229edo - 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"

2026-03-13T13:38:09Z

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 13:38, 13 March 2026
Line 157:		Line 157:
	\| [[Alphatrident]] (229)		\| [[Alphatrident]] (229)
	\|}		\|}
	<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

	== Music ==		== Music ==

FloraC: /* Regular temperament properties */ emmthird

2025-09-04T15:10:25Z

Regular temperament properties: emmthird

← Older revision		Revision as of 15:10, 4 September 2025
Line 132:		Line 132:
	\| 5/4		\| 5/4
	\| [[Würschmidt]] (5-limit)		\| [[Würschmidt]] (5-limit)
			\|-
			\| 1
			\| 75\229
			\| 393.01
			\| 2744/2187
			\| [[Emmthird]] (7-limit)
	\|-		\|-
	\| 1		\| 1

Francium: /* Music */ +link

2025-07-03T12:02:12Z

Music: +link

← Older revision		Revision as of 12:02, 3 July 2025
Line 155:		Line 155:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Don't Think About Mimes" from ''Don't'' (2025) – [https://francium223.bandcamp.com/track/dont-think-about-mimes Bandcamp] \| [https://www.youtube.com/watch?v=MNHUrF4Ff0A YouTube]		* "Don't Think About Mimes" from ''Don't'' (2025) – [https://open.spotify.com/track/4jGvn8IFTQeJwNc0y17MpQ Spotify] \| [https://francium223.bandcamp.com/track/dont-think-about-mimes Bandcamp] \| [https://www.youtube.com/watch?v=MNHUrF4Ff0A YouTube]

	[[Category:Hemiwürschmidt]]		[[Category:Hemiwürschmidt]]
	[[Category:Würschmidt]]		[[Category:Würschmidt]]

Francium: +music

2025-07-02T13:02:08Z

+music

← Older revision		Revision as of 13:02, 2 July 2025
Line 152:		Line 152:
	\|}		\|}
	<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

			== Music ==
			; [[Francium]]
			* "Don't Think About Mimes" from ''Don't'' (2025) – [https://francium223.bandcamp.com/track/dont-think-about-mimes Bandcamp] \| [https://www.youtube.com/watch?v=MNHUrF4Ff0A YouTube]

	[[Category:Hemiwürschmidt]]		[[Category:Hemiwürschmidt]]
	[[Category:Würschmidt]]		[[Category:Würschmidt]]

FloraC: Cleanup and update

2025-03-16T15:27:49Z

Cleanup and update

← Older revision		Revision as of 15:27, 16 March 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	While not highly accurate for its size, 229edo is the point where a few important temperaments meet, and is [[consistency\|distinctly consistent]] in the [[11-odd-limit]]. It [[tempering out\|tempers out]] 393216/390625 ([[würschmidt comma]]) and {{monzo\| 39 -29 3 }} ([[~~tricot~~ comma]]) in the [[5-limit]]; [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[14348907/14336000]] in the [[7-limit]]; [[3025/3024]], [[3388/3375]], [[8019/8000]], [[14641/14580]] and 15488/15435 in the [[11-limit]], notably [[support]]ing [[hemiwürschmidt]], [[newt]], and [[~~trident~~]].		While not highly accurate for its size, 229edo is the point where a few important temperaments meet, and is [[consistency\|distinctly consistent]] in the [[11-odd-limit]]. It [[tempering out\|tempers out]] 393216/390625 ([[würschmidt comma]]) and {{monzo\| 39 -29 3 }} ([[alphatricot comma]]) in the [[5-limit]]; [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[14348907/14336000]] in the [[7-limit]]; [[3025/3024]], [[3388/3375]], [[8019/8000]], [[14641/14580]] and 15488/15435 in the [[11-limit]], notably [[support]]ing [[hemiwürschmidt]], [[newt]], and [[alphatrident]].

	It extends less well to the 13-limit. Using the [[patent val]] {{val\| 229 363 532 643 792 '''847''' }}, it tempers out [[351/350]], [[1573/1568]], [[2080/2079]], and [[4096/4095]]. Using the alternative 229f val {{val\| 229 363 532 643 792 '''848''' }}, it tempers out [[352/351]], [[729/728]], [[1001/1000]], and [[1716/1715]].		It extends less well to the 13-limit. Using the [[patent val]] {{val\| 229 363 532 643 792 '''847''' }}, it tempers out [[351/350]], [[1573/1568]], [[2080/2079]], and [[4096/4095]]. Using the alternative 229f val {{val\| 229 363 532 643 792 '''848''' }}, it tempers out [[352/351]], [[729/728]], [[1001/1000]], and [[1716/1715]].
Line 23:		Line 23:
	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[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
	\|-		\|-
Line 30:		Line 30:
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| 363 -229 }}		\| {{Monzo\| 363 -229 }}
	\| {{~~mapping~~\| 229 363 }}		\| {{Mapping\| 229 363 }}
	\| −0.072		\| −0.072
	\| 0.072		\| 0.072
Line 38:		Line 38:
	\| 2.3.5		\| 2.3.5
	\| 393216/390625, {{monzo\| 39 -29 3 }}		\| 393216/390625, {{monzo\| 39 -29 3 }}
	\| {{~~mapping~~\| 229 363 532 }}		\| {{Mapping\| 229 363 532 }}
	\| −0.258		\| −0.258
	\| 0.269		\| 0.269
Line 45:		Line 45:
	\| 2.3.5.7		\| 2.3.5.7
	\| 2401/2400, 3136/3125, 14348907/14336000		\| 2401/2400, 3136/3125, 14348907/14336000
	\| {{~~mapping~~\| 229 363 532 643 }}		\| {{Mapping\| 229 363 532 643 }}
	\| −0.247		\| −0.247
	\| 0.233		\| 0.233
Line 52:		Line 52:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 2401/2400, 3025/3024, 3136/3125, 8019/8000		\| 2401/2400, 3025/3024, 3136/3125, 8019/8000
	\| {{~~mapping~~\| 229 363 532 643 792 }}		\| {{Mapping\| 229 363 532 643 792 }}
	\| −0.134		\| −0.134
	\| 0.308		\| 0.308
Line 59:		Line 59:
	\| 2.3.5.7.11.17		\| 2.3.5.7.11.17
	\| 561/560, 1089/1088, 1701/1700, 2401/2400, 3136/3125		\| 561/560, 1089/1088, 1701/1700, 2401/2400, 3136/3125
	\| {{~~mapping~~\| 229 363 532 643 792 936 }}		\| {{Mapping\| 229 363 532 643 792 936 }}
	\| −0.106		\| −0.106
	\| 0.288		\| 0.288
Line 66:		Line 66:
	\| 2.3.5.7.11.17.19		\| 2.3.5.7.11.17.19
	\| 476/475, 561/560, 1089/1088, 1216/1215, 1445/1444, 2401/2400		\| 476/475, 561/560, 1089/1088, 1216/1215, 1445/1444, 2401/2400
	\| {{~~mapping~~\| 229 363 532 643 792 936 973 }}		\| {{Mapping\| 229 363 532 643 792 936 973 }}
	\| −0.130		\| −0.130
	\| 0.273		\| 0.273
Line 73:		Line 73:
	\| 2.3.5.7.11.17.19.23		\| 2.3.5.7.11.17.19.23
	\| 476/475, 484/483, 561/560, 576/575, 736/735, 1089/1088, 1216/1215		\| 476/475, 484/483, 561/560, 576/575, 736/735, 1089/1088, 1216/1215
	\| {{~~mapping~~\| 229 363 532 643 792 936 973 1036 }}		\| {{Mapping\| 229 363 532 643 792 936 973 1036 }}
	\| −0.129		\| −0.129
	\| 0.256		\| 0.256
Line 80:		Line 80:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 351/350, 1573/1568, 2080/2079, 2197/2187, 3136/3125		\| 351/350, 1573/1568, 2080/2079, 2197/2187, 3136/3125
	\| {{~~mapping~~\| 229 363 532 643 792 847 }} (229)		\| {{Mapping\| 229 363 532 643 792 847 }} (229)
	\| −0.017		\| −0.017
	\| 0.384		\| 0.384
Line 87:		Line 87:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 352/351, 729/728, 1001/1000, 1716/1715, 3025/3024		\| 352/351, 729/728, 1001/1000, 1716/1715, 3025/3024
	\| {{~~mapping~~\| 229 363 532 643 792 848 }} (229f)		\| {{Mapping\| 229 363 532 643 792 848 }} (229f)
	\| −0.253		\| −0.253
	\| 0.387		\| 0.387
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	\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	\|-		\|-
	! Periods<br />per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br />ratio*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 149:		Line 149:
	\| 565.94		\| 565.94
	\| 18/13		\| 18/13
	\| [[~~Trident~~]] (229)		\| [[Alphatrident]] (229)
	\|}		\|}
	<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

	[[Category:Hemiwürschmidt]]		[[Category:Hemiwürschmidt]]
	[[Category:Würschmidt]]		[[Category:Würschmidt]]

ArrowHead294 at 14:20, 20 February 2025

2025-02-20T14:20:27Z

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

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T15:35:10Z

Theory: cleanup

← Older revision		Revision as of 15:35, 17 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	While not highly accurate for its size, 229edo is the point where a few important temperaments meet, and is [[distinctly consistent]] in the [[11-odd-limit]]. It [[tempers out]] 393216/390625 ([[würschmidt comma]]) and {{monzo\| 39 -29 3 }} ([[tricot comma]]) in the 5-limit; [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[14348907/14336000]] in the 7-limit; [[3025/3024]], [[3388/3375]], [[8019/8000]], [[14641/14580]] and 15488/15435 in the 11-limit, notably [[support~~\|supporting~~]] [[hemiwürschmidt]], [[newt]], and [[trident]].		While not highly accurate for its size, 229edo is the point where a few important temperaments meet, and is [[consistency\|distinctly consistent]] in the [[11-odd-limit]]. It [[tempering out\|tempers out]] 393216/390625 ([[würschmidt comma]]) and {{monzo\| 39 -29 3 }} ([[tricot comma]]) in the [[5-limit]]; [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[14348907/14336000]] in the [[7-limit]]; [[3025/3024]], [[3388/3375]], [[8019/8000]], [[14641/14580]] and 15488/15435 in the [[11-limit]], notably [[support]]ing [[hemiwürschmidt]], [[newt]], and [[trident]].

	It extends less well to the 13-limit. Using the [[patent val]] {{val\| 229 363 532 643 792 '''847''' }}, it tempers out [[351/350]], [[1573/1568]], [[2080/2079]], and [[4096/4095]]. Using the alternative 229f val {{val\| 229 363 532 643 792 '''848''' }}, it tempers out [[352/351]], [[729/728]], [[1001/1000]], and [[1716/1715]].		It extends less well to the 13-limit. Using the [[patent val]] {{val\| 229 363 532 643 792 '''847''' }}, it tempers out [[351/350]], [[1573/1568]], [[2080/2079]], and [[4096/4095]]. Using the alternative 229f val {{val\| 229 363 532 643 792 '''848''' }}, it tempers out [[352/351]], [[729/728]], [[1001/1000]], and [[1716/1715]].
Line 12:		Line 12:

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|229~~\|columns=11~~}}		{{Harmonics in equal\|229}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

ArrowHead294 at 14:19, 16 January 2025

2025-01-16T14:19:28Z

← Older revision		Revision as of 14:19, 16 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	While not highly accurate for its size, 229edo is the point where a few important temperaments meet, and is [[~~consistency\|~~distinctly consistent]] in the [[11-odd-limit]]. ~~The equal temperament~~ [[~~tempering out\|~~tempers out]] 393216/390625 ([[würschmidt comma]]) and {{monzo\| 39 -29 3 }} ([[tricot comma]]) in the 5-limit; [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[14348907/14336000]] in the 7-limit; [[3025/3024]], [[3388/3375]], [[8019/8000]], [[14641/14580]] and 15488/15435 in the 11-limit, notably [[support\|supporting]] [[hemiwürschmidt]], [[newt]], and [[trident]].		While not highly accurate for its size, 229edo is the point where a few important temperaments meet, and is [[distinctly consistent]] in the [[11-odd-limit]]. It [[tempers out]] 393216/390625 ([[würschmidt comma]]) and {{monzo\| 39 -29 3 }} ([[tricot comma]]) in the 5-limit; [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[14348907/14336000]] in the 7-limit; [[3025/3024]], [[3388/3375]], [[8019/8000]], [[14641/14580]] and 15488/15435 in the 11-limit, notably [[support\|supporting]] [[hemiwürschmidt]], [[newt]], and [[trident]].

	It extends less well to the 13-limit. Using the [[patent val]] {{val\| 229 363 532 643 792 '''847''' }}, it tempers out [[351/350]], [[1573/1568]], [[2080/2079]], and [[4096/4095]]. Using the alternative 229f val {{val\| 229 363 532 643 792 '''848''' }}, it tempers out [[352/351]], [[729/728]], [[1001/1000]], and [[1716/1715]].		It extends less well to the 13-limit. Using the [[patent val]] {{val\| 229 363 532 643 792 '''847''' }}, it tempers out [[351/350]], [[1573/1568]], [[2080/2079]], and [[4096/4095]]. Using the alternative 229f val {{val\| 229 363 532 643 792 '''848''' }}, it tempers out [[352/351]], [[729/728]], [[1001/1000]], and [[1716/1715]].

	Higher [[harmonic]]s like [[17/1\|17]], [[19/1\|19]], and [[23/1\|23]] are well approximated, so it shows great potential in the no-13 23-limit. It tempers out [[561/560]], [[1089/1088]], and [[1701/1700]] in the 17-limit; [[476/475]], [[1216/1215]], [[1445/1444]], and [[1540/1539]] in the 19-limit; and [[484/483]], [[576/575]] and [[736/735]] in the 23-limit.		Higher [[harmonic]]s like [[17/1\|17]], [[19/1\|19]], and [[23/1\|23]] are well-approximated, so it shows great potential in the no-13 23-limit. It tempers out [[561/560]], [[1089/1088]], and [[1701/1700]] in the 17-limit; [[476/475]], [[1216/1215]], [[1445/1444]], and [[1540/1539]] in the 19-limit; and [[484/483]], [[576/575]] and [[736/735]] in the 23-limit.

	The 229b [[val]] supports a [[septimal meantone]] close to the [[CTE tuning]].		The 229b [[val]] supports a [[septimal meantone]] close to the [[CTE tuning]].
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	\| {{monzo\| 363 -229 }}		\| {{monzo\| 363 -229 }}
	\| {{mapping\| 229 363 }}		\| {{mapping\| 229 363 }}
	\| ~~−0~~.072		\| −0.072
	\| 0.072		\| 0.072
	\| 1.38		\| 1.38
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	\| 393216/390625, {{monzo\| 39 -29 3 }}		\| 393216/390625, {{monzo\| 39 -29 3 }}
	\| {{mapping\| 229 363 532 }}		\| {{mapping\| 229 363 532 }}
	\| ~~−0~~.258		\| −0.258
	\| 0.269		\| 0.269
	\| 5.13		\| 5.13
Line 46:		Line 46:
	\| 2401/2400, 3136/3125, 14348907/14336000		\| 2401/2400, 3136/3125, 14348907/14336000
	\| {{mapping\| 229 363 532 643 }}		\| {{mapping\| 229 363 532 643 }}
	\| ~~−0~~.247		\| −0.247
	\| 0.233		\| 0.233
	\| 4.46		\| 4.46
Line 53:		Line 53:
	\| 2401/2400, 3025/3024, 3136/3125, 8019/8000		\| 2401/2400, 3025/3024, 3136/3125, 8019/8000
	\| {{mapping\| 229 363 532 643 792 }}		\| {{mapping\| 229 363 532 643 792 }}
	\| ~~−0~~.134		\| −0.134
	\| 0.308		\| 0.308
	\| 5.87		\| 5.87
Line 60:		Line 60:
	\| 561/560, 1089/1088, 1701/1700, 2401/2400, 3136/3125		\| 561/560, 1089/1088, 1701/1700, 2401/2400, 3136/3125
	\| {{mapping\| 229 363 532 643 792 936 }}		\| {{mapping\| 229 363 532 643 792 936 }}
	\| ~~−0~~.106		\| −0.106
	\| 0.288		\| 0.288
	\| 5.50		\| 5.50
Line 67:		Line 67:
	\| 476/475, 561/560, 1089/1088, 1216/1215, 1445/1444, 2401/2400		\| 476/475, 561/560, 1089/1088, 1216/1215, 1445/1444, 2401/2400
	\| {{mapping\| 229 363 532 643 792 936 973 }}		\| {{mapping\| 229 363 532 643 792 936 973 }}
	\| ~~−0~~.130		\| −0.130
	\| 0.273		\| 0.273
	\| 5.22		\| 5.22
Line 74:		Line 74:
	\| 476/475, 484/483, 561/560, 576/575, 736/735, 1089/1088, 1216/1215		\| 476/475, 484/483, 561/560, 576/575, 736/735, 1089/1088, 1216/1215
	\| {{mapping\| 229 363 532 643 792 936 973 1036 }}		\| {{mapping\| 229 363 532 643 792 936 973 1036 }}
	\| ~~−0~~.129		\| −0.129
	\| 0.256		\| 0.256
	\| 4.88		\| 4.88
Line 81:		Line 81:
	\| 351/350, 1573/1568, 2080/2079, 2197/2187, 3136/3125		\| 351/350, 1573/1568, 2080/2079, 2197/2187, 3136/3125
	\| {{mapping\| 229 363 532 643 792 847 }} (229)		\| {{mapping\| 229 363 532 643 792 847 }} (229)
	\| ~~−0~~.017		\| −0.017
	\| 0.384		\| 0.384
	\| 7.32		\| 7.32
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	\| 352/351, 729/728, 1001/1000, 1716/1715, 3025/3024		\| 352/351, 729/728, 1001/1000, 1716/1715, 3025/3024
	\| {{mapping\| 229 363 532 643 792 848 }} (229f)		\| {{mapping\| 229 363 532 643 792 848 }} (229f)
	\| ~~−0~~.253		\| −0.253
	\| 0.387		\| 0.387
	\| 7.39		\| 7.39
Line 151:		Line 151:
	\| [[Trident]] (229)		\| [[Trident]] (229)
	\|}		\|}
	<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:Hemiwürschmidt]]		[[Category:Hemiwürschmidt]]
	[[Category:Würschmidt]]		[[Category:Würschmidt]]

ArrowHead294 at 12:09, 16 November 2024

2024-11-16T12:09:09Z

← Older revision		Revision as of 12:09, 16 November 2024
Line 18:		Line 18:

	== 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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	\| 0.387		\| 0.387
	\| 7.39		\| 7.39
	~~{{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
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	\| 18/13		\| 18/13
	\| [[Trident]] (229)		\| [[Trident]] (229)
	~~{{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:Hemiwürschmidt]]		[[Category:Hemiwürschmidt]]
	[[Category:Würschmidt]]		[[Category:Würschmidt]]

ArrowHead294 at 05:27, 16 November 2024

2024-11-16T05:27:34Z

← Older revision		Revision as of 05:27, 16 November 2024
Line 18:		Line 18:

	== 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
	\| {{monzo\| 363 -229 }}		\| {{monzo\| 363 -229 }}
	\| {{mapping\| 229 363 }}		\| {{mapping\| 229 363 }}
	\| -0.072		\| −0.072
	\| 0.072		\| 0.072
	\| 1.38		\| 1.38
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	\| 393216/390625, {{monzo\| 39 -29 3 }}		\| 393216/390625, {{monzo\| 39 -29 3 }}
	\| {{mapping\| 229 363 532 }}		\| {{mapping\| 229 363 532 }}
	\| -0.258		\| −0.258
	\| 0.269		\| 0.269
	\| 5.13		\| 5.13
Line 45:		Line 37:
	\| 2401/2400, 3136/3125, 14348907/14336000		\| 2401/2400, 3136/3125, 14348907/14336000
	\| {{mapping\| 229 363 532 643 }}		\| {{mapping\| 229 363 532 643 }}
	\| -0.247		\| −0.247
	\| 0.233		\| 0.233
	\| 4.46		\| 4.46
Line 52:		Line 44:
	\| 2401/2400, 3025/3024, 3136/3125, 8019/8000		\| 2401/2400, 3025/3024, 3136/3125, 8019/8000
	\| {{mapping\| 229 363 532 643 792 }}		\| {{mapping\| 229 363 532 643 792 }}
	\| -0.134		\| −0.134
	\| 0.308		\| 0.308
	\| 5.87		\| 5.87
Line 59:		Line 51:
	\| 561/560, 1089/1088, 1701/1700, 2401/2400, 3136/3125		\| 561/560, 1089/1088, 1701/1700, 2401/2400, 3136/3125
	\| {{mapping\| 229 363 532 643 792 936 }}		\| {{mapping\| 229 363 532 643 792 936 }}
	\| -0.106		\| −0.106
	\| 0.288		\| 0.288
	\| 5.50		\| 5.50
Line 66:		Line 58:
	\| 476/475, 561/560, 1089/1088, 1216/1215, 1445/1444, 2401/2400		\| 476/475, 561/560, 1089/1088, 1216/1215, 1445/1444, 2401/2400
	\| {{mapping\| 229 363 532 643 792 936 973 }}		\| {{mapping\| 229 363 532 643 792 936 973 }}
	\| -0.130		\| −0.130
	\| 0.273		\| 0.273
	\| 5.22		\| 5.22
Line 73:		Line 65:
	\| 476/475, 484/483, 561/560, 576/575, 736/735, 1089/1088, 1216/1215		\| 476/475, 484/483, 561/560, 576/575, 736/735, 1089/1088, 1216/1215
	\| {{mapping\| 229 363 532 643 792 936 973 1036 }}		\| {{mapping\| 229 363 532 643 792 936 973 1036 }}
	\| -0.129		\| −0.129
	\| 0.256		\| 0.256
	\| 4.88		\| 4.88
	\|-		\|- style="border-top: double;"
	\| style="border-top: double;" \| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	~~\| style="border-top: double;"~~ \| 351/350, 1573/1568, 2080/2079, 2197/2187, 3136/3125		\| 351/350, 1573/1568, 2080/2079, 2197/2187, 3136/3125
	~~\| style="border-top: double;"~~ \| {{mapping\| 229 363 532 643 792 847 }} (229)		\| {{mapping\| 229 363 532 643 792 847 }} (229)
	\| ~~style="border-top: double~~;~~" \| -~~0.017		\| −0.017
	~~\| style="border-top: double;"~~ \| 0.384		\| 0.384
	~~\| style="border-top: double;"~~ \| 7.32		\| 7.32
	\|-		\|- style="border-top: double;"
	\| style="border-top: double;" \| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	~~\| style="border-top: double;"~~ \| 352/351, 729/728, 1001/1000, 1716/1715, 3025/3024		\| 352/351, 729/728, 1001/1000, 1716/1715, 3025/3024
	~~\| style="border-top: double;"~~ \| {{mapping\| 229 363 532 643 792 848 }} (229f)		\| {{mapping\| 229 363 532 643 792 848 }} (229f)
	\| ~~style="border-top: double~~;~~" \| -~~0.253		\| −0.253
	~~\| style="border-top: double;"~~ \| 0.387		\| 0.387
	~~\| style="border-top: double;"~~ \| 7.39		\| 7.39
	\|}		{{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 148:		Line 134:
	\| 18/13		\| 18/13
	\| [[Trident]] (229)		\| [[Trident]] (229)
	\|}		{{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:Hemiwürschmidt]]
	[[Category:Würschmidt]]		[[Category:Würschmidt]]
	~~[[Category:Hemiwürschmidt]]~~