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Breedsmic temperaments: Difference between revisions

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m Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "
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Line 61: Line 61:
Comma list: 243/242, 441/440, 65625/65536
Comma list: 243/242, 441/440, 65625/65536


Mapping: {{mapping| 1 -19 7 0 -48 | 0 22 -5 3 55 }}
{{Mapping|legend=0| 1 -19 7 0 -48 | 0 22 -5 3 55 }}


Optimal tunings:  
Optimal tunings:  
Line 76: Line 76:
Comma list: 243/242, 441/440, 625/624, 3584/3575
Comma list: 243/242, 441/440, 625/624, 3584/3575


Mapping: {{mapping| 1 -19 7 0 -48 43 | 0 22 -5 3 55 -42 }}
{{Mapping|legend=0| 1 -19 7 0 -48 43 | 0 22 -5 3 55 -42 }}


Optimal tunings:  
Optimal tunings:  
Line 91: Line 91:
Comma list: 243/242, 375/374, 441/440, 625/624, 3584/3575
Comma list: 243/242, 375/374, 441/440, 625/624, 3584/3575


Mapping: {{mapping| 1 -19 7 0 -48 43 49 | 0 22 -5 3 55 -42 -48 }}
{{Mapping|legend=0| 1 -19 7 0 -48 43 49 | 0 22 -5 3 55 -42 -48 }}


Optimal tunings:  
Optimal tunings:  
Line 106: Line 106:
Comma list: 385/384, 1331/1323, 1375/1372
Comma list: 385/384, 1331/1323, 1375/1372


Mapping: {{mapping| 1 -19 7 0 -19 | 0 22 -5 3 24 }}
{{Mapping|legend=0| 1 -19 7 0 -19 | 0 22 -5 3 24 }}


Optimal tunings:  
Optimal tunings:  
Line 121: Line 121:
Comma list: 352/351, 385/384, 625/624, 1331/1323
Comma list: 352/351, 385/384, 625/624, 1331/1323


Mapping: {{mapping| 1 -19 7 0 -19 43 | 0 22 -5 3 24 -42 }}
{{Mapping|legend=0| 1 -19 7 0 -19 43 | 0 22 -5 3 24 -42 }}


Optimal tunings:  
Optimal tunings:  
Line 136: Line 136:
Comma list: 352/351, 385/384, 561/560, 625/624, 715/714
Comma list: 352/351, 385/384, 561/560, 625/624, 715/714


Mapping: {{mapping| 1 -19 7 0 -19 43 49 | 0 22 -5 3 24 -42 -48 }}
{{Mapping|legend=0| 1 -19 7 0 -19 43 49 | 0 22 -5 3 24 -42 -48 }}


Optimal tunings:  
Optimal tunings:  
Line 153: Line 153:
Comma list: 2401/2400, 6250/6237, 65625/65536
Comma list: 2401/2400, 6250/6237, 65625/65536


Mapping: {{mapping| 1 -19 7 0 112 | 0 22 -5 3 -116 }}
{{Mapping|legend=0| 1 -19 7 0 112 | 0 22 -5 3 -116 }}


Optimal tunings:  
Optimal tunings:  
Line 168: Line 168:
Comma list: 625/624, 2080/2079, 2200/2197, 2401/2400
Comma list: 625/624, 2080/2079, 2200/2197, 2401/2400


Mapping: {{mapping| 1 -19 7 0 112 43 | 0 22 -5 3 -116 -42 }}
{{Mapping|legend=0| 1 -19 7 0 112 43 | 0 22 -5 3 -116 -42 }}


Optimal tunings:  
Optimal tunings:  
Line 183: Line 183:
Comma list: 595/594, 625/624, 833/832, 1156/1155, 2200/2197
Comma list: 595/594, 625/624, 833/832, 1156/1155, 2200/2197


Mapping: {{mapping| 1 -19 7 0 112 43 49 | 0 22 -5 3 -116 -42 -48 }}
{{Mapping|legend=0| 1 -19 7 0 112 43 49 | 0 22 -5 3 -116 -42 -48 }}


Optimal tunings:  
Optimal tunings:  
Line 198: Line 198:
Comma list: 595/594, 625/624, 833/832, 1105/1104, 1156/1155, 2200/2197
Comma list: 595/594, 625/624, 833/832, 1105/1104, 1156/1155, 2200/2197


Mapping: {{mapping| 1 -19 7 0 112 43 49 114 | 0 22 -5 3 -116 -42 -48 -117 }}
{{Mapping|legend=0| 1 -19 7 0 112 43 49 114 | 0 22 -5 3 -116 -42 -48 -117 }}


Optimal tunings:  
Optimal tunings:  
Line 213: Line 213:
Comma list: 595/594, 625/624, 784/783, 833/832, 1015/1014, 1105/1104, 1156/1155
Comma list: 595/594, 625/624, 784/783, 833/832, 1015/1014, 1105/1104, 1156/1155


Mapping: {{mapping| 1 -19 7 0 112 43 49 114 61 | 0 22 -5 3 -116 -42 -48 -117 -60 }}
{{Mapping|legend=0| 1 -19 7 0 112 43 49 114 61 | 0 22 -5 3 -116 -42 -48 -117 -60 }}


Optimal tunings:  
Optimal tunings:  
Line 228: Line 228:
Comma list: 2401/2400, 3025/3024, 65625/65536
Comma list: 2401/2400, 3025/3024, 65625/65536


Mapping: {{mapping| 1 -41 12 -3 -73 | 0 44 -10 6 79 }}
{{Mapping|legend=0| 1 -41 12 -3 -73 | 0 44 -10 6 79 }}
: mapping generators: ~2, ~88/45
: mapping generators: ~2, ~88/45


Line 244: Line 244:
Comma list: 625/624, 1575/1573, 2401/2400, 4096/4095
Comma list: 625/624, 1575/1573, 2401/2400, 4096/4095


Mapping: {{mapping| 1 -41 12 -3 -73 85 | 0 44 -10 6 79 -84 }}
{{Mapping|legend=0| 1 -41 12 -3 -73 85 | 0 44 -10 6 79 -84 }}


Optimal tunings:  
Optimal tunings:  
Line 259: Line 259:
Comma list: 625/624, 833/832, 1225/1224, 1575/1573, 4096/4095
Comma list: 625/624, 833/832, 1225/1224, 1575/1573, 4096/4095


Mapping: {{mapping| 1 -41 12 -3 -73 85 97| 0 44 -10 6 79 -84 -96 }}
{{Mapping|legend=0| 1 -41 12 -3 -73 85 97| 0 44 -10 6 79 -84 -96 }}


Optimal tunings:  
Optimal tunings:  
Line 274: Line 274:
Comma list: 2401/2400, 9801/9800, 65625/65536
Comma list: 2401/2400, 9801/9800, 65625/65536


Mapping: {{mapping| 2 -16 9 3 47 | 0 22 -5 3 -46 }}
{{Mapping|legend=0| 2 -16 9 3 47 | 0 22 -5 3 -46 }}
: mapping generators: ~99/70, ~693/512
: mapping generators: ~99/70, ~693/512


Line 312: Line 312:
Comma list: 243/242, 441/440, 1792000/1771561
Comma list: 243/242, 441/440, 1792000/1771561


Mapping: {{mapping| 1 -3 -17 -8 -8 | 0 14 59 33 35 }}
{{Mapping|legend=0| 1 -3 -17 -8 -8 | 0 14 59 33 35 }}


Optimal tunings:  
Optimal tunings:  
Line 327: Line 327:
Comma list: 243/242, 364/363, 441/440, 2200/2197
Comma list: 243/242, 364/363, 441/440, 2200/2197


Mapping: {{mapping| 1 -3 -17 -8 -8 -13 | 0 14 59 33 35 51 }}
{{Mapping|legend=0| 1 -3 -17 -8 -8 -13 | 0 14 59 33 35 51 }}


Optimal tunings:  
Optimal tunings:  
Line 342: Line 342:
Comma list: 243/242, 364/363, 441/440, 595/594, 2200/2197
Comma list: 243/242, 364/363, 441/440, 595/594, 2200/2197


Mapping: {{mapping| 1 -3 -17 -8 -8 -13 9 | 0 14 59 33 35 51 -15 }}
{{Mapping|legend=0| 1 -3 -17 -8 -8 -13 9 | 0 14 59 33 35 51 -15 }}


Optimal tunings:  
Optimal tunings:  
Line 388: Line 388:
Comma list: 243/242, 441/440, 896/891
Comma list: 243/242, 441/440, 896/891


Mapping: {{mapping| 1 1 -5 -1 2 | 0 2 25 13 5 }}
{{Mapping|legend=0| 1 1 -5 -1 2 | 0 2 25 13 5 }}


Optimal tunings:  
Optimal tunings:  
Line 403: Line 403:
Comma list: 144/143, 196/195, 243/242, 364/363
Comma list: 144/143, 196/195, 243/242, 364/363


Mapping: {{mapping| 1 1 -5 -1 2 4 | 0 2 25 13 5 -1 }}
{{Mapping|legend=0| 1 1 -5 -1 2 4 | 0 2 25 13 5 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 418: Line 418:
Comma list: 2401/2400, 3388/3375, 5120/5103
Comma list: 2401/2400, 3388/3375, 5120/5103


Mapping: {{mapping| 2 0 -35 -15 -47 | 0 2 25 13 34 }}
{{Mapping|legend=0| 2 0 -35 -15 -47 | 0 2 25 13 34 }}
: mapping generators: ~99/70, ~400/231
: mapping generators: ~99/70, ~400/231


Line 434: Line 434:
Comma list: 352/351, 676/675, 847/845, 1716/1715
Comma list: 352/351, 676/675, 847/845, 1716/1715


Mapping: {{mapping| 2 0 -35 -15 -47 -37 | 0 2 25 13 34 28 }}
{{Mapping|legend=0| 2 0 -35 -15 -47 -37 | 0 2 25 13 34 28 }}


Optimal tunings:  
Optimal tunings:  
Line 451: Line 451:
Comma list: 2401/2400, 3025/3024, 5120/5103
Comma list: 2401/2400, 3025/3024, 5120/5103


Mapping: {{mapping| 1 1 -5 -1 8 | 0 4 50 26 -31 }}
{{Mapping|legend=0| 1 1 -5 -1 8 | 0 4 50 26 -31 }}
: mapping generators: ~2, ~243/220
: mapping generators: ~2, ~243/220


Line 467: Line 467:
Comma list: 352/351, 847/845, 2401/2400, 3025/3024
Comma list: 352/351, 847/845, 2401/2400, 3025/3024


Mapping: {{mapping| 1 1 -5 -1 8 10 | 0 4 50 26 -31 -43 }}
{{Mapping|legend=0| 1 1 -5 -1 8 10 | 0 4 50 26 -31 -43 }}


Optimal tunings:  
Optimal tunings:  
Line 484: Line 484:
Comma list: 2401/2400, 4000/3993, 5120/5103
Comma list: 2401/2400, 4000/3993, 5120/5103


Mapping: {{mapping| 1 -1 -30 -14 -28 | 0 6 75 39 73 }}
{{Mapping|legend=0| 1 -1 -30 -14 -28 | 0 6 75 39 73 }}
: mapping generators: ~2, ~66/49
: mapping generators: ~2, ~66/49


Line 500: Line 500:
Comma list: 352/351, 847/845, 1575/1573, 2401/2400
Comma list: 352/351, 847/845, 1575/1573, 2401/2400


Mapping: {{mapping| 1 -1 -30 -14 -28 -20 | 0 6 75 39 73 55 }}
{{Mapping|legend=0| 1 -1 -30 -14 -28 -20 | 0 6 75 39 73 55 }}


Optimal tunings:  
Optimal tunings:  
Line 533: Line 533:
Comma list: 2401/2400, 9801/9800, 1771561/1771470
Comma list: 2401/2400, 9801/9800, 1771561/1771470


Mapping: {{mapping| 2 -6 -20 -9 -14 | 0 32 86 51 73 }}
{{Mapping|legend=0| 2 -6 -20 -9 -14 | 0 32 86 51 73 }}
: mapping generators: ~99/70, ~243/220
: mapping generators: ~99/70, ~243/220


Line 571: Line 571:
Comma list: 2401/2400, 3025/3024, 5632/5625
Comma list: 2401/2400, 3025/3024, 5632/5625


Mapping: {{mapping| 1 -7 3 1 -11 | 0 38 -3 8 64 }}
{{Mapping|legend=0| 1 -7 3 1 -11 | 0 38 -3 8 64 }}


Optimal tunings:  
Optimal tunings:  
Line 586: Line 586:
Comma list: 1001/1000, 1716/1715, 3025/3024, 4096/4095
Comma list: 1001/1000, 1716/1715, 3025/3024, 4096/4095


Mapping: {{mapping| 1 -7 3 1 -11 22 | 0 38 -3 8 64 -81 }}
{{Mapping|legend=0| 1 -7 3 1 -11 22 | 0 38 -3 8 64 -81 }}


Optimal tunings:  
Optimal tunings:  
Line 645: Line 645:
Comma list: 243/242, 441/440, 939524096/935859375
Comma list: 243/242, 441/440, 939524096/935859375


Mapping: {{mapping| 1 -1 6 4 -3 | 0 26 -37 -12 65 }}
{{Mapping|legend=0| 1 -1 6 4 -3 | 0 26 -37 -12 65 }}


Optimal tunings:  
Optimal tunings:  
Line 660: Line 660:
Comma list: 243/242, 441/440, 2200/2197, 3584/3575
Comma list: 243/242, 441/440, 2200/2197, 3584/3575


Mapping: {{mapping| 1 -1 6 4 -3 4 | 0 26 -37 -12 65 -3 }}
{{Mapping|legend=0| 1 -1 6 4 -3 4 | 0 26 -37 -12 65 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 675: Line 675:
Comma list: 243/242, 441/440, 833/832, 2200/2197, 3584/3575
Comma list: 243/242, 441/440, 833/832, 2200/2197, 3584/3575


Mapping: {{mapping| 1 -1 6 4 -3 4 2 | 0 26 -37 -12 65 -3 21 }}
{{Mapping|legend=0| 1 -1 6 4 -3 4 2 | 0 26 -37 -12 65 -3 21 }}


Optimal tunings:  
Optimal tunings:  
Line 716: Line 716:
Comma list: 2401/2400, 3025/3024, 766656/765625
Comma list: 2401/2400, 3025/3024, 766656/765625


Mapping: {{mapping| 1 -25 -16 -13 -26 | 0 74 51 44 82 }}
{{Mapping|legend=0| 1 -25 -16 -13 -26 | 0 74 51 44 82 }}


Optimal tunings:  
Optimal tunings:  
Line 731: Line 731:
Comma list: 1001/1000, 1716/1715, 3025/3024, 4225/4224
Comma list: 1001/1000, 1716/1715, 3025/3024, 4225/4224


Mapping: {{mapping| 1 -25 -16 -13 -26 -6 | 0 74 51 44 82 27 }}
{{Mapping|legend=0| 1 -25 -16 -13 -26 -6 | 0 74 51 44 82 27 }}


Optimal tunings:  
Optimal tunings:  
Line 746: Line 746:
Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 4225/4224
Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 4225/4224


Mapping: {{mapping| 1 -25 -16 -13 -26 -6 -11 | 0 74 51 44 82 27 42 }}
{{Mapping|legend=0| 1 -25 -16 -13 -26 -6 -11 | 0 74 51 44 82 27 42 }}


Optimal tunings:  
Optimal tunings:  
Line 783: Line 783:
Comma list: 2401/2400, 3025/3024, 4000/3993
Comma list: 2401/2400, 3025/3024, 4000/3993


Mapping: {{mapping| 1 -13 -14 -9 -8 | 0 42 47 34 33 }}
{{Mapping|legend=0| 1 -13 -14 -9 -8 | 0 42 47 34 33 }}


Optimal tunings:  
Optimal tunings:  
Line 798: Line 798:
Comma list: 625/624, 1575/1573, 2080/2079, 2401/2400
Comma list: 625/624, 1575/1573, 2080/2079, 2401/2400


Mapping: {{mapping| 1 -13 -14 -9 -8 -47 | 0 42 47 34 33 146 }}
{{Mapping|legend=0| 1 -13 -14 -9 -8 -47 | 0 42 47 34 33 146 }}


Optimal tunings:  
Optimal tunings:  
Line 833: Line 833:
Comma list: 243/242, 441/440, 35937/35840
Comma list: 243/242, 441/440, 35937/35840


Mapping: {{mapping| 1 -3 -29 -14 -8 | 0 6 41 22 15 }}
{{Mapping|legend=0| 1 -3 -29 -14 -8 | 0 6 41 22 15 }}


Optimal tunings:  
Optimal tunings:  
Line 848: Line 848:
Comma list: 169/168, 243/242, 364/363, 441/440
Comma list: 169/168, 243/242, 364/363, 441/440


Mapping: {{mapping| 1 -3 -29 -14 -8 -7 | 0 6 41 22 15 14 }}
{{Mapping|legend=0| 1 -3 -29 -14 -8 -7 | 0 6 41 22 15 14 }}


Optimal tunings:  
Optimal tunings:  
Line 863: Line 863:
Comma list: 169/168, 221/220, 243/242, 273/272, 364/363
Comma list: 169/168, 221/220, 243/242, 273/272, 364/363


Mapping: {{mapping| 1 -3 -29 -14 -8 -7 -28 | 0 6 41 22 15 14 42 }}
{{Mapping|legend=0| 1 -3 -29 -14 -8 -7 -28 | 0 6 41 22 15 14 42 }}


Optimal tunings:  
Optimal tunings:  
Line 898: Line 898:
Comma list: 243/242, 441/440, 78408/78125
Comma list: 243/242, 441/440, 78408/78125


Mapping: {{mapping| 1 -15 -19 -12 -38 | 0 28 36 25 70 }}
{{Mapping|legend=0| 1 -15 -19 -12 -38 | 0 28 36 25 70 }}


Optimal tunings:  
Optimal tunings:  
Line 913: Line 913:
Comma list: 243/242, 351/350, 441/440, 10985/10976
Comma list: 243/242, 351/350, 441/440, 10985/10976


Mapping: {{mapping| 1 -15 -19 -12 -38 -4 | 0 28 36 25 70 13 }}
{{Mapping|legend=0| 1 -15 -19 -12 -38 -4 | 0 28 36 25 70 13 }}


Optimal tunings:  
Optimal tunings:  
Line 946: Line 946:
Comma list: 385/384, 1375/1372, 4000/3993
Comma list: 385/384, 1375/1372, 4000/3993


Mapping: {{mapping| 1 -13 -4 -4 2 | 0 30 13 14 3 }}
{{Mapping|legend=0| 1 -13 -4 -4 2 | 0 30 13 14 3 }}


Optimal tunings:  
Optimal tunings:  
Line 961: Line 961:
Comma list: 169/168, 364/363, 385/384, 625/624
Comma list: 169/168, 364/363, 385/384, 625/624


Mapping: {{mapping| 1 -13 -4 -4 2 -7 | 0 30 13 14 3 22 }}
{{Mapping|legend=0| 1 -13 -4 -4 2 -7 | 0 30 13 14 3 22 }}


Optimal tunings:  
Optimal tunings:  
Line 994: Line 994:
Comma list: 385/384, 1375/1372, 43923/43750
Comma list: 385/384, 1375/1372, 43923/43750


Mapping: {{mapping| 1 -27 -7 -9 -4 | 0 46 15 19 12 }}
{{Mapping|legend=0| 1 -27 -7 -9 -4 | 0 46 15 19 12 }}


Optimal tunings:  
Optimal tunings:  
Line 1,009: Line 1,009:
Comma list: 385/384, 625/624, 847/845, 1375/1372
Comma list: 385/384, 625/624, 847/845, 1375/1372


Mapping: {{mapping| 1 -27 -7 -9 -4 -5 | 0 46 15 19 12 14 }}
{{Mapping|legend=0| 1 -27 -7 -9 -4 -5 | 0 46 15 19 12 14 }}


Optimal tunings:  
Optimal tunings:  
Line 1,044: Line 1,044:
Comma list: 243/242, 441/440, 1815/1792
Comma list: 243/242, 441/440, 1815/1792


Mapping: {{mapping| 1 1 9 6 2 | 0 2 -23 -11 5 }}
{{Mapping|legend=0| 1 1 9 6 2 | 0 2 -23 -11 5 }}


Optimal tunings:  
Optimal tunings:  
Line 1,079: Line 1,079:
Comma list: 243/242, 441/440, 43923/43750
Comma list: 243/242, 441/440, 43923/43750


Mapping: {{mapping| 1 -17 -34 -20 -43 | 0 22 43 27 55 }}
{{Mapping|legend=0| 1 -17 -34 -20 -43 | 0 22 43 27 55 }}


Optimal tunings:  
Optimal tunings:  
Line 1,094: Line 1,094:
Comma list: 243/242, 351/350, 441/440, 847/845
Comma list: 243/242, 351/350, 441/440, 847/845


Mapping: {{mapping| 1 -17 -34 -20 -43 -36 | 0 22 43 27 55 47 }}
{{Mapping|legend=0| 1 -17 -34 -20 -43 -36 | 0 22 43 27 55 47 }}


Optimal tunings:  
Optimal tunings:  
Line 1,109: Line 1,109:
Comma list: 243/242, 351/350, 441/440, 561/560, 847/845
Comma list: 243/242, 351/350, 441/440, 561/560, 847/845


Mapping: {{mapping| 1 -17 -34 -20 -43 -36 10 | 0 22 43 27 55 47 -7 }}
{{Mapping|legend=0| 1 -17 -34 -20 -43 -36 10 | 0 22 43 27 55 47 -7 }}


Optimal tunings:  
Optimal tunings:  
Line 1,146: Line 1,146:
Comma list: 176/175, 2401/2400, 2560/2541
Comma list: 176/175, 2401/2400, 2560/2541


Mapping: {{mapping| 1 -13 8 2 14 | 0 18 -7 1 -13 }}
{{Mapping|legend=0| 1 -13 8 2 14 | 0 18 -7 1 -13 }}


Optimal tunings:  
Optimal tunings:  
Line 1,161: Line 1,161:
Comma list: 176/175, 196/195, 364/363, 512/507
Comma list: 176/175, 196/195, 364/363, 512/507


Mapping: {{mapping| 1 -13 8 2 14 11 | 0 18 -7 1 -13 -9 }}
{{Mapping|legend=0| 1 -13 8 2 14 11 | 0 18 -7 1 -13 -9 }}


Optimal tunings:  
Optimal tunings:  
Line 1,216: Line 1,216:
Comma list: 2401/2400, 820125/819896, 2097152/2096325
Comma list: 2401/2400, 820125/819896, 2097152/2096325


Mapping: {{mapping| 1 -27 55 22 -19 | 0 70 -129 -47 55 }}
{{Mapping|legend=0| 1 -27 55 22 -19 | 0 70 -129 -47 55 }}


Optimal tunings:  
Optimal tunings:  
Line 1,231: Line 1,231:
Comma list: 2401/2400, 4096/4095, 6656/6655, 24192/24167
Comma list: 2401/2400, 4096/4095, 6656/6655, 24192/24167


Mapping: {{mapping| 1 -27 55 22 -19 -11 | 0 70 -129 -47 55 36 }}
{{Mapping|legend=0| 1 -27 55 22 -19 -11 | 0 70 -129 -47 55 36 }}


Optimal tunings:  
Optimal tunings:  
Line 1,246: Line 1,246:
Comma list: 2401/2400, 2601/2600, 4096/4095, 6656/6655, 8624/8619
Comma list: 2401/2400, 2601/2600, 4096/4095, 6656/6655, 8624/8619


Mapping: {{mapping| 1 -27 55 22 -19 -11 78 | 0 70 -129 -47 55 36 -181 }}
{{Mapping|legend=0| 1 -27 55 22 -19 -11 78 | 0 70 -129 -47 55 36 -181 }}


Optimal tunings:  
Optimal tunings:  
Line 1,261: Line 1,261:
Comma list: 2401/2400, 2601/2600, 2926/2925, 3136/3135, 3213/3211, 5985/5984
Comma list: 2401/2400, 2601/2600, 2926/2925, 3136/3135, 3213/3211, 5985/5984


Mapping: {{mapping| 1 -27 55 22 -19 -11 78 41 | 0 70 -129 -47 55 36 -181 -90 }}
{{Mapping|legend=0| 1 -27 55 22 -19 -11 78 41 | 0 70 -129 -47 55 36 -181 -90 }}


Optimal tunings:  
Optimal tunings:  
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