57edo: Difference between revisions
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Revision as of 13:22, 12 December 2019
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 | 7mus | |
| 0 | 0.0000 | 0 |
| 1 | 21.0526 | 26.9474 (1A.F28716) |
| 2 | 42.1053 | 53.8947 (35.E50E16) |
| 3 | 63.1579 | 80.8421 (50.D79416) |
| 4 | 84.2105 | 107.7895 (6B.CA1B16) |
| 5 | 105.2632 | 134.7368 (86.BCA216) |
| 6 | 126.3158 | 161.6842 (A1.AF2916) |
| 7 | 147.3684 | 188.6316 (BC.A1AF16) |
| 8 | 168.42105 | 215.57895 (D7.943616) |
| 9 | 189.4737 | 242.5263 (F2.86BD16) |
| 10 | 210.5263 | 269.4737 (10D.794316) |
| 11 | 231.57895 | 296.42105 (128.6BCA16) |
| 12 | 252.6316 | 323.3684 (143.5E5116) |
| 13 | 273.6842 | 350.3158 (15E.50D716) |
| 14 | 294.7368 | 377.2632 (17B.435E16) |
| 15 | 315.7895 | 404.2105 (194.35E516) |
| 16 | 336.8421 | 431.1579 (1AF.286C16) |
| 17 | 357.8947 | 458.1053 (1CA.1AF216) |
| 18 | 378.9474 | 485.0526 (1E5.0D7916) |
| 19 | 400 | 512 (20016) |
| 20 | 421.0526 | 538.9474 (21A.F28716) |
| 21 | 442.1053 | 565.8947 (235.E50E16) |
| 22 | 463.1579 | 592.8421 (250.D79416) |
| 23 | 484.2105 | 619.7895 (26B.CA1B16) |
| 24 | 505.2632 | 646.7368 (286.BCA216) |
| 25 | 526.3158 | 673.6842 (2A1.AF2916) |
| 26 | 547.3684 | 700.6316 (2BC.A1AF16) |
| 27 | 568.42105 | 727.57895 (2D7.943616) |
| 28 | 589.4737 | 754.5263 (2F2.86BD16) |
| 29 | 610.5263 | 781.4737 (30D.794316) |
| 30 | 631.57895 | 808.42105 (328.6BCA16) |
| 31 | 652.6316 | 835.3684 (343.5E5116) |
| 32 | 673.6842 | 862.3158 (35E.50D716) |
| 33 | 694.7368 | 889.2632 (37B.435E16) |
| 34 | 715.7895 | 916.2105 (394.35E516) |
| 35 | 736.8421 | 943.1579 (3AF.286C16) |
| 36 | 757.8947 | 970.1053 (3CA.1AF216) |
| 37 | 778.9474 | 997.0526 (3E5.0D7916) |
| 38 | 800 | 1024 (40016) |
| 39 | 821.0526 | 1050.9474 (41A.F28716) |
| 40 | 842.1053 | 1077.8947 (435.E50E16) |
| 41 | 863.1579 | 1104.8421 (450.D79416) |
| 42 | 884.2105 | 1131.7895 (46B.CA1B16) |
| 43 | 905.2632 | 1158.7368 (486.BCA216) |
| 44 | 926.3158 | 1175.6842 (4A1.AF2916) |
| 45 | 947.3684 | 1212.6316 (4BC.A1AF16) |
| 46 | 968.42105 | 1239.57895 (4D7.943616) |
| 47 | 989.4737 | 1266.5263 (4F2.86BD16) |
| 48 | 1010.5263 | 1293.4737 (50D.794316) |
| 49 | 1031.57895 | 1320.42105 (528.6BCA16) |
| 50 | 1052.6316 | 1347.3684 (543.5E5116) |
| 51 | 1073.6842 | 1374.3158 (55E.50D716) |
| 52 | 1094.7368 | 1401.2632 (57B.435E16) |
| 53 | 1115.7895 | 1428.2105 (594.35E516) |
| 54 | 1136.8421 | 1455.1579 (5AF.286C16) |
| 55 | 1157.8947 | 1482.1053 (5CA.1AF216) |
| 56 | 1178.9474 | 1509.0526 (5E5.0D7916) |
| 57 | 1200 | 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)