Immunity family
Temperaments of immunity family temper out the immunity comma, 1638400/1594323 = [16-13 2⟩ (sasayoyo).
Immunity
Immunity is naturally a 2.3.5.13 subgroup temperament as the generator serves as ~26/15 (or its octave complement ~15/13), tempering out 676/675.
Subgroup: 2.3.5
Comma list: 1638400/1594323
Mapping: [⟨1 0 -8], ⟨0 2 13]]
- mapping generators: ~2, ~1280/729
Optimal tuning (POTE): ~2 = 1\1, ~1280/729 = 952.930
Optimal ET sequence: 5, …, 29, 34
Badness: 0.184738
2.3.5.13 subgroup
Subgroup: 2.3.5.13
Comma list: 676/675, 3200/3159
Sval mapping: [⟨1 0 -8 -9], ⟨0 2 13 16]]
Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 952.6431
Optimal ET sequence: 5, …, 29, 34
Badness: 0.257
Septimal immunity
Subgroup: 2.3.5.7
Comma list: 49/48, 2240/2187
Mapping: [⟨1 0 -8 2], ⟨0 2 13 1]]
⟨⟨2 13 1 16 -4 -34]]
Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.445
Optimal ET sequence: 5, …, 29, 34, 63d
Badness: 0.077631
11-limit
Subgroup: 2.3.5.7.11
Comma list: 49/48, 55/54, 896/891
Mapping: [⟨1 0 -8 2 9], ⟨0 2 13 1 -7]]
Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.074
Optimal ET sequence: 5, 24c, 29, 63de
Badness: 0.052661
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 55/54, 91/90, 896/891
Mapping: [⟨1 0 -8 2 9 -9], ⟨0 2 13 1 -7 16]]
Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.031
Optimal ET sequence: 5, 24cf, 29
Badness: 0.037078
Impunity
Subgroup: 2.3.5.7.11
Comma list: 49/48, 100/99, 1232/1215
Mapping: [⟨1 0 -8 2 -14], ⟨0 2 13 1 22]]
Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.227
Optimal ET sequence: 5e, 24cee, 29
Badness: 0.055243
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 91/90, 100/99, 352/351
Mapping: [⟨1 0 -8 2 -14 -9], ⟨0 2 13 1 22 16]]
Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.217
Optimal ET sequence: 5e, 24ceef, 29
Badness: 0.033196
Immunized
Subgroup: 2.3.5.7
Comma list: 64/63, 8748/8575
Mapping: [⟨1 0 -8 6], ⟨0 2 13 -4]]
⟨⟨2 13 -4 16 -12 -46]]
Optimal tuning (POTE): ~2 = 1\1, ~140/81 = 953.521
Optimal ET sequence: 5, 29d, 34d, 39d, 73dd, 112cddd
Badness: 0.082592
11-limit
Subgroup: 2.3.5.7.11
Comma list: 64/63, 99/98, 1944/1925
Mapping: [⟨1 0 -8 6 13], ⟨0 2 13 -4 -12]]
Optimal tuning (POTE): ~2 = 1\1, ~55/32 = 953.397
Optimal ET sequence: 5, 29de, 34d, 39d, 73dd
Badness: 0.051515
Immune
Subgroup: 2.3.5.7
Comma list: 225/224, 781250/750141
Mapping: [⟨1 2 5 9], ⟨0 -2 -13 -30]]
⟨⟨2 13 30 16 42 33]]
Optimal tuning (POTE): ~2 = 1\1, ~1000/567 = 952.417
Optimal ET sequence: 29, 34d, 63
Badness: 0.144835
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 225/224, 1331/1323
Mapping: [⟨1 2 5 9 8], ⟨0 -2 -13 -30 -22]]
Optimal tuning (POTE): ~2 = 1\1, ~121/70 = 952.411
Optimal ET sequence: 29, 34d, 63
Badness: 0.050990
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 169/168, 225/224, 275/273
Mapping: [⟨1 2 5 9 8 7], ⟨0 -2 -13 -30 -22 -16]]
Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 952.407
Optimal ET sequence: 29, 34d, 63
Badness: 0.028521