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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 <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.

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

7-limit starling

Comma c = 126/125

7- and 9-limit minimax: 3 and 7 just, 5 1/3c sharp
[<1 0 0 0|, <0 1 0 0|, <1/3 2/3 0 1/3|, <0 0 0 1|]
Eigenmonzos: 2, 8/7, 4/3

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

Map: [<1 0 0 -5|, <0 1 0 2|, <0 0 1 2|]
Generators: 2, 3, 5
EDOs: 12, 15, 16, 19, 27, 31, 34, 43, 46, 50, 58, 65, 77, 108, 166c, 185, 243c
Badness: 0.0000699

Projection pair: 7 125/18

Scales: starling7, starling8, starling9, starling11, starling12, starling15, starling16, starling17, starling19
Music: A Seed Planted by Jake Freivald. The melody depends on tempering out 126/125.

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

11-limit

Commas: 126/125, 385/384

Map: [<1 0 0 -1 8|, <0 1 0 -2 3|, <0 0 1 3 -4]]
Generators: 2, 3, 5
EDOs: 15, 19, 27, 31, 46, 77, 96d, 127d, 173d, 204de, 300de
Badness: .000677

Thrush

Commas: 126/125, 176/175
Associated linear temperament: myna

7 and 9 limit minimax
[|1 0 0 0 0>, |0 1 0 0 0>, |1/3 2/3 0 1/3 0>,
|0 0 0 1 0>, |-10/3 4/3 0 5/3 0>]
Eigenmonzos: 2, 7/6, 4/3

Lattice basis 5/4 length 0.8576 6/5 length 0.9314
Angle(5/4, 6/5) = 74.6239 degrees
Map to lattice: [<0 1 1 1 3|, <0 1 0 -2 -2|]

Map: [<1 0 0 -1 -5|, <0 1 0 -2 -2|, <0 0 1 3 5|]
Generators: 2, 3, 5
EDOs: 12, 15, 31, 46, 58, 89, 135c, 224c
Badness: 0.000353

Projection pairs: 7 125/18 11 3125/288

Scales: thrush12

13-limit

Commas: 126/125, 176/175, 196/195

Map: [<1 0 0 -1 -5 0|, <0 1 0 -2 -2 -5|, <0 0 1 3 5 5|]
EDOs: 31, 46, 58, 89f, 104c, 135c, 193cf, 239cf, 328cf
Badness: 0.000677

Bluebird

Commas 126/125, 176/175, 144/143

Map: [<1 0 0 -1 -5 9|, <0 1 0 -2 -2 4|, <0 0 1 3 5 -5|]
EDOs: 12, 15, 31, 43, 48c, 58, 147cf, 205cef
Badness: 0.000915

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

Nightingale

Commas: 126/125, 176/175, 66/65

Map: [<1 0 0 -1 -5 -4|, <0 1 0 -2 -2 -1|, <0 0 1 3 5 4|]
EDOs: 15, 19f, 21e, 22f, 28, 31, 46, 58, 89, 108ef
Badness: 0.000837

Veery

Commas: 91/90, 126/125, 176/175

Map: [<1 0 0 -1 -5 2|, <0 1 0 -2 -2 4|, <0 0 1 3 5 -2|]
EDOs: 12, 15, 46
Badness: 0.000991

Thrasher

Commas: 56/55, 100/99

11-limit minimax
[|1 0 0 0 0>, |1 3/4 0 1/4 -3/8>,
|1 1/2 0 1/2 -1/4>, |0 0 0 1 0>,
|2 -1/2 0 1/2 1/4>]
Eigenmonzos: 2, 8/7, 11/9

Lattice basis: 6/5 length 0.9089 5/4 length 1.2007
Angle(6/5, 5/4) = 98.8447
Map to lattice: [<0 1 0 -2 -2|, <0 1 1 1 0|]

Map: [<1 0 0 -1 2|, <0 1 0 -2 -2|, <0 0 1 3 2|]
Generators: 2, 3, 5
EDOs: 12, 15, 19, 27e, 34, 46e, 58e, 61e, 73e
Badness: 0.000480

13-limit

Commas: 126/125, 100/99, 91/90

Map: [<1 0 0 -1 2 2|, <0 1 0 -2 -2 4|, <0 0 1 3 2 -2|]
EDOs: 12, 15, 18, 25e, 27e, 34, 46e, 51ce, 61e
Badness: 0.000876

Mockingbird

Commas: 126/125, 100/99, 40/39

Map: [<1 0 0 -1 2 3|, <0 1 0 -2 -2 -1|, <0 0 1 3 2 1|]
EDOs: 12f, 15, 27ef
Badness: 0.000859

Catbird

Commas: 126/125, 100/99, 78/77

Map: [<1 0 0 -1 2 0|, <0 1 0 -2 -2 -5|, <0 0 1 3 2 5|]
EDOs: 12, 15, 17c, 19, 22ef, 27e, 34, 58e
Badness: 0.000905

Aplonis

Commas: 126/125, 540/539

Map: [<1 0 0 -1 4|, <0 1 0 -2 7|, <0 0 1 3 -5|]
EDOs: 19, 31, 58, 67, 89, 197c, 286ce, 375ce
Badness: 0.000648

13-limit

Commas: 126/125, 144/143, 196/195

Map: [<1 0 0 -1 4 0|, <0 1 0 -2 7 -5|, <0 0 1 3 -5 5|]
EDOs: 19, 31, 41, 43, 50, 58, 89f, 125ce, 135ce, 147cf, 166cef, 224cef
Badness: 0.000821

Oxpecker

Commas: 121/120, 126/125

Map: [<1 0 1 2 2|, <0 1 1 1 1|, <0 0 -2 -6 -1|]
EDOs: 8d, 15, 31, 46, 77, 185e, 262cde
Badness: 0.000699

Woodpecker

Commas: 66/65, 121/120, 126/125

Map: [<1 0 1 2 2 2|, <0 1 1 1 1 1|, <0 0 -2 -6 -1 -1|]
EDOs: 15, 31, 46f, 70f, 101f
Badness: 0.001093

Treecreeper

Commas: 126/125, 1232/1215

Map: [<1 0 0 -1 -3|, <0 1 0 -2 7|, <0 0 1 3 -2|]
EDOs: 34, 46, 119c, 165c
Badness: 0.001585

13-limit

Commas: 91/90, 126/125, 352/351

Map: [<1 0 0 -1 -3 2|, <0 1 0 -2 7 4|, <0 0 1 3 -2 -2|]
EDOs: 34, 46, 172cd, 218cdf, 264bcdf, 310bcdf
Badness: 0.001588

Cuckoo

Commas: 126/125, 243/242

Map: [<1 1 0 -3 2|, <0 2 0 -4 5|, <0 0 1 3 0|]
EDOs: 31 34 58 65 89 154 185 216
Badness: 0.000933

13-limit

Commas: 126/125, 196/195, 243/242

Map: [<1 1 0 -3 2 -5|, <0 2 0 -4 5 -10|, <0 0 1 3 0 5|]
EDOs: 31 58 65f 89f 92e 154 185 216f