56ed5
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Prime factorization
23 × 7
Step size
49.7556¢
Octave
24\56ed5 (1194.13¢) (→3\7ed5)
Fifth
14\56ed5 (696.578¢) (→1\4ed5)
Semitones (A1:m2)
2:2 (99.51¢ : 99.51¢)
Consistency limit
6
Distinct consistency limit
6
| ← 55ed5 | 56ed5 | 57ed5 → |
Division of the 5th harmonic into 56 equal parts (56ed5) is related to 24 edo, but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656 cents compressed and the step size is about 49.7556 cents. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4. This tuning is also a hyperpyth, tempering out 135/133, 171/169, 225/221, and 1521/1445 in the patent val.
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 49.7556 | 36/35, 35/34 | |
| 2 | 99.5112 | 18/17 | |
| 3 | 149.2668 | 12/11 | |
| 4 | 199.0224 | 55/49 | |
| 5 | 248.7780 | 15/13 | |
| 6 | 298.5336 | 19/16 | |
| 7 | 348.2892 | 11/9 | |
| 8 | 398.0448 | 34/27 | pseudo-5/4 |
| 9 | 447.8004 | 35/27 | |
| 10 | 497.5560 | 4/3 | |
| 11 | 547.3116 | 70/51 | |
| 12 | 597.0672 | 24/17 | |
| 13 | 646.8228 | ||
| 14 | 696.5784 | meantone fifth (pseudo-3/2) | |
| 15 | 746.3340 | 20/13 | |
| 16 | 796.0896 | 19/12 | |
| 17 | 845.8452 | 44/27, 75/46 | |
| 18 | 895.6008 | 57/34 | pseudo-5/3 |
| 19 | 945.3564 | 19/11 | |
| 20 | 995.1120 | 16/9 | pseudo-9/5 |
| 21 | 1044.8676 | 64/35 | |
| 22 | 1094.6232 | 32/17 | |
| 23 | 1144.3788 | ||
| 24 | 1194.1344 | 255/128 | pseudo-octave |
| 25 | 1243.8901 | 80/39, 39/19 | |
| 26 | 1293.6457 | 19/9 | |
| 27 | 1343.4013 | 50/23 | |
| 28 | 1393.1569 | 38/17, 85/38 | meantone major second plus an octave |
| 29 | 1442.9125 | 23/10 | |
| 30 | 1492.6681 | 45/19 | |
| 31 | 1542.4237 | 39/16 | |
| 32 | 1592.1793 | 128/51 | pseudo-5/2 |
| 33 | 1641.9349 | pseudo-13/5 | |
| 34 | 1691.6905 | 85/32 | |
| 35 | 1741.4461 | 175/64 | |
| 36 | 1791.2017 | 45/16 | |
| 37 | 1840.9573 | 55/19 | |
| 38 | 1890.7129 | 170/57 | pseudo-3/1 |
| 39 | 1940.4685 | 46/15, 135/44 | |
| 40 | 1990.2241 | 60/19 | |
| 41 | 2039.9797 | 13/4 | |
| 42 | 2089.7353 | meantone major sixth plus an octave (pseudo-10/3) | |
| 43 | 2139.4909 | pseudo-17/5 | |
| 44 | 2189.2465 | 85/24 | |
| 45 | 2239.0021 | 51/14 | |
| 46 | 2288.7577 | 15/4 | pseudo-19/5 |
| 47 | 2338.5133 | 27/7 | |
| 48 | 2388.2689 | 135/34 | pseudo-4/1 |
| 49 | 2438.0245 | 45/11 | |
| 50 | 2487.7801 | 80/19 | pseudo-21/5 |
| 51 | 2537.5357 | 13/3 | |
| 52 | 2587.2913 | 49/11 | |
| 53 | 2637.0469 | 55/12 | |
| 54 | 2686.8025 | 85/18 | |
| 55 | 2736.5581 | 34/7 | |
| 56 | 2786.3137 | exact 5/1 | just major third plus two octaves |