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Aberschismic temperaments: Difference between revisions

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[[Comma list]]: 5120/5103, 235298/234375
[[Comma list]]: 5120/5103, 235298/234375


[[Mapping]]: [{{val| 1 0 61 71 }}, {{val| 0 1 -37 -43 }}]
{{Mapping|legend=1| 1 0 61 71 | 0 1 -37 -43 }}


{{Multival|legend=1| 1 -37 -43 -61 -71 4 }}
{{Multival|legend=1| 1 -37 -43 -61 -71 4 }}
Line 52: Line 52:
[[Comma list]]: 686/675, 5120/5103
[[Comma list]]: 686/675, 5120/5103


[[Mapping]]: [{{val| 1 0 -31 -21 }}, {{val| 0 1 21 15 }}]
{{Mapping|legend=1| 1 0 -31 -21 | 0 1 21 15 }}


{{Multival|legend=1| 1 21 15 31 21 -24 }}
{{Multival|legend=1| 1 21 15 31 21 -24 }}
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Comma list: 121/120, 441/440, 686/675
Comma list: 121/120, 441/440, 686/675


Mapping: [{{val| 1 0 -31 -21 -14 }}, {{val| 0 1 21 15 11 }}]
Mapping: {{mapping| 1 0 -31 -21 -14 | 0 1 21 15 11 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.250
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.250
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Comma list: 91/90, 121/120, 169/168, 352/351
Comma list: 91/90, 121/120, 169/168, 352/351


Mapping: [{{val| 1 0 -31 -21 -14 -9 }}, {{val| 0 1 21 15 11 8 }}]
Mapping: {{mapping| 1 0 -31 -21 -14 -9 | 0 1 21 15 11 8 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.214
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.214
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Comma list: 91/90, 121/120, 136/135, 154/153, 169/168
Comma list: 91/90, 121/120, 136/135, 154/153, 169/168


Mapping: [{{val| 1 0 -31 -21 -14 -9 -34 }}, {{val| 0 1 21 15 11 8 24 }}]
Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 | 0 1 21 15 11 8 24 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.229
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.229
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Comma list: 91/90, 121/120, 133/132, 136/135, 154/153, 169/168
Comma list: 91/90, 121/120, 133/132, 136/135, 154/153, 169/168


Mapping: [{{val| 1 0 -31 -21 -14 -9 -34 9 }}, {{val| 0 1 21 15 11 8 24 -3 }}]
Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 9 | 0 1 21 15 11 8 24 -3 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.135
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.135
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Comma list: 91/90, 121/120, 133/132, 136/135, 154/153, 161/160, 169/168
Comma list: 91/90, 121/120, 133/132, 136/135, 154/153, 161/160, 169/168


Mapping: [{{val| 1 0 -31 -21 -14 -9 -34 9 -5 }}, {{val| 0 1 21 15 11 8 24 -3 6 }}]
Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 9 -5 | 0 1 21 15 11 8 24 -3 6 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.141
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.141
Line 132: Line 132:
Comma list: 77/76, 91/90, 121/120, 136/135, 153/152, 169/168
Comma list: 77/76, 91/90, 121/120, 136/135, 153/152, 169/168


Mapping: [{{val| 1 0 -31 -21 -14 -9 -34 -37 }}, {{val| 0 1 21 15 11 8 24 26 }}]
Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 -37 | 0 1 21 15 11 8 24 26 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.123
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.123
Line 145: Line 145:
Comma list: 77/76, 91/90, 115/114, 121/120, 136/135, 153/152, 161/160
Comma list: 77/76, 91/90, 115/114, 121/120, 136/135, 153/152, 161/160


Mapping: [{{val| 1 0 -31 -21 -14 -9 -34 -37 -5 }}, {{val| 0 1 21 15 11 8 24 26 6 }}]
Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 -37 -5 | 0 1 21 15 11 8 24 26 6 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.114
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.114
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[[Comma list]]: 5120/5103, 50421/50000
[[Comma list]]: 5120/5103, 50421/50000


[[Mapping]]: [{{val| 29 46 0 14 }}, {{val| 0 0 1 1 }}]
{{Mapping|legend=1| 29 46 0 14 | 0 0 1 1 }}


{{Multival|legend=1| 0 29 29 46 46 -14 }}
{{Multival|legend=1| 0 29 29 46 46 -14 }}
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Comma list: 441/440, 896/891, 3388/3375
Comma list: 441/440, 896/891, 3388/3375


Mapping: [{{val| 29 46 0 14 33 }}, {{val| 0 0 1 1 1 }}]
Mapping: {{mapping| 29 46 0 14 33 | 0 0 1 1 1 }}


Optimal tuning (POTE): ~45/44 = 1\29, ~5/4 = 388.460
Optimal tuning (POTE): ~45/44 = 1\29, ~5/4 = 388.460
Line 191: Line 191:
Comma list: 196/195, 352/351, 364/363, 676/675
Comma list: 196/195, 352/351, 364/363, 676/675


Mapping: [{{val| 29 46 0 14 33 40 }}, {{val| 0 0 1 1 1 1 }}]
Mapping: {{mapping| 29 46 0 14 33 40 | 0 0 1 1 1 1 }}


Optimal tuning (POTE): ~45/44 = 1\29, ~5/4 = 388.354
Optimal tuning (POTE): ~45/44 = 1\29, ~5/4 = 388.354
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[[Comma list]]: 5120/5103, 5832000/5764801
[[Comma list]]: 5120/5103, 5832000/5764801


[[Mapping]]: [{{val| 1 1 -4 0 }}, {{val| 0 5 54 24 }}]
{{Mapping|legend=1| 1 1 -4 0 | 0 5 54 24 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~160/147 = 140.493
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~160/147 = 140.493
Line 217: Line 217:
Comma list: 540/539, 1331/1323, 5120/5103
Comma list: 540/539, 1331/1323, 5120/5103


Mapping: [{{val| 1 1 -4 0 1 }}, {{val| 0 5 54 24 21 }}]
Mapping: {{mapping| 1 1 -4 0 1 | 0 5 54 24 21 }}


Optimal tuning (POTE): ~2 = 1\1, ~88/81 = 140.489
Optimal tuning (POTE): ~2 = 1\1, ~88/81 = 140.489
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Comma list: 352/351, 540/539, 729/728, 1331/1323
Comma list: 352/351, 540/539, 729/728, 1331/1323


Mapping: [{{val| 1 1 -4 0 1 3 }}, {{val| 0 5 54 24 21 6 }}]
Mapping: {{mapping| 1 1 -4 0 1 3 | 0 5 54 24 21 6 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.496
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.496
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Comma list: 352/351, 442/441, 540/539, 715/714, 847/845
Comma list: 352/351, 442/441, 540/539, 715/714, 847/845


Mapping: [{{val| 1 1 -4 0 1 3 -2 }}, {{val| 0 5 54 24 21 6 52 }}]
Mapping: {{mapping| 1 1 -4 0 1 3 -2 | 0 5 54 24 21 6 52 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.497
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.497
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Comma list: 352/351, 400/399, 442/441, 456/455, 495/494, 715/714
Comma list: 352/351, 400/399, 442/441, 456/455, 495/494, 715/714


Mapping: [{{val| 1 1 -4 0 1 3 -2 -5 }}, {{val| 0 5 54 24 21 6 52 79 }}]
Mapping: {{mapping| 1 1 -4 0 1 3 -2 -5 | 0 5 54 24 21 6 52 79 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.496
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.496
Line 269: Line 269:
[[Comma list]]: 5120/5103, 420175/419904
[[Comma list]]: 5120/5103, 420175/419904


[[Mapping]]: [{{val| 1 3 10 2 }}, {{val| 0 -7 -38 4 }}]
{{Mapping|legend=1| 1 3 10 2 | 0 -7 -38 4 }}


{{Multival|legend=1| 7 38 -4 44 -26 -116 }}
{{Multival|legend=1| 7 38 -4 44 -26 -116 }}
Line 284: Line 284:
Comma list: 5120/5103, 9801/9800, 14641/14580
Comma list: 5120/5103, 9801/9800, 14641/14580


Mapping: [{{val| 2 6 20 4 15 }}, {{val| 0 -7 -38 4 -20 }}]
Mapping: {{mapping| 2 6 20 4 15 | 0 -7 -38 4 -20 }}


Optimal tuning (POTE): ~2 = 1\1, ~121/105 = 242.4511
Optimal tuning (POTE): ~2 = 1\1, ~121/105 = 242.4511
Line 297: Line 297:
Comma list: 352/351, 847/845, 1716/1715, 14641/14580
Comma list: 352/351, 847/845, 1716/1715, 14641/14580


Mapping: [{{val| 2 6 20 4 15 7 }}, {{val| 0 -7 -38 4 -20 1 }}]
Mapping: {{mapping| 2 6 20 4 15 7 | 0 -7 -38 4 -20 1 }}


Optimal tuning (POTE): ~2 = 1\1, ~121/105 = 242.4448
Optimal tuning (POTE): ~2 = 1\1, ~121/105 = 242.4448
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[[Comma list]]: 5120/5103, 7558272/7503125
[[Comma list]]: 5120/5103, 7558272/7503125


[[Mapping]]: [{{val| 1 6 19 -7 }}, {{val| 0 -9 -34 20 }}]
{{Mapping|legend=1| 1 6 19 -7 | 0 -9 -34 20 }}


{{Multival|legend=1| 9 34 -20 33 -57 -142 }}
{{Multival|legend=1| 9 34 -20 33 -57 -142 }}
Line 327: Line 327:
Comma list: 176/175, 5120/5103, 41503/41472
Comma list: 176/175, 5120/5103, 41503/41472


Mapping: [{{val| 1 6 19 -7 27 }}, {{val| 0 -9 -34 20 -48 }}]
Mapping: {{mapping| 1 6 19 -7 27 | 0 -9 -34 20 -48 }}


Optimal tuning (POTE): ~2 = 1\1, ~108/77 = 588.545
Optimal tuning (POTE): ~2 = 1\1, ~108/77 = 588.545
Line 340: Line 340:
Comma list: 176/175, 351/350, 847/845, 2197/2187
Comma list: 176/175, 351/350, 847/845, 2197/2187


Mapping: [{{val| 1 6 19 -7 27 14 }}, {{val| 0 -9 -34 20 -48 -21 }}]
Mapping: {{mapping| 1 6 19 -7 27 14 | 0 -9 -34 20 -48 -21 }}


Optimal tuning (POTE): ~2 = 1\1, ~108/77 = 588.544
Optimal tuning (POTE): ~2 = 1\1, ~108/77 = 588.544
Line 353: Line 353:
[[Comma list]]: 5120/5103, 1071875/1062882
[[Comma list]]: 5120/5103, 1071875/1062882


[[Mapping]]: [{{val| 2 3 4 6 }}, {{val| 0 4 15 -9 }}]
{{Mapping|legend=1| 2 3 4 6 | 0 4 15 -9 }}


{{Multival|legend=1| 8 30 -18 29 -51 -126 }}
{{Multival|legend=1| 8 30 -18 29 -51 -126 }}
Line 368: Line 368:
Comma list: 385/384, 1331/1323, 2200/2187
Comma list: 385/384, 1331/1323, 2200/2187


Mapping: [{{val| 2 3 4 6 7 }}, {{val| 0 4 15 -9 -2 }}]
Mapping: {{mapping| 2 3 4 6 7 | 0 4 15 -9 -2 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~64/63 = 25.693
Optimal tuning (POTE): ~99/70 = 1\2, ~64/63 = 25.693
Line 381: Line 381:
Comma list: 325/324, 352/351, 385/384, 1331/1323
Comma list: 325/324, 352/351, 385/384, 1331/1323


Mapping: [{{val| 2 3 4 6 7 8 }}, {{val| 0 4 15 -9 -2 -14 }}]
Mapping: {{mapping| 2 3 4 6 7 8 | 0 4 15 -9 -2 -14 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~66/65 = 25.697
Optimal tuning (POTE): ~99/70 = 1\2, ~66/65 = 25.697
Line 394: Line 394:
Comma list: 289/288, 325/324, 352/351, 385/384, 561/560
Comma list: 289/288, 325/324, 352/351, 385/384, 561/560


Mapping: [{{val| 2 3 4 6 7 8 8 }}, {{val| 0 4 15 -9 -2 -14 4 }}]
Mapping: {{mapping| 2 3 4 6 7 8 8 | 0 4 15 -9 -2 -14 4 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.701
Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.701
Line 407: Line 407:
Comma list: 190/189, 209/208, 289/288, 352/351, 385/384, 561/560
Comma list: 190/189, 209/208, 289/288, 352/351, 385/384, 561/560


Mapping: [{{val| 2 3 4 6 7 8 8 9 }}, {{val| 0 4 15 -9 -2 -14 4 -12 }}]
Mapping: {{mapping| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 -12 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.660
Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.660
Line 420: Line 420:
Comma list: 190/189, 209/208, 253/252, 289/288, 323/322, 352/351, 385/384
Comma list: 190/189, 209/208, 253/252, 289/288, 323/322, 352/351, 385/384


Mapping: [{{val| 2 3 4 6 7 8 8 9 9 }}, {{val| 0 4 15 -9 -2 -14 4 -12 1 }}]
Mapping: {{mapping| 2 3 4 6 7 8 8 9 9 | 0 4 15 -9 -2 -14 4 -12 1 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.661
Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.661
Line 435: Line 435:
[[Comma list]]: 5120/5103, 3828125/3779136
[[Comma list]]: 5120/5103, 3828125/3779136


[[Mapping]]: [{{val| 1 8 18 -20 }}, {{val| 0 -9 -22 32 }}]
{{Mapping|legend=1| 1 8 18 -20 | 0 -9 -22 32 }}


: mapping generators: ~2, ~105/64
: mapping generators: ~2, ~105/64
Line 450: Line 450:
Comma list: 385/384, 2200/2187, 4000/3993
Comma list: 385/384, 2200/2187, 4000/3993


Mapping: [{{val| 1 8 18 -20 17 }}, {{val| 0 -9 -22 32 -19 }}]
Mapping: {{mapping| 1 8 18 -20 17 | 0 -9 -22 32 -19 }}


Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2397
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2397
Line 463: Line 463:
Comma list: 325/324, 352/351, 385/384, 1575/1573
Comma list: 325/324, 352/351, 385/384, 1575/1573


Mapping: [{{val| 1 8 18 -20 17 -2 }}, {{val| 0 -9 -22 32 -19 8 }}]
Mapping: {{mapping| 1 8 18 -20 17 -2 | 0 -9 -22 32 -19 8 }}


Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2369
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2369
Line 476: Line 476:
Comma list: 325/324, 352/351, 375/374, 385/384, 595/594
Comma list: 325/324, 352/351, 375/374, 385/384, 595/594


Mapping: [{{val| 1 8 18 -20 17 -2 44 }}, {{val| 0 -9 -22 32 -19 8 -56 }}]
Mapping: {{mapping| 1 8 18 -20 17 -2 44 | 0 -9 -22 32 -19 8 -56 }}


Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2495
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2495
Line 489: Line 489:
Comma list: 325/324, 352/351, 375/374, 385/384, 400/399, 595/594
Comma list: 325/324, 352/351, 375/374, 385/384, 400/399, 595/594


Mapping: [{{val| 1 8 18 -20 17 -2 44 52 }}, {{val| 0 -9 -22 32 -19 8 -56 -67 }}]
Mapping: {{mapping| 1 8 18 -20 17 -2 44 52 | 0 -9 -22 32 -19 8 -56 -67 }}


Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2534
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2534
Line 502: Line 502:
Comma list: 300/299, 325/324, 352/351, 375/374, 385/384, 400/399, 484/483
Comma list: 300/299, 325/324, 352/351, 375/374, 385/384, 400/399, 484/483


Mapping: [{{val| 1 8 18 -20 17 -2 44 52 48 }}, {{val| 0 -9 -22 32 -19 8 -56 -67 -61 }}]
Mapping: {{mapping| 1 8 18 -20 17 -2 44 52 48 | 0 -9 -22 32 -19 8 -56 -67 -61 }}


Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2576
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2576
Line 512: Line 512:
[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Hemifamity temperaments| ]] <!-- main article -->
[[Category:Hemifamity temperaments| ]] <!-- main article -->
[[Category:Hamifamity| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
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