214edo - 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"

2026-03-13T13:31:46Z

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 112:		Line 112:
	\| [[Kwazy]]		\| [[Kwazy]]
	\|}		\|}
	<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:Browser]]		[[Category:Browser]]

ArrowHead294 at 22:45, 20 February 2025

2025-02-20T22:45:37Z

← Older revision		Revision as of 22:45, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|214~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 19:45, 15 January 2025

2025-01-15T19:45:47Z

← Older revision		Revision as of 19:45, 15 January 2025
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 214 factors into ~~2 × 107~~, 214edo contains [[2edo]] and [[107edo]] as its subsets.		Since 214 factors into {{factorisation\|214}}, 214edo contains [[2edo]] and [[107edo]] as its subsets.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 40:		Line 40:
	\| 6144/6125, 16875/16807, 78732/78125		\| 6144/6125, 16875/16807, 78732/78125
	\| {{mapping\| 214 339 497 601 }}		\| {{mapping\| 214 339 497 601 }}
	\| ~~−0~~.0169		\| −0.0169
	\| 0.4137		\| 0.4137
	\| 7.38		\| 7.38
Line 61:		Line 61:
	\| 351/350, 540/539, 715/714, 847/845, 936/935, 4096/4095		\| 351/350, 540/539, 715/714, 847/845, 936/935, 4096/4095
	\| {{mapping\| 214 339 497 601 740 792 875 }}		\| {{mapping\| 214 339 497 601 740 792 875 }}
	\| ~~−0~~.0144		\| −0.0144
	\| 0.4012		\| 0.4012
	\| 7.15		\| 7.15
Line 112:		Line 112:
	\| [[Kwazy]]		\| [[Kwazy]]
	\|}		\|}
	<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:Browser]]		[[Category:Browser]]

ArrowHead294: Partial undo

2024-11-16T12:38:44Z

Partial undo

← Older revision		Revision as of 12:38, 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:
	\| 0.4012		\| 0.4012
	\| 7.15		\| 7.15
	~~{{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 95:		Line 111:
	\| 1125/1024		\| 1125/1024
	\| [[Kwazy]]		\| [[Kwazy]]
	~~{{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:Browser]]		[[Category:Browser]]

ArrowHead294 at 04:14, 16 November 2024

2024-11-16T04:14:04Z

← Older revision		Revision as of 04:14, 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 39:		Line 31:
	\| 6144/6125, 16875/16807, 78732/78125		\| 6144/6125, 16875/16807, 78732/78125
	\| {{mapping\| 214 339 497 601 }}		\| {{mapping\| 214 339 497 601 }}
	\| -0.0169		\| −0.0169
	\| 0.4137		\| 0.4137
	\| 7.38		\| 7.38
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	\| 351/350, 540/539, 715/714, 847/845, 936/935, 4096/4095		\| 351/350, 540/539, 715/714, 847/845, 936/935, 4096/4095
	\| {{mapping\| 214 339 497 601 740 792 875 }}		\| {{mapping\| 214 339 497 601 740 792 875 }}
	\| -0.0144		\| −0.0144
	\| 0.4012		\| 0.4012
	\| 7.15		\| 7.15
	\|}		{{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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	\| 1125/1024		\| 1125/1024
	\| [[Kwazy]]		\| [[Kwazy]]
	\|}		{{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:Browser]]		[[Category:Browser]]

FloraC: /* Rank-2 temperaments */ +browser

2024-04-03T08:53:20Z

Rank-2 temperaments: +browser

← Older revision		Revision as of 08:53, 3 April 2024
Line 73:		Line 73:
	! Associated<br>Ratio*		! Associated<br>Ratio*
	! Temperaments		! Temperaments
			\|-
			\| 1
			\| 27\214
			\| 151.40
			\| 12/11
			\| [[Browser]]
	\|-		\|-
	\| 1		\| 1
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	\|}		\|}
	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<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:Browser]]

FloraC: Review

2024-04-03T08:45:46Z

Review

← Older revision		Revision as of 08:45, 3 April 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	214edo is (uniquely) consistent through the [[7-odd-limit]]. The patent val for 214edo is {{val\| 214 339 497 601 740 792 }}, which [[tempering out\|tempers out]] the following commas: 78732/78125 ([[sensipent comma]]) and {{monzo\| -51 19 9 }} (untriton comma) in the 5-limit; 6144/6125 ([[porwell comma]]), 16875/16807 ([[mirkwai comma]]), 321489/320000 (varunisma), and {{monzo\| 22 -1 -10 1 }} (quasiorwellisma) in the 7-limit; [[540/539]] ~~and~~ [[~~1375~~/~~1372~~]] in the 11-limit; [[351/350]], [[847/845]], ~~and~~ [[1188/1183]] in the 13-limit. It can be viewed as a 2.13/5 [[subgroup]] temperament, as its approximations for lower prime limits are very poor but this makes 214edo an exceptionally xenharmonic tuning.		214edo is (uniquely) consistent through the [[7-odd-limit]]. The patent val for 214edo is {{val\| 214 339 497 601 740 792 }}, which [[tempering out\|tempers out]] the following commas: 78732/78125 ([[sensipent comma]]) and {{monzo\| -51 19 9 }} (untriton comma) in the 5-limit; 6144/6125 ([[porwell comma]]), 16875/16807 ([[mirkwai comma]]), 321489/320000 (varunisma), and {{monzo\| 22 -1 -10 1 }} (quasiorwellisma) in the 7-limit; [[540/539]], 1375/1372, [[5632/5625]], in the 11-limit; [[351/350]], [[847/845]], [[1001/1000]], [[1188/1183]], [[1573/1568]], and [[4096/4095]] in the 13-limit. It can be viewed as a 2.3.5.13.19.23 [[subgroup]] temperament, as its approximations for lower prime limits are very poor but this makes 214edo an exceptionally xenharmonic tuning.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	214 factors into 2 × 107, ~~with~~ [[2edo]] and [[107edo]] as its ~~subset edos~~.		Since 214 factors into 2 × 107, 214edo contains [[2edo]] and [[107edo]] as its subsets.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 44:		Line 44:
	\|-		\|-
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 540/539, 1375/1372, ~~3025~~/~~3024~~, ~~5632~~/~~5625~~		\| 540/539, 1375/1372, 5632/5625, 72171/71680
	\| {{mapping\| 214 339 497 601 740 }}		\| {{mapping\| 214 339 497 601 740 }}
	\| +0.0897		\| +0.0897
Line 51:		Line 51:
	\|-		\|-
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 540/539, 847/845~~, 1001/1000~~, 1375/1372, ~~5632~~/~~5625~~		\| 351/350, 540/539, 847/845, 1375/1372, 4096/4095
	\| {{mapping\| 214 339 497 601 740 792 }}		\| {{mapping\| 214 339 497 601 740 792 }}
	\| +0.0480		\| +0.0480
Line 58:		Line 58:
	\|-		\|-
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 351/350, 715/714, 936/935, ~~1275/1274, 5544/5525, 5850~~/~~5831~~		\| 351/350, 540/539, 715/714, 847/845, 936/935, 4096/4095
	\| {{mapping\| 214 339 497 601 740 792 875 }}		\| {{mapping\| 214 339 497 601 740 792 875 }}
	\| -0.0144		\| -0.0144
Line 83:		Line 83:
	\| 79\214		\| 79\214
	\| 442.99		\| 442.99
	\| 9/7		\| 162/125
	\| [[~~Sensi~~]]		\| [[Sensipent]]
	\|-		\|-
	\| 1		\| 1
Line 96:		Line 96:
	\| 157.01		\| 157.01
	\| 35/32		\| 35/32
	\| [[Bison]]		\| [[Bison]] (214e)
	\|-		\|-
	\| 2		\| 2

FloraC: Cleanup

2024-04-03T08:31:50Z

Cleanup

← Older revision		Revision as of 08:31, 3 April 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|214}}		{{EDO intro\|214}}
	==Theory==
	~~214et~~ is (uniquely) consistent through the [[7-odd-limit]]. The patent val for 214edo is {{val\| 214 339 497 601 740 792 }}, which tempers out the following commas: 78732/78125 ([[sensipent comma]]) and {{monzo\| -51 19 9 }} (untriton comma) in the 5-limit; [[6144/6125]] ~~(porwell~~), 16875/16807 (mirkwai), 321489/320000 (varunisma), and {{monzo\| 22 -1 -10 1 }} (quasiorwellisma) in the 7-limit; [[540/539]] and 1375/1372 in the 11-limit; ~~1188/1183,~~ [[351/350]] ~~and~~ [[847/845]] in the 13-limit. It can be viewed as a 2.13/5 subgroup temperament, as its approximations for lower prime limits are very poor but this makes 214edo an exceptionally xenharmonic tuning.		== Theory ==
	===Prime harmonics===		214edo is (uniquely) consistent through the [[7-odd-limit]]. The patent val for 214edo is {{val\| 214 339 497 601 740 792 }}, which [[tempering out\|tempers out]] the following commas: 78732/78125 ([[sensipent comma]]) and {{monzo\| -51 19 9 }} (untriton comma) in the 5-limit; 6144/6125 ([[porwell comma]]), 16875/16807 ([[mirkwai comma]]), 321489/320000 (varunisma), and {{monzo\| 22 -1 -10 1 }} (quasiorwellisma) in the 7-limit; [[540/539]] and [[1375/1372]] in the 11-limit; [[351/350]], [[847/845]], and [[1188/1183]] in the 13-limit. It can be viewed as a 2.13/5 [[subgroup]] temperament, as its approximations for lower prime limits are very poor but this makes 214edo an exceptionally xenharmonic tuning.

			=== Prime harmonics ===
	{{Harmonics in equal\|214}}		{{Harmonics in equal\|214}}
	===Subsets and supersets===
			=== Subsets and supersets ===
	214 factors into 2 × 107, with [[2edo]] and [[107edo]] as its subset edos.		214 factors into 2 × 107, with [[2edo]] and [[107edo]] as its subset edos.
	==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\|-339 214}}		\| {{monzo\| -339 214 }}
	\|{{~~val~~\|214 339}}		\| {{mapping\| 214 339 }}
	\| +0.3219		\| +0.3219
	\| 0.3220		\| 0.3220
	\| 5.74		\| 5.74
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|78732/78125, {{monzo\|-49 28 2}}		\| 78732/78125, {{monzo\| -49 28 2 }}
	\|{{~~val~~\|214 339 497}}		\| {{mapping\| 214 339 497 }}
	\| +0.1281		\| +0.1281
	\| 0.3797		\| 0.3797
	\| 6.77		\| 6.77
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|6144/6125, 16875/16807, 78732/78125		\| 6144/6125, 16875/16807, 78732/78125
	\|{{~~val~~\|214 339 497 601}}		\| {{mapping\| 214 339 497 601 }}
	\| -0.0169		\| -0.0169
	\| 0.4137		\| 0.4137
	\| 7.38		\| 7.38
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|540/539, 1375/1372, 3025/3024, 5632/5625		\| 540/539, 1375/1372, 3025/3024, 5632/5625
	\|{{~~val~~\|214 339 497 601 740}}		\| {{mapping\| 214 339 497 601 740 }}
	\| +0.0897		\| +0.0897
	\| 0.4270		\| 0.4270
	\| 7.61		\| 7.61
	\|-		\|-
	\|2.3.5.7.11.13		\| 2.3.5.7.11.13
	\|540/539, 847/845, 1001/1000, 1375/1372, 5632/5625		\| 540/539, 847/845, 1001/1000, 1375/1372, 5632/5625
	\|{{~~val~~\|214 339 497 601 740 792}}		\| {{mapping\| 214 339 497 601 740 792 }}
	\| +0.0480		\| +0.0480
	\| 0.4008		\| 0.4008
	\| 7.15		\| 7.15
	\|-		\|-
	\|2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\|351/350, 715/714, 936/935, 1275/1274, 5544/5525, 5850/5831		\| 351/350, 715/714, 936/935, 1275/1274, 5544/5525, 5850/5831
	\|{{~~val~~\|214 339 497 601 740 792 875}}		\| {{mapping\| 214 339 497 601 740 792 875 }}
	\| -0.0144		\| -0.0144
	\| 0.4012		\| 0.4012
	\| 7.15		\| 7.15
	\|}		\|}

	=== 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
	\|69\214		\| 69\214
	\|386.92		\| 386.92
	\|5/4		\| 5/4
	\|[[Grendel]]		\| [[Grendel]]
	\|-		\|-
	\|1		\| 1
	\|79\214		\| 79\214
	\|442.99		\| 442.99
	\|9/7		\| 9/7
	\|[[Sensi]]		\| [[Sensi]]
	\|-		\|-
	\|1		\| 1
	\|105\214		\| 105\214
	\|588.79		\| 588.79
	\|7/5		\| 7/5
	\|[[~~Untriton]] / [[aufo~~]]		\| [[Aufo]]
	\|-		\|-
	\|2		\| 2
	\|28\214		\| 28\214
	\|157.01		\| 157.01
	\|35/32		\| 35/32
	\|[[Bison]]		\| [[Bison]]
	\|-		\|-
	\|2		\| 2
	\|29\214		\| 29\214
	\|162.62		\| 162.62
	\|1125/1024		\| 1125/1024
	\|[[Kwazy]]		\| [[Kwazy]]
	\|}		\|}
			<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 17:07, 19 October 2023

2023-10-19T17:07:41Z

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''214edo''' is the equal division of the [[octave]] into 214 parts of 5.6075 [[cent]]s each. It is (uniquely) consistent through the [[7-odd-limit]]. The patent val for 214edo is {{val| 214 339 497 601 740 792 }}, which tempers out the following commas: 78732/78125 ([[sensipent comma]]) and {{monzo| -51 19 9 }} (untriton comma) in the 5-limit; [[6144/6125]] (porwell), 16875/16807 (mirkwai), 321489/320000 (varunisma), and {{monzo| 22 -1 -10 1 }} (quasiorwellisma) in the 7-limit; [[540/539]] and 1375/1372 in the 11-limit; 1188/1183, [[351/350]] and [[847/845]] in the 13-limit. It can be viewed as a 2.13/5 subgroup temperament, as its approximations for lower prime limits are very poor but this makes 214edo an exceptionally xenharmonic tuning.
+{{EDO intro|214}}
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->

Plumtree: Infobox ET added

2022-10-04T21:22:51Z

Infobox ET added

← Older revision		Revision as of 21:22, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''214edo''' is the equal division of the [[octave]] into 214 parts of 5.6075 [[cent]]s each. It is (uniquely) consistent through the [[7-odd-limit]]. The patent val for 214edo is {{val\| 214 339 497 601 740 792 }}, which tempers out the following commas: 78732/78125 ([[sensipent comma]]) and {{monzo\| -51 19 9 }} (untriton comma) in the 5-limit; [[6144/6125]] (porwell), 16875/16807 (mirkwai), 321489/320000 (varunisma), and {{monzo\| 22 -1 -10 1 }} (quasiorwellisma) in the 7-limit; [[540/539]] and 1375/1372 in the 11-limit; 1188/1183, [[351/350]] and [[847/845]] in the 13-limit. It can be viewed as a 2.13/5 subgroup temperament, as its approximations for lower prime limits are very poor but this makes 214edo an exceptionally xenharmonic tuning.		'''214edo''' is the equal division of the [[octave]] into 214 parts of 5.6075 [[cent]]s each. It is (uniquely) consistent through the [[7-odd-limit]]. The patent val for 214edo is {{val\| 214 339 497 601 740 792 }}, which tempers out the following commas: 78732/78125 ([[sensipent comma]]) and {{monzo\| -51 19 9 }} (untriton comma) in the 5-limit; [[6144/6125]] (porwell), 16875/16807 (mirkwai), 321489/320000 (varunisma), and {{monzo\| 22 -1 -10 1 }} (quasiorwellisma) in the 7-limit; [[540/539]] and 1375/1372 in the 11-limit; 1188/1183, [[351/350]] and [[847/845]] in the 13-limit. It can be viewed as a 2.13/5 subgroup temperament, as its approximations for lower prime limits are very poor but this makes 214edo an exceptionally xenharmonic tuning.

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->