67ed4
Jump to navigation
Jump to search
Prime factorization
67 (prime)
Step size
35.8209¢
Octave
34\67ed4 (1217.91¢)
Twelfth
53\67ed4 (1898.51¢)
Consistency limit
1
Distinct consistency limit
1
 |
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 65ed4 | 67ed4 | 69ed4 → |
67 equal divisions of the 4th harmonic (abbreviated 67ed4) is a nonoctave tuning system that divides the interval of 4/1 into 67 equal parts of about 35.8 ¢ each. Each step represents a frequency ratio of 41/67, or the 67th root of 4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 35.821 | |
| 2 | 71.642 | 26/25 |
| 3 | 107.463 | 33/31 |
| 4 | 143.284 | 25/23 |
| 5 | 179.104 | |
| 6 | 214.925 | 17/15, 26/23 |
| 7 | 250.746 | 15/13 |
| 8 | 286.567 | 13/11 |
| 9 | 322.388 | 35/29 |
| 10 | 358.209 | |
| 11 | 394.03 | |
| 12 | 429.851 | |
| 13 | 465.672 | 17/13 |
| 14 | 501.493 | |
| 15 | 537.313 | 15/11 |
| 16 | 573.134 | |
| 17 | 608.955 | 27/19 |
| 18 | 644.776 | |
| 19 | 680.597 | 34/23 |
| 20 | 716.418 | |
| 21 | 752.239 | 17/11 |
| 22 | 788.06 | |
| 23 | 823.881 | 29/18 |
| 24 | 859.701 | 23/14 |
| 25 | 895.522 | |
| 26 | 931.343 | |
| 27 | 967.164 | |
| 28 | 1002.985 | 25/14 |
| 29 | 1038.806 | 31/17 |
| 30 | 1074.627 | 13/7 |
| 31 | 1110.448 | |
| 32 | 1146.269 | 33/17 |
| 33 | 1182.09 | |
| 34 | 1217.91 | |
| 35 | 1253.731 | 31/15, 35/17 |
| 36 | 1289.552 | |
| 37 | 1325.373 | |
| 38 | 1361.194 | 11/5 |
| 39 | 1397.015 | |
| 40 | 1432.836 | |
| 41 | 1468.657 | 7/3 |
| 42 | 1504.478 | 31/13 |
| 43 | 1540.299 | |
| 44 | 1576.119 | |
| 45 | 1611.94 | 33/13 |
| 46 | 1647.761 | |
| 47 | 1683.582 | |
| 48 | 1719.403 | |
| 49 | 1755.224 | |
| 50 | 1791.045 | 31/11 |
| 51 | 1826.866 | |
| 52 | 1862.687 | |
| 53 | 1898.507 | 3/1 |
| 54 | 1934.328 | |
| 55 | 1970.149 | |
| 56 | 2005.97 | 35/11 |
| 57 | 2041.791 | |
| 58 | 2077.612 | |
| 59 | 2113.433 | |
| 60 | 2149.254 | |
| 61 | 2185.075 | |
| 62 | 2220.896 | 18/5 |
| 63 | 2256.716 | |
| 64 | 2292.537 | |
| 65 | 2328.358 | 23/6 |
| 66 | 2364.179 | |
| 67 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +17.9 | -3.4 | +0.0 | +7.7 | +14.5 | -1.7 | +17.9 | -6.9 | -10.2 | +3.9 | -3.4 |
| Relative (%) | +50.0 | -9.6 | +0.0 | +21.5 | +40.4 | -4.6 | +50.0 | -19.2 | -28.5 | +10.9 | -9.6 | |
| Steps (reduced) |
34 (34) |
53 (53) |
67 (0) |
78 (11) |
87 (20) |
94 (27) |
101 (34) |
106 (39) |
111 (44) |
116 (49) |
120 (53) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.3 | +16.2 | +4.3 | +0.0 | +2.5 | +11.0 | -10.9 | +7.7 | -5.1 | -14.0 | +16.5 |
| Relative (%) | +3.5 | +45.4 | +11.9 | +0.0 | +7.0 | +30.8 | -30.6 | +21.5 | -14.3 | -39.1 | +46.1 | |
| Steps (reduced) |
124 (57) |
128 (61) |
131 (64) |
134 (0) |
137 (3) |
140 (6) |
142 (8) |
145 (11) |
147 (13) |
149 (15) |
152 (18) | |