| Prime factorization
|
53 (prime)
|
| Step size
|
63.5628¢
|
| Octave
|
19\53ed7 (1207.69¢)
|
| Twelfth
|
30\53ed7 (1906.88¢)
|
| Consistency limit
|
10
|
| Distinct consistency limit
|
6
|
Division of the 7th harmonic into 53 equal parts (53ed7) is related to 19edo, 30edt, and Carlos Beta, but with the 7/1 rather than the 2/1 being just. The octave is about 7.6923 cents stretched and the step size is about 63.5628 cents. The patent val has a generally sharp tendency for harmonics up to 16, with exception for 11th harmonic.
| degree
|
cents value
|
corresponding
JI intervals
|
comments
|
| 0
|
0.0000
|
exact 1/1
|
|
| 1
|
63.5628
|
28/27, 27/26
|
|
| 2
|
127.1255
|
14/13
|
|
| 3
|
190.6883
|
19/17
|
|
| 4
|
254.2510
|
22/19
|
|
| 5
|
317.8138
|
6/5, 77/64
|
|
| 6
|
381.3765
|
96/77
|
|
| 7
|
444.9393
|
22/17
|
|
| 8
|
508.5020
|
|
|
| 9
|
572.0648
|
32/23
|
|
| 10
|
635.6275
|
13/9
|
|
| 11
|
699.1903
|
3/2
|
|
| 12
|
762.7530
|
14/9
|
|
| 13
|
826.3158
|
|
|
| 14
|
889.8785
|
77/46
|
|
| 15
|
953.4413
|
26/15
|
|
| 16
|
1017.0040
|
9/5
|
|
| 17
|
1080.5668
|
28/15
|
|
| 18
|
1144.1296
|
64/33
|
|
| 19
|
1207.6923
|
161/80
|
pseudo-octave
|
| 20
|
1271.2551
|
25/12
|
|
| 21
|
1334.8178
|
54/25
|
|
| 22
|
1398.3806
|
56/25, 110/49
|
|
| 23
|
1461.9433
|
|
|
| 24
|
1525.5061
|
|
|
| 25
|
1589.0688
|
5/2
|
|
| 26
|
1652.6316
|
13/5
|
|
| 27
|
1716.1943
|
35/13
|
|
| 28
|
1779.7571
|
14/5
|
|
| 29
|
1843.3198
|
|
|
| 30
|
1906.8826
|
|
pseudo-3/1
|
| 31
|
1970.4453
|
25/8
|
|
| 32
|
2034.0081
|
68/21
|
|
| 33
|
2097.5708
|
84/25
|
|
| 34
|
2161.1336
|
80/23
|
|
| 35
|
2224.6964
|
76/21
|
|
| 36
|
2288.2591
|
15/4
|
|
| 37
|
2351.8219
|
35/9
|
|
| 38
|
2415.3846
|
105/26
|
pseudo-4/1
|
| 39
|
2478.9474
|
46/11, 88/21
|
|
| 40
|
2542.5101
|
100/23
|
|
| 41
|
2606.0729
|
9/2
|
|
| 42
|
2669.6356
|
14/3
|
|
| 43
|
2733.1984
|
63/13
|
|
| 44
|
2796.7611
|
161/32
|
pseudo-5/1
|
| 45
|
2860.3239
|
|
|
| 46
|
2923.8866
|
119/22
|
|
| 47
|
2987.4494
|
|
|
| 48
|
3051.0121
|
64/11, 35/6
|
|
| 49
|
3114.5749
|
133/22
|
pseudo-6/1
|
| 50
|
3178.1376
|
119/19
|
|
| 51
|
3241.7004
|
13/2
|
|
| 52
|
3305.2632
|
27/4
|
|
| 53
|
3368.8259
|
exact 7/1
|
harmonic seventh plus two octaves
|