# 53edt

 ← 52edt 53edt 54edt →
Prime factorization 53 (prime)
Step size 35.8859¢
Octave 33\53edt (1184.24¢)
Consistency limit 2
Distinct consistency limit 2

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 hekts corresponding
JI intervals
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