57ed6
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Prime factorization
3 × 19
Step size
54.4203¢
Octave
22\57ed6 (1197.25¢)
Twelfth
35\57ed6 (1904.71¢)
Consistency limit
12
Distinct consistency limit
8
| ← 56ed6 | 57ed6 | 58ed6 → |
Division of the sixth harmonic into 57 equal parts (57ED6) is very nearly identical to 22 EDO, but with the 6/1 rather than the 2/1 being just. The octave is about 2.754 ¢ compressed and the step size is about 54.4203 ¢. The local zeta peak around 22 is located at 22.025147, which has a step size of 54.483 ¢ and an octave of 1198.63 ¢ (which is compressed by 1.37 ¢), making 57ed6 very close to optimal for 22edo.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 54.42 | 30/29, 31/30, 32/31, 33/32, 34/33 |
| 2 | 108.841 | 16/15, 17/16, 33/31 |
| 3 | 163.261 | 11/10, 34/31 |
| 4 | 217.681 | 17/15, 25/22 |
| 5 | 272.101 | 34/29 |
| 6 | 326.522 | 23/19, 29/24 |
| 7 | 380.942 | |
| 8 | 435.362 | 9/7 |
| 9 | 489.782 | |
| 10 | 544.203 | 26/19 |
| 11 | 598.623 | 17/12, 24/17 |
| 12 | 653.043 | 16/11, 19/13 |
| 13 | 707.463 | |
| 14 | 761.884 | 14/9, 31/20 |
| 15 | 816.304 | 8/5 |
| 16 | 870.724 | 33/20 |
| 17 | 925.144 | 29/17 |
| 18 | 979.565 | 30/17 |
| 19 | 1033.985 | 20/11, 29/16 |
| 20 | 1088.405 | 15/8 |
| 21 | 1142.826 | 29/15, 31/16 |
| 22 | 1197.246 | 2/1 |
| 23 | 1251.666 | 33/16 |
| 24 | 1306.086 | 17/8 |
| 25 | 1360.507 | 11/5 |
| 26 | 1414.927 | 34/15 |
| 27 | 1469.347 | 7/3 |
| 28 | 1523.767 | 29/12 |
| 29 | 1578.188 | |
| 30 | 1632.608 | 18/7 |
| 31 | 1687.028 | |
| 32 | 1741.448 | 30/11 |
| 33 | 1795.869 | 31/11 |
| 34 | 1850.289 | 32/11 |
| 35 | 1904.709 | 3/1 |
| 36 | 1959.129 | 31/10 |
| 37 | 2013.55 | 16/5 |
| 38 | 2067.97 | 33/10 |
| 39 | 2122.39 | 17/5 |
| 40 | 2176.811 | |
| 41 | 2231.231 | 29/8 |
| 42 | 2285.651 | 15/4 |
| 43 | 2340.071 | 27/7 |
| 44 | 2394.492 | |
| 45 | 2448.912 | 33/8 |
| 46 | 2503.332 | 17/4 |
| 47 | 2557.752 | |
| 48 | 2612.173 | |
| 49 | 2666.593 | 14/3 |
| 50 | 2721.013 | |
| 51 | 2775.433 | |
| 52 | 2829.854 | |
| 53 | 2884.274 | |
| 54 | 2938.694 | |
| 55 | 2993.114 | |
| 56 | 3047.535 | 29/5 |
| 57 | 3101.955 | 6/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.8 | +2.8 | -5.5 | -10.9 | +0.0 | +5.2 | -8.3 | +5.5 | -13.6 | -15.4 | -2.8 |
| Relative (%) | -5.1 | +5.1 | -10.1 | -20.0 | +0.0 | +9.6 | -15.2 | +10.1 | -25.1 | -28.3 | -5.1 | |
| Steps (reduced) |
22 (22) |
35 (35) |
44 (44) |
51 (51) |
57 (0) |
62 (5) |
66 (9) |
70 (13) |
73 (16) |
76 (19) |
79 (22) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +21.9 | +2.5 | -8.1 | -11.0 | -7.1 | +2.8 | +18.0 | -16.4 | +8.0 | -18.1 | +13.8 |
| Relative (%) | +40.3 | +4.6 | -14.9 | -20.2 | -13.1 | +5.1 | +33.1 | -30.1 | +14.7 | -33.3 | +25.3 | |
| Steps (reduced) |
82 (25) |
84 (27) |
86 (29) |
88 (31) |
90 (33) |
92 (35) |
94 (37) |
95 (38) |
97 (40) |
98 (41) |
100 (43) | |