57edo

← 56edo

57edo

58edo →

Prime factorization	3 × 19
Step size	21.0526 ¢
Fifth	33\57 (694.737 ¢) (→ 11\19)
Semitones (A1:m2)	3:6 (63.16 ¢ : 126.3 ¢)
Dual sharp fifth	34\57 (715.789 ¢)
Dual flat fifth	33\57 (694.737 ¢) (→ 11\19)
Dual major 2nd	10\57 (210.526 ¢)
Consistency limit	7
Distinct consistency limit	7

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	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	168.42105
9	189.4737
10	210.5263
11	231.57895
12	252.6316
13	273.6842
14	294.7368
15	315.7895
16	336.8421
17	357.8947
18	378.9474
19	400
20	421.0526
21	442.1053
22	463.1579
23	484.2105
24	505.2632
25	526.3158
26	547.3684
27	568.42105
28	589.4737
29	610.5263
30	631.57895
31	652.6316
32	673.6842
33	694.7368
34	715.7895
35	736.8421
36	757.8947
37	778.9474
38	800
39	821.0526
40	842.1053
41	863.1579
42	884.2105
43	905.2632
44	926.3158
45	947.3684
46	968.42105
47	989.4737
48	1010.5263
49	1031.57895
50	1052.6316
51	1073.6842
52	1094.7368
53	1115.7895
54	1136.8421
55	1157.8947
56	1178.9474
57	1200

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)