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{{Technical data page}}
The head of the starling [[family|family]] is starling, which tempers out [[126/125|126/125]], the [[starling_comma|starling comma]] or [[septimal_semicomma|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|77edo]]. Other possible tunings are [[108edo|108edo]] and [[185edo|185edo]], and the nonpatent [[135edo|135edo]] val <135 214 314 379|.


In starling, (6/5)^3 = 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 [[Starling_temperaments|valentine temperament]], 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 }}


=7-limit starling=
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 }}.
[[Comma|Comma]] c = 126/125


7- and 9-limit minimax: 3 and 7 just, 5 1/3c sharp
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.


[<1 0 0 0|, <0 1 0 0|, <1/3 2/3 0 1/3|, <0 0 0 1|]
[[Subgroup]]: 2.3.5.7


Eigenmonzos: 2, 8/7, 4/3
[[Comma list]]: [[126/125]]


Minkowski lattice basis: 6/5 length 1.068, 5/4 length 1.206
{{Mapping|legend=1| 1 0 0 -1 | 0 1 0 -2 | 0 0 1 3 }}
: mapping generators: ~2, ~3, ~5


Angle(6/5, 5/4) = 100.364 degrees
[[Mapping to lattice]]: [{{val| 0 1 0 -2 }}, {{val| 0 1 1 1 }}]


Map to lattice: [<0 1 0 -2|, <0 1 1 1|]
[[Minkowski lattice basis]]:  
: ~6/5 length = 1.068, ~5/4 length = 1.206
: angle (~6/5, ~5/4) = 100.364°


Map: [<1 0 0 -5|, <0 1 0 2|, <0 0 1 2|]
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.7931{{c}}, ~3/2 = 701.1306{{c}}, ~5/4 = 390.0298{{c}}
: [[error map]]: {{val| -0.207 -1.031 +3.302 -1.618 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.0811{{c}}, ~5/4 = 389.8833{{c}}
: error map: {{val| 0.000 -0.874 +3.570 -1.338 }}


Generators: 2, 3, 5
[[Minimax tuning]]:
* 7- and [[9-odd-limit]]: 3 and 7 just, 5 1/3-comma sharp
: {{monzo list| 1 0 0 0 | 0 1 0 0 | 1/3 2/3 0 1/3 | 0 0 0 1 }}
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7


[[EDO|EDOs]]: 12, 15, 16, 19, 27, 31, 34, 43, 46, 50, 58, 65, [[77edo|77]], [[108edo|108]], [[166edo|166c]], [[185edo|185]], [[243edo|243c]]
{{Optimal ET sequence|legend=1| 7d, 8d, 12, 19, 27, 31, 46, 58, 77, 135c, 166c }}


Badness: 0.0000699
[[Badness]] (Sintel): 0.308


[[Projection_pair|Projection pair]]: 7 125/18
[[Projection pair]]: <code>7 125/18</code>


Scales: [[starling7|starling7]], [[starling8|starling8]], [[starling9|starling9]], [[starling11|starling11]], [[starling12|starling12]], [[starling15|starling15]], [[starling16|starling16]], [[starling17|starling17]], [[starling19|starling19]]
{{Databox|[[Minkowski blocks]]|
* 7: 25/24, 81/80
* 8: 16/15, 648/625
* 9: 27/25, 128/125
* 11: 16/15, 15625/15552
* 12: 128/125, 628/625
* 15: 128/125, 250/243
* 16: 648/625, 3125/3072
* 17: 25/24, 20480/19683
* 19: 81/80, 3125/3072
* 27: 128/125, 78732/78125
* 28: 648/625, 16875/16384
* 31: 81/80, 1990656/1953125
* 34: 15625/15552, 2048/2025
}}


Music: [https://soundcloud.com/jdfreivald/a-seed-planted-starling-pure A Seed Planted] by Jake Freivald. The melody depends on tempering out 126/125.
=== Overview to extensions ===
Temperaments discussed elsewhere include
* ''[[Erato]]'' (+81/80) → [[Didymus rank-3 family #Erato|Didymus rank-3 family]]
* ''[[Sensigh]]'' (+245/243) → [[Sengic family #Sensigh|Sengic family]]
* ''[[Oxpecker]]'' (+121/120) → [[Biyatismic clan #Oxpecker|Biyatismic clan]]
* ''[[Cuckoo]]'' (+243/242) → [[Rastmic rank-3 clan #Cuckoo|Rastmic rank-3 clan]]


==[[Minkowski_blocks|Minkowski blocks]]==
Considered below are thrush, starnova, thrasher, aplonis, and treecreeper.
7: 25/24, 81/80


8: 16/15, 648/625
== Thrush ==
{{Main| Starling and thrush }}


9: 27/25, 128/125
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]].


11: 16/15, 15625/15552
[[Subgroup]]: 2.3.5.7.11


12: 128/125, 628/625
[[Comma list]]: 126/125, 176/175


15: 128/125, 250/243
{{Mapping|legend=1| 1 0 0 -1 -5 | 0 1 0 -2 -2 | 0 0 1 3 5 }}


16: 648/625, 3125/3072
Mapping to lattice: [{{val| 0 1 1 1 3 }}, {{val| 0 1 0 -2 -2 }}]


17: 25/24, 20480/19683
Lattice basis:  
: ~5/4 length = 0.8576, ~6/5 length = 0.9314
: angle(~5/4, ~6/5) = 74.6239°


19: 81/80, 3125/3072
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.4742{{c}}, ~3/2 = 701.6379{{c}}, ~5/4 = 391.0192{{c}}
: [[error map]]: {{val| -0.526 -0.843 +3.654 -0.621 -1.075 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.6298{{c}}, ~5/4 = 390.8558{{c}}
: error map: {{val| 0.000 -0.325 +4.542 +0.482 -0.298 }}


27: 128/125, 78732/78125
[[Minimax tuning]]:  
* 7- and [[9-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 1/3 2/3 0 1/3 0 }}, {{monzo| 0 0 0 1 0 }}, {{monzo| -10/3 4/3 0 5/3 0 }}]
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7


28: 648/625, 16875/16384
{{Optimal ET sequence|legend=1| 12, 15, 19e, 27e, 31, 46, 58, 89, 135c, 193c, 224c }}


31: 81/80, 1990656/1953125
[[Badness]] (Sintel): 0.424


34: 15625/15552, 2048/2025
[[Projection pair]]s: <code>7 125/18</code> <code>11 3125/288</code>


==11-limit==
=== 13-limit ===
Commas: 126/125, 385/384
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 0 0 -1 8|, &lt;0 1 0 -2 3|, &lt;0 0 1 3 -4]]
Comma list: 126/125, 176/175, 196/195


Generators: 2, 3, 5
Mapping: {{mapping| 1 0 0 -1 -5 0 | 0 1 0 -2 -2 -5 | 0 0 1 3 5 5 }}


EDOs: 15, 19, 27, 31, 46, 77, 96d, 127d, 173d, 204de, 300de
Optimal tunings:  
* WE: ~2 = 1199.2727{{c}}, ~3/2 = 702.2858{{c}}, ~5/4 = 391.3567{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.4562{{c}}, ~5/4 = 391.2080{{c}}


Badness: .000677
{{Optimal ET sequence|legend=0| 12f, 19e, 27e, 31, 46, 58, 104c, 135c, 193cf }}


=Thrush=
Badness (Sintel): 0.633
[[Comma|Commas]]: 126/125, 176/175


Associated linear temperament: [[Starling_temperaments|myna]]
=== Bluebird ===
{{Distinguish| Bluebirds }}


7 and 9 limit minimax
Subgroup: 2.3.5.7.11.13


[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;, |1/3 2/3 0 1/3 0&gt;,
Comma list: 126/125, 144/143, 176/175
|0 0 0 1 0&gt;, |-10/3 4/3 0 5/3 0&gt;]


[[Eigenmonzo|Eigenmonzos]]: 2, 7/6, 4/3
Mapping: {{mapping| 1 0 0 -1 -5 9 | 0 1 0 -2 -2 4 | 0 0 1 3 5 -5 }}


Lattice basis 5/4 length 0.8576 6/5 length 0.9314
Optimal tunings:
* WE: ~2 = 1198.7153{{c}}, ~3/2 = 701.647{{c}}, ~5/4 = 391.9180{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.6263{{c}}, ~5/4 = 391.7786{{c}}


Angle(5/4, 6/5) = 74.6239 degrees
{{Optimal ET sequence|legend=0| 12, 15, 27e, 31, 43, 58, 205cceff, 263ccdeefff }}


Map to lattice: [&lt;0 1 1 1 3|, &lt;0 1 0 -2 -2|]
Badness (Sintel): 0.856


Map: [&lt;1 0 0 -1 -5|, &lt;0 1 0 -2 -2|, &lt;0 0 1 3 5|]
Projection pairs: <code>7 125/18</code> <code>11 3125/288</code> <code>13 41472/3125</code>


[[generator|Generators]]: 2, 3, 5
=== Nightingale ===
Subgroup: 2.3.5.7.11.13


EDOs: 12, 15, 31, 46, 58, 89, 135c, 224c
Comma list: 66/65, 126/125, 176/175


Badness: 0.000353
Mapping: {{mapping| 1 0 0 -1 -5 -4 | 0 1 0 -2 -2 -1 | 0 0 1 3 5 4 }}


Projection pairs: 7 125/18 11 3125/288
Optimal tunings:  
* WE: ~2 = 1200.1476{{c}}, ~3/2 = 699.2886{{c}}, ~5/4 = 388.2054{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.2840{{c}}, ~5/4 = 388.2437{{c}}


Scales: [[thrush12|thrush12]]
{{Optimal ET sequence|legend=0| 12f, 15, 19e, 27eff, 31 }}


==13-limit==
Badness (Sintel): 0.783
Commas: 126/125, 176/175, 196/195


Map: [&lt;1 0 0 -1 -5 0|, &lt;0 1 0 -2 -2 -5|, &lt;0 0 1 3 5 5|]
=== Veery ===
Subgroup: 2.3.5.7.11.13


EDOs: 31, 46, 58, 89f, 104c, 135c, 193cf, 239cf, 328cf
Comma list: 91/90, 126/125, 176/175


Badness: 0.000677
Mapping: {{mapping| 1 0 0 -1 -5 2 | 0 1 0 -2 -2 4 | 0 0 1 3 5 -2 }}


==Bluebird==
Optimal tunings:
Commas 126/125, 176/175, 144/143
* WE: ~2 = 1199.7998{{c}}, ~3/2 = 704.4117{{c}}, ~5/4 = 391.7571{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.3959{{c}}, ~5/4 = 391.6910{{c}}


Map: [&lt;1 0 0 -1 -5 9|, &lt;0 1 0 -2 -2 4|, &lt;0 0 1 3 5 -5|]
{{Optimal ET sequence|legend=0| 12, 15, 19e, 27e, 31f, 46 }}


EDOs: 12, 15, 31, 43, 48c, 58, 147cf, 205cef
Badness (Sintel): 0.927


Badness: 0.000915
== Starnova ==
Starnova tempers out [[385/384]]. This temperament used to be known as ''undecimal starling'', but was decanonicalized in 2026. The name ''starnova'' was proposed by [[Flora Canou]] after [[Gene Ward Smith]]'s [[Star]] and [[Nova]] scales.  


Projection pairs: 7 125/18 11 3125/288 13 41472/3125
[[Subgroup]]: 2.3.5.7.11


==Nightingale==
[[Comma list]]: 126/125, 385/384
Commas: 126/125, 176/175, 66/65


Map: [&lt;1 0 0 -1 -5 -4|, &lt;0 1 0 -2 -2 -1|, &lt;0 0 1 3 5 4|]
{{Mapping|legend=1| 1 0 0 -1 8 | 0 1 0 -2 3 | 0 0 1 3 -4 }}


[[EDO|EDOs]]: [[15edo|15]], [[19edo|19f]], [[21edo|21e]], [[22edo|22f]], [[28edo|28]], [[31edo|31]], [[46edo|46]], [[58edo|58]], [[89edo|89]], [[108edo|108ef]]
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.6133{{c}}, ~3/2 = 700.4314{{c}}, ~5/4 = 388.3236{{c}}
: [[error map]]: {{val| +0.613 -0.910 +3.237 -2.878 -1.478 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.4020{{c}}, ~5/4 = 388.3631{{c}}
: error map: {{val| 0.000 -1.553 +2.049 -4.541 -3.564 }}


Badness: 0.000837
{{Optimal ET sequence|legend=1| 12e, 15, 19, 27, 31, 46, 77, 96d, 127d, 173d, 204de }}


==Veery==
[[Badness]] (Sintel): 0.813
Commas: 91/90, 126/125, 176/175


Map: [&lt;1 0 0 -1 -5 2|, &lt;0 1 0 -2 -2 4|, &lt;0 0 1 3 5 -2|]
[[Projection pair]]s: <code>7 125/18</code> <code>11 6912/625</code>


EDOs: 12, 15, 46
Scales: [[Star and Nova]]


Badness: 0.000991
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


=Thrasher=
Comma list: 126/125, 196/195, 385/384
[[Comma|Commas]]: 56/55, 100/99


11-limit minimax
Mapping: {{mapping| 1 0 0 -1 8 0 | 0 1 0 -2 3 -5 | 0 0 1 3 -4 5 }}


[|1 0 0 0 0&gt;, |1 3/4 0 1/4 -3/8&gt;,
Optimal tunings:
|1 1/2 0 1/2 -1/4&gt;, |0 0 0 1 0&gt;,
* WE: ~2 = 1200.5083{{c}}, ~3/2 = 700.7452{{c}}, ~5/4 = 388.4655{{c}}
|2 -1/2 0 1/2 1/4&gt;]
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.5708{{c}}, ~5/4 = 388.4346{{c}}


[[Eigenmonzo|Eigenmonzos]]: 2, 8/7, 11/9
{{Optimal ET sequence|legend=0| 15f, 19, 27, 31, 46, 77, 96d }}


Lattice basis: 6/5 length 0.9089 5/4 length 1.2007
Badness (Sintel): 1.07


Angle(6/5, 5/4) = 98.8447
== Thrasher ==
{{See also| Ptolemismic clan }}


Map to lattice: [&lt;0 1 0 -2 -2|, &lt;0 1 1 1 0|]
[[Subgroup]]: 2.3.5.7.11


Map: [&lt;1 0 0 -1 2|, &lt;0 1 0 -2 -2|, &lt;0 0 1 3 2|]
[[Comma list]]: 56/55, 100/99


[[generator|Generators]]: 2, 3, 5
{{Mapping|legend=1| 1 0 0 -1 2 | 0 1 0 -2 -2 | 0 0 1 3 2 }}


EDOs: 12, 15, 19, 27e, 34, 46e, 58e, 61e, 73e
Mapping to lattice: [{{val| 0 1 0 -2 -2 }}, {{val| 0 1 1 1 0 }}]


Badness: 0.000480
Lattice basis:  
: ~6/5 length = 0.9089, ~5/4 length = 1.2007
: angle (~6/5, ~5/4) = 98.8447°


==13-limit==
[[Optimal tuning]]s:
Commas: 126/125, 100/99, 91/90
* [[WE]]: ~2 = 1196.9183{{c}}, ~3/2 = 706.1793{{c}}, ~5/4 = 394.5223{{c}}
: [[error map]]: {{val| -3.082 +1.143 +2.045 -6.863 +13.041 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 706.2523{{c}}, ~5/4 = 392.7970{{c}}
: error map: {{val| 0.000 +4.297 +6.483 -2.940 +21.771 }}


Map: [&lt;1 0 0 -1 2 2|, &lt;0 1 0 -2 -2 4|, &lt;0 0 1 3 2 -2|]
[[Minimax tuning]]:
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 1 3/4 0 1/4 -3/8 }}, {{monzo| 1 1/2 0 1/2 -1/4 }}, {{monzo| 0 0 0 1 0 }}, {{monzo| 2 -1/2 0 1/2 1/4 }}]
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7.11/9


EDOs: 12, 15, 18, 25e, 27e, 34, 46e, 51ce, 61e
{{Optimal ET sequence|legend=1| 7d, 8d, 12, 15, 19, 27e }} *


Badness: 0.000876
<nowiki>*</nowiki> [[optimal patent val]]: [[34edo|34]]


==Mockingbird==
[[Badness]] (Sintel): 0.577
Commas: 126/125, 100/99, 40/39


Map: [&lt;1 0 0 -1 2 3|, &lt;0 1 0 -2 -2 -1|, &lt;0 0 1 3 2 1|]
Scales: [[Thrasher chromatic]], [[Thrasher diatonic]]


EDOs: 12f, 15, 27ef
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Badness: 0.000859
Comma list: 56/55, 91/90, 100/99


==Catbird==
Mapping: {{mapping| 1 0 0 -1 2 2 | 0 1 0 -2 -2 4 | 0 0 1 3 2 -2 }}
Commas: 126/125, 100/99, 78/77


Map: [&lt;1 0 0 -1 2 0|, &lt;0 1 0 -2 -2 -5|, &lt;0 0 1 3 2 5|]
Optimal tunings:  
* WE: ~2 = 1197.4723{{c}}, ~3/2 = 707.3847{{c}}, ~5/4 = 394.2040{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 707.1440{{c}}, ~5/4 = 392.7909{{c}}


[[EDO|EDOs]]: [[12edo|12]], [[15edo|15]], [[17edo|17c]], [[19edo|19]], [[22edo|22ef]], [[27edo|27e]], [[34edo|34]], [[58edo|58e]]
{{Optimal ET sequence|legend=0| 7d, 8d, 12, 15, 19, 27e, 69bceef }} *


Badness: 0.000905
<nowiki>*</nowiki> optimal patent val: [[34edo|34]]


=Aplonis=
Badness (Sintel): 0.820
Commas: 126/125, 540/539


Map: [&lt;1 0 0 -1 4|, &lt;0 1 0 -2 7|, &lt;0 0 1 3 -5|]
=== Mockingbird ===
Subgroup: 2.3.5.7.11.13


EDOs: 19, 31, 58, 67, 89, 197c, 286ce, 375ce
Comma list: 40/39, 56/55, 100/99


Badness: 0.000648
Mapping: {{mapping| 1 0 0 -1 2 3 | 0 1 0 -2 -2 -1 | 0 0 1 3 2 1 }}


==13-limit==
Optimal tunings:
Commas: 126/125, 144/143, 196/195
* WE: ~2 = 1193.3128{{c}}, ~3/2 = 710.0779{{c}}, ~5/4 = 400.7221{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 711.2922{{c}}, ~5/4 = 398.0867{{c}}


Map: [&lt;1 0 0 -1 4 0|, &lt;0 1 0 -2 7 -5|, &lt;0 0 1 3 -5 5|]
{{Optimal ET sequence|legend=0| 7d, 8d, 12f, 15, 27eff }}


EDOs: 19, 31, 41, 43, 50, 58, 89f, 125ce, 135ce, 147cf, 166cef, 224cef
Badness (Sintel): 0.804


Badness: 0.000821
=== Catbird ===
Subgroup: 2.3.5.7.11.13


=Oxpecker=
Comma list: 56/55, 78/77, 100/99
Commas: 121/120, 126/125


Map: [&lt;1 0 1 2 2|, &lt;0 1 1 1 1|, &lt;0 0 -2 -6 -1|]
Mapping: {{mapping| 1 0 0 -1 2 0 | 0 1 0 -2 -2 -5 | 0 0 1 3 2 5 }}


EDOs: 8d, 15, 31, 46, 77, 185e, 262cde
Optimal tunings:  
* WE: ~2 = 1196.8488{{c}}, ~3/2 = 704.8749{{c}}, ~5/4 = 394.9837{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.9205{{c}}, ~5/4 = 393.2290{{c}}


Badness: 0.000699
{{Optimal ET sequence|legend=0| 7df, 8d, 12f, 19, 27e, 66cdeeef }}


==Woodpecker==
Badness (Sintel): 0.846
Commas: 66/65, 121/120, 126/125


Map: [&lt;1 0 1 2 2 2|, &lt;0 1 1 1 1 1|, &lt;0 0 -2 -6 -1 -1|]
== Aplonis ==
[[Subgroup]]: 2.3.5.7.11


EDOs: 15, 31, 46f, 70f, 101f
[[Comma list]]: 126/125, 540/539


Badness: 0.001093
{{Mapping|legend=1| 1 0 0 -1 4 | 0 1 0 -2 7 | 0 0 1 3 -5 }}


=Treecreeper=
[[Optimal tuning]]s:
Commas: 126/125, 1232/1215
* [[WE]]: ~2 = 1199.6006{{c}}, ~3/2 = 700.5746{{c}}, ~5/4 = 390.2558{{c}}
: [[error map]]: {{val| -0.399 -1.780 +3.143 -0.406 +1.026 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.4342{{c}}, ~5/4 = 389.9796{{c}}
: error map: {{val| 0.000 -1.521 +3.666 +0.244 +1.824 }}


Map: [&lt;1 0 0 -1 -3|, &lt;0 1 0 -2 7|, &lt;0 0 1 3 -2|]
{{Optimal ET sequence|legend=1| 12e, 19, 27e, 31, 58, 89, 197c, 228c }}


EDOs: 34, 46, 119c, 165c
[[Badness]] (Sintel): 0.778


Badness: 0.001585
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


==13-limit==
Comma list: 126/125, 144/143, 196/195
Commas: 91/90, 126/125, 352/351


Map: [&lt;1 0 0 -1 -3 2|, &lt;0 1 0 -2 7 4|, &lt;0 0 1 3 -2 -2|]
Mapping: {{mapping| 1 0 0 -1 4 0 | 0 1 0 -2 7 -5 | 0 0 1 3 -5 5 }}


EDOs: 34, 46, 172cd, 218cdf, 264bcdf, 310bcdf
Optimal tunings:  
* WE: ~2 = 1199.0609{{c}}, ~3/2 = 701.2333{{c}}, ~5/4 = 390.8385{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.0203{{c}}, ~5/4 = 390.2413{{c}}


Badness: 0.001588
{{Optimal ET sequence|legend=0| 8d, 19, 27e, 31, 50, 58, 166cef, 224ceeff }}


=Cuckoo=
Badness (Sintel): 0.768
Commas: 126/125, 243/242


Map: [&lt;1 1 0 -3 2|, &lt;0 2 0 -4 5|, &lt;0 0 1 3 0|]
== Treecreeper ==
[[Subgroup]]: 2.3.5.7.11


EDOs: 31 34 58 65 89 154 185 216
[[Comma list]]: 126/125, 1232/1215


Badness: 0.000933
{{Mapping|legend=1| 1 0 0 -1 -3 | 0 1 0 -2 7 | 0 0 1 3 -2 }}


==13-limit==
[[Optimal tuning]]s:
Commas: 126/125, 196/195, 243/242
* [[WE]]: ~2 = 1198.8957{{c}}, ~3/2 = 704.9055{{c}}, ~5/4 = 392.8725{{c}}
: [[error map]]: {{val| -1.104 +1.846 +4.350 -3.332 -2.725 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 705.0045{{c}}, ~5/4 = 392.3159{{c}}
: error map: {{val| 0.000 +3.050 +6.002 -1.887 -0.918 }}


Map: [&lt;1 1 0 -3 2 -5|, &lt;0 2 0 -4 5 -10|, &lt;0 0 1 3 0 5|]
{{Optimal ET sequence|legend=1| 7d, 12e, 19e, 27e, 39d, 46, 119c }}


EDOs: 31 58 65f 89f 92e 154 185 216f
[[Badness]] (Sintel): 1.91
[[Category:bluebird]]
 
[[Category:catbird]]
=== 13-limit ===
[[Category:family]]
Subgroup: 2.3.5.7.11.13
[[Category:index]]
 
[[Category:list]]
Comma list: 91/90, 126/125, 352/351
[[Category:listen]]
 
[[Category:mockingbird]]
Mapping: {{mapping| 1 0 0 -1 -3 2 | 0 1 0 -2 7 4 | 0 0 1 3 -2 -2 }}
[[Category:nightingale]]
 
[[Category:overview]]
Optimal tunings:  
[[Category:planar]]
* WE: ~2 = 1199.7878{{c}}, ~3/2 = 704.6703{{c}}, ~5/4 = 391.3513{{c}}
[[Category:sound_example]]
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.7011{{c}}, ~5/4 = 391.2846{{c}}
[[Category:starling]]
 
[[Category:theory]]
{{Optimal ET sequence|legend=0| 7d, 12e, 19e, 27e, 46 }}
[[Category:thrasher]]
 
[[Category:thrush]]
Badness (Sintel): 1.48
 
[[Category:Starling family| ]] <!-- main article -->
[[Category:Temperament families]]
[[Category:Catalogs of rank-3 temperaments]]
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