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__FORCETOC__
{{Technical data page}}
=Immunity=
The '''immunity family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[immunity comma]], 1638400/1594323 ({{monzo| 16 -13 2 }}).
Comma: 1638400/1594323


POTE generator: ~729/640 = 247.070
== 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]].  


Map: [<1 0 -8|, <0 2 13|]
[[Subgroup]]: 2.3.5


EDOs: 5, 29, 34
[[Comma list]]: 1638400/1594323


Badness: 0.18473
{{Mapping|legend=1| 1 0 -8 | 0 2 13 }}


==7-limit==
: mapping generators: ~2, ~1280/729
Commas: 49/48, 2240/2187


POTE generator: ~8/7 = 247.555
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~1280/729 = 952.706
: [[error map]]: {{val| 0.000 +3.456 -1.141 }}
* [[POTE]]: ~2 = 1200.000, ~1280/729 = 952.930
: error map: {{val| 0.000 +3.905 +1.775 }}


Map: [<1 0 -8 2|, <0 2 13 1|]
{{Optimal ET sequence|legend=1| 5, …, 29, 34 }}


Wedgie: <<2 13 1 16 -4 -34||
[[Badness]] (Smith): 0.184738


EDOs: 5, 29, 34
=== 2.3.5.13 subgroup ===
Subgroup: 2.3.5.13


Badness: 0.0776
Comma list: 676/675, 3200/3159


==11-limit==
Sval mapping: {{mapping| 1 0 -8 -9 | 0 2 13 16 }}
Commas: 49/48, 55/54, 896/891


POTE generator: ~8/7 = 247.926
Optimal tunings:  
* CTE: ~2 = 1200.000, ~26/15 = 952.643
* CWE: ~2 = 1200.000, ~26/15 = 952.789


Map: [<1 0 -8 2 9|, <0 2 13 1 -7|]
{{Optimal ET sequence|legend=0| 5, …, 29, 34 }}


EDOs: 5, 29, 63de, 92cde
Badness (Smith): 0.257


Badness: 0.0527
== Septimal immunity ==
{{See also| Semaphoresmic clan }}


==13-limit==
[[Subgroup]]: 2.3.5.7
Commas: 49/48, 55/54, 91/90, 896/891


POTE generator: ~8/7 = 247.97
[[Comma list]]: 49/48, 2240/2187


Map: [<1 0 -8 2 9 -9|, <0 2 13 1 -7 16|]
{{Mapping|legend=1| 1 0 -8 2 | 0 2 13 1 }}


EDOs: 5, 29, 92cde
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~7/4 = 952.767
: [[error map]]: {{val| 0.000 +3.580 -0.337 -16.058 }}
* [[POTE]]: ~2 = 1200.000, ~7/4 = 952.445
: error map: {{val| 0.000 +2.936 -4.525 -16.381 }}


Badness: 0.0371
{{Optimal ET sequence|legend=1| 5, …, 29, 34, 63d }}


==Impunity==
[[Badness]] (Smith): 0.077631
Commas: 49/48, 100/99, 1232/1215


POTE generator: ~8/7 = 247.773
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [<1 0 -8 2 -14|, <0 2 13 1 22|]
Comma list: 49/48, 55/54, 896/891


EDOs: 29, 63d, 92cd
Mapping: {{mapping| 1 0 -8 2 9 | 0 2 13 1 -7 }}


Badness: 0.0552
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/4 = 952.442
* POTE: ~2 = 1200.000, ~7/4 = 952.074


===13-limit===
{{Optimal ET sequence|legend=0| 5, 24c, 29, 63de }}
Commas: 49/48, 91/90, 100/99, 352/351


POTE generator: ~8/7 = 247.783
Badness (Smith): 0.052661


Map: [<1 0 -8 2 -14 -9|, <0 2 13 1 22 16|]
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


EDOs: 29, 63d, 92cd
Comma list: 49/48, 55/54, 91/90, 896/891


Badness: 0.0332
Mapping: {{mapping| 1 0 -8 2 9 -9 | 0 2 13 1 -7 16 }}


=Immunized=
Optimal tunings:
Commas: 64/63, 8748/8575
* CTE: ~2 = 1200.000, ~7/4 = 952.472
* POTE: ~2 = 1200.000, ~7/4 = 952.031


POTE generator: ~81/70 = 246.479
{{Optimal ET sequence|legend=0| 5, 24cf, 29 }}


Map: [<1 0 -8 6|, <0 2 13 -4|]
Badness (Smith): 0.037078


Wedgie: <<2 13 -4 16 -12 -46||
=== Impunity ===
Subgroup: 2.3.5.7.11


EDOs: 5, 34d, 39d, 73d
Comma list: 49/48, 100/99, 1232/1215


Badness: 0.0826
Mapping: {{mapping| 1 0 -8 2 -14 | 0 2 13 1 22 }}


==11-limit==
Optimal tunings:
Commas: 64/63, 99/98, 1944/1925
* CTE: ~2 = 1200.000, ~7/4 = 952.528
* POTE: ~2 = 1200.000, ~7/4 = 952.227


POTE generator: ~81/70 = 246.603
{{Optimal ET sequence|legend=0| 5e, 24cee, 29 }}


Map: [<1 0 -8 6 13|, <0 2 13 -4 -12|]
Badness (Smith): 0.055243


EDOs: 5, 34d, 39d, 73d
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Badness: 0.0515
Comma list: 49/48, 91/90, 100/99, 352/351
 
Mapping: {{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|legend=0| 5e, 24ceef, 29 }}
 
Badness (Smith): 0.033196
 
== Immunized ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 64/63, 8748/8575
 
{{Mapping|legend=1| 1 0 -8 6 | 0 2 13 -4 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~140/81 = 953.001
: [[error map]]: {{val| 0.000 +4.047 +2.669 +19.170 }}
* [[POTE]]: ~2 = 1200.000, ~140/81 = 953.521
: error map: {{val| 0.000 +5.088 +9.463 +17.089 }}
 
{{Optimal ET sequence|legend=1| 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: {{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|legend=0| 5, 29de, 34d, 39d, 73dd }}
 
Badness (Smith): 0.051515
 
== Immune ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 781250/750141
 
{{Mapping|legend=1| 1 2 5 9 | 0 -2 -13 -30 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~1000/567 = 952.386
: [[error map]]: {{val| 0.000 +2.818 -5.292 +2.763 }}
* [[POTE]]: ~2 = 1200.000, ~1000/567 = 952.417
: error map: {{val| 0.000 +2.879 -4.893 +3.683 }}
 
{{Optimal ET sequence|legend=1| 29, 34d, 63 }}
 
[[Badness]] (Smith): 0.144835
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 100/99, 225/224, 1331/1323
 
Mapping: {{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|legend=0| 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: {{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|legend=0| 29, 34d, 63 }}
 
Badness (Smith): 0.028521
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Immunity family| ]] <!-- Main article -->
[[Category:Immunity| ]] <!-- Key article -->
[[Category:Rank 2]]
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