57ed6
| ← 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 | 54.4 | 30/29, 31/30, 32/31, 33/32, 34/33 |
| 2 | 108.8 | 16/15, 17/16, 33/31 |
| 3 | 163.3 | 11/10, 34/31 |
| 4 | 217.7 | 17/15, 25/22 |
| 5 | 272.1 | 34/29 |
| 6 | 326.5 | 23/19, 29/24 |
| 7 | 380.9 | |
| 8 | 435.4 | 9/7 |
| 9 | 489.8 | |
| 10 | 544.2 | 26/19 |
| 11 | 598.6 | 17/12, 24/17 |
| 12 | 653 | 16/11, 19/13 |
| 13 | 707.5 | |
| 14 | 761.9 | 14/9, 31/20 |
| 15 | 816.3 | 8/5 |
| 16 | 870.7 | 33/20 |
| 17 | 925.1 | 29/17 |
| 18 | 979.6 | 30/17 |
| 19 | 1034 | 20/11, 29/16 |
| 20 | 1088.4 | 15/8 |
| 21 | 1142.8 | 29/15, 31/16 |
| 22 | 1197.2 | 2/1 |
| 23 | 1251.7 | 33/16 |
| 24 | 1306.1 | 17/8 |
| 25 | 1360.5 | 11/5 |
| 26 | 1414.9 | 34/15 |
| 27 | 1469.3 | 7/3 |
| 28 | 1523.8 | 29/12 |
| 29 | 1578.2 | |
| 30 | 1632.6 | 18/7 |
| 31 | 1687 | |
| 32 | 1741.4 | 30/11 |
| 33 | 1795.9 | 31/11 |
| 34 | 1850.3 | 32/11 |
| 35 | 1904.7 | 3/1 |
| 36 | 1959.1 | 31/10 |
| 37 | 2013.5 | 16/5 |
| 38 | 2068 | 33/10 |
| 39 | 2122.4 | 17/5 |
| 40 | 2176.8 | |
| 41 | 2231.2 | 29/8 |
| 42 | 2285.7 | 15/4 |
| 43 | 2340.1 | 27/7 |
| 44 | 2394.5 | |
| 45 | 2448.9 | 33/8 |
| 46 | 2503.3 | 17/4 |
| 47 | 2557.8 | |
| 48 | 2612.2 | |
| 49 | 2666.6 | 14/3 |
| 50 | 2721 | |
| 51 | 2775.4 | |
| 52 | 2829.9 | |
| 53 | 2884.3 | |
| 54 | 2938.7 | |
| 55 | 2993.1 | |
| 56 | 3047.5 | 29/5 |
| 57 | 3102 | 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) | |
|
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