Starling family - Revision history

Xenllium at 12:46, 4 May 2026

2026-05-04T12:46:45Z

← Older revision		Revision as of 12:46, 4 May 2026
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	[[Badness]] (Sintel): 0.424		[[Badness]] (Sintel): 0.424

	[[Projection pair]]s: <code>7 125/18 11 3125/288</code>		[[Projection pair]]s: <code>7 125/18</code> <code>11 3125/288</code>

	=== 13-limit ===		=== 13-limit ===
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	Badness (Sintel): 0.856		Badness (Sintel): 0.856

	Projection pairs: <code>7 125/18 11 3125/288 13 41472/3125</code>		Projection pairs: <code>7 125/18</code> <code>11 3125/288</code> <code>13 41472/3125</code>

	=== Nightingale ===		=== Nightingale ===
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	[[Badness]] (Sintel): 0.813		[[Badness]] (Sintel): 0.813

			[[Projection pair]]s: <code>7 125/18</code> <code>11 6912/625</code>

	Scales: [[Star and Nova]]		Scales: [[Star and Nova]]

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

			Comma list: 126/125, 196/195, 385/384

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

			Optimal tunings:
			* WE: ~2 = 1200.5083{{c}}, ~3/2 = 700.7452{{c}}, ~5/4 = 388.4655{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.5708{{c}}, ~5/4 = 388.4346{{c}}

			{{Optimal ET sequence\|legend=0\| 15f, 19, 27, 31, 46, 77, 96d }}

			Badness (Sintel): 1.07

	== Thrasher ==		== Thrasher ==
	{{See also\| Ptolemismic clan ~~#Thrasher~~ }}		{{See also\| Ptolemismic clan }}

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

FloraC: Update

2026-04-11T10:10:54Z

Update

← Older revision		Revision as of 10:10, 11 April 2026
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	Temperaments discussed elsewhere include		Temperaments discussed elsewhere include
	* ''[[Erato]]'' (+81/80) → [[Didymus rank-3 family #Erato\|Didymus rank-3 family]]		* ''[[Erato]]'' (+81/80) → [[Didymus rank-3 family #Erato\|Didymus rank-3 family]]
	* ''[[Sensigh]]'' (+245/243) → [[~~Sensamagic~~ family #Sensigh\|~~Sensamagic~~ family]]		* ''[[Sensigh]]'' (+245/243) → [[Sengic family #Sensigh\|Sengic family]]
	* ''[[Oxpecker]]'' (+121/120) → [[Biyatismic clan #Oxpecker\|Biyatismic clan]]		* ''[[Oxpecker]]'' (+121/120) → [[Biyatismic clan #Oxpecker\|Biyatismic clan]]
	* ''[[Cuckoo]]'' (+243/242) → [[Rastmic rank-3 clan #Cuckoo\|Rastmic rank-3 clan]]		* ''[[Cuckoo]]'' (+243/242) → [[Rastmic rank-3 clan #Cuckoo\|Rastmic rank-3 clan]]

FloraC: Decanonicalize undecimal starling

2026-02-12T06:31:06Z

Decanonicalize undecimal starling

@@ Line 63: / Line 63: @@
 * ''[[Cuckoo]]'' (+243/242) → [[Rastmic rank-3 clan #Cuckoo|Rastmic rank-3 clan]]
-Considered below are starling, thrush, thrasher, aplonis, and treecreeper.
+Considered below are thrush, starnova, thrasher, aplonis, and treecreeper.
 == Thrush ==
@@ Line 179: / Line 162: @@
 Badness (Sintel): 0.927
 == Thrasher ==

FloraC: Dissolve associated temps into generic description

2025-12-12T15:40:23Z

Dissolve associated temps into generic description

← Older revision		Revision as of 15:40, 12 December 2025
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	== Thrush ==		== Thrush ==
	{{Main\| Starling and thrush }}		{{Main\| Starling and thrush }}

			Thrush is the main extension of starling into the [[11-limit]]. It may be described as 12 & 15 & 31, and is loosely [[associated temperament\|associated]] with [[myna]].

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11
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	[[Projection pair]]s: <code>7 125/18 11 3125/288</code>		[[Projection pair]]s: <code>7 125/18 11 3125/288</code>

	~~[[Associated temperament]]: [[myna]]~~

	=== 13-limit ===		=== 13-limit ===

FloraC: Switch to Sintel's badness and + missing tunings

2025-12-12T15:25:12Z

Switch to Sintel's badness and + missing tunings

Show changes

FloraC: Move harmony-related contents to the dedicated temp article

2025-12-12T13:41:57Z

Move harmony-related contents to the dedicated temp article

← Older revision		Revision as of 13:41, 12 December 2025
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	The head of the starling family is starling, which tempers out 126/125. Starling has a normal generator list of {2, 3, 5}; hence a [[5-limit]] scale can be converted to starling simply by tempering it. One way to do that, and an excellent starling tuning, is given by [[77edo]]. Other possible tunings are [[108edo]] and [[185edo]], and [[135edo]] in the nonpatent 135c val {{val\| 135 214 '''314''' 379 }}.		The head of the starling family is starling, which tempers out 126/125. Starling has a normal generator list of {2, 3, 5}; hence a [[5-limit]] scale can be converted to starling simply by tempering it. One way to do that, and an excellent starling tuning, is given by [[77edo]]. Other possible tunings are [[108edo]] and [[185edo]], and [[135edo]] in the nonpatent 135c val {{val\| 135 214 '''314''' 379 }}.

	In starling, (6/5)<sup>3</sup> = (126/125)⋅(12/7), and minor thirds and major sixths are low-complexity intervals. A suitable 5-limit scale to temper via starling will be one where there are chains of minor thirds. Starling has a 6/5, 6/5, 6/5, 7/6 versions of the [[diminished seventh chord]], which is very characteristic of it. Since this is a chord of [[meantone]] in wide use in Western {{w\|common practice}} harmony long before [[12edo]] established itself as the standard tuning, it is arguably more authentic to tune it as three stacked minor thirds and an augmented second, which is what it is in meantone, than as the modern version of four stacked very flat minor thirds.

	Because no appreciable tuning accuracy is lost by including [[1029/1024]] along with 126/125 in the comma list, which leads to [[valentine]], there is a close relationship between the two. Even if tempering a 5-limit scale, one can assume valentine tempering.		Because no appreciable tuning accuracy is lost by including [[1029/1024]] along with 126/125 in the comma list, which leads to [[valentine]], there is a close relationship between the two. Even if tempering a 5-limit scale, one can assume valentine tempering.

FloraC: Proper intro

2025-12-12T13:35:05Z

Proper intro

← Older revision		Revision as of 13:35, 12 December 2025
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	{{Technical data page}}		{{Technical data page}}
	The head of the '''starling family''' is starling, which tempers out [[126/125]], the starling comma or septimal semicomma. Starling has a normal list basis of [2, 3, 5]; hence a 5-limit scale can be converted to starling simply by tempering it. One way to do that, and an excellent starling tuning, is given by [[77edo]]. Other possible tunings are [[108edo]] and [[185edo]], and the nonpatent [[135edo]] val {{val\| 135 214 314 379 }} (135c).

	In starling, (~~6/5)<sup>3</sup> =~~ 126/125 ~~× 12/7~~, ~~and minor thirds/major sixths are low complexity intervals. A suitable 5~~-limit scale to temper via starling will be one where there are chains of minor thirds. Starling has a 6/5-6/5-6/5-7/6 versions of the diminished seventh chord which is very characteristic of it. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, ~~it is arguably more authentic to tune it~~ as ~~three stacked minor thirds and an augmented second, which is what it is in meantone, than as the modern version of four stacked very flat minor thirds~~.		The '''starling family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[starling comma]] ([[ratio]]: 126/125, {{monzo\|legend=1\| 1 2 -3 1 }}), also known as ''septimal semicomma''.

	Because no appreciable tuning accuracy is lost by including [[1029/1024]] along with 126/125 in the comma list, which leads to [[valentine]], there is a close relationship between the two. Even if tempering a 5-limit scale, one can assume valentine tempering.		== Starling ==
			{{Main\| Starling and thrush }}

	~~Temperaments discussed elsewhere include~~		The head of the starling family is starling, which tempers out 126/125. Starling has a normal generator list of {2, 3, 5}; hence a [[5-limit]] scale can be converted to starling simply by tempering it. One way to do that, and an excellent starling tuning, is given by [[77edo]]. Other possible tunings are [[108edo]] and [[185edo]], and [[135edo]] in the nonpatent 135c val {{val\| 135 214 '''314''' 379 }}.
	* ''[[~~Erato~~]]~~'' (+81/80) →~~ [[~~Didymus rank-3 family #Erato\|Didymus rank-3 family~~]]
	* ''[[~~Sensigh~~]]~~'' (+245/243) →~~ [[~~Sensamagic family #Sensigh\|Sensamagic family~~]]
	* ''[[~~Oxpecker~~]]'' ~~(+121/120) → [[Biyatismic clan #Oxpecker\|Biyatismic clan]]~~
	* ''~~[[Cuckoo]]~~'' ~~(+243/242) → [[Rastmic rank-3 clan #Cuckoo\|Rastmic rank-3 clan]]~~

	~~Considered below~~ are starling, ~~thrush~~, ~~thrasher~~, ~~aplonis~~, and ~~treecreeper~~.		In starling, (6/5)<sup>3</sup> = (126/125)⋅(12/7), and minor thirds and major sixths are low-complexity intervals. A suitable 5-limit scale to temper via starling will be one where there are chains of minor thirds. Starling has a 6/5, 6/5, 6/5, 7/6 versions of the [[diminished seventh chord]], which is very characteristic of it. Since this is a chord of [[meantone]] in wide use in Western {{w\|common practice}} harmony long before [[12edo]] established itself as the standard tuning, it is arguably more authentic to tune it as three stacked minor thirds and an augmented second, which is what it is in meantone, than as the modern version of four stacked very flat minor thirds.

	~~== Starling ==~~		Because no appreciable tuning accuracy is lost by including [[1029/1024]] along with 126/125 in the comma list, which leads to [[valentine]], there is a close relationship between the two. Even if tempering a 5-limit scale, one can assume valentine tempering.
	~~{{Main\| Starling and thrush }}~~

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	* 34: 15625/15552, 2048/2025		* 34: 15625/15552, 2048/2025
	}}		}}

			=== Overview to extensions ===
			Temperaments discussed elsewhere include
			* ''[[Erato]]'' (+81/80) → [[Didymus rank-3 family #Erato\|Didymus rank-3 family]]
			* ''[[Sensigh]]'' (+245/243) → [[Sensamagic family #Sensigh\|Sensamagic family]]
			* ''[[Oxpecker]]'' (+121/120) → [[Biyatismic clan #Oxpecker\|Biyatismic clan]]
			* ''[[Cuckoo]]'' (+243/242) → [[Rastmic rank-3 clan #Cuckoo\|Rastmic rank-3 clan]]

			Considered below are starling, thrush, thrasher, aplonis, and treecreeper.

	== Undecimal starling ==		== Undecimal starling ==

FloraC: Units & misc. cleanup

2025-12-12T13:02:57Z

Units & misc. cleanup

Show changes

FloraC: Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

2025-11-27T12:17:15Z

Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

← Older revision		Revision as of 12:17, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Starling family\| ]] <!-- main article -->		[[Category:Starling family\| ]] <!-- main article -->
	[[Category:Starling\| ]] <!-- key article -->		[[Category:Starling\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: /* Thrush */ distinguish

2025-09-10T14:30:42Z

Thrush: distinguish

← Older revision		Revision as of 14:30, 10 September 2025
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	=== Bluebird ===		=== Bluebird ===
			{{Distinguish\| Bluebirds }}

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13