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Augmented family: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Update keys
Line 10: Line 10:
[[Comma list]]: 128/125
[[Comma list]]: 128/125


[[Mapping]]: [{{val| 3 0 7 }}, {{val| 0 1 0 }}]
{{Mapping|legend=1| 3 0 7 | 0 1 0 }}


Mapping generators: ~5/4, ~3
: mapping generators: ~5/4, ~3


[[Optimal tuning]] ([[CTE]]): ~5/4 = 1\3, ~3/2 = 701.9550
[[Optimal tuning]] ([[CTE]]): ~5/4 = 1\3, ~3/2 = 701.9550
Line 28: Line 28:
[[Comma list]]: 36/35, 128/125
[[Comma list]]: 36/35, 128/125


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


{{Multival|legend=1| 3 0 6 -7 1 14 }}
{{Multival|legend=1| 3 0 6 -7 1 14 }}
Line 43: Line 43:
Comma list: 36/35, 45/44, 56/55
Comma list: 36/35, 45/44, 56/55


Mapping: [{{val| 3 0 7 -1 1 }}, {{val| 0 1 0 2 2 }}]
Mapping: {{mapping| 3 0 7 -1 1 | 0 1 0 2 2 }}


Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 687.6853
Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 687.6853
Line 56: Line 56:
Comma list: 27/26, 36/35, 45/44, 56/55
Comma list: 27/26, 36/35, 45/44, 56/55


Mapping: [{{val| 3 0 7 -1 1 -3 }}, {{val| 0 1 0 2 2 3 }}]
Mapping: {{mapping| 3 0 7 -1 1 -3 | 0 1 0 2 2 3 }}


Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 685.0836
Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 685.0836
Line 69: Line 69:
Comma list: 26/25, 36/35, 45/44, 56/55
Comma list: 26/25, 36/35, 45/44, 56/55


Mapping: [{{val| 3 0 7 -1 1 11 }}, {{val| 0 1 0 2 2 0 }}]
Mapping: {{mapping| 3 0 7 -1 1 11 | 0 1 0 2 2 0 }}


Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 687.6853
Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 687.6853
Line 82: Line 82:
[[Comma list]]: 64/63, 126/125
[[Comma list]]: 64/63, 126/125


[[Mapping]]: [{{val| 3 0 7 18 }}, {{val| 0 1 0 -2 }}]
{{Mapping|legend=1| 3 0 7 18 | 0 1 0 -2 }}


{{Multival|legend=1| 3 0 -6 -7 -18 -14 }}
{{Multival|legend=1| 3 0 -6 -7 -18 -14 }}
Line 97: Line 97:
Comma list: 56/55, 64/63, 100/99
Comma list: 56/55, 64/63, 100/99


Mapping: [{{val| 3 0 7 18 20 }}, {{val| 0 1 0 -2 -2 }}]
Mapping: {{mapping| 3 0 7 18 20 | 0 1 0 -2 -2 }}


Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 713.5701
Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 713.5701
Line 110: Line 110:
Comma list: 40/39, 56/55, 64/63, 66/65
Comma list: 40/39, 56/55, 64/63, 66/65


Mapping: [{{val| 3 0 7 18 20 16 }}, {{val| 0 1 0 -2 -2 -1 }}]
Mapping: {{mapping| 3 0 7 18 20 16 | 0 1 0 -2 -2 -1 }}


Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 716.1234
Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 716.1234
Line 123: Line 123:
Comma list: 56/55, 64/63, 91/90, 100/99
Comma list: 56/55, 64/63, 91/90, 100/99


Mapping: [{{val| 3 0 7 18 20 -8 }}, {{val| 0 1 0 -2 -2 4 }}]
Mapping: {{mapping| 3 0 7 18 20 -8 | 0 1 0 -2 -2 4 }}


Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 711.9020
Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 711.9020
Line 136: Line 136:
Comma list: 56/55, 64/63, 78/77, 100/99
Comma list: 56/55, 64/63, 78/77, 100/99


Mapping: [{{val| 3 0 7 18 20 35 }}, {{val| 0 1 0 -2 -2 -5 }}]
Mapping: {{mapping| 3 0 7 18 20 35 | 0 1 0 -2 -2 -5 }}


Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 712.5722
Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 712.5722
Line 149: Line 149:
Comma list: 55/54, 64/63, 77/75
Comma list: 55/54, 64/63, 77/75


Mapping: [{{val| 3 0 7 18 -4 }}, {{val| 0 1 0 -2 3 }}]
Mapping: {{mapping| 3 0 7 18 -4 | 0 1 0 -2 3 }}


Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 713.0025
Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 713.0025
Line 166: Line 166:
[[Comma list]]: 28/27, 128/125
[[Comma list]]: 28/27, 128/125


[[Mapping]]: [{{val| 3 0 7 -6 }}, {{val| 0 1 0 3 }}]
{{Mapping|legend=1| 3 0 7 -6 | 0 1 0 3 }}


{{Multival|legend=1| 3 0 9 -7 6 21 }}
{{Multival|legend=1| 3 0 9 -7 6 21 }}
Line 181: Line 181:
Comma list: 28/27, 55/54, 128/125
Comma list: 28/27, 55/54, 128/125


Mapping: [{{val| 3 0 7 -6 -4 }}, {{val| 0 1 0 3 3 }}]
Mapping: {{mapping| 3 0 7 -6 -4 | 0 1 0 3 3 }}


Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 717.5172
Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 717.5172
Line 194: Line 194:
[[Comma list]]: 21/20, 128/125
[[Comma list]]: 21/20, 128/125


[[Mapping]]: [{{val| 3 0 7 13 }}, {{val| 0 1 0 -1 }}]
{{Mapping|legend=1| 3 0 7 13 | 0 1 0 -1 }}


{{Multival|legend=1| 3 0 -3 -7 -13 -7 }}
{{Multival|legend=1| 3 0 -3 -7 -13 -7 }}
Line 209: Line 209:
Comma list: 21/20, 33/32, 128/125
Comma list: 21/20, 33/32, 128/125


Mapping: [{{val| 3 0 7 13 15 }}, {{val| 0 1 0 -1 -1 }}]
Mapping: {{mapping| 3 0 7 13 15 | 0 1 0 -1 -1 }}


Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 679.881
Optimal tuning (CTE): ~5/4 = 1\3, ~3/2 = 679.881
Line 222: Line 222:
[[Comma list]]: 50/49, 128/125
[[Comma list]]: 50/49, 128/125


[[Mapping]]: [{{val| 6 0 14 17 }}, {{val| 0 1 0 0 }}]
{{Mapping|legend=1| 6 0 14 17 | 0 1 0 0 }}


Mapping generators: ~28/25, ~3
: mapping generators: ~28/25, ~3


{{Multival|legend=1| 6 0 0 -14 -17 0 }}
{{Multival|legend=1| 6 0 0 -14 -17 0 }}
Line 239: Line 239:
Comma list: 50/49, 56/55, 125/121
Comma list: 50/49, 56/55, 125/121


Mapping: [{{val| 6 0 14 17 21 }}, {{val| 0 1 0 0 0 }}]
Mapping: {{mapping| 6 0 14 17 21 | 0 1 0 0 0 }}


Optimal tuning (CTE): ~28/25 = 1\6, ~3/2 = 701.9550
Optimal tuning (CTE): ~28/25 = 1\6, ~3/2 = 701.9550
Line 252: Line 252:
Comma list: 50/49, 56/55, 66/65, 105/104
Comma list: 50/49, 56/55, 66/65, 105/104


Mapping: [{{val| 6 0 14 17 21 13 }}, {{val| 0 1 0 0 0 1 }}]
Mapping: {{mapping| 6 0 14 17 21 13 | 0 1 0 0 0 1 }}


Optimal tuning (CTE): ~28/25 = 1\6, ~3/2 = 692.4327
Optimal tuning (CTE): ~28/25 = 1\6, ~3/2 = 692.4327
Line 267: Line 267:
[[Comma list]]: 49/48, 128/125
[[Comma list]]: 49/48, 128/125


[[Mapping]]: [{{val| 3 0 7 6 }}, {{val| 0 2 0 1 }}]
{{Mapping|legend=1| 3 0 7 6 | 0 2 0 1 }}


Mapping generators: ~5/4, ~7/4
: mapping generators: ~5/4, ~7/4


{{Multival|legend=1| 6 0 3 -14 -12 7 }}
{{Multival|legend=1| 6 0 3 -14 -12 7 }}
Line 284: Line 284:
Comma list: 49/48, 56/55, 77/75
Comma list: 49/48, 56/55, 77/75


Mapping: [{{val| 3 0 7 6 8 }}, {{val| 0 2 0 1 1 }}]
Mapping: {{mapping| 3 0 7 6 8 | 0 2 0 1 1 }}


Optimal tuning (CTE): ~5/4 = 1\3, ~7/4 = 952.2495
Optimal tuning (CTE): ~5/4 = 1\3, ~7/4 = 952.2495
Line 301: Line 301:
Comma list: 49/48, 56/55, 66/65, 77/75
Comma list: 49/48, 56/55, 66/65, 77/75


Mapping: [{{val| 3 0 7 6 8 4 }}, {{val| 0 2 0 1 1 3 }}]
Mapping: {{mapping| 3 0 7 6 8 4 | 0 2 0 1 1 3 }}


Optimal tuning (CTE): ~5/4 = 1\3, ~7/4 = 950.8049
Optimal tuning (CTE): ~5/4 = 1\3, ~7/4 = 950.8049
Line 317: Line 317:
Comma list: 49/48, 56/55, 77/75, 507/500
Comma list: 49/48, 56/55, 77/75, 507/500


Mapping: [{{val| 6 0 14 12 16 27 }}, {{val| 0 2 0 1 1 -1 }}]
Mapping: {{mapping| 6 0 14 12 16 27 | 0 2 0 1 1 -1 }}


Mapping generators: ~44/39, ~7/4
: mapping generators: ~44/39, ~7/4


Optimal tuning (CTE): ~44/39 = 1\6, ~7/4 = 952.5307
Optimal tuning (CTE): ~44/39 = 1\6, ~7/4 = 952.5307
Line 332: Line 332:
[[Comma list]]: 128/125, 245/243
[[Comma list]]: 128/125, 245/243


[[Mapping]]: [{{val| 3 1 7 -1 }}, {{val| 0 2 0 5 }}]
{{Mapping|legend=1| 3 1 7 -1 | 0 2 0 5 }}


Mapping generators: ~5/4, ~14/9
: mapping generators: ~5/4, ~14/9


{{Multival|legend=1| 6 0 15 -14 7 35 }}
{{Multival|legend=1| 6 0 15 -14 7 35 }}
Line 349: Line 349:
Comma list: 56/55, 128/125, 243/242
Comma list: 56/55, 128/125, 243/242


Mapping: [{{val| 3 1 7 -1 1 }}, {{val| 0 2 0 5 5 }}]
Mapping: {{mapping| 3 1 7 -1 1 | 0 2 0 5 5 }}


Optimal tuning (CTE): ~5/4 = 1\3, ~14/9 = 752.0512 (~36/35 = 47.9488)
Optimal tuning (CTE): ~5/4 = 1\3, ~14/9 = 752.0512 (~36/35 = 47.9488)
Line 362: Line 362:
Comma list: 56/55, 91/90, 128/125, 245/243
Comma list: 56/55, 91/90, 128/125, 245/243


Mapping: [{{val| 3 1 7 -1 1 13 }}, {{val| 0 2 0 5 5 -1 }}]
Mapping: {{mapping| 3 1 7 -1 1 13 | 0 2 0 5 5 -1 }}


Optimal tuning (CTE): ~5/4 = 1\3, ~14/9 = 752.1284 (or ~36/35 = 47.8716)
Optimal tuning (CTE): ~5/4 = 1\3, ~14/9 = 752.1284 (or ~36/35 = 47.8716)
Line 375: Line 375:
[[Comma list]]: 128/125, 1323/1250
[[Comma list]]: 128/125, 1323/1250


[[Mapping]]: [{{val| 3 1 7 14 }}, {{val| 0 2 0 -3 }}]
{{Mapping|legend=1| 3 1 7 14 | 0 2 0 -3 }}


Mapping generators: ~5/4, ~32/21
: mapping generators: ~5/4, ~32/21


{{Multival|legend=1| 6 0 -9 -14 -31 -21 }}
{{Multival|legend=1| 6 0 -9 -14 -31 -21 }}
Line 392: Line 392:
Comma list: 56/55, 128/125, 1323/1250
Comma list: 56/55, 128/125, 1323/1250


Mapping: [{{val| 3 1 7 14 16 }}, {{val| 0 2 0 -3 -3 }}]
Mapping: {{mapping| 3 1 7 14 16 | 0 2 0 -3 -3 }}


Optimal tuning (CTE): ~5/4 = 1\3, ~32/21 = 748.2962 (~33/32 = 51.7038)
Optimal tuning (CTE): ~5/4 = 1\3, ~32/21 = 748.2962 (~33/32 = 51.7038)
Line 405: Line 405:
Comma list: 56/55, 66/65, 105/104, 507/500
Comma list: 56/55, 66/65, 105/104, 507/500


Mapping: [{{val| 3 1 7 14 16 13 }}, {{val| 0 2 0 -3 -3 -1 }}]
Mapping: {{mapping| 3 1 7 14 16 13 | 0 2 0 -3 -3 -1 }}


Optimal tuning (CTE): ~5/4 = 1\3, ~32/21 = 748.5255 (~33/32 = 51.4745)
Optimal tuning (CTE): ~5/4 = 1\3, ~32/21 = 748.5255 (~33/32 = 51.4745)
Line 418: Line 418:
[[Comma list]]: 128/125, 2401/2400
[[Comma list]]: 128/125, 2401/2400


[[Mapping]]: [{{val| 3 3 7 8 }}, {{val| 0 4 0 1 }}]
{{Mapping|legend=1| 3 3 7 8 | 0 4 0 1 }}


Mapping generators: ~5/4, ~28/25
: mapping generators: ~5/4, ~28/25


{{Multival|legend=1| 12 0 3 -28 -29 7 }}
{{Multival|legend=1| 12 0 3 -28 -29 7 }}
Line 435: Line 435:
Comma list: 56/55, 128/125, 2401/2400
Comma list: 56/55, 128/125, 2401/2400


Mapping: [{{val| 3 3 7 8 10 }}, {{val| 0 4 0 1 1 }}]
Mapping: {{mapping| 3 3 7 8 10 | 0 4 0 1 1 }}


Optimal tuning (CTE): ~5/4 = 1\3, ~11/10 = 175.0533
Optimal tuning (CTE): ~5/4 = 1\3, ~11/10 = 175.0533
Line 448: Line 448:
Comma list: 56/55, 78/77, 128/125, 507/500
Comma list: 56/55, 78/77, 128/125, 507/500


Mapping: [{{val| 3 3 7 8 10 12 }}, {{val| 0 4 0 1 1 -2 }}]
Mapping: {{mapping| 3 3 7 8 10 12 | 0 4 0 1 1 -2 }}


Optimal tuning (CTE): ~5/4 = 1\3, ~11/10 = 175.2524
Optimal tuning (CTE): ~5/4 = 1\3, ~11/10 = 175.2524
Line 461: Line 461:
[[Comma list]]: 128/125, 12005/11664
[[Comma list]]: 128/125, 12005/11664


[[Mapping]]: [{{val| 6 1 14 4 }}, {{val| 0 2 0 3 }}]
{{Mapping|legend=1| 6 1 14 4 | 0 2 0 3 }}


Mapping generators: ~54/49, ~45/28
: mapping generators: ~54/49, ~45/28


{{Multival|legend=1| 12 0 18 -28 -5 42 }}
{{Multival|legend=1| 12 0 18 -28 -5 42 }}
Line 478: Line 478:
Comma list: 56/55, 128/125, 3773/3645
Comma list: 56/55, 128/125, 3773/3645


Mapping: [{{val| 6 1 14 4 8 }}, {{val| 0 2 0 3 3 }}]
Mapping: {{mapping| 6 1 14 4 8 | 0 2 0 3 3 }}


Optimal tuning (CTE): ~54/49 = 1\6, ~18/11 = 852.5968 (~36/35 = 52.5968)
Optimal tuning (CTE): ~54/49 = 1\6, ~18/11 = 852.5968 (~36/35 = 52.5968)
Line 493: Line 493:
[[Comma list]]: 128/125, 686/675
[[Comma list]]: 128/125, 686/675


[[Mapping]]: [{{val| 9 0 21 11 }}, {{val| 0 1 0 1 }}]
{{Mapping|legend=1| 9 0 21 11 | 0 1 0 1 }}


Mapping generators: ~49/45, ~3
: mapping generators: ~49/45, ~3


{{Multival|legend=1| 9 0 9 -21 -11 21 }}
{{Multival|legend=1| 9 0 9 -21 -11 21 }}
Line 510: Line 510:
Comma list: 56/55, 128/125, 540/539
Comma list: 56/55, 128/125, 540/539


Mapping: [{{val| 9 0 21 11 17 }}, {{val| 0 1 0 1 1 }}]
Mapping: {{mapping| 9 0 21 11 17 | 0 1 0 1 1 }}


Optimal tuning (CTE): ~12/11 = 1\9, ~3/2 = 699.6216
Optimal tuning (CTE): ~12/11 = 1\9, ~3/2 = 699.6216
Line 523: Line 523:
Comma list: 56/55, 78/77, 91/90, 128/125
Comma list: 56/55, 78/77, 91/90, 128/125


Mapping: [{{val| 9 0 21 11 17 19 }}, {{val| 0 1 0 1 1 1 }}]
Mapping: {{mapping| 9 0 21 11 17 19 | 0 1 0 1 1 1 }}


Optimal tuning (CTE): ~14/13 = 1\9, ~3/2 = 700.4330
Optimal tuning (CTE): ~14/13 = 1\9, ~3/2 = 700.4330
Line 536: Line 536:
[[Comma list]]: 128/125, 360/343
[[Comma list]]: 128/125, 360/343


[[Mapping]]: [{{val| 3 1 7 6 }}, {{val| 0 3 0 2 }}]
{{Mapping|legend=1| 3 1 7 6 | 0 3 0 2 }}


Mapping generators: ~5/4, ~48/35
: mapping generators: ~5/4, ~48/35


[[Optimal tuning]] ([[CTE]]): ~5/4 = 1\3, ~48/35 = 498.6367
[[Optimal tuning]] ([[CTE]]): ~5/4 = 1\3, ~48/35 = 498.6367
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