56edf
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Prime factorization
23 × 7
Step size
12.5349¢
Octave
96\56edf (1203.35¢) (→12\7edf)
Twelfth
152\56edf (1905.31¢) (→19\7edf)
Consistency limit
2
Distinct consistency limit
2
| ← 55edf | 56edf | 57edf → |
56EDF is the equal division of the just perfect fifth into 56 parts of 12.5349 cents each, corresponding to 95.7326 edo. 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.
| ed3/2 | |
|---|---|
| 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 |
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, [[1]], [[2]]
POTE generator: ~13504609503/13421772800 = 12.5359
Mapping: [<1 1 -1 1 3|, <[56 318 173|0 56 318 173] 44|]