Immunity family: Difference between revisions
+CTE tunings. +error maps. Spell the periods in cents. Note the badness metric being used. Misc. cleanup |
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{{Technical data page}} | |||
The '''immunity family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[immunity comma]], 1638400/1594323 ({{monzo| 16 -13 2 }}). | The '''immunity family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[immunity comma]], 1638400/1594323 ({{monzo| 16 -13 2 }}). | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
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[[Category:Immunity family| ]] <!-- Main article --> | [[Category:Immunity family| ]] <!-- Main article --> | ||
[[Category:Immunity| ]] <!-- Key article --> | [[Category:Immunity| ]] <!-- Key article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Latest revision as of 00:39, 24 June 2025
- 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, 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]]
- 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]]
- 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]]
- 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