57edo
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57 tone equal temperament[edit]
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[edit]
| 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)