57edo
| ← 56edo | 57edo | 58edo → |
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
Just approximation
Script error: No such module "primes_in_edo".
Intervals
| Degree | Cents | Ups and downs notation (flat fifth 11\19) | Ups and downs notation (sharp fifth 34\57) |
|---|---|---|---|
| 0 | 0.0000 | D | D |
| 1 | 21.0526 | ^D, ^E♭♭♭ | ^D, E♭ |
| 2 | 42.1053 | vD♯, vE♭♭ | ^^D, ^E♭ |
| 3 | 63.1579 | D♯, E♭♭ | ^3D, ^^E♭ |
| 4 | 84.2105 | ^D♯, ^E♭♭ | ^4D, ^3E♭ |
| 5 | 105.2632 | vD𝄪, vE♭ | ^5D, ^4E♭ |
| 6 | 126.3158 | D𝄪, E♭ | v4D♯, v5E |
| 7 | 147.3684 | ^D𝄪, ^E♭ | v3D♯, v4E |
| 8 | 168.42105 | vD♯𝄪, vE | vvD♯, v3E |
| 9 | 189.4737 | E | vD♯, vvE |
| 10 | 210.5263 | ^E, ^F♭♭ | D♯, vE |
| 11 | 231.57895 | vE♯, vF♭ | E |
| 12 | 252.6316 | E♯, F♭ | F |
| 13 | 273.6842 | ^E♯, ^F♭ | ^F, G♭ |
| 14 | 294.7368 | vE𝄪, vF | ^^F, ^G♭ |
| 15 | 315.7895 | F | ^3F, ^^G♭ |
| 16 | 336.8421 | ^F, ^G♭♭♭ | ^4F, ^3G♭ |
| 17 | 357.8947 | vF♯, vG♭♭ | ^5F, ^4G♭ |
| 18 | 378.9474 | F♯, G♭♭ | v4F♯, v5G |
| 19 | 400 | ^F♯, ^G♭♭ | v3F♯, v4G |
| 20 | 421.0526 | vF𝄪, vG♭ | vvF♯, v3G |
| 21 | 442.1053 | F𝄪, G♭ | vF♯, vvG |
| 22 | 463.1579 | ^F𝄪, ^G♭ | F♯, vG |
| 23 | 484.2105 | vF♯𝄪, vG | G |
| 24 | 505.2632 | G | ^G, A♭ |
| 25 | 526.3158 | ^G, ^A♭♭♭ | ^^G, ^A♭ |
| 26 | 547.3684 | vG♯, vA♭♭ | ^3G, ^^A♭ |
| 27 | 568.42105 | G♯, A♭♭ | ^4G, ^3A♭ |
| 28 | 589.4737 | ^G♯, ^A♭♭ | ^5G, ^4A♭ |
| 29 | 610.5263 | vG𝄪, vA♭ | v4G♯, v5A |
| 30 | 631.57895 | G𝄪, A♭ | v3G♯, v4A |
| 31 | 652.6316 | ^G𝄪, ^A♭ | vvG♯, v3A |
| 32 | 673.6842 | vG♯𝄪, vA | vG♯, vvA |
| 33 | 694.7368 | A | G♯, vA |
| 34 | 715.7895 | ^A, ^B♭♭♭ | A |
| 35 | 736.8421 | vA♯, vB♭♭ | ^A, B♭ |
| 36 | 757.8947 | A♯, B♭♭ | ^^A, ^B♭ |
| 37 | 778.9474 | ^A♯, ^B♭♭ | ^3A, ^^B♭ |
| 38 | 800 | vA𝄪, vB♭ | ^4A, ^3B♭ |
| 39 | 821.0526 | A𝄪, B♭ | ^5A, ^4B♭ |
| 40 | 842.1053 | ^A𝄪, ^B♭ | v4A♯, v5B |
| 41 | 863.1579 | vA♯𝄪, vB | v3A♯, v4B |
| 42 | 884.2105 | B | vvA♯, v3B |
| 43 | 905.2632 | ^B, ^C♭♭ | vA♯, vvB |
| 44 | 926.3158 | vB♯, vC♭ | A♯, vB |
| 45 | 947.3684 | B♯, C♭ | B |
| 46 | 968.42105 | ^B♯, ^C♭ | C |
| 47 | 989.4737 | vB𝄪, vC | ^C, D♭ |
| 48 | 1010.5263 | C | ^^C, ^D♭ |
| 49 | 1031.57895 | ^C, ^D♭♭♭ | ^3C, ^^D♭ |
| 50 | 1052.6316 | vC♯, vD♭♭ | ^4C, ^3D♭ |
| 51 | 1073.6842 | C♯, D♭♭ | ^5C, ^4D♭ |
| 52 | 1094.7368 | ^C♯, ^D♭♭ | v4C♯, v5D |
| 53 | 1115.7895 | vC𝄪, vD♭ | v3C♯, v4D |
| 54 | 1136.8421 | C𝄪, D♭ | vvC♯, v3D |
| 55 | 1157.8947 | ^C𝄪, ^D♭ | vC♯, vvD |
| 56 | 1178.9474 | vC♯𝄪, vD | C♯, vD |
| 57 | 1200 | D | D |
Scales 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)