53edt
53EDT is the equal division of the third harmonic into 53 parts of 35.8859 cents each, corresponding to 33.4393 edo. It has a generally sharp tendency, in the sense that if 3 is pure, 5, 7, 11, 13, and 17 are all sharp. It tempers out 413343/390625 and 823543/820125 in the 7-limit; 891/875, 3087/3025, and 164025/161051 in the 11-limit; 637/625, 729/715, 847/845, and 1575/1573 in the 13-limit; 189/187, 429/425, 459/455, and 833/825 in the 17-limit; 171/169, 247/245, 361/357, and 855/847 in the 19-limit (no-twos subgroup).
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 35.8859 | 50/49, 49/48 | |
| 2 | 71.7719 | 25/24 | |
| 3 | 107.6578 | ||
| 4 | 143.5438 | 38/35 | |
| 5 | 179.4297 | 51/46, 132/119 | |
| 6 | 215.3157 | ||
| 7 | 251.2016 | ||
| 8 | 287.0875 | ||
| 9 | 322.9735 | ||
| 10 | 358.8594 | 16/13 | |
| 11 | 394.7454 | 49/39 | |
| 12 | 430.6313 | 50/39 | |
| 13 | 466.5173 | ||
| 14 | 502.4032 | ||
| 15 | 538.2892 | 15/11 | |
| 16 | 574.1751 | 39/28 | |
| 17 | 610.0610 | ||
| 18 | 645.9470 | ||
| 19 | 681.8329 | 126/85 | |
| 20 | 717.7189 | ||
| 21 | 753.6048 | 17/11 | |
| 22 | 789.4908 | 30/19 | |
| 23 | 825.3767 | ||
| 24 | 861.2626 | ||
| 25 | 897.1486 | ||
| 26 | 933.0345 | 12/7 | |
| 27 | 968.9205 | 7/4 | |
| 28 | 1004.8064 | ||
| 29 | 1040.6924 | ||
| 30 | 1076.5783 | ||
| 31 | 1112.4642 | 19/10 | |
| 32 | 1148.3502 | 33/17 | |
| 33 | 1184.2361 | ||
| 34 | 1220.1221 | 85/42 | |
| 35 | 1256.0080 | 95/46 | |
| 36 | 1291.8940 | ||
| 37 | 1327.7799 | 28/13 | |
| 38 | 1363.6658 | 11/5 | |
| 39 | 1399.5518 | 128/57 | |
| 40 | 1435.4377 | ||
| 41 | 1471.3237 | 117/50 | |
| 42 | 1507.2096 | 117/49 | |
| 43 | 1543.0956 | 39/16 | |
| 44 | 1578.9815 | ||
| 45 | 1614.8675 | ||
| 46 | 1650.7534 | ||
| 47 | 1686.6393 | ||
| 48 | 1722.5253 | 119/44 | |
| 49 | 1758.4112 | ||
| 50 | 1794.2972 | ||
| 51 | 1830.1831 | 72/25 | |
| 52 | 1866.0691 | ||
| 53 | 1901.9550 | exact 3/1 |