68ed12
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Prime factorization
22 × 17
Step size
63.264¢
Octave
19\68ed12 (1202.02¢)
Twelfth
30\68ed12 (1897.92¢) (→15\34ed12)
Consistency limit
10
Distinct consistency limit
6
| ← 67ed12 | 68ed12 | 69ed12 → |
Division of the twelfth harmonic into 68 equal parts (68ED12) is very nearly identical to 19 EDO, but with the 12/1 rather than the 2/1 being just. The octave is about 2.02 cents stretched and the step size is about 63.264 cents.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 63.264 | 27/26, 28/27, 29/28 |
| 2 | 126.528 | 14/13, 29/27 |
| 3 | 189.792 | 19/17, 29/26 |
| 4 | 253.056 | 22/19, 29/25, 37/32 |
| 5 | 316.32 | 6/5 |
| 6 | 379.584 | |
| 7 | 442.848 | 22/17, 31/24 |
| 8 | 506.112 | |
| 9 | 569.376 | 25/18, 32/23 |
| 10 | 632.64 | 36/25 |
| 11 | 695.904 | |
| 12 | 759.169 | 31/20 |
| 13 | 822.433 | 29/18, 37/23 |
| 14 | 885.697 | 5/3 |
| 15 | 948.961 | 19/11, 26/15 |
| 16 | 1012.225 | |
| 17 | 1075.489 | 13/7 |
| 18 | 1138.753 | 27/14, 29/15 |
| 19 | 1202.017 | 2/1 |
| 20 | 1265.281 | 27/13 |
| 21 | 1328.545 | 28/13 |
| 22 | 1391.809 | 29/13 |
| 23 | 1455.073 | 37/16 |
| 24 | 1518.337 | 12/5 |
| 25 | 1581.601 | |
| 26 | 1644.865 | 31/12 |
| 27 | 1708.129 | |
| 28 | 1771.393 | 25/9 |
| 29 | 1834.657 | 26/9 |
| 30 | 1897.921 | |
| 31 | 1961.185 | 28/9, 31/10 |
| 32 | 2024.449 | 29/9 |
| 33 | 2087.713 | 10/3 |
| 34 | 2150.978 | |
| 35 | 2214.242 | 18/5 |
| 36 | 2277.506 | |
| 37 | 2340.77 | 27/7 |
| 38 | 2404.034 | |
| 39 | 2467.298 | 25/6 |
| 40 | 2530.562 | |
| 41 | 2593.826 | |
| 42 | 2657.09 | |
| 43 | 2720.354 | |
| 44 | 2783.618 | 5/1 |
| 45 | 2846.882 | 31/6 |
| 46 | 2910.146 | |
| 47 | 2973.41 | |
| 48 | 3036.674 | |
| 49 | 3099.938 | 6/1 |
| 50 | 3163.202 | |
| 51 | 3226.466 | |
| 52 | 3289.73 | |
| 53 | 3352.994 | |
| 54 | 3416.258 | 36/5 |
| 55 | 3479.522 | |
| 56 | 3542.786 | 31/4 |
| 57 | 3606.051 | |
| 58 | 3669.315 | 25/3 |
| 59 | 3732.579 | |
| 60 | 3795.843 | |
| 61 | 3859.107 | |
| 62 | 3922.371 | |
| 63 | 3985.635 | 10/1 |
| 64 | 4048.899 | |
| 65 | 4112.163 | |
| 66 | 4175.427 | |
| 67 | 4238.691 | |
| 68 | 4301.955 | 12/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.0 | -4.0 | +4.0 | -2.7 | -2.0 | -15.8 | +6.1 | -8.1 | -0.7 | +24.1 | +0.0 |
| Relative (%) | +3.2 | -6.4 | +6.4 | -4.3 | -3.2 | -25.0 | +9.6 | -12.8 | -1.1 | +38.1 | +0.0 | |
| Steps (reduced) |
19 (19) |
30 (30) |
38 (38) |
44 (44) |
49 (49) |
53 (53) |
57 (57) |
60 (60) |
63 (63) |
66 (66) |
68 (0) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -12.0 | -13.8 | -6.7 | +8.1 | +29.6 | -6.1 | +26.9 | +1.3 | -19.9 | +26.1 | +12.4 |
| Relative (%) | -19.0 | -21.8 | -10.6 | +12.8 | +46.9 | -9.6 | +42.5 | +2.1 | -31.4 | +41.3 | +19.7 | |
| Steps (reduced) |
70 (2) |
72 (4) |
74 (6) |
76 (8) |
78 (10) |
79 (11) |
81 (13) |
82 (14) |
83 (15) |
85 (17) |
86 (18) | |