53edt
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Prime factorization
53 (prime)
Step size
35.8859¢
Octave
33\53edt (1184.24¢)
Consistency limit
2
Distinct consistency limit
2
| ← 52edt | 53edt | 54edt → |
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).
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -15.8 | +0.0 | +4.4 | +12.8 | -15.8 | +4.5 | -11.4 | +0.0 | -3.0 | +11.5 | +4.4 |
| Relative (%) | -43.9 | +0.0 | +12.1 | +35.6 | -43.9 | +12.4 | -31.8 | +0.0 | -8.3 | +31.9 | +12.1 | |
| Steps (reduced) |
33 (33) |
53 (0) |
67 (14) |
78 (25) |
86 (33) |
94 (41) |
100 (47) |
106 (0) |
111 (5) |
116 (10) |
120 (14) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +9.3 | -11.3 | +12.8 | +8.7 | +11.4 | -15.8 | -1.7 | +17.1 | +4.5 | -4.3 | -9.5 |
| Relative (%) | +26.0 | -31.5 | +35.6 | +24.3 | +31.8 | -43.9 | -4.8 | +47.8 | +12.4 | -12.0 | -26.5 | |
| Steps (reduced) |
124 (18) |
127 (21) |
131 (25) |
134 (28) |
137 (31) |
139 (33) |
142 (36) |
145 (39) |
147 (41) |
149 (43) |
151 (45) | |
Intervals
| degree | cents value | hekts | corresponding JI intervals |
comments |
|---|---|---|---|---|
| 0 | exact 1/1 | |||
| 1 | 35.8859 | 24.5283 | 50/49, 49/48 | |
| 2 | 71.7719 | 49.0566 | 25/24 | |
| 3 | 107.6578 | 73.5849 | 17/16, 16/15 | |
| 4 | 143.5438 | 98.1132 | 38/35 | |
| 5 | 179.4297 | 122.6415 | 51/46, 132/119 | |
| 6 | 215.3157 | 147.1698 | 17/15 | |
| 7 | 251.2016 | 171.6981 | 15/13 | |
| 8 | 287.0875 | 196.2264 | 33/28, 13/11 | |
| 9 | 322.9735 | 220.7547 | 6/5 | |
| 10 | 358.8594 | 245.283 | 16/13 | |
| 11 | 394.7454 | 269.8113 | 5/4, 49/39 | |
| 12 | 430.6313 | 594.3396 | 9/7, 50/39 | |
| 13 | 466.5173 | 318.8679 | 21/16 | |
| 14 | 502.4032 | 343.3962 | 4/3, 171/128 | |
| 15 | 538.2892 | 367.9245 | 15/11 | |
| 16 | 574.1751 | 392.4528 | 39/28 | |
| 17 | 610.061 | 416.9811 | 10/7 | |
| 18 | 645.947 | 441.5094 | 35/24 | |
| 19 | 681.8329 | 466.0377 | 126/85, 40/27 | |
| 20 | 717.7189 | 490.566 | pseudo-3/2 | |
| 21 | 753.6048 | 515.0943 | 17/11 | |
| 22 | 789.4908 | 539.6226 | 30/19 | |
| 23 | 825.3767 | 564.1509 | 13/8 | |
| 24 | 861.2626 | 588.67945 | ||
| 25 | 897.1486 | 613.20755 | 42/25, 32/19 | |
| 26 | 933.0345 | 637.73585 | 12/7 | |
| 27 | 968.9205 | 662.26415 | 7/4 | |
| 28 | 1004.8064 | 686.79245 | 25/14, 57/32 | |
| 29 | 1040.6924 | 711.32075 | ||
| 30 | 1076.5783 | 735.8491 | 24/13 | |
| 31 | 1112.4642 | 760.3774 | 19/10 | |
| 32 | 1148.3502 | 784.9057 | 33/17 | |
| 33 | 1184.2361 | 809.434 | pseudooctave | |
| 34 | 1220.1221 | 833.9623 | 85/42, 81/40 | |
| 35 | 1256.008 | 858.4906 | 95/46 | |
| 36 | 1291.894 | 883.0189 | 21/10 | |
| 37 | 1327.7799 | 907.5472 | 28/13 | |
| 38 | 1363.6658 | 932.0755 | 11/5 | |
| 39 | 1399.5518 | 956.6038 | 9/4, 128/57 | |
| 40 | 1435.4377 | 981.1321 | 16/7 | |
| 41 | 1471.3237 | 1005.3304 | 7/3, 117/50 | |
| 42 | 1507.2096 | 1303.1887 | 12/5, 117/49 | |
| 43 | 1543.0956 | 1054.717 | 39/16 | |
| 44 | 1578.9815 | 1079.2453 | 5/2 | |
| 45 | 1614.8675 | 1130.7736 | 28/11, 33/13 | |
| 46 | 1650.7534 | 1128.3019 | 13/5 | |
| 47 | 1686.6393 | 1152.8302 | 45/17 | |
| 48 | 1722.5253 | 1177.3585 | 119/44 | |
| 49 | 1758.4112 | 1201.8868 | 105/38 | |
| 50 | 1794.2972 | 1226.4151 | 48/17, 45/16 | |
| 51 | 1830.1831 | 1250.9434 | 72/25 | |
| 52 | 1866.0691 | 1275.4717 | 147/50, 144/49 | |
| 53 | 1901.955 | 1300 | exact 3/1 | |