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 pions 7mus
0 0
1 21.0526 22.3158 26.9474 (1A.F28716)
2 42.1053 44.6316 53.8947 (35.E50E16)
3 63.1579 66.9474 80.8421 (50.D79416)
4 84.2105 89.2632 107.7895 (6B.CA1B16)
5 105.2632 111.57895 134.7368 (86.BCA216)
6 126.3158 133.8947 161.6842 (A1.AF2916)
7 147.3684 156.2105 188.6316 (BC.A1AF16)
8 168.42105 178.5263 215.57895 (D7.943616)
9 189.4737 200.8421 242.5263 (F2.86BD16)
10 210.5263 223.1579 269.4737 (10D.794316)
11 231.57895 245.4737 296.42105 (128.6BCA16)
12 252.6316 267.7895 323.3684 (143.5E5116)
13 273.6842 290.1053 350.3158 (15E.50D716)
14 294.7368 312.42105 377.2632 (17B.435E16)
15 315.7895 334.7368 404.2105 (194.35E516)
16 336.8421 357.0526 431.1579 (1AF.286C16)
17 357.8947 379.3684 458.1053 (1CA.1AF216)
18 378.9474 401.6842 485.0526 (1E5.0D7916)
19 400 424 512 (20016)
20 421.0526 446.3158 538.9474 (21A.F28716)
21 442.1053 468.6316 565.8947 (235.E50E16)
22 463.1579 490.9474 592.8421 (250.D79416)
23 484.2105 513.2632 619.7895 (26B.CA1B16)
24 505.2632 535.57895 646.7368 (286.BCA216)
25 526.3158 557.8947 673.6842 (2A1.AF2916)
26 547.3684 580.2105 700.6316 (2BC.A1AF16)
27 568.42105 602.5263 727.57895 (2D7.943616)
28 589.4737 624.8421 754.5263 (2F2.86BD16)
29 610.5263 647.1579 781.4737 (30D.794316)
30 631.57895 669.4737 808.42105 (328.6BCA16)
31 652.6316 691.7895 835.3684 (343.5E5116)
32 673.6842 714.1053 862.3158 (35E.50D716)
33 694.7368 736.42105 889.2632 (37B.435E16)
34 715.7895 758.7368 916.2105 (394.35E516)
35 736.8421 781.0526 943.1579 (3AF.286C16)
36 757.8947 803.3684 970.1053 (3CA.1AF216)
37 778.9474 825.6842 997.0526 (3E5.0D7916)
38 800 848 1024 (40016)
39 821.0526 870.3158 1050.9474 (41A.F28716)
40 842.1053 892.6316 1077.8947 (435.E50E16)
41 863.1579 914.9474 1104.8421 (450.D79416)
42 884.2105 937.2632 1131.7895 (46B.CA1B16)
43 905.2632 959.57895 1158.7368 (486.BCA216)
44 926.3158 981.8947 1175.6842 (4A1.AF2916)
45 947.3684 1004.2105 1212.6316 (4BC.A1AF16)
46 968.42105 1026.5263 1239.57895 (4D7.943616)
47 989.4737 1048.8421 1266.5263 (4F2.86BD16)
48 1010.5263 1071.1579 1293.4737 (50D.794316)
49 1031.57895 1093.4737 1320.42105 (528.6BCA16)
50 1052.6316 1115.7895 1347.3684 (543.5E5116)
51 1073.6842 1138.1053 1374.3158 (55E.50D716)
52 1094.7368 1160.42105 1401.2632 (57B.435E16)
53 1115.7895 1182.7368 1428.2105 (594.35E516)
54 1136.8421 1205.0526 1455.1579 (5AF.286C16)
55 1157.8947 1227.3684 1482.1053 (5CA.1AF216)
56 1178.9474 1249.6842 1509.0526 (5E5.0D7916)
57 1200 1272 1536 (60016)

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)