Breed family - Revision history

FloraC: /* Freya */

2026-07-12T13:29:29Z

Freya

← Older revision		Revision as of 13:29, 12 July 2026
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	== Freya ==		== Freya ==
	Freya tempers out [[3025/3024]] and [[41503/41472]], so it splits breed's [[28/27]] into two [[55/54]]~[[56/55]]'s and [[8/7]] into two [[77/72]]'s. It also takes the [[225/224]][[~]][[1029/1024]] [[kleisma (interval region)\|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.		Freya tempers out [[3025/3024]] and [[41503/41472]], so it splits breed's [[28/27]] into two [[55/54]]~[[56/55]]'s and [[8/7]] into two [[77/72]]'s. It also takes the [[225/224]][[~]][[1029/1024]] [[kleisma #As an interval region\|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.

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

Hkm: /* 17-limit */

2026-06-09T22:21:03Z

17-limit

← Older revision		Revision as of 22:21, 9 June 2026
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	Subgroup: 2.3.5.7.11.13.17		Subgroup: 2.3.5.7.11.13.17

	Comma list: 715/714, 936/935, 1001/1000, 1225/1224~~, 1716/1715~~		Comma list: 715/714, 936/935, 1001/1000, 1225/1224

	Mapping: {{mapping\| 1 1 -1 1 5 -6 -5 \| 0 2 3 2 1 6 6 \| 0 0 4 2 -3 13 12 }}		Mapping: {{mapping\| 1 1 -1 1 5 -6 -5 \| 0 2 3 2 1 6 6 \| 0 0 4 2 -3 13 12 }}

FloraC: Text replacement - "rank-3 temperament" to "rank-3 temperament"

2026-06-08T08:36:26Z

Text replacement - "rank-3 temperament" to "rank-3 temperament"

← Older revision		Revision as of 08:36, 8 June 2026
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	{{Technical data page}}		{{Technical data page}}
	The '''breed family''' of [[rank-3 ~~temperament\|rank-3]] [[regular temperament\|~~temperament]]s are [[microtemperament]]s which [[tempering out\|temper out]] [[2401/2400]].		The '''breed family''' of [[rank-3 temperament]]s are [[microtemperament]]s which [[tempering out\|temper out]] [[2401/2400]].

	== Breed ==		== Breed ==

FloraC: Formatting

2026-04-04T12:04:57Z

Formatting

← Older revision		Revision as of 12:04, 4 April 2026
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	[[Badness]] (Sintel): 0.204		[[Badness]] (Sintel): 0.204

	[[Projection pair]]s: ~3 ~~= ~~~2401/800, ~5 ~~= ~~~22880495169/4575312500, ~7 ~~= ~~~1058841/151250, ~11 ~~= ~~~33275/3024 to 2.49/5.77/3		[[Projection pair]]s: <code>3 2401/800, 5 22880495169/4575312500, 7 1058841/151250, 11 33275/3024</code> to 2.49/5.77/3

	=== 13-limit ===		=== 13-limit ===
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	* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9526{{c}}, ~70/39 = 1013.3747{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9526{{c}}, ~70/39 = 1013.3747{{c}}

	{{Optimal ET sequence\|legend=0\| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} ~~<nowiki>~~*~~</nowiki>~~		{{Optimal ET sequence\|legend=0\| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} *
	<nowiki>*~~</nowiki> [[~~optimal patent val]]: [[1241edo\|1241]]
			<nowiki/>* optimal patent val: [[1241edo\|1241]]

	Badness (Sintel): 0.873		Badness (Sintel): 0.873

Squib: /* Freya */

2026-03-27T02:28:28Z

Freya

← Older revision		Revision as of 02:28, 27 March 2026
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	== Freya ==		== Freya ==
	Freya tempers out [[3025/3024]] and [[41503/41472]], so it splits breed's [[28/27]] into two [[55/54]]~[[56/55]]'s and [[8/7]] into two [[77/72]]'s. It also takes ~~breed's~~ [[225/224]][[~]][[1029/1024]] [[kleisma (interval region)\|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.		Freya tempers out [[3025/3024]] and [[41503/41472]], so it splits breed's [[28/27]] into two [[55/54]]~[[56/55]]'s and [[8/7]] into two [[77/72]]'s. It also takes the [[225/224]][[~]][[1029/1024]] [[kleisma (interval region)\|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.

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

FloraC: /* Ennealimmic */ could go with parentheses to indicate both breeds

2026-03-23T11:09:30Z

Ennealimmic: could go with parentheses to indicate both breeds

← Older revision		Revision as of 11:09, 23 March 2026
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	: error map: {{val\| 0.000 +0.021 -0.016 -0.183 -0.040 }}		: error map: {{val\| 0.000 +0.021 -0.016 -0.183 -0.040 }}

	{{Optimal ET sequence\|legend=1\| 72~~, …~~, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd, 6903dd }}		{{Optimal ET sequence\|legend=1\| 72, 171(e), 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd, 6903dd }}

	[[Badness]] (Sintel): 0.330		[[Badness]] (Sintel): 0.330
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	* CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3905{{c}}, ~11/8 = 551.7085{{c}}		* CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3905{{c}}, ~11/8 = 551.7085{{c}}

	{{Optimal ET sequence\|legend=0\| 72~~, …~~, 171, 198, 270, 639, 711, 981, 1692e }}		{{Optimal ET sequence\|legend=0\| 72, 171(ef), 198, 270, 639, 711, 981, 1692e }}

	Badness (Sintel): 0.706		Badness (Sintel): 0.706

FloraC: Cleanup. - idiosyncratic approaches

2026-02-16T09:13:24Z

Cleanup. - idiosyncratic approaches

← Older revision		Revision as of 09:13, 16 February 2026
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	== Freya ==		== Freya ==
	Freya takes breed's [[225/224]]~[[1029/1024]] [[kleisma (interval region)\|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament~~. (Breed is already a detemperament of 7-limit miracle.)~~		Freya tempers out [[3025/3024]] and [[41503/41472]], so it splits breed's [[28/27]] into two [[55/54]]~[[56/55]]'s and [[8/7]] into two [[77/72]]'s. It also takes breed's [[225/224]][[~]][[1029/1024]] [[kleisma (interval region)\|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.

	~~It also splits breed's [[8/7]] into two [[77/72]]s and [[28/27]] into two [[55/54]]~[[56/55]]s~~.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11
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	==== 17-limit ====		==== 17-limit ====
	~~Equave 10/7 and 16-note scales with that period are of interest.~~

	Subgroup: 2.3.5.7.11.13.17		Subgroup: 2.3.5.7.11.13.17

Squib: /* Freya */

2026-02-16T02:26:14Z

Freya

← Older revision		Revision as of 02:26, 16 February 2026
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	== Freya ==		== Freya ==
	Freya takes breed's [[225/224]]~[[1029/1024]] [[kleisma (interval region)\|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.		Freya takes breed's [[225/224]]~[[1029/1024]] [[kleisma (interval region)\|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament. (Breed is already a detemperament of 7-limit miracle.)

	It also splits breed's [[8/7]] into two [[77/72]]s and [[28/27]] into two [[55/54]]~[[56/55]]s.		It also splits breed's [[8/7]] into two [[77/72]]s and [[28/27]] into two [[55/54]]~[[56/55]]s.

Squib: /* Freya */+link

2026-02-15T22:36:46Z

Freya: +link

← Older revision		Revision as of 22:36, 15 February 2026
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	== Freya ==		== Freya ==
	Freya takes breed's [[225/224]]~[[1029/1024]] kleisma to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.		Freya takes breed's [[225/224]]~[[1029/1024]] [[kleisma (interval region)\|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.

	It also splits breed's [[8/7]] into two [[77/72]]s and [[28/27]] into two [[55/54]]~[[56/55]]s.		It also splits breed's [[8/7]] into two [[77/72]]s and [[28/27]] into two [[55/54]]~[[56/55]]s.

Overthink: /* Freya */ 225/224~1029/1024 is more of a kleisma

2026-02-15T22:29:15Z

Freya: 225/224~1029/1024 is more of a kleisma

← Older revision		Revision as of 22:29, 15 February 2026
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	== Freya ==		== Freya ==
	Freya takes breed's [[225/224]]~[[1029/1024]] ~~comma~~ to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.		Freya takes breed's [[225/224]]~[[1029/1024]] kleisma to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.

	It also splits breed's [[8/7]] into two [[77/72]]s and [[28/27]] into two [[55/54]]~[[56/55]]s.		It also splits breed's [[8/7]] into two [[77/72]]s and [[28/27]] into two [[55/54]]~[[56/55]]s.
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	=== 13-limit ===		=== 13-limit ===
	Freya's canonical 13-limit extension maps [[352/351]] to the half-~~comma~~. It has [[miraculous]] as a sub-temperament.		Freya's canonical 13-limit extension maps [[352/351]] to the half-kleisma. It has [[miraculous]] as a sub-temperament.

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13
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	=== Eir ===		=== Eir ===
	[[User:VIxen\|VIxen]] named this extension after a healer goddess or valkyrie from the Norse mythology, as it is an extension of freya with the [[ibnsinma]] that evokes associations with medicine. It maps [[325/324]], [[364/363]], and [[729/728]] to the half-~~comma~~ and has [[manna]] as a sub-temperament.		[[User:VIxen\|VIxen]] named this extension after a healer goddess or valkyrie from the Norse mythology, as it is an extension of freya with the [[ibnsinma]] that evokes associations with medicine. It maps [[325/324]], [[364/363]], and [[729/728]] to the half-kleisma and has [[manna]] as a sub-temperament.

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13
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	=== Heimlaug ===		=== Heimlaug ===
	VIxen named this extension after a völva (seeress) from the Gull-Þóris saga of Icelanders. It is an extension of freya with the [[1001/1000\|fairytale comma]] and the [[936/935\|ainisma]], both adding to the mystical theme. The one of prophecy is bolstered by that this extension has [[benediction]] as a subtemperament. It maps [[351/350]] and [[625/624]] to the half-~~comma~~.		VIxen named this extension after a völva (seeress) from the Gull-Þóris saga of Icelanders. It is an extension of freya with the [[1001/1000\|fairytale comma]] and the [[936/935\|ainisma]], both adding to the mystical theme. The one of prophecy is bolstered by that this extension has [[benediction]] as a subtemperament. It maps [[351/350]] and [[625/624]] to the half-kleisma.

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13