Immunity family

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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 sequence5, …, 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 sequence5, …, 29, 34

Badness: 0.257

Septimal immunity

See also: Slendro clan

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]]

Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.445

Optimal ET sequence5, …, 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 sequence5, 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 sequence5, 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 sequence5e, 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 sequence5e, 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]]

Wedgie⟨⟨2 13 -4 16 -12 -46]]

Optimal tuning (POTE): ~2 = 1\1, ~140/81 = 953.521

Optimal ET sequence5, 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 sequence5, 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]]

Wedgie⟨⟨2 13 30 16 42 33]]

Optimal tuning (POTE): ~2 = 1\1, ~1000/567 = 952.417

Optimal ET sequence29, 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 sequence29, 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 sequence29, 34d, 63

Badness: 0.028521