Unicorn family: Difference between revisions

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Line 2: Line 2:


= Unicorn =
= Unicorn =
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 13: Line 12:
{{Val list|legend=1| 19, 58, 77, 96, 173, 269 }}
{{Val list|legend=1| 19, 58, 77, 96, 173, 269 }}


[[Badness]]: 0.1505
[[Badness]]: 0.150487


= Alicorn =
= Alicorn =
Line 30: Line 29:
{{Val list|legend=1| 19, 39d, 58, 77, 135c }}
{{Val list|legend=1| 19, 39d, 58, 77, 135c }}


[[Badness]]: 0.0409
[[Badness]]: 0.040913


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 42: Line 40:
POTE generator: ~28/27 = 62.101
POTE generator: ~28/27 = 62.101


{{Val list|legend=1| 19, 39d, 58 }}
Vals: {{Val list| 19, 39d, 58 }}


Badness: 0.0392
Badness: 0.039156


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


Line 56: Line 53:
POTE generator: ~28/27 = 62.119
POTE generator: ~28/27 = 62.119


{{Val list|legend=1| 19, 39df, 58 }}
Vals: {{Val list| 19, 39df, 58 }}


Badness: 0.0237
Badness: 0.023667


== Camahueto ==
== Camahueto ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 70: Line 66:
POTE generator: ~28/27 = 62.431
POTE generator: ~28/27 = 62.431


{{Val list|legend=1| 19, 58e, 77, 96d, 173d }}
Vals: {{Val list| 19, 58e, 77, 96d, 173d }}


Badness: 0.0659
Badness: 0.065940


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


Line 84: Line 79:
POTE generator: ~28/27 = 62.434
POTE generator: ~28/27 = 62.434


{{Val list|legend=1| 19, 58e, 77, 96d, 173d }}
Vals: {{Val list| 19, 58e, 77, 96d, 173d }}


Badness: 0.0362
Badness: 0.036155


== Qilin ==
== Qilin ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 98: Line 92:
POTE generator: ~28/27 = 62.196
POTE generator: ~28/27 = 62.196


{{Val list|legend=1| 58, 77, 135c, 193c, 328c }}
Vals: {{Val list| 58, 77, 135c, 193c, 328cc }}


Badness: 0.0414
Badness: 0.041426


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


Line 112: Line 105:
POTE generator: ~28/27 = 62.197
POTE generator: ~28/27 = 62.197


{{Val list|legend=1| 58, 77, 135c, 193cf, 328cf }}
Vals: {{Val list| 58, 77, 135c, 193cf, 328ccff }}


Badness: 0.0228
Badness: 0.022842


== Monocerus ==
== Monocerus ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 126: Line 118:
POTE generator: ~28/27 = 62.292
POTE generator: ~28/27 = 62.292


{{Val list|legend=1| 58, 96d, 154, 212ce, 366de }}
Vals: {{Val list| 58, 96d, 154, 212ce, 366cce }}


Badness: 0.0528
Badness: 0.052757


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


Line 140: Line 131:
POTE generator: ~28/27 = 62.301
POTE generator: ~28/27 = 62.301


{{Val list|legend=1| 58, 96d, 154, 366cef }}
Vals: {{Val list| 58, 96d, 154, 366ccef }}


Badness: 0.0288
Badness: 0.028795


= Rhinoceros =
= Rhinoceros =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 156: Line 146:
[[POTE generator]]: ~21/20 = 62.920
[[POTE generator]]: ~21/20 = 62.920


{{Val list|legend=1| 19 }}
{{Val list|legend=1| 1c, 19 }}


[[Badness]]: 0.0819
[[Badness]]: 0.081864


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 170: Line 159:
POTE generator: ~21/20 = 62.874
POTE generator: ~21/20 = 62.874


{{Val list|legend=1| 19 }}
Vals: {{Val list| 19 }}


Badness: 0.0593
Badness: 0.059319


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


Line 184: Line 172:
POTE generator: ~21/20 = 63.043
POTE generator: ~21/20 = 63.043


{{Val list|legend=1| 19 }}
Vals: {{Val list| 19 }}


Badness: 0.0393
Badness: 0.039343


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]

Revision as of 15:07, 18 May 2021

The unicorn family tempers out the unicorn comma, 1594323/1562500 = [-2 13 -8⟩.

Unicorn

Subgroup: 2.3.5

Comma list: 1594323/1562500

Mapping: [⟨1 2 3], ⟨0 -8 -13]]

POTE generator: ~250/243 = 62.458

Template:Val list

Badness: 0.150487

Alicorn

See also: Starling temperaments § Alicorn

Subgroup: 2.3.5.7

Comma list: 126/125, 10976/10935

Mapping: [⟨1 2 3 4], ⟨0 -8 -13 -23]]

Wedgie: ⟨⟨ 8 13 23 2 14 17 ]]

POTE generator: ~28/27 = 62.278

Template:Val list

Badness: 0.040913

11-limit

Subgroup: 2.3.5.7.11

Comma list: 126/125, 540/539, 896/891

Mapping: [⟨1 2 3 4 3], ⟨0 -8 -13 -23 9]]

POTE generator: ~28/27 = 62.101

Vals: Template:Val list

Badness: 0.039156

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 144/143, 196/195, 676/675

Mapping: [⟨1 2 3 4 3 5], ⟨0 -8 -13 -23 9 -25]]

POTE generator: ~28/27 = 62.119

Vals: Template:Val list

Badness: 0.023667

Camahueto

Subgroup: 2.3.5.7.11

Comma list: 126/125, 385/384, 10976/10935

Mapping: [⟨1 2 3 4 2], ⟨0 -8 -13 -23 28]]

POTE generator: ~28/27 = 62.431

Vals: Template:Val list

Badness: 0.065940

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 196/195, 385/384, 676/675

Mapping: [⟨1 2 3 4 2 5], ⟨0 -8 -13 -23 28 -25]]

POTE generator: ~28/27 = 62.434

Vals: Template:Val list

Badness: 0.036155

Qilin

Subgroup: 2.3.5.7.11

Comma list: 126/125, 176/175, 10976/10935

Mapping: [⟨1 2 3 4 6], ⟨0 -8 -13 -23 -49]]

POTE generator: ~28/27 = 62.196

Vals: Template:Val list

Badness: 0.041426

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 176/175, 196/195, 2200/2197

Mapping: [⟨1 2 3 4 6 5], ⟨0 -8 -13 -23 -49 -25]]

POTE generator: ~28/27 = 62.197

Vals: Template:Val list

Badness: 0.022842

Monocerus

Subgroup: 2.3.5.7.11

Comma list: 126/125, 243/242, 5488/5445

Mapping: [⟨2 4 6 8 9], ⟨0 -8 -13 -23 -20]]

POTE generator: ~28/27 = 62.292

Vals: Template:Val list

Badness: 0.052757

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 196/195, 364/363, 676/675

Mapping: [⟨2 4 6 8 9 10], ⟨0 -8 -13 -23 -20 -25]]

POTE generator: ~28/27 = 62.301

Vals: Template:Val list

Badness: 0.028795

Rhinoceros

Subgroup: 2.3.5.7

Comma list: 49/48, 4375/4374

Mapping: [⟨1 2 3 3], ⟨0 -8 -13 -4]]

Wedgie: ⟨⟨ 8 13 4 2 -16 -27 ]]

POTE generator: ~21/20 = 62.920

Template:Val list

Badness: 0.081864

11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 100/99, 126/121

Mapping: [⟨1 2 3 3 4], ⟨0 -8 -13 -4 -10]]

POTE generator: ~21/20 = 62.874

Vals: Template:Val list

Badness: 0.059319

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 78/77, 100/99, 126/121

Mapping: [⟨1 2 3 3 4 4], ⟨0 -8 -13 -4 -10 -6]]

POTE generator: ~21/20 = 63.043

Vals: Template:Val list

Badness: 0.039343

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