Passion family
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
The passion family tempers out the passion comma, 262144/253125 = [18 -4 -5⟩ 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
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.670
Optimal ET sequence: 12, 49, 61, 73
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]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.153
Optimal ET sequence: 12, 37, 49, 110bcd
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]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.019
Optimal ET sequence: 12, 37, 49
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]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 97.910
Optimal ET sequence: 12f, 25f, 37, 49f
Badness: 0.030886
Passionate
Subgroup: 2.3.5.7
Comma list: 126/125, 131072/127575
Mapping: [⟨1 2 2 1], ⟨0 -5 4 22]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.817
Optimal ET sequence: 12, 61, 73, 85c
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]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.721
Optimal ET sequence: 12, 61, 73, 158bccee
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]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.627
Optimal ET sequence: 12f, 61, 73f
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]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.791
Optimal ET sequence: 12f, 61f, 73, 85ce
Badness: 0.056386
Passive
Subgroup: 2.3.5.7
Comma list: 225/224, 256/245
Mapping: [⟨1 2 2 3], ⟨0 -5 4 -2]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.809
Optimal ET sequence: 1, 11, 12, 49dd
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
Optimal tuning (POTE): ~2 = 1\1, ~48/35 = 550.9374
Optimal ET sequence: 13d, 24, 37, 61, 98b
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]]
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 550.9007
Optimal ET sequence: 13d, 24, 37, 61
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]]
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 550.9062
Optimal ET sequence: 13d, 24, 37, 61
Badness: 0.045864