| 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
|
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
|
|