Immunity 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 immunity family of temperaments tempers out the immunity comma (monzo: [16 -13 2⟩, ratio: 1638400/1594323).
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
- WE: ~2 = 1198.9215 ¢, ~1280/729 = 952.0734 ¢
- error map: ⟨-1.079 +2.192 -0.731]
- CWE: ~2 = 1200.0000 ¢, ~1280/729 = 952.8424 ¢
- error map: ⟨0.000 +3.730 +0.638]
Optimal ET sequence: 5, …, 29, 34
Badness (Sintel): 4.33
2.3.5.13 subgroup
Subgroup: 2.3.5.13
Comma list: 676/675, 3200/3159
Subgroup-val mapping: [⟨1 0 -8 -9], ⟨0 2 13 16]]
Optimal tunings:
- WE: ~2 = 1198.8955 ¢, ~26/15 = 952.0049 ¢
- CWE: ~2 = 1200.0000 ¢, ~26/15 = 952.7890 ¢
Optimal ET sequence: 5, …, 29, 34
Badness (Sintel): 0.858
Overview to extensions
The second comma of the comma list defines which 7-limit family member we are looking at:
Septimal immunity
Subgroup: 2.3.5.7
Comma list: 49/48, 2240/2187
Mapping: [⟨1 0 -8 2], ⟨0 2 13 1]]
- WE: ~2 = 1201.4508 ¢, ~7/4 = 953.5968 ¢
- error map: ⟨+1.451 +5.239 -1.162 -12.327]
- CWE: ~2 = 1200.0000 ¢, ~7/4 = 952.5376 ¢
- error map: ⟨0.000 +3.120 -3.325 -16.288]
Optimal ET sequence: 5, …, 29, 34, 63d
Badness (Sintel): 1.96
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:
- WE: ~2 = 1202.6033 ¢, ~7/4 = 954.1395 ¢
- CWE: ~2 = 1200.0000 ¢, ~7/4 = 952.1429 ¢
Optimal ET sequence: 5, 24c, 29, 63de
Badness (Sintel): 1.74
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:
- WE: ~2 = 1202.5640 ¢, ~7/4 = 954.0648 ¢
- CWE: ~2 = 1200.0000 ¢, ~7/4 = 952.1117 ¢
Optimal ET sequence: 5, 24cf, 29
Badness (Sintel): 1.53
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:
- WE: ~2 = 1201.6023 ¢, ~7/4 = 953.4988 ¢
- CWE: ~2 = 1200.0000 ¢, ~7/4 = 952.3120 ¢
Optimal ET sequence: 5e, 24cee, 29
Badness (Sintel): 1.83
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:
- WE: ~2 = 1200.5826 ¢, ~7/4 = 952.4725 ¢
- CWE: ~2 = 1200.0000 ¢, ~7/4 = 952.3038 ¢
Optimal ET sequence: 5e, 24ceef, 29
Badness (Sintel): 1.37
Immunized
Subgroup: 2.3.5.7
Comma list: 64/63, 8748/8575
Mapping: [⟨1 0 -8 6], ⟨0 2 13 -4]]
- WE: ~2 = 1196.6463 ¢, ~140/81 = 950.8564 ¢
- error map: ⟨-3.354 -0.242 +1.649 +7.626]
- CWE: ~2 = 1200.0000 ¢, ~140/81 = 953.3954 ¢
- error map: ⟨0.000 +4.836 +7.827 +17.592]
Optimal ET sequence: 5, 29d, 34d, 39d, 73dd, 112cddd
Badness (Sintel): 2.09
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:
- WE: ~2 = 1196.9902 ¢, ~55/32 = 951.0056 ¢
- CWE: ~2 = 1200.0000 ¢, ~55/32 = 953.3755 ¢
Optimal ET sequence: 5, 29de, 34d, 39d, 73dd
Badness (Sintel): 1.70
Immune
Subgroup: 2.3.5.7
Comma list: 225/224, 781250/750141
Mapping: [⟨1 2 5 9], ⟨0 -2 -13 -30]]
- WE: ~2 = 1199.7353 ¢, ~1000/567 = 952.2068 ¢
- error map: ⟨-0.265 +2.459 -5.507 +2.939]
- CWE: ~2 = 1200.0000 ¢, ~1000/567 = 952.4061 ¢
- error map: ⟨0.000 +2.857 -5.034 +3.357]
Optimal ET sequence: 29, 34d, 63
Badness (Sintel): 3.67
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:
- WE: ~2 = 1199.7081 ¢, ~121/70 = 952.1793 ¢
- CWE: ~2 = 1200.0000 ¢, ~121/70 = 952.3983 ¢
Optimal ET sequence: 29, 34d, 63
Badness (Sintel): 1.69
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:
- WE: ~2 = 1199.8625 ¢, ~26/15 = 952.2977 ¢
- CWE: ~2 = 1200.0000 ¢, ~26/15 = 952.4008 ¢
Optimal ET sequence: 29, 34d, 63
Badness (Sintel): 1.18