207edo - 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"

2026-03-13T13:31:53Z

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
Line 94:		Line 94:
	\| [[Helmholtz (temperament)\|Helmholtz]]		\| [[Helmholtz (temperament)\|Helmholtz]]
	\|}		\|}
	<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

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

2025-04-17T02:29:25Z

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

← Older revision		Revision as of 02:29, 17 April 2025
Line 92:		Line 92:
	\| 498.55		\| 498.55
	\| 4/3		\| 4/3
	\| [[Helmholtz temperament\|Helmholtz]]		\| [[Helmholtz (temperament)\|Helmholtz]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

Nick Vuci: Edited Helmholtz redirect

2025-04-16T15:37:24Z

Edited Helmholtz redirect

← Older revision		Revision as of 15:37, 16 April 2025
Line 92:		Line 92:
	\| 498.55		\| 498.55
	\| 4/3		\| 4/3
	\| [[Helmholtz]]		\| [[Helmholtz temperament\|Helmholtz]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

ArrowHead294 at 14:15, 20 February 2025

2025-02-20T14:15:13Z

← Older revision		Revision as of 14:15, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|207~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:03, 15 January 2025

2025-01-15T18:03:39Z

← Older revision		Revision as of 18:03, 15 January 2025
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 207 factors into ~~3<sup>2</sup> × 23~~, 207edo has subset edos {{EDOs\| 3, 9, 23, and 69 }}.		Since 207 factors into {{factorisation\|207}}, 207edo has subset edos {{EDOs\| 3, 9, 23, and 69 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 33:		Line 33:
	\| 32805/32768, {{monzo\| 2 31 -22 }}		\| 32805/32768, {{monzo\| 2 31 -22 }}
	\| {{mapping\| 207 328 481 }}		\| {{mapping\| 207 328 481 }}
	\| ~~−0~~.1942		\| −0.1942
	\| 0.5166		\| 0.5166
	\| 8.91		\| 8.91
Line 40:		Line 40:
	\| 6144/6125, 19683/19600, 50421/50000		\| 6144/6125, 19683/19600, 50421/50000
	\| {{mapping\| 207 328 481 581 }}		\| {{mapping\| 207 328 481 581 }}
	\| ~~−0~~.0825		\| −0.0825
	\| 0.4874		\| 0.4874
	\| 8.41		\| 8.41
Line 47:		Line 47:
	\| 441/440, 3388/3375, 6144/6125, 19683/19600		\| 441/440, 3388/3375, 6144/6125, 19683/19600
	\| {{mapping\| 207 328 481 581 716 }}		\| {{mapping\| 207 328 481 581 716 }}
	\| ~~−0~~.0317		\| −0.0317
	\| 0.4477		\| 0.4477
	\| 7.72		\| 7.72
Line 54:		Line 54:
	\| 351/350, 441/440, 676/675, 847/845, 3584/3575		\| 351/350, 441/440, 676/675, 847/845, 3584/3575
	\| {{mapping\| 207 328 481 581 716 766 }}		\| {{mapping\| 207 328 481 581 716 766 }}
	\| ~~−0~~.0287		\| −0.0287
	\| 0.4087		\| 0.4087
	\| 7.05		\| 7.05
Line 61:		Line 61:
	\| 351/350, 441/440, 561/560, 676/675, 847/845, 1089/1088		\| 351/350, 441/440, 561/560, 676/675, 847/845, 1089/1088
	\| {{mapping\| 207 328 481 581 716 766 846 }}		\| {{mapping\| 207 328 481 581 716 766 846 }}
	\| ~~−0~~.0034		\| −0.0034
	\| 0.3834		\| 0.3834
	\| 6.61		\| 6.61
Line 94:		Line 94:
	\| [[Helmholtz]]		\| [[Helmholtz]]
	\|}		\|}
	<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

2024-11-16T12:56:17Z

Partial undo

← Older revision		Revision as of 12:56, 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 55:		Line 64:
	\| 0.3834		\| 0.3834
	\| 6.61		\| 6.61
	~~{{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 77:		Line 93:
	\| 4/3		\| 4/3
	\| [[Helmholtz]]		\| [[Helmholtz]]
	~~{{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 03:11, 16 November 2024

2024-11-16T03:11:40Z

← Older revision		Revision as of 03:11, 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 32:		Line 24:
	\| 32805/32768, {{monzo\| 2 31 -22 }}		\| 32805/32768, {{monzo\| 2 31 -22 }}
	\| {{mapping\| 207 328 481 }}		\| {{mapping\| 207 328 481 }}
	\| -0.1942		\| −0.1942
	\| 0.5166		\| 0.5166
	\| 8.91		\| 8.91
Line 39:		Line 31:
	\| 6144/6125, 19683/19600, 50421/50000		\| 6144/6125, 19683/19600, 50421/50000
	\| {{mapping\| 207 328 481 581 }}		\| {{mapping\| 207 328 481 581 }}
	\| -0.0825		\| −0.0825
	\| 0.4874		\| 0.4874
	\| 8.41		\| 8.41
Line 46:		Line 38:
	\| 441/440, 3388/3375, 6144/6125, 19683/19600		\| 441/440, 3388/3375, 6144/6125, 19683/19600
	\| {{mapping\| 207 328 481 581 716 }}		\| {{mapping\| 207 328 481 581 716 }}
	\| -0.0317		\| −0.0317
	\| 0.4477		\| 0.4477
	\| 7.72		\| 7.72
Line 53:		Line 45:
	\| 351/350, 441/440, 676/675, 847/845, 3584/3575		\| 351/350, 441/440, 676/675, 847/845, 3584/3575
	\| {{mapping\| 207 328 481 581 716 766 }}		\| {{mapping\| 207 328 481 581 716 766 }}
	\| -0.0287		\| −0.0287
	\| 0.4087		\| 0.4087
	\| 7.05		\| 7.05
Line 60:		Line 52:
	\| 351/350, 441/440, 561/560, 676/675, 847/845, 1089/1088		\| 351/350, 441/440, 561/560, 676/675, 847/845, 1089/1088
	\| {{mapping\| 207 328 481 581 716 766 846 }}		\| {{mapping\| 207 328 481 581 716 766 846 }}
	\| -0.0034		\| −0.0034
	\| 0.3834		\| 0.3834
	\| 6.61		\| 6.61
	\|}		{{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
Line 91:		Line 77:
	\| 4/3		\| 4/3
	\| [[Helmholtz]]		\| [[Helmholtz]]
	\|}		{{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}}

FloraC: /* Regular temperament properties */ review +1

2024-04-13T10:49:01Z

Regular temperament properties: review +1

← Older revision		Revision as of 10:49, 13 April 2024
Line 23:		Line 23:
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{monzo\|-328 207}}		\| {{monzo\| -328 207 }}
	\| {{~~val~~\|207 328}}		\| {{mapping\| 207 328 }}
	\| +0.1595		\| +0.1595
	\| 0.1596		\| 0.1596
Line 30:		Line 30:
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| 32805/32768, {{monzo\|2 31 -22}}		\| 32805/32768, {{monzo\| 2 31 -22 }}
	\| {{~~val~~\|207 328 481}}		\| {{mapping\| 207 328 481 }}
	\| -0.1942		\| -0.1942
	\| 0.5166		\| 0.5166
Line 37:		Line 37:
	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
	\| 6144/6125, 19683/19600, ~~32805~~/~~32768~~		\| 6144/6125, 19683/19600, 50421/50000
	\| {{~~val~~\|207 328 481 581}}		\| {{mapping\| 207 328 481 581 }}
	\| -0.0825		\| -0.0825
	\| 0.4874		\| 0.4874
Line 44:		Line 44:
	\|-		\|-
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 441/440, 3388/3375, ~~3773~~/~~3750~~, ~~6144~~/~~6125~~		\| 441/440, 3388/3375, 6144/6125, 19683/19600
	\| {{~~val~~\|207 328 481 581 716}}		\| {{mapping\| 207 328 481 581 716 }}
	\| -0.0317		\| -0.0317
	\| 0.4477		\| 0.4477
Line 52:		Line 52:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 351/350, 441/440, 676/675, 847/845, 3584/3575		\| 351/350, 441/440, 676/675, 847/845, 3584/3575
	\| {{~~val~~\|207 328 481 581 716 766}}		\| {{mapping\| 207 328 481 581 716 766 }}
	\| -0.0287		\| -0.0287
	\| 0.4087		\| 0.4087
Line 58:		Line 58:
	\|-		\|-
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 441/440, 561/560, 676/675, ~~936/935, 1632~~/~~1625~~, ~~8624~~/~~8619~~		\| 351/350, 441/440, 561/560, 676/675, 847/845, 1089/1088
	\| {{~~val~~\|207 328 481 581 716 766 846}}		\| {{mapping\| 207 328 481 581 716 766 846 }}
	\| -0.0034		\| -0.0034
	\| 0.3834		\| 0.3834

FloraC: Review

2024-04-13T10:34:30Z

Review

← Older revision		Revision as of 10:34, 13 April 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|207}}		{{EDO intro\|207}}
	==Theory==
	It tempers out 32805/32768 in the 5-limit, 6144/6125 and 19683/19600 in the 7-limit, 441/440 and 43923/43904 in the 11-limit, and 351/350, ~~847/845,~~ 676/675, 729/728, 1716/1715 in the 13-limit. It serves as ~~the patent val~~ in the 11- and 13-~~limits~~ for [[~~Cataharry_temperaments#Swetneus\|~~swetneus ~~temperament~~]]. It is significantly more accurate on the 2.3.7.11.13 subgroup, a favorite of many people, and one which contains both 729/728 and 10648/10647, which it tempers out.		== Theory ==
	===Prime harmonics===		207et [[tempering out\|tempers out]] 32805/32768 ([[schisma]]) in the 5-limit, [[6144/6125]] and [[19683/19600]] in the 7-limit, [[441/440]] and 43923/43904 in the 11-limit, and [[351/350]], [[676/675]], [[729/728]], [[847/845]], [[1716/1715]] in the 13-limit. It serves as a tuning in the 11- and 13-limit for the [[swetneus]] temperament. It is significantly more accurate on the 2.3.7.11.13 [[subgroup]], a favorite of many people, and one which contains both 729/728 and [[10648/10647]], which it tempers out.

			=== Prime harmonics ===
	{{Harmonics in equal\|207}}		{{Harmonics in equal\|207}}
	===Subsets and supersets===
	207 factors into 3<sup>2</sup> × 23, ~~with~~ subset edos {{EDOs\|3, 9, 23, and 69}}.		=== Subsets and supersets ===
	==Regular temperament properties==		Since 207 factors into 3<sup>2</sup> × 23, 207edo has subset edos {{EDOs\| 3, 9, 23, and 69 }}.

			== 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\|-328 207}}		\| {{monzo\|-328 207}}
	\|{{val\|207 328}}		\| {{val\|207 328}}
	\| +0.1595		\| +0.1595
	\| 0.1596		\| 0.1596
	\| 2.75		\| 2.75
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|32805/32768, {{monzo\|2 31 -22}}		\| 32805/32768, {{monzo\|2 31 -22}}
	\|{{val\|207 328 481}}		\| {{val\|207 328 481}}
	\| -0.1942		\| -0.1942
	\| 0.5166		\| 0.5166
	\| 8.91		\| 8.91
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|6144/6125, 19683/19600, 32805/32768		\| 6144/6125, 19683/19600, 32805/32768
	\|{{val\|207 328 481 581}}		\| {{val\|207 328 481 581}}
	\| -0.0825		\| -0.0825
	\| 0.4874		\| 0.4874
	\|8.41		\| 8.41
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|441/440, 3388/3375, 3773/3750, 6144/6125		\| 441/440, 3388/3375, 3773/3750, 6144/6125
	\|{{val\|207 328 481 581 716}}		\| {{val\|207 328 481 581 716}}
	\| -0.0317		\| -0.0317
	\| 0.4477		\| 0.4477
	\| 7.72		\| 7.72
	\|-		\|-
	\|2.3.5.7.11.13		\| 2.3.5.7.11.13
	\|351/350, 441/440, 676/675, 847/845, 3584/3575		\| 351/350, 441/440, 676/675, 847/845, 3584/3575
	\|{{val\|207 328 481 581 716 766}}		\| {{val\|207 328 481 581 716 766}}
	\| -0.0287		\| -0.0287
	\| 0.4087		\| 0.4087
	\| 7.05		\| 7.05
	\|-		\|-
	\|2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\|441/440, 561/560, 676/675, 936/935, 1632/1625, 8624/8619		\| 441/440, 561/560, 676/675, 936/935, 1632/1625, 8624/8619
	\|{{val\|207 328 481 581 716 766 846}}		\| {{val\|207 328 481 581 716 766 846}}
	\| -0.0034		\| -0.0034
	\| 0.3834		\| 0.3834
	\| 6.61		\| 6.61
	\|}		\|}

	=== 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
	\|25\207		\| 25\207
	\|144.93		\| 144.93
	\|49/45		\| 49/45
	\|[[Swetneus]]		\| [[Swetneus]]
	\|-		\|-
	\|1		\| 1
	\|43\207		\| 43\207
	\|249.28		\| 249.28
	\|15/13		\| 15/13
	\|[[Hemischis]]		\| [[Hemischis]]
	\|-		\|-
	\|1		\| 1
	\|86\207		\| 86\207
	\|498.55		\| 498.55
	\|4/3		\| 4/3
	\|[[Helmholtz]]		\| [[Helmholtz]]
	\|}		\|}
			<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:Equal divisions of~~ the octave\|~~###~~]] ~~<!-- 3-digit number -->~~

Francium at 19:08, 18 October 2023

2023-10-18T19:08:37Z

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-The 207 equal division of the octave, 207edo, divides the octave into 207 equal parts of size 5.797 cents each. It tempers out 32805/32768 in the 5-limit, 6144/6125 and 19683/19600 in the 7-limit, 441/440 and 43923/43904 in the 11-limit, and 351/350, 847/845, 676/675, 729/728, 1716/1715 in the 13-limit. It serves as the patent val in the 11- and 13-limits for [[Cataharry_temperaments#Swetneus|swetneus temperament]]. It is significantly more accurate on the 2.3.7.11.13 subgroup, a favorite of many people, and one which contains both 729/728 and 10648/10647, which it tempers out.
+{{EDO intro|207}}
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->