Quatracot]]		\| [[Quatracot]]
	\|}		\|}
	<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:Quatracot]]		[[Category:Quatracot]]

ArrowHead294: Partial undo

2024-11-16T13:06:05Z

Partial undo

← Older revision		Revision as of 13:06, 16 November 2024
Line 12:		Line 12:

	== 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
Line 48:		Line 57:
	\| 0.1330		\| 0.1330
	\| 7.07		\| 7.07
	~~{{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 70:		Line 86:
	\| 448/405		\| 448/405
	\| [[Quatracot]]		\| [[Quatracot]]
	~~{{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:Quatracot]]		[[Category:Quatracot]]

ArrowHead294 at 02:37, 16 November 2024

2024-11-16T02:37:12Z

← Older revision		Revision as of 02:37, 16 November 2024
Line 12:		Line 12:

	== 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<br>8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
Line 56:		Line 48:
	\| 0.1330		\| 0.1330
	\| 7.07		\| 7.07
	\|}		{{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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	\| 448/405		\| 448/405
	\| [[Quatracot]]		\| [[Quatracot]]
	\|}		{{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:Quatracot]]		[[Category:Quatracot]]

FloraC: Cleanup and correct the comma bases

2023-10-25T10:22:45Z

Cleanup and correct the comma bases

← Older revision		Revision as of 10:22, 25 October 2023
Line 11:		Line 11:
	Since 638 factors as 2 × 11 × 29, 638edo has subset edos {{EDOs\| 2, 11, 22, 29, 58, and 319 }}.		Since 638 factors as 2 × 11 × 29, 638edo has subset edos {{EDOs\| 2, 11, 22, 29, 58, and 319 }}.

	==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
	\|{{monzo\|-1011 638}}		\| {{monzo\| -1011 638 }}
	\|{{~~val~~\|638 1011}}		\| {{mapping\| 638 1011 }}
	\| 0.1223		\| +0.1223
	\| 0.1223		\| 0.1223
	\| 6.50		\| 6.50
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|-51 19 9}}, {{monzo\|-16 35 -17}}		\| {{monzo\| -51 19 9 }}, {{monzo\| -16 35 -17 }}
	\|{{~~val~~\|638 1011 1481}}		\| {{mapping\| 638 1011 1481 }}
	\| 0.1869		\| +0.1869
	\| 0.1353		\| 0.1353
	\| 7.19		\| 7.19
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|4375/4374, 2100875/2097152, ~~5250987/5242880~~		\| 4375/4374, 2100875/2097152, {{monzo\| -11 5 11 -8 }}
	\|{{~~val~~\|638 1011 1481 1791}}		\| {{mapping\| 638 1011 1481 1791 }}
	\| 0.1556		\| +0.1556
	\| 0.1291		\| 0.1291
	\| 6.86		\| 6.86
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|3025/3024, 4375/4374, ~~9801~~/~~9800~~, ~~43923~~/~~43904~~		\| 3025/3024, 4375/4374, 825000/823543, 1265625/1261568
	\|{{~~val~~\|638 1011 1481 1791 2207}}		\| {{mapping\| 638 1011 1481 1791 2207 }}
	\| 0.1373		\| +0.1373
	\| 0.1212		\| 0.1212
	\| 6.44		\| 6.44
	\|-		\|-
	\|2.3.5.7.11.13		\| 2.3.5.7.11.13
	\|625/624, 729/728, 1575/1573, ~~4225~~/~~4224~~, ~~78975~~/~~78848~~		\| 625/624, 729/728, 1575/1573, 2200/2197, 823680/823543
	\|{{~~val~~\|638 1011 1481 1791 2207 2361}}		\| {{mapping\| 638 1011 1481 1791 2207 2361 }}
	\| 0.1043		\| +0.1043
	\| 0.1330		\| 0.1330
	\| 7.07		\| 7.07
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	\|+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
	\|97\638		\| 97\638
	\|182.45		\| 182.45
	\|10/9		\| 10/9
	\|[[~~Minortone]] / [[mitonic~~]]		\| [[Mitonic]]
	\|-		\|-
	\|1		\| 1
	\|313\638		\| 313\638
	\|588.71		\| 588.71
	\|7/5		\| 7/5
	\|[[Untriton]]		\| [[Untriton]]
	\|-		\|-
	\|2		\| 2
	\|94\638		\| 94\638
	\|176.80		\| 176.80
	\|448/405		\| 448/405
	\|[[Quatracot]]		\| [[Quatracot]]
	\|}		\|}
			<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:Quatracot]]		[[Category:Quatracot]]

Francium: +regular temperament properties

2023-10-25T09:16:42Z

+regular temperament properties

@@ Line 2: / Line 2: @@
 {{EDO intro|638}}
 The equal temperament [[tempering out|tempers out]] the minortone comma, {{monzo| -16 35 -17 }}, in the 5-limit, [[4375/4374]] in the 7-limit, [[3025/3024]], [[9801/9800]], and 43923/43904, in the 11-limit; and [[625/624]], [[729/728]], [[1575/1573]], [[2200/2197]] and [[4225/4224]] in the 13-limit. It supplies the [[optimal patent val]] for [[quatracot]], the 224 & 414 temperament.
@@ Line 9: / Line 10: @@
 === Subsets and supersets ===
 Since 638 factors as 2 × 11 × 29, 638edo has subset edos {{EDOs| 2, 11, 22, 29, 58, and 319 }}.
 [[Category:Quatracot]]

FloraC: -typo

2023-10-25T07:34:33Z

-typo

← Older revision		Revision as of 07:34, 25 October 2023
Line 10:		Line 10:
	Since 638 factors as 2 × 11 × 29, 638edo has subset edos {{EDOs\| 2, 11, 22, 29, 58, and 319 }}.		Since 638 factors as 2 × 11 × 29, 638edo has subset edos {{EDOs\| 2, 11, 22, 29, 58, and 319 }}.

	[[~~Categories~~:Quatracot]]		[[Category:Quatracot]]

FloraC: +category

2023-10-25T07:34:16Z

+category

← Older revision		Revision as of 07:34, 25 October 2023
Line 9:		Line 9:
	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 638 factors as 2 × 11 × 29, 638edo has subset edos {{EDOs\| 2, 11, 22, 29, 58, and 319 }}.		Since 638 factors as 2 × 11 × 29, 638edo has subset edos {{EDOs\| 2, 11, 22, 29, 58, and 319 }}.

			[[Categories:Quatracot]]

FloraC: Adopt template: EDO intro; +prime error table; +subsets and supersets

2023-10-25T07:32:17Z

Adopt template: EDO intro; +prime error table; +subsets and supersets

← Older revision		Revision as of 07:32, 25 October 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	The '''638 equal temperament''' divides the octave into 638 equal parts of 1.881 cents each. It tempers out the minortone comma, \| -16 35 -17 >, in the 5-limit, 4375/4374 in the 7-limit, 43923/43904, 3025/3024, 9801/9800 in the 11-limit, and 625/624, 729/728, 1575/1573, 2200/2197 and 4225/4224 in the 13-limit. It supplies the optimal patent val for [[Ragismic_microtemperaments#Quatracot\|~~quatracot temperament]].~~ 638 ~~factors as 21129.~~		{{EDO intro\|638}}

	[[~~Category:Equal divisions of the octave~~\|~~###~~]] <!-- 3-~~digit number~~ -->		The equal temperament [[tempering out\|tempers out]] the minortone comma, {{monzo\| -16 35 -17 }}, in the 5-limit, [[4375/4374]] in the 7-limit, [[3025/3024]], [[9801/9800]], and 43923/43904, in the 11-limit; and [[625/624]], [[729/728]], [[1575/1573]], [[2200/2197]] and [[4225/4224]] in the 13-limit. It supplies the [[optimal patent val]] for [[quatracot]], the 224 & 414 temperament.

			=== Odd harmonics ===
			{{Harmonics in equal\|638}}

			=== Subsets and supersets ===
			Since 638 factors as 2 × 11 × 29, 638edo has subset edos {{EDOs\| 2, 11, 22, 29, 58, and 319 }}.