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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


[[Category:Theory]]
Comma list: 49/48, 91/90, 100/99, 352/351
[[Category:Temperament family]]
 
[[Category:Immunity]]
Mapping: {{mapping| 1 0 -8 2 -14 -9 | 0 2 13 1 22 16 }}
[[Category:Rank 2]]
 
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:Immunity family| ]] <!-- Main article -->
[[Category:Immunity| ]] <!-- Key article -->
[[Category:Temperament families]]
[[Category:Catalogs of rank-2 temperaments]]

Latest revision as of 12:01, 14 August 2026

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

Optimal tunings:

  • CTE: ~2 = 1200.0000¢, ~1280/729 = 952.7056¢
error map: ⟨0.000 +3.456 -1.141]
  • CWE: ~2 = 1200.0000¢, ~1280/729 = 952.8424¢
error map: ⟨0.000 +3.730 +0.638]

Optimal ET sequence: 5, …, 29, 34

Badness (Sintel): 4.334

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 = 1200.0000¢, ~26/15 = 952.6431¢
  • 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

See also: Semaphoresmic clan

Subgroup: 2.3.5.7

Comma list: 49/48, 2240/2187

Mapping: [⟨1 0 -8 2], ⟨0 2 13 1]]

Optimal tunings:

  • CTE: ~2 = 1200.0000¢, ~7/4 = 952.7674¢
error map: ⟨0.000 +3.580 -0.337 -16.058]
  • 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): 1.965

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 = 1200.0000¢, ~7/4 = 952.4418¢
  • CWE: ~2 = 1200.0000¢, ~7/4 = 952.1429¢

Optimal ET sequence: 5, 24c, 29, 63de

Badness (Sintel): 1.741

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 = 1200.0000¢, ~7/4 = 952.4723¢
  • CWE: ~2 = 1200.0000¢, ~7/4 = 952.1117¢

Optimal ET sequence: 5, 24cf, 29

Badness (Sintel): 1.532

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 = 1200.0000¢, ~7/4 = 952.5282¢
  • CWE: ~2 = 1200.0000¢, ~7/4 = 952.3120¢

Optimal ET sequence: 5e, 24cee, 29

Badness (Sintel): 1.826

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 = 1200.0000¢, ~7/4 = 952.5292¢
  • CWE: ~2 = 1200.0000¢, ~7/4 = 952.3038¢

Optimal ET sequence: 5e, 24ceef, 29

Badness (Sintel): 1.372

Immunized

Subgroup: 2.3.5.7

Comma list: 64/63, 8748/8575

Mapping: [⟨1 0 -8 6], ⟨0 2 13 -4]]

Optimal tunings:

  • CTE: ~2 = 1200.0000¢, ~140/81 = 953.0010¢
error map: ⟨0.000 +4.047 +2.669 +19.170]
  • 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): 2.090

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 = 1200.0000¢, ~55/32 = 953.2713¢
  • CWE: ~2 = 1200.0000¢, ~55/32 = 953.3755¢

Optimal ET sequence: 5, 29de, 34d, 39d, 73dd

Badness (Sintel): 1.703

Immune

Subgroup: 2.3.5.7

Comma list: 225/224, 781250/750141

Mapping: [⟨1 2 5 9], ⟨0 -2 -13 -30]]

Optimal tunings:

  • CTE: ~2 = 1200.0000¢, ~1000/567 = 952.3863¢
error map: ⟨0.000 +2.818 -5.292 +2.763]
  • 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): 3.665

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 = 1200.0000¢, ~121/70 = 952.3747¢
  • CWE: ~2 = 1200.0000¢, ~121/70 = 952.3983¢

Optimal ET sequence: 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: [⟨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: 29, 34d, 63

Badness (Sintel): 1.179

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