157edt
| ← 156edt | 157edt | 158edt → |
Division of the third harmonic into 157 equal parts (157EDT) is related to 99edo, but with the 3/1 rather than the 2/1 being just. The octave is about 0.6781 cents compressed and the step size is about 12.1144 cents. It is consistent to the 12-integer-limit. In comparison, 99edo is only consistent up to the 10-integer-limit. 157edt is notable for it's excellent 5/3, as a convergent to log3(5), and can be used effectively both with and without twos.
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 12.1 | 8.3 | |
| 2 | 24.2 | 16.6 | |
| 3 | 36.3 | 24.8 | 47/46, 48/47, 49/48, 50/49 |
| 4 | 48.5 | 33.1 | 36/35, 37/36 |
| 5 | 60.6 | 41.4 | 29/28, 57/55 |
| 6 | 72.7 | 49.7 | 24/23, 49/47 |
| 7 | 84.8 | 58 | 21/20 |
| 8 | 96.9 | 66.2 | 37/35, 55/52 |
| 9 | 109 | 74.5 | 33/31, 49/46 |
| 10 | 121.1 | 82.8 | 44/41 |
| 11 | 133.3 | 91.1 | 27/25 |
| 12 | 145.4 | 99.4 | 25/23, 37/34 |
| 13 | 157.5 | 107.6 | 23/21, 57/52 |
| 14 | 169.6 | 115.9 | 32/29, 43/39, 54/49 |
| 15 | 181.7 | 124.2 | 10/9 |
| 16 | 193.8 | 132.5 | 19/17, 47/42 |
| 17 | 205.9 | 140.8 | |
| 18 | 218.1 | 149 | 17/15, 42/37 |
| 19 | 230.2 | 157.3 | 8/7 |
| 20 | 242.3 | 165.6 | 23/20 |
| 21 | 254.4 | 173.9 | 22/19, 51/44 |
| 22 | 266.5 | 182.2 | 7/6 |
| 23 | 278.6 | 190.4 | 27/23, 47/40 |
| 24 | 290.7 | 198.7 | 58/49 |
| 25 | 302.9 | 207 | 25/21, 56/47 |
| 26 | 315 | 215.3 | 6/5 |
| 27 | 327.1 | 223.6 | 29/24 |
| 28 | 339.2 | 231.8 | 28/23, 45/37 |
| 29 | 351.3 | 240.1 | 38/31, 49/40 |
| 30 | 363.4 | 248.4 | 37/30, 58/47 |
| 31 | 375.5 | 256.7 | 36/29, 41/33, 46/37 |
| 32 | 387.7 | 265 | 5/4 |
| 33 | 399.8 | 273.2 | 34/27 |
| 34 | 411.9 | 281.5 | 33/26, 52/41 |
| 35 | 424 | 289.8 | 23/18 |
| 36 | 436.1 | 298.1 | 9/7 |
| 37 | 448.2 | 306.4 | 35/27, 57/44 |
| 38 | 460.3 | 314.6 | 30/23, 47/36 |
| 39 | 472.5 | 322.9 | 46/35 |
| 40 | 484.6 | 331.2 | 41/31, 45/34 |
| 41 | 496.7 | 339.5 | 4/3 |
| 42 | 508.8 | 347.8 | 51/38, 55/41 |
| 43 | 520.9 | 356.1 | 27/20, 50/37 |
| 44 | 533 | 364.3 | 34/25, 49/36 |
| 45 | 545.1 | 372.6 | 37/27 |
| 46 | 557.3 | 380.9 | 40/29 |
| 47 | 569.4 | 389.2 | 25/18, 57/41 |
| 48 | 581.5 | 397.5 | 7/5 |
| 49 | 593.6 | 405.7 | 31/22 |
| 50 | 605.7 | 414 | 44/31 |
| 51 | 617.8 | 422.3 | 10/7 |
| 52 | 629.9 | 430.6 | 36/25 |
| 53 | 642.1 | 438.9 | 29/20, 42/29 |
| 54 | 654.2 | 447.1 | 35/24, 54/37 |
| 55 | 666.3 | 455.4 | 25/17, 47/32 |
| 56 | 678.4 | 463.7 | 37/25 |
| 57 | 690.5 | 472 | |
| 58 | 702.6 | 480.3 | 3/2 |
| 59 | 714.7 | 488.5 | |
| 60 | 726.9 | 496.8 | 35/23 |
| 61 | 739 | 505.1 | 23/15, 49/32 |
| 62 | 751.1 | 513.4 | 54/35 |
| 63 | 763.2 | 521.7 | |
| 64 | 775.3 | 529.9 | 36/23 |
| 65 | 787.4 | 538.2 | 41/26, 52/33 |
| 66 | 799.5 | 546.5 | 27/17, 46/29 |
| 67 | 811.7 | 554.8 | |
| 68 | 823.8 | 563.1 | 37/23 |
| 69 | 835.9 | 571.3 | 47/29 |
| 70 | 848 | 579.6 | 31/19, 49/30 |
| 71 | 860.1 | 587.9 | 23/14 |
| 72 | 872.2 | 596.2 | 43/26, 48/29 |
| 73 | 884.3 | 604.5 | 5/3 |
| 74 | 896.5 | 612.7 | 47/28, 52/31 |
| 75 | 908.6 | 621 | 49/29 |
| 76 | 920.7 | 629.3 | |
| 77 | 932.8 | 637.6 | 12/7 |
| 78 | 944.9 | 645.9 | 19/11 |
| 79 | 957 | 654.1 | 33/19, 40/23 |
| 80 | 969.1 | 662.4 | 7/4 |
| 81 | 981.3 | 670.7 | 37/21 |
| 82 | 993.4 | 679 | 55/31 |
| 83 | 1005.5 | 687.3 | |
| 84 | 1017.6 | 695.5 | 9/5 |
| 85 | 1029.7 | 703.8 | 29/16 |
| 86 | 1041.8 | 712.1 | 42/23 |
| 87 | 1053.9 | 720.4 | 57/31 |
| 88 | 1066.1 | 728.7 | 37/20, 50/27 |
| 89 | 1078.2 | 736.9 | 41/22 |
| 90 | 1090.3 | 745.2 | |
| 91 | 1102.4 | 753.5 | 17/9 |
| 92 | 1114.5 | 761.8 | 40/21 |
| 93 | 1126.6 | 770.1 | 23/12 |
| 94 | 1138.8 | 778.3 | 56/29 |
| 95 | 1150.9 | 786.6 | 35/18 |
| 96 | 1163 | 794.9 | 45/23, 47/24 |
| 97 | 1175.1 | 803.2 | |
| 98 | 1187.2 | 811.5 | |
| 99 | 1199.3 | 819.7 | 2/1 |
| 100 | 1211.4 | 828 | |
| 101 | 1223.6 | 836.3 | |
| 102 | 1235.7 | 844.6 | 49/24, 51/25 |
| 103 | 1247.8 | 852.9 | 37/18 |
| 104 | 1259.9 | 861.1 | 29/14 |
| 105 | 1272 | 869.4 | 25/12 |
| 106 | 1284.1 | 877.7 | 21/10 |
| 107 | 1296.2 | 886 | 55/26 |
| 108 | 1308.4 | 894.3 | 49/23 |
| 109 | 1320.5 | 902.5 | 15/7 |
| 110 | 1332.6 | 910.8 | 41/19, 54/25 |
| 111 | 1344.7 | 919.1 | 50/23 |
| 112 | 1356.8 | 927.4 | 46/21 |
| 113 | 1368.9 | 935.7 | |
| 114 | 1381 | 943.9 | 20/9 |
| 115 | 1393.2 | 952.2 | 38/17 |
| 116 | 1405.3 | 960.5 | 9/4 |
| 117 | 1417.4 | 968.8 | 34/15 |
| 118 | 1429.5 | 977.1 | |
| 119 | 1441.6 | 985.4 | 23/10 |
| 120 | 1453.7 | 993.6 | 44/19 |
| 121 | 1465.8 | 1001.9 | 7/3 |
| 122 | 1478 | 1010.2 | 47/20, 54/23 |
| 123 | 1490.1 | 1018.5 | 26/11 |
| 124 | 1502.2 | 1026.8 | 50/21 |
| 125 | 1514.3 | 1035 | 12/5 |
| 126 | 1526.4 | 1043.3 | 29/12 |
| 127 | 1538.5 | 1051.6 | |
| 128 | 1550.6 | 1059.9 | 49/20 |
| 129 | 1562.8 | 1068.2 | 37/15 |
| 130 | 1574.9 | 1076.4 | |
| 131 | 1587 | 1084.7 | 5/2 |
| 132 | 1599.1 | 1093 | |
| 133 | 1611.2 | 1101.3 | |
| 134 | 1623.3 | 1109.6 | 23/9 |
| 135 | 1635.4 | 1117.8 | 18/7 |
| 136 | 1647.6 | 1126.1 | 44/17, 57/22 |
| 137 | 1659.7 | 1134.4 | |
| 138 | 1671.8 | 1142.7 | 21/8 |
| 139 | 1683.9 | 1151 | 37/14, 45/17 |
| 140 | 1696 | 1159.2 | |
| 141 | 1708.1 | 1167.5 | 51/19 |
| 142 | 1720.2 | 1175.8 | 27/10 |
| 143 | 1732.4 | 1184.1 | 49/18 |
| 144 | 1744.5 | 1192.4 | 52/19 |
| 145 | 1756.6 | 1200.6 | |
| 146 | 1768.7 | 1208.9 | 25/9 |
| 147 | 1780.8 | 1217.2 | |
| 148 | 1792.9 | 1225.5 | 31/11 |
| 149 | 1805 | 1233.8 | |
| 150 | 1817.2 | 1242 | 20/7 |
| 151 | 1829.3 | 1250.3 | 23/8 |
| 152 | 1841.4 | 1258.6 | 55/19 |
| 153 | 1853.5 | 1266.9 | 35/12 |
| 154 | 1865.6 | 1275.2 | 47/16 |
| 155 | 1877.7 | 1283.4 | |
| 156 | 1889.8 | 1291.7 | |
| 157 | 1902 | 1300 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.68 | +0.00 | -1.36 | -0.01 | -0.68 | -1.03 | -2.03 | +0.00 | -0.69 | +3.91 | -1.36 |
| Relative (%) | -5.6 | +0.0 | -11.2 | -0.1 | -5.6 | -8.5 | -16.8 | +0.0 | -5.7 | +32.3 | -11.2 | |
| Steps (reduced) |
99 (99) |
157 (0) |
198 (41) |
230 (73) |
256 (99) |
278 (121) |
297 (140) |
314 (0) |
329 (15) |
343 (29) |
355 (41) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.44 | -1.71 | -0.01 | -2.71 | +1.36 | -0.68 | +2.63 | -1.37 | -1.03 | +3.23 | -1.04 |
| Relative (%) | +44.9 | -14.1 | -0.1 | -22.4 | +11.2 | -5.6 | +21.7 | -11.3 | -8.5 | +26.7 | -8.6 | |
| Steps (reduced) |
367 (53) |
377 (63) |
387 (73) |
396 (82) |
405 (91) |
413 (99) |
421 (107) |
428 (114) |
435 (121) |
442 (128) |
448 (134) | |