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57 tone equal temperament


57edo divides the octave into 57 parts of size 21.053. It can be used to tune mothra temperament, and is an excellent tuning for the 2.5/3.7.11.13.17.19 just intonation subgroup. One way to describe 57 is that it has a 5-limit part consisting of three versions of 19, plus a no-threes no-fives part which is much more accurate. A good generator to exploit the 2.5/3.7.11.13.17.19 aspect of 57 is the approximate 11/8, which is 26\57. This gives the 19-limit 46&57 temperament Heinz.

5-limit commas: 81/80, 3125/3072

7-limit commas: 81/80, 3125/3072, 1029/1024

11-limit commas: 99/98, 385/384, 441/440, 625/616

Intervals

Degree
Size (Cents)
0
0.0000
1
21.0526
2
42.1053
3
63.1579
4
84.2105
5
105.2632
6
126.3158
7
147.3684
8
168.4211
9
189.4737
10
210.5263
11
231.5789
12
252.6316
13
273.6842
14
294.7368
15
315.7895
16
336.8421
17
357.8947
18
378.9474
19
400.0000
20
421.0526
21
442.1053
22
463.1579
23
484.2105
24
505.2632
25
526.3158
26
547.3684
27
568.4211
28
589.4737
29
610.5263
30
631.5789
31
652.6316
32
673.6842
33
694.7368
34
715.7895
35
736.8421
36
757.8947
37
778.9474
38
800.0000
39
821.0526
40
842.1053
41
863.1579
42
884.2105
43
905.2632
44
926.3158
45
947.3684
46
968.4211
47
989.4737
48
1010.5263
49
1031.5789
50
1052.6316
51
1073.6842
52
1094.7368
53
1115.7895
54
1136.8421
55
1157.8947
56
1178.9474
57
1200.0000

Modes of 57edo
2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 - 3MOS of type 18L 21s (augene)