Unicorn family: Difference between revisions
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The '''unicorn family''' tempers out the [[unicorn comma]], 1594323/1562500 = {{monzo| -2 13 -8 }}. | The '''unicorn family''' tempers out the [[unicorn comma]], 1594323/1562500 = {{monzo| -2 13 -8 }}. | ||
== | == Unicorn == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 14: | Line 14: | ||
[[Badness]]: 0.150487 | [[Badness]]: 0.150487 | ||
== Septimal unicorn | == Septimal unicorn == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 29: | Line 29: | ||
[[Badness]]: 0.040913 | [[Badness]]: 0.040913 | ||
=== Alicorn | === Alicorn === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 42: | Line 42: | ||
Badness: 0.039156 | Badness: 0.039156 | ||
==== 13-limit | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 55: | Line 55: | ||
Badness: 0.023667 | Badness: 0.023667 | ||
=== Camahueto | === Camahueto === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 68: | Line 68: | ||
Badness: 0.065940 | Badness: 0.065940 | ||
==== 13-limit | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 81: | Line 81: | ||
Badness: 0.036155 | Badness: 0.036155 | ||
=== Qilin | === Qilin === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 94: | Line 94: | ||
Badness: 0.041426 | Badness: 0.041426 | ||
==== 13-limit | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 107: | Line 107: | ||
Badness: 0.022842 | Badness: 0.022842 | ||
=== Monocerus | === Monocerus === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 120: | Line 120: | ||
Badness: 0.052757 | Badness: 0.052757 | ||
==== 13-limit | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 133: | Line 133: | ||
Badness: 0.028795 | Badness: 0.028795 | ||
== Rhinoceros | == Rhinoceros == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 148: | Line 148: | ||
[[Badness]]: 0.081864 | [[Badness]]: 0.081864 | ||
=== 11-limit | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 161: | Line 161: | ||
Badness: 0.059319 | Badness: 0.059319 | ||
=== 13-limit | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 176: | Line 176: | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Unicorn]] | [[Category:Unicorn family| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Revision as of 17:11, 9 November 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
Badness: 0.150487
Septimal unicorn
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
Badness: 0.040913
Alicorn
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
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