Passion family: Difference between revisions
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== Passive == | == Passive == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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{{Val list|legend=1| 13d, 24, 37, 61, 98b }} | {{Val list|legend=1| 13d, 24, 37, 61, 98b }} | ||
[[Badness]]: 0. | [[Badness]]: 0.209095 | ||
=== 11-limit === | === 11-limit === | ||
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Vals: {{val list| 13d, 24, 37, 61 }} | Vals: {{val list| 13d, 24, 37, 61 }} | ||
Badness: 0. | Badness: 0.077504 | ||
=== 13-limit === | === 13-limit === | ||
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Vals: {{val list| 13d, 24, 37, 61 }} | Vals: {{val list| 13d, 24, 37, 61 }} | ||
Badness: 0. | Badness: 0.045864 | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Passion family]] <!-- main article --> | [[Category:Passion family| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Revision as of 12:17, 19 October 2021
The passion family tempers out 262144/253125 in the 5-limit, which equates five instances of 16/15 with 4/3.
Passion
Subgroup: 2.3.5
Comma list: 262144/253125
Mapping: [⟨1 2 2], ⟨0 -5 4]]
Mapping generators: ~2, ~16/15
POTE generator: ~16/15 = 98.670
Badness: 0.168550
Septimal passion
Subgroup: 2.3.5.7
Comma list: 64/63, 3125/3087
Mapping: [⟨1 2 2 2], ⟨0 -5 4 10]]
Mapping generators: 2, 16/15
Wedgie: ⟨⟨ 5 -4 -10 -18 -30 -12 ]]
POTE generator: ~16/15 = 98.153
Badness: 0.062327
11-limit
Subgroup: 2.3.5.7.11
Comma list: 64/63, 100/99, 1375/1372
Mapping: [⟨1 2 2 2 2], ⟨0 -5 4 10 18]]
POTE generator: ~16/15 = 98.019
Vals: Template:Val list
Badness: 0.040809
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 64/63, 100/99, 196/195, 275/273
Mapping: [⟨1 2 2 2 2 2], ⟨0 -5 4 10 18 21]]
POTE generator: ~16/15 = 97.910
Vals: Template:Val list
Badness: 0.030886
Passionate
Subgroup: 2.3.5.7
Comma list: 126/125, 131072/127575
Mapping: [⟨1 2 2 1], ⟨0 -5 4 22]]
Wedgie: ⟨⟨ 5 -4 -22 -18 -49 -40 ]]
POTE generator: ~16/15 = 98.817
Badness: 0.121293
11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 8192/8019
Mapping: [⟨1 2 2 1 1], ⟨0 -5 4 22 30]]
POTE generator: ~16/15 = 98.721
Vals: Template:Val list
Badness: 0.068322
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 176/175, 343/338, 364/363
Mapping: [⟨1 2 2 1 1 1], ⟨0 -5 4 22 30 33]]
POTE generator: ~16/15 = 98.627
Vals: Template:Val list
Badness: 0.052302
Pash
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 176/175, 196/195, 1352/1331
Mapping: [⟨1 2 2 1 1 0], ⟨0 -5 4 22 30 45]]
POTE generator: ~16/15 = 98.791
Vals: Template:Val list
Badness: 0.056386
Passive
Subgroup: 2.3.5.7
Comma list: 225/224, 256/245
Mapping: [⟨1 2 2 3], ⟨0 -5 4 -2]]
POTE generator: ~16/15 = 98.809
Badness: 0.075055
Freivald
Subgroup: 2.3.5.7
Comma list: 6144/6125, 6272/6075
Mapping: [⟨1 7 -2 12], ⟨0 -10 8 -17]]
Mapping generator: ~2, ~35/24
POTE generator: ~48/35 = 550.9374
Badness: 0.209095
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 2744/2673
Mapping: [⟨1 7 -2 12 4], ⟨0 -10 8 -17 -1]]
POTE generator: ~11/8 = 550.9007
Vals: Template:Val list
Badness: 0.077504
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 176/175, 512/507
Mapping: [⟨1 7 -2 12 4 1], ⟨0 -10 8 -17 -1 5]]
POTE generator: ~11/8 = 550.9062
Vals: Template:Val list
Badness: 0.045864