Immunity family: Difference between revisions

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== Immunity ==
== Immunity ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


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


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


[[POTE generator]]: ~729/640 = 247.070
: mapping generators: ~2, ~1280/729
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~1280/729 = 952.930


{{Optimal ET sequence|legend=1| 5, 29, 34 }}
{{Optimal ET sequence|legend=1| 5, 29, 34 }}
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[[Badness]]: 0.184738
[[Badness]]: 0.184738


=== 7-limit ===
== Septimal immunity ==
Subgroup: 2.3.5.7
{{See also| Slendro clan }}
 
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 49/48, 2240/2187
[[Comma list]]: 49/48, 2240/2187


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


{{Multival|legend=1|2 13 1 16 -4 -34}}
{{Multival|legend=1| 2 13 1 16 -4 -34 }}


[[POTE generator]]: ~7/6 = 247.555
[[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 }}
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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: [{{val| 1 0 -8 2 9 }}, {{val| 0 2 13 1 -7 }}]


POTE generator: ~7/6 = 247.926
Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.074


{{Optimal ET sequence|legend=1| 5, 24c, 29, 63de, 92cddee }}
{{Optimal ET sequence|legend=1| 5, 24c, 29, 63de, 92cddee }}
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Mapping: [{{val|1 0 -8 2 9 -9}}, {{val|0 2 13 1 -7 16}}]
Mapping: [{{val|1 0 -8 2 9 -9}}, {{val|0 2 13 1 -7 16}}]


POTE generator: ~7/6 = 247.969
Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.031


{{Optimal ET sequence|legend=1| 5, 24cf, 29, 92cddee }}
{{Optimal ET sequence|legend=1| 5, 24cf, 29, 92cddee }}
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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: [{{val| 1 0 -8 2 -14 }}, {{val| 0 2 13 1 22 }}]


POTE generator: ~7/6 = 247.773
Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.227


{{Optimal ET sequence|legend=1| 29, 63d, 92cdd }}
{{Optimal ET sequence|legend=1| 29, 63d, 92cdd }}
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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: [{{val| 1 0 -8 2 -14 -9 }}, {{val| 0 2 13 1 22 16 }}]


POTE generator: ~7/6 = 247.783
Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.217


{{Optimal ET sequence|legend=1| 29, 63d, 92cdd }}
{{Optimal ET sequence|legend=1| 29, 63d, 92cdd }}
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== Immunized ==
== Immunized ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 64/63, 8748/8575
[[Comma list]]: 64/63, 8748/8575


[[Mapping]]: [{{val|1 0 -8 6}}, {{val|0 2 13 -4}}]
[[Mapping]]: [{{val| 1 0 -8 6 }}, {{val| 0 2 13 -4 }}]


{{Multival|legend=1|2 13 -4 16 -12 -46}}
{{Multival|legend=1|2 13 -4 16 -12 -46}}


[[POTE generator]]: ~81/70 = 246.479
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~140/81 = 953.521


{{Optimal ET sequence|legend=1| 5, 34d, 39d, 73dd }}
{{Optimal ET sequence|legend=1| 5, 34d, 39d, 73dd }}
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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: [{{val| 1 0 -8 6 13 }}, {{val| 0 2 13 -4 -12 }}]


POTE generator: ~64/55 = 246.603
Optimal tuning (POTE): ~2 = 1\1, ~55/32 = 953.397


{{Optimal ET sequence|legend=1| 5, 34d, 39d, 73dd }}
{{Optimal ET sequence|legend=1| 5, 34d, 39d, 73dd }}
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== Immune ==
== Immune ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 781250/750141
[[Comma list]]: 225/224, 781250/750141


[[Mapping]]: [{{val|1 2 5 9}}, {{val|0 -2 -13 -30}}]
[[Mapping]]: [{{val| 1 2 5 9 }}, {{val| 0 -2 -13 -30 }}]


{{Multival|legend=1|2 13 30 16 42 33}}
{{Multival|legend=1| 2 13 30 16 42 33 }}


[[POTE generator]]: ~567/500 = 247.583
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~1000/567 = 952.417


{{Optimal ET sequence|legend=1| 29, 34d, 63 }}
{{Optimal ET sequence|legend=1| 29, 34d, 63 }}
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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: [{{val| 1 2 5 9 8 }}, {{val| 0 -2 -13 -30 -22 }}]


POTE generator: ~140/121 = 247.589
Optimal tuning (POTE): ~2 = 1\1, ~121/70 = 952.411


{{Optimal ET sequence|legend=1| 29, 34d, 63 }}
{{Optimal ET sequence|legend=1| 29, 34d, 63 }}
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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: [{{val| 1 2 5 9 8 7 }}, {{val| 0 -2 -13 -30 -22 -16 }}]


POTE generator: ~15/13 = 247.593
Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 952.407


{{Optimal ET sequence|legend=1| 29, 34d, 63 }}
{{Optimal ET sequence|legend=1| 29, 34d, 63 }}
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[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Immunity family| ]] <!-- main article -->
[[Category:Immunity family| ]] <!-- main article -->
[[Category:Immunity]]
[[Category:Immunity| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Revision as of 07:35, 15 May 2023

Temperaments of immunity family temper out the immunity comma, 1638400/1594323 = [16-13 2⟩ (sasayoyo).

Immunity

Subgroup: 2.3.5

Comma list: 1638400/1594323

Mapping: [⟨1 0 -8], ⟨0 2 13]]

mapping generators: ~2, ~1280/729

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

Optimal ET sequence: 5, 29, 34

Badness: 0.184738

Septimal immunity

See also: Slendro clan

Subgroup: 2.3.5.7

Comma list: 49/48, 2240/2187

Mapping: [⟨1 0 -8 2], ⟨0 2 13 1]]

Wedgie: ⟨⟨ 2 13 1 16 -4 -34 ]]

Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.445

Optimal ET sequence: 5, 29, 34, 63d

Badness: 0.077631

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 tuning (POTE): ~2 = 1\1, ~7/4 = 952.074

Optimal ET sequence: 5, 24c, 29, 63de, 92cddee

Badness: 0.052661

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 tuning (POTE): ~2 = 1\1, ~7/4 = 952.031

Optimal ET sequence: 5, 24cf, 29, 92cddee

Badness: 0.037078

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 tuning (POTE): ~2 = 1\1, ~7/4 = 952.227

Optimal ET sequence: 29, 63d, 92cdd

Badness: 0.055243

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 tuning (POTE): ~2 = 1\1, ~7/4 = 952.217

Optimal ET sequence: 29, 63d, 92cdd

Badness: 0.033196

Immunized

Subgroup: 2.3.5.7

Comma list: 64/63, 8748/8575

Mapping: [⟨1 0 -8 6], ⟨0 2 13 -4]]

Wedgie: ⟨⟨ 2 13 -4 16 -12 -46 ]]

Optimal tuning (POTE): ~2 = 1\1, ~140/81 = 953.521

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

Badness: 0.082592

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 tuning (POTE): ~2 = 1\1, ~55/32 = 953.397

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

Badness: 0.051515

Immune

Subgroup: 2.3.5.7

Comma list: 225/224, 781250/750141

Mapping: [⟨1 2 5 9], ⟨0 -2 -13 -30]]

Wedgie: ⟨⟨ 2 13 30 16 42 33 ]]

Optimal tuning (POTE): ~2 = 1\1, ~1000/567 = 952.417

Optimal ET sequence: 29, 34d, 63

Badness: 0.144835

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 tuning (POTE): ~2 = 1\1, ~121/70 = 952.411

Optimal ET sequence: 29, 34d, 63

Badness: 0.050990

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 tuning (POTE): ~2 = 1\1, ~26/15 = 952.407

Optimal ET sequence: 29, 34d, 63

Badness: 0.028521

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