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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 ==
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
[[Subgroup]]: 2.3.5


[[Comma list]]: 1638400/1594323
[[Comma list]]: 1638400/1594323


[[Mapping]]: [{{val| 1 0 -8 }}, {{val| 0 2 13 }}]
{{Mapping|legend=1| 1 0 -8 | 0 2 13 }}


: 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 }}
 
[[Badness]] (Smith): 0.184738
 
=== 2.3.5.13 subgroup ===
Subgroup: 2.3.5.13
 
Comma list: 676/675, 3200/3159
 
Sval mapping: {{mapping| 1 0 -8 -9 | 0 2 13 16 }}
 
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]]: 0.184738
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
Line 23: Line 45:
[[Comma list]]: 49/48, 2240/2187
[[Comma list]]: 49/48, 2240/2187


[[Mapping]]: [{{val| 1 0 -8 2 }}, {{val| 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
: [[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 tuning]] ([[POTE]]): ~2 = 1\1, ~7/4 = 952.445
{{Optimal ET sequence|legend=1| 5, …, 29, 34, 63d }}


{{Optimal ET sequence|legend=1| 5, 29, 34, 63d }}
[[Badness]] (Smith): 0.077631
 
[[Badness]]: 0.077631


=== 11-limit ===
=== 11-limit ===
Line 38: Line 62:
Comma list: 49/48, 55/54, 896/891
Comma list: 49/48, 55/54, 896/891


Mapping: [{{val| 1 0 -8 2 9 }}, {{val| 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, 92cddee }}
{{Optimal ET sequence|legend=0| 5, 24c, 29, 63de }}


Badness: 0.052661
Badness (Smith): 0.052661


==== 13-limit ====
==== 13-limit ====
Line 51: Line 77:
Comma list: 49/48, 55/54, 91/90, 896/891
Comma list: 49/48, 55/54, 91/90, 896/891


Mapping: [{{val|1 0 -8 2 9 -9}}, {{val|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, 92cddee }}
{{Optimal ET sequence|legend=0| 5, 24cf, 29 }}


Badness: 0.037078
Badness (Smith): 0.037078


=== Impunity ===
=== Impunity ===
Line 64: Line 92:
Comma list: 49/48, 100/99, 1232/1215
Comma list: 49/48, 100/99, 1232/1215


Mapping: [{{val| 1 0 -8 2 -14 }}, {{val| 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| 29, 63d, 92cdd }}
{{Optimal ET sequence|legend=0| 5e, 24cee, 29 }}


Badness: 0.055243
Badness (Smith): 0.055243


==== 13-limit ====
==== 13-limit ====
Line 77: Line 107:
Comma list: 49/48, 91/90, 100/99, 352/351
Comma list: 49/48, 91/90, 100/99, 352/351


Mapping: [{{val| 1 0 -8 2 -14 -9 }}, {{val| 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| 29, 63d, 92cdd }}
{{Optimal ET sequence|legend=0| 5e, 24ceef, 29 }}


Badness: 0.033196
Badness (Smith): 0.033196


== Immunized ==
== Immunized ==
Line 90: Line 122:
[[Comma list]]: 64/63, 8748/8575
[[Comma list]]: 64/63, 8748/8575


[[Mapping]]: [{{val| 1 0 -8 6 }}, {{val| 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]] ([[POTE]]): ~2 = 1\1, ~140/81 = 953.521
[[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, 34d, 39d, 73dd }}
{{Optimal ET sequence|legend=1| 5, 29d, 34d, 39d, 73dd, 112cddd }}


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


=== 11-limit ===
=== 11-limit ===
Line 105: Line 139:
Comma list: 64/63, 99/98, 1944/1925  
Comma list: 64/63, 99/98, 1944/1925  


Mapping: [{{val| 1 0 -8 6 13 }}, {{val| 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, 34d, 39d, 73dd }}
{{Optimal ET sequence|legend=0| 5, 29de, 34d, 39d, 73dd }}


Badness: 0.051515
Badness (Smith): 0.051515


== Immune ==
== Immune ==
Line 118: Line 154:
[[Comma list]]: 225/224, 781250/750141
[[Comma list]]: 225/224, 781250/750141


[[Mapping]]: [{{val| 1 2 5 9 }}, {{val| 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]] ([[POTE]]): ~2 = 1\1, ~1000/567 = 952.417
[[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 }}
{{Optimal ET sequence|legend=1| 29, 34d, 63 }}


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


=== 11-limit ===
=== 11-limit ===
Line 133: Line 171:
Comma list: 100/99, 225/224, 1331/1323
Comma list: 100/99, 225/224, 1331/1323


Mapping: [{{val| 1 2 5 9 8 }}, {{val| 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 ===
Line 146: Line 186:
Comma list: 100/99, 169/168, 225/224, 275/273
Comma list: 100/99, 169/168, 225/224, 275/273


Mapping: [{{val| 1 2 5 9 8 7 }}, {{val| 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:Immunity family| ]] <!-- main article -->
[[Category:Pages with mostly numerical content]]
[[Category:Immunity| ]] <!-- key article -->
[[Category:Immunity family| ]] <!-- Main article -->
[[Category:Immunity| ]] <!-- Key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Immunity_family"