Starling family: Difference between revisions

Revision as of 09:13, 8 June 2021

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.

Starling

Subgroup: 2.3.5.7

Comma list: 126/125

Mapping: [<1 0 0 -5|, <0 1 0 2|, <0 0 1 2|]

Mapping generators: ~2, ~3, ~5

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 degrees

Minimax tuning:

7- and 9-odd-limit: 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

Template:Val list

Badness: 0.0699 × 10^-3

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

Undecimal starling

Subgroup: 2.3.5.7.11

Comma list: 126/125, 385/384

Mapping: [<1 0 0 -1 8|, <0 1 0 -2 3|, <0 0 1 3 -4]]

Mapping generators: ~2, ~3, ~5

Template:Val list

Badness: 0.677 × 10^-3

Thrush

Subgroup: 2.3.5.7.11

Comma list: 126/125, 176/175

Mapping: [<1 0 0 -1 -5|, <0 1 0 -2 -2|, <0 0 1 3 5|]

Mapping generators: ~2, ~3, ~5

Minimax tuning:

7- and 9-odd-limit

[|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

Map to lattice: [<0 1 1 1 3|, <0 1 0 -2 -2|]

Lattice basis:

5/4 length = 0.8576, 6/5 length = 0.9314

Angle(5/4, 6/5) = 74.6239 degrees

Template:Val list

Badness: 0.353 × 10^-3

Projection pairs: 7 125/18 11 3125/288

Associated temperament: myna

Scales: thrush12

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 176/175, 196/195

Mapping: [<1 0 0 -1 -5 0|, <0 1 0 -2 -2 -5|, <0 0 1 3 5 5|]

Vals: Template:Val list

Badness: 0.677 × 10^-3

Bluebird

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 176/175, 144/143

Mapping: [<1 0 0 -1 -5 9|, <0 1 0 -2 -2 4|, <0 0 1 3 5 -5|]

Vals: Template:Val list

Badness: 0.915 × 10^-3

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

Nightingale

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 176/175, 66/65

Mapping: [<1 0 0 -1 -5 -4|, <0 1 0 -2 -2 -1|, <0 0 1 3 5 4|]

Vals: Template:Val list

Badness: 0.837 × 10^-3

Veery

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 126/125, 176/175

Mapping: [<1 0 0 -1 -5 2|, <0 1 0 -2 -2 4|, <0 0 1 3 5 -2|]

Vals: Template:Val list

Badness: 0.991 × 10^-3

Thrasher

Subgroup: 2.3.5.7.11

Comma list: 56/55, 100/99

Mapping: [<1 0 0 -1 2|, <0 1 0 -2 -2|, <0 0 1 3 2|]

Mapping generators: ~2, ~3, ~5

Map to lattice: [<0 1 0 -2 -2|, <0 1 1 1 0|]

Lattice basis:

6/5 length = 0.9089, 5/4 length = 1.2007

Angle (6/5, 5/4) = 98.8447

Minimax tuning:

11-odd-limit

Comma list: 126/125, 243/242

Mapping: [<1 1 0 -3 2|, <0 2 0 -4 5|, <0 0 1 3 0|]

Template:Val list

Badness: 0.933 × 10^-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 196/195, 243/242

Mapping: [<1 1 0 -3 2 -5|, <0 2 0 -4 5 -10|, <0 0 1 3 0 5|]

Vals: Template:Val list

Starling family: Difference between revisions

Revision as of 09:13, 8 June 2021

Contents

Starling

Undecimal starling

Thrush

13-limit

Bluebird

Nightingale

Veery

Thrasher

13-limit

Mockingbird

Catbird

Aplonis

13-limit

Oxpecker

Woodpecker

Treecreeper

13-limit

Cuckoo

13-limit

Navigation menu

@@ Line 1: / Line 1: @@
-__FORCETOC__
 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 }}.
@@ Line 7: / Line 6: @@
 == Starling  ==
-[[Comma]] c = 126/125
+Subgroup: 2.3.5.7
-- and 9-limit minimax: 3 and 7 just, 5 1/3c sharp
+[[Comma list]]: [[126/125]]
-[&lt;1 0 0 0|, &lt;0 1 0 0|, &lt;1/3 2/3 0 1/3|, &lt;0 0 0 1|]
+[[Mapping]]: [&lt;1 0 0 -5|, &lt;0 1 0 2|, &lt;0 0 1 2|]
-Eigenmonzos: 2, 8/7, 4/3
+Mapping generators: ~2, ~3, ~5
-Minkowski lattice basis: 6/5 length 1.068, 5/4 length 1.206
-Angle(6/5, 5/4) = 100.364 degrees
 Map to lattice: [&lt;0 1 0 -2|, &lt;0 1 1 1|]
-Map: [&lt;1 0 0 -5|, &lt;0 1 0 2|, &lt;0 0 1 2|]
+Minkowski lattice basis:
+: 6/5 length = 1.068, 5/4 length = 1.206
+: Angle (6/5, 5/4) = 100.364 degrees
-Generators: 2, 3, 5
+[[Minimax tuning]]:
+* 7- and [[9-odd-limit]]: 3 and 7 just, 5 1/3c sharp
+: [&lt;1 0 0 0|, &lt;0 1 0 0|, &lt;1/3 2/3 0 1/3|, &lt;0 0 0 1|]
+: Eigenmonzos: 2, 8/7, 4/3
-[[EDO|EDOs]]: 12, 15, 16, 19, 27, 31, 34, 43, 46, 50, 58, 65, [[77edo|77]], [[108edo|108]], [[166edo|166c]], [[185edo|185]], [[243edo|243c]]
+{{Val list|legend=1| 12, 15, 16, 19, 27, 31, 34, 43, 46, 50, 58, 65, 77, 108, 166c, 185, 243c }}
-Badness: 0.0000699
+[[Badness]]: 0.0699 × 10<sup>-3</sup>
 [[Projection pair]]: 7 125/18
@@ Line 33: / Line 33: @@
 Scales: [[starling7]], [[starling8]], [[starling9]], [[starling11]], [[starling12]], [[starling15]], [[starling16]], [[starling17]], [[starling19]]
-Music: [https://soundcloud.com/jdfreivald/a-seed-planted-starling-pure A Seed Planted] by Jake Freivald. The melody depends on tempering out 126/125.
+; Music
+* [https://soundcloud.com/jdfreivald/a-seed-planted-starling-pure A Seed Planted] by [[Jake Freivald]]. The melody depends on tempering out 126/125.
+<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div style="line-height:1.6;">[[Minkowski blocks]]</div>
+<div class="mw-collapsible-content">
-=== [[Minkowski blocks]]  ===
+* 7: 25/24, 81/80
-: 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
-: 16/15, 648/625
+</div></div>
-: 27/25, 128/125
+== Undecimal starling ==
+Subgroup: 2.3.5.7.11
-: 16/15, 15625/15552
+[[Comma list]]: 126/125, 385/384
-: 128/125, 628/625
+[[Mapping]]: [&lt;1 0 0 -1 8|, &lt;0 1 0 -2 3|, &lt;0 0 1 3 -4]]
-: 128/125, 250/243
+Mapping generators: ~2, ~3, ~5
-: 648/625, 3125/3072
+{{Val list|legend=1| 15, 19, 27, 31, 46, 77, 96d, 127d, 173d, 204de, 300de }}
-: 25/24, 20480/19683
+[[Badness]]: 0.677 × 10<sup>-3</sup>
-: 81/80, 3125/3072
+== Thrush ==
+Subgroup: 2.3.5.7.11
-: 128/125, 78732/78125
+[[Comma list]]: 126/125, 176/175
-: 648/625, 16875/16384
+[[Mapping]]: [&lt;1 0 0 -1 -5|, &lt;0 1 0 -2 -2|, &lt;0 0 1 3 5|]
-: 81/80, 1990656/1953125
+Mapping generators: ~2, ~3, ~5
-: 15625/15552, 2048/2025
+[[Minimax tuning]]:
+* 7- and [[9-odd-limit]]
+: [|1 0 0 0 0&gt;, |0 1 0 0 0&gt;, |1/3 2/3 0 1/3 0&gt;, |0 0 0 1 0&gt;, |-10/3 4/3 0 5/3 0&gt;]
+: [[Eigenmonzo]]s: 2, 7/6, 4/3
-=== 11-limit  ===
+Map to lattice: [&lt;0 1 1 1 3|, &lt;0 1 0 -2 -2|]
-Commas: 126/125, 385/384
-Map: [&lt;1 0 0 -1 8|, &lt;0 1 0 -2 3|, &lt;0 0 1 3 -4]]
+Lattice basis:
+: 5/4 length = 0.8576, 6/5 length = 0.9314
+: Angle(5/4, 6/5) = 74.6239 degrees
-Generators: 2, 3, 5
+{{Val list|legend=1| 12, 15, 31, 46, 58, 89, 135c, 224c }}
-EDOs: 15, 19, 27, 31, 46, 77, 96d, 127d, 173d, 204de, 300de
+[[Badness]]: 0.353 × 10<sup>-3</sup>
-Badness: .000677
+[[Projection pair]]s: 7 125/18 11 3125/288
-== Thrush  ==
+[[Associated temperament]]: [[Starling temperaments #Myna|myna]]
-[[Commas]]: 126/125, 176/175
-Associated linear temperament: [[Starling temperaments #Myna|myna]]
+Scales: [[thrush12]]
-and 9 limit minimax
+=== 13-limit ===
+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, 176/175, 196/195
-|0 0 0 1 0&gt;, |-10/3 4/3 0 5/3 0&gt;]
-[[Eigenmonzo]]s: 2, 7/6, 4/3
+Mapping: [&lt;1 0 0 -1 -5 0|, &lt;0 1 0 -2 -2 -5|, &lt;0 0 1 3 5 5|]
-Lattice basis 5/4 length 0.8576 6/5 length 0.9314
+Vals: {{Val list| 31, 46, 58, 89f, 104c, 135c, 193cf, 239cf, 328cf }}
-Angle(5/4, 6/5) = 74.6239 degrees
+Badness: 0.677 × 10<sup>-3</sup>
-Map to lattice: [&lt;0 1 1 1 3|, &lt;0 1 0 -2 -2|]
+=== Bluebird ===
+Subgroup: 2.3.5.7.11.13
-Map: [&lt;1 0 0 -1 -5|, &lt;0 1 0 -2 -2|, &lt;0 0 1 3 5|]
+Comma list: 126/125, 176/175, 144/143
-[[Generator]]s: 2, 3, 5
+Mapping: [&lt;1 0 0 -1 -5 9|, &lt;0 1 0 -2 -2 4|, &lt;0 0 1 3 5 -5|]
-EDOs: 12, 15, 31, 46, 58, 89, 135c, 224c
+Vals: {{Val list| 12, 15, 31, 43, 48c, 58, 147cf, 205cef }}
-Badness: 0.000353
+Badness: 0.915 × 10<sup>-3</sup>
-Projection pairs: 7 125/18 11 3125/288
+Projection pairs: 7 125/18 11 3125/288 13 41472/3125
-Scales: [[thrush12]]
+=== Nightingale ===
+Subgroup: 2.3.5.7.11.13
-=== 13-limit  ===
+Comma list: 126/125, 176/175, 66/65
-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|]
+Mapping: [&lt;1 0 0 -1 -5 -4|, &lt;0 1 0 -2 -2 -1|, &lt;0 0 1 3 5 4|]
-EDOs: 31, 46, 58, 89f, 104c, 135c, 193cf, 239cf, 328cf
+Vals: {{Val list| 15, 19f, 21e, 22f, 28, 31, 46, 58, 89, 108ef }}
-Badness: 0.000677
+Badness: 0.837 × 10<sup>-3</sup>
-=== Bluebird  ===
+=== Veery ===
-Commas 126/125, 176/175, 144/143
+Subgroup: 2.3.5.7.11.13
-Map: [&lt;1 0 0 -1 -5 9|, &lt;0 1 0 -2 -2 4|, &lt;0 0 1 3 5 -5|]
+Comma list: 91/90, 126/125, 176/175
-EDOs: 12, 15, 31, 43, 48c, 58, 147cf, 205cef
+Mapping: [&lt;1 0 0 -1 -5 2|, &lt;0 1 0 -2 -2 4|, &lt;0 0 1 3 5 -2|]
-Badness: 0.000915
+Vals: {{Val list| 12, 15, 46 }}
-Projection pairs: 7 125/18 11 3125/288 13 41472/3125
+Badness: 0.991 × 10<sup>-3</sup>
-=== Nightingale  ===
+== Thrasher ==
-Commas: 126/125, 176/175, 66/65
+Subgroup: 2.3.5.7.11
-Map: [&lt;1 0 0 -1 -5 -4|, &lt;0 1 0 -2 -2 -1|, &lt;0 0 1 3 5 4|]
+[[Comma list]]: 56/55, 100/99
-[[EDO|EDOs]]: [[15edo|15]], [[19edo|19f]], [[21edo|21e]], [[22edo|22f]], [[28edo|28]], [[31edo|31]], [[46edo|46]], [[58edo|58]], [[89edo|89]], [[108edo|108ef]]
+[[Mapping]]: [&lt;1 0 0 -1 2|, &lt;0 1 0 -2 -2|, &lt;0 0 1 3 2|]
-Badness: 0.000837
+Mapping generators: ~2, ~3, ~5
-=== Veery  ===
+Map to lattice: [&lt;0 1 0 -2 -2|, &lt;0 1 1 1 0|]
-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|]
+Lattice basis:
+: 6/5 length = 0.9089, 5/4 length = 1.2007
+: Angle (6/5, 5/4) = 98.8447
-EDOs: 12, 15, 46
+[[Minimax tuning]]:
+* [[11-odd-limit]]
+: [|1 0 0 0 0&gt;, |1 3/4 0 1/4 -3/8&gt;, |1 1/2 0 1/2 -1/4&gt;, |0 0 0 1 0&gt;, |2 -1/2 0 1/2 1/4&gt;]
+: [[Eigenmonzo]]s: 2, 8/7, 11/9
-Badness: 0.000991
+{{Val list|legend=1| 12, 15, 19, 27e, 34, 46e, 58e, 61e, 73e }}
-== Thrasher  ==
+[[Badness]]: 0.480 × 10<sup>-3</sup>
-[[Comma]]s: 56/55, 100/99
--limit minimax
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-[|1 0 0 0 0&gt;, |1 3/4 0 1/4 -3/8&gt;,
+Comma list: 126/125, 100/99, 91/90
-|1 1/2 0 1/2 -1/4&gt;, |0 0 0 1 0&gt;,
-|2 -1/2 0 1/2 1/4&gt;]
-[[Eigenmonzo]]s: 2, 8/7, 11/9
+Mapping: [&lt;1 0 0 -1 2 2|, &lt;0 1 0 -2 -2 4|, &lt;0 0 1 3 2 -2|]
-Lattice basis: 6/5 length 0.9089 5/4 length 1.2007
+Vals: {{Val list| 12, 15, 18, 25e, 27e, 34, 46e, 51ce, 61e }}
-Angle(6/5, 5/4) = 98.8447
+Badness: 0.876 × 10<sup>-3</sup>
-Map to lattice: [&lt;0 1 0 -2 -2|, &lt;0 1 1 1 0|]
+=== Mockingbird ===
+Subgroup: 2.3.5.7.11.13
-Map: [&lt;1 0 0 -1 2|, &lt;0 1 0 -2 -2|, &lt;0 0 1 3 2|]
+Comma list: 40/39, 100/99, 126/125
-[[Generator]]s: 2, 3, 5
+Mapping: [&lt;1 0 0 -1 2 3|, &lt;0 1 0 -2 -2 -1|, &lt;0 0 1 3 2 1|]
-EDOs: 12, 15, 19, 27e, 34, 46e, 58e, 61e, 73e
+Vals: {{Val list| 12f, 15, 27ef }}
-Badness: 0.000480
+Badness: 0.859 × 10<sup>-3</sup>
-=== 13-limit  ===
+=== Catbird ===
-Commas: 126/125, 100/99, 91/90
+Subgroup: 2.3.5.7.11.13
-Map: [&lt;1 0 0 -1 2 2|, &lt;0 1 0 -2 -2 4|, &lt;0 0 1 3 2 -2|]
+Comma list: 78/77, 100/99, 126/125
-EDOs: 12, 15, 18, 25e, 27e, 34, 46e, 51ce, 61e
+Mapping: [&lt;1 0 0 -1 2 0|, &lt;0 1 0 -2 -2 -5|, &lt;0 0 1 3 2 5|]
-Badness: 0.000876
+Vals: {{Val list| 12, 15, 17c, 19, 22ef], 27e, 34, 58e }}
-=== Mockingbird  ===
+Badness: 0.905 × 10<sup>-3</sup>
-Commas: 40/39, 100/99, 126/125
-Map: [&lt;1 0 0 -1 2 3|, &lt;0 1 0 -2 -2 -1|, &lt;0 0 1 3 2 1|]
+== Aplonis ==
+Subgroup: 2.3.5.7.11
-EDOs: 12f, 15, 27ef
+[[Comma list]]: 126/125, 540/539
-Badness: 0.000859
+[[Mapping]]: [&lt;1 0 0 -1 4|, &lt;0 1 0 -2 7|, &lt;0 0 1 3 -5|]
-=== Catbird  ===
+{{Val list|legend=1| 19, 31, 58, 67, 89, 197c, 286ce, 375ce }}
-Commas: 78/77, 100/99, 126/125
-Map: [&lt;1 0 0 -1 2 0|, &lt;0 1 0 -2 -2 -5|, &lt;0 0 1 3 2 5|]
+[[Badness]]: 0.648 × 10<sup>-3</sup>
-[[EDO|EDOs]]: [[12edo|12]], [[15edo|15]], [[17edo|17c]], [[19edo|19]], [[22edo|22ef]], [[27edo|27e]], [[34edo|34]], [[58edo|58e]]
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-Badness: 0.000905
+Comma list: 126/125, 144/143, 196/195
-== Aplonis  ==
+Mapping: [&lt;1 0 0 -1 4 0|, &lt;0 1 0 -2 7 -5|, &lt;0 0 1 3 -5 5|]
-Commas: 126/125, 540/539
-Map: [&lt;1 0 0 -1 4|, &lt;0 1 0 -2 7|, &lt;0 0 1 3 -5|]
+Vals: {{Val list| 19, 31, 41, 43, 50, 58, 89f, 125ce, 135ce, 147cf, 166cef, 224cef }}
-EDOs: 19, 31, 58, 67, 89, 197c, 286ce, 375ce
+Badness: 0.821 × 10<sup>-3</sup>
-Badness: 0.000648
+== Oxpecker ==
+Subgroup: 2.3.5.7.11
-=== 13-limit  ===
+[[Comma list]]: 121/120, 126/125
-Commas: 126/125, 144/143, 196/195
-Map: [&lt;1 0 0 -1 4 0|, &lt;0 1 0 -2 7 -5|, &lt;0 0 1 3 -5 5|]
+[[Mapping]]: [&lt;1 0 1 2 2|, &lt;0 1 1 1 1|, &lt;0 0 -2 -6 -1|]
-EDOs: 19, 31, 41, 43, 50, 58, 89f, 125ce, 135ce, 147cf, 166cef, 224cef
+{{Val list|legend=1| 8d, 15, 31, 46, 77, 185e, 262cde }}
-Badness: 0.000821
+[[Badness]]: 0.699 × 10<sup>-3</sup>
-== Oxpecker  ==
+=== Woodpecker ===
-Commas: 121/120, 126/125
+Subgroup: 2.3.5.7.11.13
-Map: [&lt;1 0 1 2 2|, &lt;0 1 1 1 1|, &lt;0 0 -2 -6 -1|]
+Comma list: 66/65, 121/120, 126/125
-EDOs: 8d, 15, 31, 46, 77, 185e, 262cde
+Mapping: [&lt;1 0 1 2 2 2|, &lt;0 1 1 1 1 1|, &lt;0 0 -2 -6 -1 -1|]
-Badness: 0.000699
+Vals: {{Val list| 15, 31, 46f, 70f, 101f }}
-=== Woodpecker  ===
+Badness: 1.093 × 10<sup>-3</sup>
-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|]
+== Treecreeper ==
+Subgroup: 2.3.5.7.11
-EDOs: 15, 31, 46f, 70f, 101f
+[[Comma list]]: 126/125, 1232/1215
-Badness: 0.001093
+[[Mapping]]: [&lt;1 0 0 -1 -3|, &lt;0 1 0 -2 7|, &lt;0 0 1 3 -2|]
-== Treecreeper  ==
+{{Val list|legend=1| 34, 46, 119c, 165c }}
-Commas: 126/125, 1232/1215
-Map: [&lt;1 0 0 -1 -3|, &lt;0 1 0 -2 7|, &lt;0 0 1 3 -2|]
+[[Badness]]: 1.585 × 10<sup>-3</sup>
-EDOs: 34, 46, 119c, 165c
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-Badness: 0.001585
+Comma list: 91/90, 126/125, 352/351
-=== 13-limit  ===
+Mapping: [&lt;1 0 0 -1 -3 2|, &lt;0 1 0 -2 7 4|, &lt;0 0 1 3 -2 -2|]
-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|]
+Vals: {{Val list| 34, 46, 172cd, 218cdf, 264bcdf, 310bcdf }}
-EDOs: 34, 46, 172cd, 218cdf, 264bcdf, 310bcdf
+Badness: 1.588 × 10<sup>-3</sup>
-Badness: 0.001588
+== Cuckoo ==
+Subgroup: 2.3.5.7.11
-== Cuckoo  ==
+[[Comma list]]: 126/125, 243/242
-Commas: 126/125, 243/242
-Map: [&lt;1 1 0 -3 2|, &lt;0 2 0 -4 5|, &lt;0 0 1 3 0|]
+[[Mapping]]: [&lt;1 1 0 -3 2|, &lt;0 2 0 -4 5|, &lt;0 0 1 3 0|]
-EDOs: 31, 34, 58, 65, 89, 154, 185, 216
+{{Val list|legend=1| 31, 34, 58, 65, 89, 154, 185, 216 }}
-Badness: 0.000933
+[[Badness]]: 0.933 × 10<sup>-3</sup>
 === 13-limit  ===
-Commas: 126/125, 196/195, 243/242
+Subgroup: 2.3.5.7.11.13
+Comma list: 126/125, 196/195, 243/242
-Map: [&lt;1 1 0 -3 2 -5|, &lt;0 2 0 -4 5 -10|, &lt;0 0 1 3 0 5|]
+Mapping: [&lt;1 1 0 -3 2 -5|, &lt;0 2 0 -4 5 -10|, &lt;0 0 1 3 0 5|]
-EDOs: 31, 58, 65f, 89f, 92e, 154, 185, 216f
+Vals: {{Val list| 31, 58, 65f, 89f, 92e, 154, 185, 216f }}
-[[Category:Theory]]
+[[Category:Regular temperament theory]]
 [[Category:Temperament family]]
-[[Category:Starling]]
+[[Category:Starling family| ]] <!-- main article -->
 [[Category:Thrush]]
 [[Category:Rank 3]]
 [[Category:Listen]]

Starling family: Difference between revisions

Revision as of 09:13, 8 June 2021

Starling

Undecimal starling

Thrush

13-limit

Bluebird

Nightingale

Veery

Thrasher

13-limit

Mockingbird

Catbird

Aplonis

13-limit

Oxpecker

Woodpecker

Treecreeper

13-limit

Cuckoo

13-limit

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