Werckismic temperaments - Revision history

FloraC: Naming of the history temp (reference thread #96550)

2026-03-14T08:25:06Z

Naming of the history temp (reference thread #96550)

← Older revision		Revision as of 08:25, 14 March 2026
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	: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #History]].''		: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #History]].''

	History splits the perfect fourth into six, each for [[21/20]][[~]][[22/21]]. A recommendable tuning is given by [[289edo]].		History, named by [[Graham Breed]] some time before 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_96550.html#96556 Yahoo! Tuning Group \| ''Madagascar<nowiki>[</nowiki>19<nowiki>]</nowiki>'']</ref>, splits the perfect fourth into six, each for [[21/20]][[~]][[22/21]]. A recommendable tuning is given by [[289edo]].

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11
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	Badness (Sintel): 1.284		Badness (Sintel): 1.284

			== References ==

	[[Category:Temperament collections]]		[[Category:Temperament collections]]

Xenllium at 05:07, 21 February 2026

2026-02-21T05:07:59Z

← Older revision		Revision as of 05:07, 21 February 2026
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	* ''[[Tiberius]]'' (+2048/2025) → [[Diaschismic rank-3 family #Tiberius\|Diaschismic rank-3 family]]		* ''[[Tiberius]]'' (+2048/2025) → [[Diaschismic rank-3 family #Tiberius\|Diaschismic rank-3 family]]
	* ''[[Belobog]]'' (+3136/3125) → [[Hemimean family #Belobog\|Hemimean family]]		* ''[[Belobog]]'' (+3136/3125) → [[Hemimean family #Belobog\|Hemimean family]]
			* ''[[Landy]]'' (+4375/4356) → [[Landscape family #Landy\|Landscape family]]
	* ''[[Turan]]'' (+10976/10935) → [[Hemimage family #Turan\|Hemimage family]]		* ''[[Turan]]'' (+10976/10935) → [[Hemimage family #Turan\|Hemimage family]]
	* ''[[Snape]]'' (+19683/19600) → [[Cataharry family #Snape\|Cataharry family]]		* ''[[Snape]]'' (+19683/19600) → [[Cataharry family #Snape\|Cataharry family]]

Xenllium: /* Seminaiad */

2026-02-16T23:42:41Z

Seminaiad

← Older revision		Revision as of 23:42, 16 February 2026
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	== Seminaiad ==		== Seminaiad ==
	: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Seminaiad]].''		: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Seminaiad]].''

			Named by [[User:Xenllium\|Xenllium]] in 2026, seminaiad is a weak extension of [[No-threes subgroup temperaments #No-threes naiad\|no-threes naiad]]. It splits ~13/5 in two to represent ~21/13.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

Xenllium: /* Seminaiad */

2026-02-16T23:25:51Z

Seminaiad

← Older revision		Revision as of 23:25, 16 February 2026
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	Badness (Sintel): 1.748		Badness (Sintel): 1.748

			==== Seminaiadia ====
			Subgroup: 2.3.5.7.11.13.17

			Comma list: 441/440, 833/832, 847/845, 1001/1000

			Mapping: {{mapping\| 1 5 0 -2 3 2 12 \| 0 -11 0 8 -6 -2 -18 \| 0 0 1 1 1 1 -1 }}

			Optimal tunings:
			* WE: ~2 = 1199.925{{c}}, ~26/21 = 372.566{{c}}, ~5/4 = 387.117{{c}}
			* CWE: ~2 = 1200.000{{c}}, ~26/21 = 372.594{{c}}, ~5/4 = 387.080{{c}}

			{{Optimal ET sequence\|legend=0\| 16, 29, 45ef, 58, 87, 103, 145, 161, 190 }}

			Badness (Sintel): 1.284

	[[Category:Temperament collections]]		[[Category:Temperament collections]]

Xenllium: /* Seminaiad */

2026-02-15T23:46:50Z

Seminaiad

← Older revision		Revision as of 23:46, 15 February 2026
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	[[Badness]] (Sintel): 2.582		[[Badness]] (Sintel): 2.582

	==== 13-limit ====		=== 13-limit ===
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

	Comma list: 441/440, 847/845, 1001/1000		Comma list: 441/440, 847/845, 1001/1000

	Mapping: {{mapping\| 1 5 0 -2 3 2 \| 0 -11 0 8 -6 -2 \| 0 0 1 1 1 1 }}		Mapping: {{mapping\| 1 5 0 -2 3 2 \| 0 -11 0 8 -6 -2 \| 0 0 1 1 1 1 }}

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	Badness (Sintel): 0.944		Badness (Sintel): 0.944

			==== 17-limit ====
			Subgroup: 2.3.5.7.11.13.17

			Comma list: 170/169, 221/220, 441/440, 847/845

			Mapping: {{mapping\| 1 5 0 -2 3 2 3 \| 0 -11 0 8 -6 -2 -4 \| 0 0 1 1 1 1 1 }}

			Optimal tunings:
			* WE: ~2 = 1200.375{{c}}, ~21/17 = 372.711{{c}}, ~5/4 = 386.747{{c}}
			* CWE: ~2 = 1200.000{{c}}, ~21/17 = 372.573{{c}}, ~5/4 = 387.138{{c}}

			{{Optimal ET sequence\|legend=0\| 16, 29g, 45efg, 58, 87g }}

			Badness (Sintel): 1.748

	[[Category:Temperament collections]]		[[Category:Temperament collections]]

Xenllium at 23:37, 15 February 2026

2026-02-15T23:37:21Z

← Older revision		Revision as of 23:37, 15 February 2026
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	Badness (Sintel): 1.38		Badness (Sintel): 1.38

			== Seminaiad ==
			: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Seminaiad]].''

			[[Subgroup]]: 2.3.5.7.11

			[[Comma list]]: 441/440, 1127357/1125000

			{{Mapping\|legend=1\| 1 5 0 -2 3 \| 0 -11 0 8 -6 \| 0 0 1 1 1 }}
			: mapping generators: ~2, ~150/121, ~5

			[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1200.203{{c}}, ~150/121 = 372.665{{c}}, ~5/4 = 386.499{{c}}
			: [[error map]]: {{val\| +0.203 -0.257 +0.592 -1.004 +0.206 }}
			* [[CWE]]: ~2 = 1200.000{{c}}, ~150/121 = 372.591{{c}}, ~5/4 = 386.702{{c}}
			: error map: {{val\| 0.000 -0.453 +0.388 -1.399 -0.161 }}

			{{Optimal ET sequence\|legend=1\| 16, 29, 45e, 58, 87, 103, 145, 161, 190 }}

			[[Badness]] (Sintel): 2.582

			==== 13-limit ====
			Subgroup: 2.3.5.7.11.13

			Comma list: 441/440, 847/845, 1001/1000
			Mapping: {{mapping\| 1 5 0 -2 3 2 \| 0 -11 0 8 -6 -2 \| 0 0 1 1 1 1 }}

			Optimal tunings:
			* WE: ~2 = 1200.161{{c}}, ~26/21 = 372.652{{c}}, ~5/4 = 386.381{{c}}
			* CWE: ~2 = 1200.000{{c}}, ~26/21 = 372.593{{c}}, ~5/4 = 386.546{{c}}

			{{Optimal ET sequence\|legend=0\| 16, 29, 45ef, 58, 87, 103, 145, 161, 190 }}

			Badness (Sintel): 0.944

	[[Category:Temperament collections]]		[[Category:Temperament collections]]

Xenllium at 05:39, 31 January 2026

2026-01-31T05:39:24Z

← Older revision		Revision as of 05:39, 31 January 2026
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	== History ==		== History ==
			: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #History]].''

	History splits the perfect fourth into six, each for [[21/20]][[~]][[22/21]]. A recommendable tuning is given by [[289edo]].		History splits the perfect fourth into six, each for [[21/20]][[~]][[22/21]]. A recommendable tuning is given by [[289edo]].

FloraC: Improve intro

2025-12-24T11:03:36Z

Improve intro

← Older revision		Revision as of 11:03, 24 December 2025
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	{{Technical data page}}		{{Technical data page}}
	This is a collection of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out]] the [[werckisma]], 441/440 = {{monzo\| -3 2 -1 2 -1 }}. For the rank-4 werckismic temperament, see [[Catalog of rank-4 temperaments #Werckismic (441/440)]].		This is a collection of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out]] the [[werckisma]] ([[ratio]]: 441/440, {{monzo\|legend=1\| -3 2 -1 2 -1 }}). For the rank-4 werckismic temperament, see [[Catalog of rank-4 temperaments #Werckismic (441/440)]].

	Temperaments discussed elsewhere are:		Temperaments discussed elsewhere are:

FloraC: /* Trimyna */

2025-12-24T10:58:51Z

Trimyna

← Older revision		Revision as of 10:58, 24 December 2025
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	Comma list: 196/195, 352/351, 1001/1000		Comma list: 196/195, 352/351, 1001/1000

	Mapping: {{mapping\| 1 ~~4 0~~ 0 5 -2 \| 0 -5 0 1 -8 7 \| 0 0 1 1 1 1 }}		Mapping: {{mapping\| 1 -1 0 1 -3 5 \| 0 5 0 -1 8 -7 \| 0 0 1 1 1 1 }}

	Optimal tunings:		Optimal tunings:

FloraC: /* Trimyna */

2025-12-24T10:57:50Z

Trimyna

← Older revision		Revision as of 10:57, 24 December 2025
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	: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Trimyna]].''		: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Trimyna]].''

	Trimyna can be described as the 27e & 29 & 31 temperament. All three equal temperaments have a fairly accurate tritone for ~~~7/5 (or~~ ~10/7), and trimyna takes it as one of its generators. The name ''trimyna'' is a contraction of ''[[tritonic]]'' and ''[[myna]]''.		Trimyna can be described as the {{nowrap\| 27e & 29 & 31 }} temperament. All three equal temperaments have a fairly accurate tritone for ~10/7, and trimyna takes it as one of its generators, five of which get us to the [[6/1\|6th]] [[harmonic]]. The name ''trimyna'' is a contraction of ''[[tritonic]]'' and ''[[myna]]''.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

← Older revision		Revision as of 05:07, 21 February 2026
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	* ''[[Tiberius]]'' (+2048/2025) → [[Diaschismic rank-3 family #Tiberius\|Diaschismic rank-3 family]]		* ''[[Tiberius]]'' (+2048/2025) → [[Diaschismic rank-3 family #Tiberius\|Diaschismic rank-3 family]]
	* ''[[Belobog]]'' (+3136/3125) → [[Hemimean family #Belobog\|Hemimean family]]		* ''[[Belobog]]'' (+3136/3125) → [[Hemimean family #Belobog\|Hemimean family]]
			* ''[[Landy]]'' (+4375/4356) → [[Landscape family #Landy\|Landscape family]]
	* ''[[Turan]]'' (+10976/10935) → [[Hemimage family #Turan\|Hemimage family]]		* ''[[Turan]]'' (+10976/10935) → [[Hemimage family #Turan\|Hemimage family]]
	* ''[[Snape]]'' (+19683/19600) → [[Cataharry family #Snape\|Cataharry family]]		* ''[[Snape]]'' (+19683/19600) → [[Cataharry family #Snape\|Cataharry family]]