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Immunity family: Difference between revisions

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


== Immunity ==
== Immunity ==
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: mapping generators: ~2, ~1280/729
: mapping generators: ~2, ~1280/729


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~1280/729 = 952.930
[[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 }}


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


[[Badness]]: 0.184738
[[Badness]] (Smith): 0.184738


=== 2.3.5.13 subgroup ===
=== 2.3.5.13 subgroup ===
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Sval mapping: {{mapping| 1 0 -8 -9 | 0 2 13 16 }}
Sval mapping: {{mapping| 1 0 -8 -9 | 0 2 13 16 }}


Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 952.6431
Optimal tunings:
* CTE: ~2 = 1200.000, ~26/15 = 952.643
* CWE: ~2 = 1200.000, ~26/15 = 952.789


{{Optimal ET sequence|legend=1| 5, …, 29, 34 }}
{{Optimal ET sequence|legend=0| 5, …, 29, 34 }}


Badness: 0.257
Badness (Smith): 0.257


== Septimal immunity ==
== Septimal immunity ==
{{See also| Slendro clan }}
{{See also| Semaphoresmic clan }}


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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{{Mapping|legend=1| 1 0 -8 2 | 0 2 13 1 }}
{{Mapping|legend=1| 1 0 -8 2 | 0 2 13 1 }}


{{Multival|legend=1| 2 13 1 16 -4 -34 }}
[[Optimal tuning]]s:
 
* [[CTE]]: ~2 = 1200.000, ~7/4 = 952.767
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/4 = 952.445
: [[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 }}


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


[[Badness]]: 0.077631
[[Badness]] (Smith): 0.077631


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 0 -8 2 9 | 0 2 13 1 -7 }}
Mapping: {{mapping| 1 0 -8 2 9 | 0 2 13 1 -7 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.074
Optimal tunings:
* CTE: ~2 = 1200.000, ~7/4 = 952.442
* POTE: ~2 = 1200.000, ~7/4 = 952.074


{{Optimal ET sequence|legend=1| 5, 24c, 29, 63de }}
{{Optimal ET sequence|legend=0| 5, 24c, 29, 63de }}


Badness: 0.052661
Badness (Smith): 0.052661


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 1 0 -8 2 9 -9 | 0 2 13 1 -7 16 }}
Mapping: {{mapping| 1 0 -8 2 9 -9 | 0 2 13 1 -7 16 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.031
Optimal tunings:
* CTE: ~2 = 1200.000, ~7/4 = 952.472
* POTE: ~2 = 1200.000, ~7/4 = 952.031


{{Optimal ET sequence|legend=1| 5, 24cf, 29 }}
{{Optimal ET sequence|legend=0| 5, 24cf, 29 }}


Badness: 0.037078
Badness (Smith): 0.037078


=== Impunity ===
=== Impunity ===
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Mapping: {{mapping| 1 0 -8 2 -14 | 0 2 13 1 22 }}
Mapping: {{mapping| 1 0 -8 2 -14 | 0 2 13 1 22 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.227
Optimal tunings:
* CTE: ~2 = 1200.000, ~7/4 = 952.528
* POTE: ~2 = 1200.000, ~7/4 = 952.227


{{Optimal ET sequence|legend=1| 5e, 24cee, 29 }}
{{Optimal ET sequence|legend=0| 5e, 24cee, 29 }}


Badness: 0.055243
Badness (Smith): 0.055243


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 1 0 -8 2 -14 -9 | 0 2 13 1 22 16 }}
Mapping: {{mapping| 1 0 -8 2 -14 -9 | 0 2 13 1 22 16 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.217
Optimal tunings:
* CTE: ~2 = 1200.000, ~7/4 = 952.529
* POTE: ~2 = 1200.000, ~7/4 = 952.217


{{Optimal ET sequence|legend=1| 5e, 24ceef, 29 }}
{{Optimal ET sequence|legend=0| 5e, 24ceef, 29 }}


Badness: 0.033196
Badness (Smith): 0.033196


== Immunized ==
== Immunized ==
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{{Mapping|legend=1| 1 0 -8 6 | 0 2 13 -4 }}
{{Mapping|legend=1| 1 0 -8 6 | 0 2 13 -4 }}


{{Multival|legend=1| 2 13 -4 16 -12 -46 }}
[[Optimal tuning]]s:
 
* [[CTE]]: ~2 = 1200.000, ~140/81 = 953.001
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~140/81 = 953.521
: [[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 }}
{{Optimal ET sequence|legend=1| 5, 29d, 34d, 39d, 73dd, 112cddd }}


[[Badness]]: 0.082592
[[Badness]] (Smith): 0.082592


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 0 -8 6 13 | 0 2 13 -4 -12 }}
Mapping: {{mapping| 1 0 -8 6 13 | 0 2 13 -4 -12 }}


Optimal tuning (POTE): ~2 = 1\1, ~55/32 = 953.397
Optimal tunings:
* CTE: ~2 = 1200.000, ~55/32 = 953.271
* POTE: ~2 = 1200.000, ~55/32 = 953.397


{{Optimal ET sequence|legend=1| 5, 29de, 34d, 39d, 73dd }}
{{Optimal ET sequence|legend=0| 5, 29de, 34d, 39d, 73dd }}


Badness: 0.051515
Badness (Smith): 0.051515


== Immune ==
== Immune ==
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{{Mapping|legend=1| 1 2 5 9 | 0 -2 -13 -30 }}
{{Mapping|legend=1| 1 2 5 9 | 0 -2 -13 -30 }}


{{Multival|legend=1| 2 13 30 16 42 33 }}
[[Optimal tuning]]s:
 
* [[CTE]]: ~2 = 1200.000, ~1000/567 = 952.386
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~1000/567 = 952.417
: [[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 }}
{{Optimal ET sequence|legend=1| 29, 34d, 63 }}


[[Badness]]: 0.144835
[[Badness]] (Smith): 0.144835


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 2 5 9 8 | 0 -2 -13 -30 -22 }}
Mapping: {{mapping| 1 2 5 9 8 | 0 -2 -13 -30 -22 }}


Optimal tuning (POTE): ~2 = 1\1, ~121/70 = 952.411
Optimal tunings:
* CTE: ~2 = 1200.000, ~121/70 = 952.375
* POTE: ~2 = 1200.000, ~121/70 = 952.411


{{Optimal ET sequence|legend=1| 29, 34d, 63 }}
{{Optimal ET sequence|legend=0| 29, 34d, 63 }}


Badness: 0.050990
Badness (Smith): 0.050990


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 2 5 9 8 7 | 0 -2 -13 -30 -22 -16 }}
Mapping: {{mapping| 1 2 5 9 8 7 | 0 -2 -13 -30 -22 -16 }}


Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 952.407
Optimal tunings:
* CTE: ~2 = 1200.000, ~26/15 = 952.389
* POTE: ~2 = 1200.000, ~26/15 = 952.407


{{Optimal ET sequence|legend=1| 29, 34d, 63 }}
{{Optimal ET sequence|legend=0| 29, 34d, 63 }}


Badness: 0.028521
Badness (Smith): 0.028521


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Immunity family| ]] <!-- Main article -->
[[Category:Immunity family| ]] <!-- Main article -->
[[Category:Immunity| ]] <!-- Key article -->
[[Category:Immunity| ]] <!-- Key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Immunity_family"