57edo

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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)