56edt
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Prime factorization
23 × 7
Step size
33.9635¢
Octave
35\56edt (1188.72¢) (→5\8edt)
Consistency limit
2
Distinct consistency limit
2
| ← 55edt | 56edt | 57edt → |
The 56 equal division of 3, the tritave, divides it into 56 equal parts of 33.963 cents each, corresponding to 35.332 edo. It tempers out 245/243 in the 7-limit, 1331/1323 in the 11-limit and 275/273 in the 13-limit. It supports the 3.5.7.11.13 temperament with mapping [<1 5 0 1 10|, <0 -6 3 2 -13|]. 56edt is the twelfth no-twos zeta peak edt.
Harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0 | -1.3 | -6.4 | +0.0 | -7.8 | +8.7 | -1.3 | -14.2 | -3.0 | -6.4 | +5.9 |
| Relative (%) | +0.0 | -3.9 | -19.0 | +0.0 | -22.9 | +25.6 | -3.9 | -41.9 | -8.8 | -19.0 | +17.3 | |
| Steps (reduced) |
56 (0) |
82 (26) |
99 (43) |
112 (0) |
122 (10) |
131 (19) |
138 (26) |
144 (32) |
150 (38) |
155 (43) |
160 (48) | |
| Harmonic | 25 | 27 | 29 | 31 | 33 | 35 | 37 | 39 | 41 | 43 | 45 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.6 | +0.0 | +12.1 | -1.4 | -7.8 | -7.7 | -2.1 | +8.7 | -10.0 | +9.5 | -1.3 |
| Relative (%) | -7.7 | +0.0 | +35.7 | -4.2 | -22.9 | -22.8 | -6.1 | +25.6 | -29.3 | +27.9 | -3.9 | |
| Steps (reduced) |
164 (52) |
168 (0) |
172 (4) |
175 (7) |
178 (10) |
181 (13) |
184 (16) |
187 (19) |
189 (21) |
192 (24) |
194 (26) | |
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 33.963 | |
| 2 | 67.927 | 26/25, 27/26 |
| 3 | 101.89 | 18/17 |
| 4 | 135.854 | 27/25 |
| 5 | 169.817 | 11/10, 21/19 |
| 6 | 203.781 | |
| 7 | 237.744 | 31/27 |
| 8 | 271.708 | 7/6 |
| 9 | 305.671 | 25/21, 31/26 |
| 10 | 339.635 | 17/14 |
| 11 | 373.598 | 26/21, 31/25 |
| 12 | 407.562 | 19/15 |
| 13 | 441.525 | 22/17 |
| 14 | 475.489 | 25/19 |
| 15 | 509.452 | |
| 16 | 543.416 | 26/19 |
| 17 | 577.379 | |
| 18 | 611.343 | 27/19 |
| 19 | 645.306 | |
| 20 | 679.27 | |
| 21 | 713.233 | |
| 22 | 747.197 | |
| 23 | 781.16 | 11/7 |
| 24 | 815.124 | |
| 25 | 849.087 | 18/11, 31/19 |
| 26 | 883.051 | 5/3 |
| 27 | 917.014 | 17/10 |
| 28 | 950.978 | 19/11, 26/15, 33/19 |
| 29 | 984.941 | 23/13, 30/17 |
| 30 | 1018.904 | 9/5 |
| 31 | 1052.868 | 11/6 |
| 32 | 1086.831 | |
| 33 | 1120.795 | 21/11 |
| 34 | 1154.758 | |
| 35 | 1188.722 | |
| 36 | 1222.685 | |
| 37 | 1256.649 | 31/15 |
| 38 | 1290.612 | 19/9 |
| 39 | 1324.576 | |
| 40 | 1358.539 | |
| 41 | 1392.503 | 29/13 |
| 42 | 1426.466 | |
| 43 | 1460.43 | |
| 44 | 1494.393 | |
| 45 | 1528.357 | |
| 46 | 1562.32 | |
| 47 | 1596.284 | |
| 48 | 1630.247 | 18/7 |
| 49 | 1664.211 | |
| 50 | 1698.174 | |
| 51 | 1732.138 | 19/7, 30/11 |
| 52 | 1766.101 | 25/9 |
| 53 | 1800.065 | 17/6 |
| 54 | 1834.028 | 26/9 |
| 55 | 1867.992 | |
| 56 | 1901.955 | 3/1 |