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Porwell temperaments: Difference between revisions

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Line 55: Line 55:
Comma list: 121/120, 176/175, 10976/10935
Comma list: 121/120, 176/175, 10976/10935


Mapping: {{mapping| 11 0 43 -4 38 | 0 1 -1 2 0 }}
{{Mapping|legend=0| 11 0 43 -4 38 | 0 1 -1 2 0 }}


Optimal tunings:  
Optimal tunings:  
Line 70: Line 70:
Comma list: 121/120, 176/175, 351/350, 4459/4455
Comma list: 121/120, 176/175, 351/350, 4459/4455


Mapping: {{mapping| 11 0 43 -4 38 93 | 0 1 -1 2 0 -3 }}
{{Mapping|legend=0| 11 0 43 -4 38 93 | 0 1 -1 2 0 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 85: Line 85:
Comma list: 121/120, 154/153, 176/175, 273/272, 2025/2023
Comma list: 121/120, 154/153, 176/175, 273/272, 2025/2023


Mapping: {{mapping| 11 0 43 -4 38 93 45 | 0 1 -1 2 0 -3 0 }}
{{Mapping|legend=0| 11 0 43 -4 38 93 45 | 0 1 -1 2 0 -3 0 }}


Optimal tunings:  
Optimal tunings:  
Line 100: Line 100:
Comma list: 540/539, 896/891, 4375/4356
Comma list: 540/539, 896/891, 4375/4356


Mapping: {{mapping| 11 0 43 -4 73 | 0 1 -1 2 -2 }}
{{Mapping|legend=0| 11 0 43 -4 73 | 0 1 -1 2 -2 }}


Optimal tunings:  
Optimal tunings:  
Line 115: Line 115:
Comma list: 352/351, 364/363, 540/539, 625/624
Comma list: 352/351, 364/363, 540/539, 625/624


Mapping: {{mapping| 11 0 43 -4 73 128 | 0 1 -1 2 -2 -5 }}
{{Mapping|legend=0| 11 0 43 -4 73 128 | 0 1 -1 2 -2 -5 }}


Optimal tunings:  
Optimal tunings:  
Line 130: Line 130:
Comma list: 256/255, 352/351, 364/363, 375/374, 540/539
Comma list: 256/255, 352/351, 364/363, 375/374, 540/539


Mapping: {{mapping| 11 0 43 -4 73 128 45 | 0 1 -1 2 -2 -5 0 }}
{{Mapping|legend=0| 11 0 43 -4 73 128 45 | 0 1 -1 2 -2 -5 0 }}


Optimal tunings:  
Optimal tunings:  
Line 145: Line 145:
Comma list: 3388/3375, 6144/6125, 9801/9800
Comma list: 3388/3375, 6144/6125, 9801/9800


Mapping: {{mapping| 22 0 86 -8 111 | 0 1 -1 2 -1 }}
{{Mapping|legend=0| 22 0 86 -8 111 | 0 1 -1 2 -1 }}
: mapping generators: ~33/32, ~3
: mapping generators: ~33/32, ~3


Line 183: Line 183:
Comma list: 441/440, 1344/1331, 4375/4356
Comma list: 441/440, 1344/1331, 4375/4356


Mapping: {{mapping| 3 2 5 10 10 | 0 7 5 -4 1 }}
{{Mapping|legend=0| 3 2 5 10 10 | 0 7 5 -4 1 }}


Optimal tunings:  
Optimal tunings:  
Line 198: Line 198:
Comma list: 144/143, 364/363, 441/440, 625/624
Comma list: 144/143, 364/363, 441/440, 625/624


Mapping: {{mapping| 3 2 5 10 10 6 | 0 7 5 -4 1 13 }}
{{Mapping|legend=0| 3 2 5 10 10 6 | 0 7 5 -4 1 13 }}


Optimal tunings:  
Optimal tunings:  
Line 213: Line 213:
Comma list: 121/120, 176/175, 250047/250000
Comma list: 121/120, 176/175, 250047/250000


Mapping: {{mapping| 3 2 5 10 8 | 0 7 5 -4 6 }}
{{Mapping|legend=0| 3 2 5 10 8 | 0 7 5 -4 6 }}


Optimal tunings:  
Optimal tunings:  
Line 250: Line 250:
Comma list: 540/539, 1375/1372, 5632/5625
Comma list: 540/539, 1375/1372, 5632/5625


Mapping: {{mapping| 1 -14 3 -6 -25 | 0 23 -1 13 42 }}
{{Mapping|legend=0| 1 -14 3 -6 -25 | 0 23 -1 13 42 }}


Optimal tunings:  
Optimal tunings:  
Line 265: Line 265:
Comma list: 352/351, 540/539, 625/624, 1375/1372
Comma list: 352/351, 540/539, 625/624, 1375/1372


Mapping: {{mapping| 1 -14 3 -6 -25 22 | 0 23 -1 13 42 -27 }}
{{Mapping|legend=0| 1 -14 3 -6 -25 22 | 0 23 -1 13 42 -27 }}


Optimal tunings:  
Optimal tunings:  
Line 280: Line 280:
Comma list: 256/255, 352/351, 625/624, 715/714, 1275/1274
Comma list: 256/255, 352/351, 625/624, 715/714, 1275/1274


Mapping: {{mapping| 1 -14 3 -6 -25 22 19 | 0 23 -1 13 42 -27 -22 }}
{{Mapping|legend=0| 1 -14 3 -6 -25 22 19 | 0 23 -1 13 42 -27 -22 }}


Optimal tunings:  
Optimal tunings:  
Line 295: Line 295:
Comma list: 256/255, 352/351, 375/374, 400/399, 456/455, 715/714
Comma list: 256/255, 352/351, 375/374, 400/399, 456/455, 715/714


Mapping: {{mapping| 1 -14 3 -6 -25 22 19 30 | 0 23 -1 13 42 -27 -22 -38 }}
{{Mapping|legend=0| 1 -14 3 -6 -25 22 19 30 | 0 23 -1 13 42 -27 -22 -38 }}


Optimal tunings:  
Optimal tunings:  
Line 332: Line 332:
Comma list: 121/120, 176/175, 177147/175616
Comma list: 121/120, 176/175, 177147/175616


Mapping: {{mapping| 1 -3 12 -14 6 | 0 9 -19 33 -5 }}
{{Mapping|legend=0| 1 -3 12 -14 6 | 0 9 -19 33 -5 }}


Optimal tunings:  
Optimal tunings:  
Line 347: Line 347:
Comma list: 121/120, 176/175, 351/350, 58806/57967
Comma list: 121/120, 176/175, 351/350, 58806/57967


Mapping: {{mapping| 1 -3 12 -14 6 20 | 0 9 -19 33 -5 -32 }}
{{Mapping|legend=0| 1 -3 12 -14 6 20 | 0 9 -19 33 -5 -32 }}


Optimal tunings:  
Optimal tunings:  
Line 362: Line 362:
Comma list: 540/539, 5632/5625, 72171/71680
Comma list: 540/539, 5632/5625, 72171/71680


Mapping: {{mapping| 1 -3 12 -14 33 | 0 9 -19 33 -58 }}
{{Mapping|legend=0| 1 -3 12 -14 33 | 0 9 -19 33 -58 }}


Optimal tunings:  
Optimal tunings:  
Line 377: Line 377:
Comma list: 351/350, 540/539, 847/845, 4096/4095
Comma list: 351/350, 540/539, 847/845, 4096/4095


Mapping: {{mapping| 1 -3 12 -14 33 20 | 0 9 -19 33 -58 -32 }}
{{Mapping|legend=0| 1 -3 12 -14 33 20 | 0 9 -19 33 -58 -32 }}


Optimal tunings:  
Optimal tunings:  
Line 413: Line 413:
Comma list: 441/440, 6144/6125, 72171/71680
Comma list: 441/440, 6144/6125, 72171/71680


Mapping: {{mapping| 7 0 -17 64 124 | 0 1 3 -4 -9 }}
{{Mapping|legend=0| 7 0 -17 64 124 | 0 1 3 -4 -9 }}


Optimal tunings:  
Optimal tunings:  
Line 428: Line 428:
Comma list: 351/350, 441/440, 1188/1183, 3584/3575
Comma list: 351/350, 441/440, 1188/1183, 3584/3575


Mapping: {{mapping| 7 0 -17 64 124 37 | 0 1 3 -4 -9 -1 }}
{{Mapping|legend=0| 7 0 -17 64 124 37 | 0 1 3 -4 -9 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 443: Line 443:
Comma list: 351/350, 441/440, 561/560, 1188/1183, 1632/1625
Comma list: 351/350, 441/440, 561/560, 1188/1183, 1632/1625


Mapping: {{mapping| 7 0 -17 64 124 37 -49 | 0 1 3 -4 -9 -1 7 }}
{{Mapping|legend=0| 7 0 -17 64 124 37 -49 | 0 1 3 -4 -9 -1 7 }}


Optimal tunings:  
Optimal tunings:  
Line 458: Line 458:
Comma list: 324/323, 351/350, 441/440, 456/455, 476/475, 495/494
Comma list: 324/323, 351/350, 441/440, 456/455, 476/475, 495/494


Mapping: {{mapping| 7 0 -17 64 124 37 -49 63 | 0 1 3 -4 -9 -1 7 -3 }}
{{Mapping|legend=0| 7 0 -17 64 124 37 -49 63 | 0 1 3 -4 -9 -1 7 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 473: Line 473:
Comma list: 276/275, 324/323, 351/350, 441/440, 456/455, 476/475, 495/494
Comma list: 276/275, 324/323, 351/350, 441/440, 456/455, 476/475, 495/494


Mapping: {{mapping| 7 0 -17 64 124 37 -49 63 76 | 0 1 3 -4 -9 -1 7 -3 -4 }}
{{Mapping|legend=0| 7 0 -17 64 124 37 -49 63 76 | 0 1 3 -4 -9 -1 7 -3 -4 }}


Optimal tunings:  
Optimal tunings:  
Line 488: Line 488:
Comma list: 261/260, 276/275, 324/323, 351/350, 441/440, 456/455, 476/475, 495/494
Comma list: 261/260, 276/275, 324/323, 351/350, 441/440, 456/455, 476/475, 495/494


Mapping: {{mapping| 7 0 -17 64 124 37 -49 63 76 34 | 0 1 3 -4 -9 -1 7 -3 -4 0 }}
{{Mapping|legend=0| 7 0 -17 64 124 37 -49 63 76 34 | 0 1 3 -4 -9 -1 7 -3 -4 0 }}


Optimal tunings:  
Optimal tunings:  
Line 525: Line 525:
Comma list: 896/891, 2200/2187, 6144/6125
Comma list: 896/891, 2200/2187, 6144/6125


Mapping: {{mapping| 1 0 -31 52 59 | 0 1 21 -31 -35 }}
{{Mapping|legend=0| 1 0 -31 52 59 | 0 1 21 -31 -35 }}


Optimal tunings:  
Optimal tunings:  
Line 540: Line 540:
Comma list: 325/324, 352/351, 364/363, 1716/1715
Comma list: 325/324, 352/351, 364/363, 1716/1715


Mapping: {{mapping| 1 0 -31 52 59 64 | 0 1 21 -31 -35 -38 }}
{{Mapping|legend=0| 1 0 -31 52 59 64 | 0 1 21 -31 -35 -38 }}


Optimal tunings:  
Optimal tunings:  
Line 555: Line 555:
Comma list: 256/255, 325/324, 352/351, 364/363, 1716/1715
Comma list: 256/255, 325/324, 352/351, 364/363, 1716/1715


Mapping: {{mapping| 1 0 -31 52 59 64 39 | 0 1 21 -31 -35 -38 -22 }}
{{Mapping|legend=0| 1 0 -31 52 59 64 39 | 0 1 21 -31 -35 -38 -22 }}


Optimal tunings:  
Optimal tunings:  
Line 592: Line 592:
Comma list: 2200/2187, 3388/3375, 6144/6125
Comma list: 2200/2187, 3388/3375, 6144/6125


Mapping: {{mapping| 1 -9 -12 19 -42 | 0 17 23 -26 73 }}
{{Mapping|legend=0| 1 -9 -12 19 -42 | 0 17 23 -26 73 }}


Optimal tunings:  
Optimal tunings:  
Line 607: Line 607:
Comma list: 325/324, 352/351, 1001/1000, 2704/2695
Comma list: 325/324, 352/351, 1001/1000, 2704/2695


Mapping: {{mapping| 1 -9 -12 19 -42 -10 | 0 17 23 -26 73 22 }}
{{Mapping|legend=0| 1 -9 -12 19 -42 -10 | 0 17 23 -26 73 22 }}


Optimal tunings:  
Optimal tunings:  
Line 644: Line 644:
Comma list: 3025/3024, 4000/3993, 6144/6125
Comma list: 3025/3024, 4000/3993, 6144/6125


Mapping: {{mapping| 1 -16 -11 14 -4 | 0 33 25 -21 14 }}
{{Mapping|legend=0| 1 -16 -11 14 -4 | 0 33 25 -21 14 }}


Optimal tunings:  
Optimal tunings:  
Line 681: Line 681:
Comma list: 1375/1372, 2560/2541, 4375/4356
Comma list: 1375/1372, 2560/2541, 4375/4356


Mapping: {{mapping| 1 -23 -4 0 14 | 0 35 9 4 -15 }}
{{Mapping|legend=0| 1 -23 -4 0 14 | 0 35 9 4 -15 }}


Optimal tunings:  
Optimal tunings:  
Line 696: Line 696:
Comma list: 364/363, 625/624, 640/637, 1375/1372
Comma list: 364/363, 625/624, 640/637, 1375/1372


Mapping: {{mapping| 1 12 5 4 -1 4 | 0 -35 -9 -4 15 -1 }}
{{Mapping|legend=0| 1 12 5 4 -1 4 | 0 -35 -9 -4 15 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 733: Line 733:
Comma list: 441/440, 6144/6125, 35937/35840
Comma list: 441/440, 6144/6125, 35937/35840


Mapping: {{mapping| 23 0 17 101 116 | 0 1 1 -1 -1 }}
{{Mapping|legend=0| 23 0 17 101 116 | 0 1 1 -1 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 748: Line 748:
Comma list: 351/350, 441/440, 847/845, 3584/3575
Comma list: 351/350, 441/440, 847/845, 3584/3575


Mapping: {{mapping| 23 0 17 101 116 158 | 0 1 1 -1 -1 -2 }}
{{Mapping|legend=0| 23 0 17 101 116 158 | 0 1 1 -1 -1 -2 }}


Optimal tunings:  
Optimal tunings:  
Line 763: Line 763:
Comma list: 351/350, 441/440, 561/560, 847/845, 1089/1088
Comma list: 351/350, 441/440, 561/560, 847/845, 1089/1088


Mapping: {{mapping| 23 0 17 101 116 158 94 | 0 1 1 -1 -1 -2 0 }}
{{Mapping|legend=0| 23 0 17 101 116 158 94 | 0 1 1 -1 -1 -2 0 }}


Optimal tunings:  
Optimal tunings:  
Line 778: Line 778:
Comma list: 351/350, 441/440, 456/455, 476/475, 513/512, 847/845
Comma list: 351/350, 441/440, 456/455, 476/475, 513/512, 847/845


Mapping: {{mapping| 23 0 17 101 116 158 94 207 | 0 1 1 -1 -1 -2 0 -3 }}
{{Mapping|legend=0| 23 0 17 101 116 158 94 207 | 0 1 1 -1 -1 -2 0 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 793: Line 793:
Comma list: 276/275, 351/350, 391/390, 441/440, 456/455, 476/475, 847/845
Comma list: 276/275, 351/350, 391/390, 441/440, 456/455, 476/475, 847/845


Mapping: {{mapping| 23 0 17 101 116 158 94 207 104 | 0 1 1 -1 -1 -2 0 -3 0 }}
{{Mapping|legend=0| 23 0 17 101 116 158 94 207 104 | 0 1 1 -1 -1 -2 0 -3 0 }}


Optimal tunings:  
Optimal tunings:  
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