56edf
56EDF is the equal division of the just perfect fifth into 56 parts of 12.5349 cents each, corresponding to 95.7326 edo.
| ← 55edf | 56edf | 57edf → |
It is related to the regular temperament which tempers out 2401/2400 and |91 -80 13 2> in the 7-limit, which is supported by 383, 670, 1053, 1436, and 1723 EDOs.
Related regular temperaments
7-limit 383&670
Commas: 2401/2400, |91 -80 13 2>
POTE generator: ~|-33 32 -4 -3> = 12.5357
Mapping: [<1 1 -1 1|, <0 56 318 173|]
EDOs: 383, 670, 1053, 1436, 1723
11-limit 383&670
Commas: 2401/2400, 14348907/14348180, 26214400/26198073
POTE generator: ~13504609503/13421772800 = 12.5359
Mapping: [<1 1 -1 1 3|, <0 56 318 173 44|]
Intervals
| 56ed3/2 | |
|---|---|
| 1 | 12.5349 |
| 2 | 25.0698 |
| 3 | 37.6047 |
| 4 | 50.1396 |
| 5 | 62.67455 |
| 6 | 75.2095 |
| 7 | 87.7444 |
| 8 | 100.2793 |
| 9 | 112.8142 |
| 10 | 125.3491 |
| 11 | 137.884 |
| 12 | 150.4189 |
| 13 | 162.9538 |
| 14 | 175.48875 |
| 15 | 188.2366 |
| 16 | 200.5586 |
| 17 | 213.0935 |
| 18 | 225.6284 |
| 19 | 238.1633 |
| 20 | 250.6982 |
| 21 | 263.2331 |
| 22 | 275.768 |
| 23 | 288.30295 |
| 24 | 300.8379 |
| 25 | 313.3728 |
| 26 | 325.9077 |
| 27 | 338.4426 |
| 28 | 350.9775 |
| 29 | 363.5214 |
| 30 | 376.0473 |
| 31 | 388.5822 |
| 32 | 401.1171 |
| 33 | 413.65205 |
| 34 | 426.187 |
| 35 | 438.7219 |
| 36 | 451.2568 |
| 37 | 463.7917 |
| 38 | 476.3266 |
| 39 | 488.8615 |
| 40 | 501.3964 |
| 41 | 513.9313 |
| 42 | 526.46625 |
| 43 | 539.0012 |
| 44 | 551.536 |
| 45 | 564.071 |
| 46 | 576.6059 |
| 47 | 589.1408 |
| 48 | 601.6757 |
| 49 | 614.2106 |
| 50 | 626.7455 |
| 51 | 639.28045 |
| 52 | 651.8154 |
| 53 | 664.3503 |
| 54 | 676.8852 |
| 55 | 689.4201 |
| 56 | 701.955 |
| 57 | 714.4899 |
| 58 | 727.0248 |
| 59 | 739.5597 |
| 60 | 752.0946 |
| 61 | 764.62955 |
| 62 | 777.1645 |
| 63 | 789.6994 |
| 64 | 802.2343 |
| 65 | 814.7692 |
| 66 | 827.3041 |
| 67 | 839.839 |
| 68 | 852.3739 |
| 69 | 864.9088 |
| 70 | 877.44375 |
| 71 | 889.9787 |
| 72 | 902.5136 |
| 73 | 915.0485 |
| 74 | 927.5834 |
| 75 | 940.1183 |
| 76 | 952.6532 |
| 77 | 965.1881 |
| 78 | 977.723 |
| 79 | 990.25795 |
| 80 | 1002.7929 |
| 81 | 1015.3278 |
| 82 | 1027.8627 |
| 83 | 1040.3976 |
| 84 | 1052.9325 |
| 85 | 1065.4674 |
| 86 | 1078.0023 |
| 87 | 1090.5372 |
| 88 | 1103.0721 |
| 89 | 1115.6071 |
| 90 | 1128.142 |
| 91 | 1140.6769 |
| 92 | 1153.2118 |
| 93 | 1165.7467 |
| 94 | 1178.2816 |
| 95 | 1190.8165 |
| 96 | 1203.3514 |
| 97 | 1215.8863 |
| 98 | 1228.42125 |
| 99 | 1240.9561 |
| 100 | 1253.4911 |
| 101 | 1266.026 |
| 102 | 1278.5609 |
| 103 | 1291.0958 |
| 104 | 1303.6307 |
| 105 | 1316.1656 |
| 106 | 1328.7005 |
| 107 | 1341.23545 |
| 108 | 1353.7704 |
| 109 | 1366.3053 |
| 110 | 1378.8418 |
| 111 | 1391.3751 |
| 112 | 1403.91 |
|
Todo: complete table
Add a third column that comments on the intervals, either what JI they approximate, what they are named, or how they can be used musically. |