Immunity family
The immunity family of temperaments tempers out the immunity comma, 1638400/1594323 ([16 -13 2⟩).
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
- CTE: ~2 = 1200.000, ~1280/729 = 952.706
- error map: ⟨0.000 +3.456 -1.141]
- POTE: ~2 = 1200.000, ~1280/729 = 952.930
- error map: ⟨0.000 +3.905 +1.775]
Optimal ET sequence: 5, …, 29, 34
Badness (Smith): 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 tunings:
- CTE: ~2 = 1200.000, ~26/15 = 952.643
- CWE: ~2 = 1200.000, ~26/15 = 952.789
Optimal ET sequence: 5, …, 29, 34
Badness (Smith): 0.257
Septimal immunity
Subgroup: 2.3.5.7
Comma list: 49/48, 2240/2187
Mapping: [⟨1 0 -8 2], ⟨0 2 13 1]]
Wedgie: ⟨⟨ 2 13 1 16 -4 -34 ]]
- CTE: ~2 = 1200.000, ~7/4 = 952.767
- error map: ⟨0.000 +3.580 -0.337 -16.058]
- POTE: ~2 = 1200.000, ~7/4 = 952.445
- error map: ⟨0.000 +2.936 -4.525 -16.381]
Optimal ET sequence: 5, …, 29, 34, 63d
Badness (Smith): 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 tunings:
- CTE: ~2 = 1200.000, ~7/4 = 952.442
- POTE: ~2 = 1200.000, ~7/4 = 952.074
Optimal ET sequence: 5, 24c, 29, 63de
Badness (Smith): 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 tunings:
- CTE: ~2 = 1200.000, ~7/4 = 952.472
- POTE: ~2 = 1200.000, ~7/4 = 952.031
Optimal ET sequence: 5, 24cf, 29
Badness (Smith): 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 tunings:
- CTE: ~2 = 1200.000, ~7/4 = 952.528
- POTE: ~2 = 1200.000, ~7/4 = 952.227
Optimal ET sequence: 5e, 24cee, 29
Badness (Smith): 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 tunings:
- CTE: ~2 = 1200.000, ~7/4 = 952.529
- POTE: ~2 = 1200.000, ~7/4 = 952.217
Optimal ET sequence: 5e, 24ceef, 29
Badness (Smith): 0.033196
Immunized
Subgroup: 2.3.5.7
Comma list: 64/63, 8748/8575
Mapping: [⟨1 0 -8 6], ⟨0 2 13 -4]]
Wedgie: ⟨⟨ 2 13 -4 16 -12 -46 ]]
- CTE: ~2 = 1200.000, ~140/81 = 953.001
- error map: ⟨0.000 +4.047 +2.669 +19.170]
- POTE: ~2 = 1200.000, ~140/81 = 953.521
- error map: ⟨0.000 +5.088 +9.463 +17.089]
Optimal ET sequence: 5, 29d, 34d, 39d, 73dd, 112cddd
Badness (Smith): 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 tunings:
- CTE: ~2 = 1200.000, ~55/32 = 953.271
- POTE: ~2 = 1200.000, ~55/32 = 953.397
Optimal ET sequence: 5, 29de, 34d, 39d, 73dd
Badness (Smith): 0.051515
Immune
Subgroup: 2.3.5.7
Comma list: 225/224, 781250/750141
Mapping: [⟨1 2 5 9], ⟨0 -2 -13 -30]]
Wedgie: ⟨⟨ 2 13 30 16 42 33 ]]
- CTE: ~2 = 1200.000, ~1000/567 = 952.386
- error map: ⟨0.000 +2.818 -5.292 +2.763]
- POTE: ~2 = 1200.000, ~1000/567 = 952.417
- error map: ⟨0.000 +2.879 -4.893 +3.683]
Optimal ET sequence: 29, 34d, 63
Badness (Smith): 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 tunings:
- CTE: ~2 = 1200.000, ~121/70 = 952.375
- POTE: ~2 = 1200.000, ~121/70 = 952.411
Optimal ET sequence: 29, 34d, 63
Badness (Smith): 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 tunings:
- CTE: ~2 = 1200.000, ~26/15 = 952.389
- POTE: ~2 = 1200.000, ~26/15 = 952.407
Optimal ET sequence: 29, 34d, 63
Badness (Smith): 0.028521