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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 = 1200.0000¢, ~1280/729 = 952.7056¢
: [[error map]]: {{val| 0.000 +3.456 -1.141 }}
* [[CWE]]: ~2 = 1200.0000¢, ~1280/729 = 952.8424¢
: error map: {{val| 0.000 +3.730 +0.638 }}


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]] (Sintel): 4.334


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 = 1200.0000¢, ~26/15 = 952.6431¢
* CWE: ~2 = 1200.0000¢, ~26/15 = 952.7890¢


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 (Sintel): 0.858


Badness: 0.0527
=== Overview to extensions ===
The second comma of the comma list defines which 7-limit family member we are looking at:  
* Septimal immunity adds [[49/48]];
* Immunized adds [[64/63]];
* Immune adds [[225/224]].


==13-limit==
== Septimal immunity ==
Commas: 49/48, 55/54, 91/90, 896/891
{{See also| Semaphoresmic clan }}


POTE generator: ~8/7 = 247.97
[[Subgroup]]: 2.3.5.7


Map: [<1 0 -8 2 9 -9|, <0 2 13 1 -7 16|]
[[Comma list]]: 49/48, 2240/2187


EDOs: 5, 29, 92cde
{{Mapping|legend=1| 1 0 -8 2 | 0 2 13 1 }}


Badness: 0.0371
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000¢, ~7/4 = 952.7674¢
: [[error map]]: {{val| 0.000 +3.580 -0.337 -16.058 }}
* [[CWE]]: ~2 = 1200.0000¢, ~7/4 = 952.5376¢
: error map: {{val| 0.000 +3.120 -3.325 -16.288 }}


==Impunity==
{{Optimal ET sequence|legend=1| 5, …, 29, 34, 63d }}
Commas: 49/48, 100/99, 1232/1215


POTE generator: ~8/7 = 247.773
[[Badness]] (Sintel): 1.965


Map: [<1 0 -8 2 -14|, <0 2 13 1 22|]
=== 11-limit ===
Subgroup: 2.3.5.7.11


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


Badness: 0.0552
Mapping: {{mapping| 1 0 -8 2 9 | 0 2 13 1 -7 }}


===13-limit===
Optimal tunings:
Commas: 49/48, 91/90, 100/99, 352/351
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.4418¢
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.1429¢


POTE generator: ~8/7 = 247.783
{{Optimal ET sequence|legend=0| 5, 24c, 29, 63de }}


Map: [<1 0 -8 2 -14 -9|, <0 2 13 1 22 16|]
Badness (Sintel): 1.741


EDOs: 29, 63d, 92cd
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Badness: 0.0332
Comma list: 49/48, 55/54, 91/90, 896/891


=Immunized=
Mapping: {{mapping| 1 0 -8 2 9 -9 | 0 2 13 1 -7 16 }}
Commas: 64/63, 8748/8575


POTE generator: ~81/70 = 246.479
Optimal tunings:  
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.4723¢
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.1117¢


Map: [<1 0 -8 6|, <0 2 13 -4|]
{{Optimal ET sequence|legend=0| 5, 24cf, 29 }}


Wedgie: <<2 13 -4 16 -12 -46||
Badness (Sintel): 1.532


EDOs: 5, 34d, 39d, 73d
=== Impunity ===
Subgroup: 2.3.5.7.11


Badness: 0.0826
Comma list: 49/48, 100/99, 1232/1215


==11-limit==
Mapping: {{mapping| 1 0 -8 2 -14 | 0 2 13 1 22 }}
Commas: 64/63, 99/98, 1944/1925


POTE generator: ~81/70 = 246.603
Optimal tunings:  
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.5282¢
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.3120¢


Map: [<1 0 -8 6 13|, <0 2 13 -4 -12|]
{{Optimal ET sequence|legend=0| 5e, 24cee, 29 }}


EDOs: 5, 34d, 39d, 73d
Badness (Sintel): 1.826


Badness: 0.0515
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
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 = 1200.0000¢, ~7/4 = 952.5292¢
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.3038¢
 
{{Optimal ET sequence|legend=0| 5e, 24ceef, 29 }}
 
Badness (Sintel): 1.372
 
== 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 = 1200.0000¢, ~140/81 = 953.0010¢
: [[error map]]: {{val| 0.000 +4.047 +2.669 +19.170 }}
* [[CWE]]: ~2 = 1200.0000¢, ~140/81 = 953.3954¢
: error map: {{val| 0.000 +4.836 +7.827 +17.592 }}
 
{{Optimal ET sequence|legend=1| 5, 29d, 34d, 39d, 73dd, 112cddd }}
 
[[Badness]] (Sintel): 2.090
 
=== 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 = 1200.0000¢, ~55/32 = 953.2713¢
* CWE: ~2 = 1200.0000¢, ~55/32 = 953.3755¢
 
{{Optimal ET sequence|legend=0| 5, 29de, 34d, 39d, 73dd }}
 
Badness (Sintel): 1.703
 
== 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 = 1200.0000¢, ~1000/567 = 952.3863¢
: [[error map]]: {{val| 0.000 +2.818 -5.292 +2.763 }}
* [[CWE]]: ~2 = 1200.0000¢, ~1000/567 = 952.4061¢
: error map: {{val| 0.000 +2.857 -5.034 +3.357 }}
 
{{Optimal ET sequence|legend=1| 29, 34d, 63 }}
 
[[Badness]] (Sintel): 3.665
 
=== 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 = 1200.0000¢, ~121/70 = 952.3747¢
* CWE: ~2 = 1200.0000¢, ~121/70 = 952.3983¢
 
{{Optimal ET sequence|legend=0| 29, 34d, 63 }}
 
Badness (Sintel): 1.686
 
=== 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 = 1200.0000¢, ~26/15 = 952.3891¢
* CWE: ~2 = 1200.0000¢, ~26/15 = 952.4008¢
 
{{Optimal ET sequence|legend=0| 29, 34d, 63 }}
 
Badness (Sintel): 1.179
 
[[Category:Temperament families]]
[[Category:Immunity family| ]] <!-- Main article -->
[[Category:Immunity| ]] <!-- Key article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Immunity_family"