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Immunity family: Difference between revisions

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== Immunity ==
== 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]].  
Immunity is naturally a [[2.3.5.13 subgroup|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
[[Subgroup]]: 2.3.5
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{{Mapping|legend=1| 1 0 -8 | 0 2 13 }}
{{Mapping|legend=1| 1 0 -8 | 0 2 13 }}
: mapping generators: ~2, ~1280/729
: mapping generators: ~2, ~1280/729


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


{{Optimal ET sequence|legend=1| 5, …, 29, 34 }}
{{Optimal ET sequence|legend=1| 5, …, 29, 34 }}


[[Badness]] (Sintel): 4.334
[[Badness]] (Sintel): 4.33


=== 2.3.5.13 subgroup ===
=== 2.3.5.13 subgroup ===
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Comma list: 676/675, 3200/3159
Comma list: 676/675, 3200/3159


Sval mapping: {{mapping| 1 0 -8 -9 | 0 2 13 16 }}
Subgroup-val mapping: {{mapping| 1 0 -8 -9 | 0 2 13 16 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000¢, ~26/15 = 952.6431¢
* CTE: ~2 = 1200.0000{{c}}, ~26/15 = 952.6431{{c}}
* CWE: ~2 = 1200.0000¢, ~26/15 = 952.7890¢
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 952.7890{{c}}


{{Optimal ET sequence|legend=0| 5, …, 29, 34 }}
{{Optimal ET sequence|legend=0| 5, …, 29, 34 }}
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000¢, ~7/4 = 952.7674¢
* [[CTE]]: ~2 = 1200.0000{{c}}, ~7/4 = 952.7674{{c}}
: [[error map]]: {{val| 0.000 +3.580 -0.337 -16.058 }}
: [[error map]]: {{val| 0.000 +3.580 -0.337 -16.058 }}
* [[CWE]]: ~2 = 1200.0000¢, ~7/4 = 952.5376¢
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 952.5376{{c}}
: error map: {{val| 0.000 +3.120 -3.325 -16.288 }}
: error map: {{val| 0.000 +3.120 -3.325 -16.288 }}


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


[[Badness]] (Sintel): 1.965
[[Badness]] (Sintel): 1.96


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.4418¢
* CTE: ~2 = 1200.0000{{c}}, ~7/4 = 952.4418{{c}}
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.1429¢
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 952.1429{{c}}


{{Optimal ET sequence|legend=0| 5, 24c, 29, 63de }}
{{Optimal ET sequence|legend=0| 5, 24c, 29, 63de }}


Badness (Sintel): 1.741
Badness (Sintel): 1.74


==== 13-limit ====
==== 13-limit ====
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.4723¢
* CTE: ~2 = 1200.0000{{c}}, ~7/4 = 952.4723{{c}}
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.1117¢
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 952.1117{{c}}


{{Optimal ET sequence|legend=0| 5, 24cf, 29 }}
{{Optimal ET sequence|legend=0| 5, 24cf, 29 }}


Badness (Sintel): 1.532
Badness (Sintel): 1.53


=== Impunity ===
=== Impunity ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.5282¢
* CTE: ~2 = 1200.0000{{c}}, ~7/4 = 952.5282{{c}}
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.3120¢
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 952.3120{{c}}


{{Optimal ET sequence|legend=0| 5e, 24cee, 29 }}
{{Optimal ET sequence|legend=0| 5e, 24cee, 29 }}


Badness (Sintel): 1.826
Badness (Sintel): 1.83


==== 13-limit ====
==== 13-limit ====
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.5292¢
* CTE: ~2 = 1200.0000{{c}}, ~7/4 = 952.5292{{c}}
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.3038¢
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 952.3038{{c}}


{{Optimal ET sequence|legend=0| 5e, 24ceef, 29 }}
{{Optimal ET sequence|legend=0| 5e, 24ceef, 29 }}


Badness (Sintel): 1.372
Badness (Sintel): 1.37


== Immunized ==
== Immunized ==
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000¢, ~140/81 = 953.0010¢
* [[CTE]]: ~2 = 1200.0000{{c}}, ~140/81 = 953.0010{{c}}
: [[error map]]: {{val| 0.000 +4.047 +2.669 +19.170 }}
: [[error map]]: {{val| 0.000 +4.047 +2.669 +19.170 }}
* [[CWE]]: ~2 = 1200.0000¢, ~140/81 = 953.3954¢
* [[CWE]]: ~2 = 1200.0000{{c}}, ~140/81 = 953.3954{{c}}
: error map: {{val| 0.000 +4.836 +7.827 +17.592 }}
: error map: {{val| 0.000 +4.836 +7.827 +17.592 }}


{{Optimal ET sequence|legend=1| 5, 29d, 34d, 39d, 73dd, 112cddd }}
{{Optimal ET sequence|legend=1| 5, 29d, 34d, 39d, 73dd, 112cddd }}


[[Badness]] (Sintel): 2.090
[[Badness]] (Sintel): 2.09


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000¢, ~55/32 = 953.2713¢
* CTE: ~2 = 1200.0000{{c}}, ~55/32 = 953.2713{{c}}
* CWE: ~2 = 1200.0000¢, ~55/32 = 953.3755¢
* CWE: ~2 = 1200.0000{{c}}, ~55/32 = 953.3755{{c}}


{{Optimal ET sequence|legend=0| 5, 29de, 34d, 39d, 73dd }}
{{Optimal ET sequence|legend=0| 5, 29de, 34d, 39d, 73dd }}


Badness (Sintel): 1.703
Badness (Sintel): 1.70


== Immune ==
== Immune ==
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000¢, ~1000/567 = 952.3863¢
* [[CTE]]: ~2 = 1200.0000{{c}}, ~1000/567 = 952.3863{{c}}
: [[error map]]: {{val| 0.000 +2.818 -5.292 +2.763 }}
: [[error map]]: {{val| 0.000 +2.818 -5.292 +2.763 }}
* [[CWE]]: ~2 = 1200.0000¢, ~1000/567 = 952.4061¢
* [[CWE]]: ~2 = 1200.0000{{c}}, ~1000/567 = 952.4061{{c}}
: error map: {{val| 0.000 +2.857 -5.034 +3.357 }}
: error map: {{val| 0.000 +2.857 -5.034 +3.357 }}


{{Optimal ET sequence|legend=1| 29, 34d, 63 }}
{{Optimal ET sequence|legend=1| 29, 34d, 63 }}


[[Badness]] (Sintel): 3.665
[[Badness]] (Sintel): 3.67


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000¢, ~121/70 = 952.3747¢
* CTE: ~2 = 1200.0000{{c}}, ~121/70 = 952.3747{{c}}
* CWE: ~2 = 1200.0000¢, ~121/70 = 952.3983¢
* CWE: ~2 = 1200.0000{{c}}, ~121/70 = 952.3983{{c}}


{{Optimal ET sequence|legend=0| 29, 34d, 63 }}
{{Optimal ET sequence|legend=0| 29, 34d, 63 }}


Badness (Sintel): 1.686
Badness (Sintel): 1.69


=== 13-limit ===
=== 13-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000¢, ~26/15 = 952.3891¢
* CTE: ~2 = 1200.0000{{c}}, ~26/15 = 952.3891{{c}}
* CWE: ~2 = 1200.0000¢, ~26/15 = 952.4008¢
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 952.4008{{c}}


{{Optimal ET sequence|legend=0| 29, 34d, 63 }}
{{Optimal ET sequence|legend=0| 29, 34d, 63 }}


Badness (Sintel): 1.179
Badness (Sintel): 1.18


[[Category:Immunity family| ]] <!-- Main article -->
[[Category:Immunity family| ]] <!-- Main article -->
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