Immunity family: Difference between revisions

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Line 6: Line 6:
[[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
Line 23: Line 23:
[[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 }}
{{Multival|legend=1| 2 13 1 16 -4 -34 }}
Line 38: Line 38:
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 tuning (POTE): ~2 = 1\1, ~7/4 = 952.074
Line 51: Line 51:
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 tuning (POTE): ~2 = 1\1, ~7/4 = 952.031
Line 64: Line 64:
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 tuning (POTE): ~2 = 1\1, ~7/4 = 952.227
Line 77: Line 77:
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 tuning (POTE): ~2 = 1\1, ~7/4 = 952.217
Line 90: Line 90:
[[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}}
{{Multival|legend=1| 2 13 -4 16 -12 -46 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~140/81 = 953.521
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~140/81 = 953.521
Line 105: Line 105:
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 tuning (POTE): ~2 = 1\1, ~55/32 = 953.397
Line 118: Line 118:
[[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 }}
{{Multival|legend=1| 2 13 30 16 42 33 }}
Line 133: Line 133:
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 tuning (POTE): ~2 = 1\1, ~121/70 = 952.411
Line 146: Line 146:
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 tuning (POTE): ~2 = 1\1, ~26/15 = 952.407

Revision as of 11:50, 26 August 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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