67ed7/3
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Prime factorization
67 (prime)
Step size
21.8936¢
Octave
55\67ed7/3 (1204.15¢)
Twelfth
87\67ed7/3 (1904.74¢)
Consistency limit
4
Distinct consistency limit
4
 |
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67 equal divisions of 7/3 (abbreviated 67ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 67 equal parts of about 21.9 ¢ each. Each step represents a frequency ratio of (7/3)1/67, or the 67th root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 21.9 | |
| 2 | 43.8 | |
| 3 | 65.7 | 27/26, 28/27 |
| 4 | 87.6 | 20/19, 21/20 |
| 5 | 109.5 | 33/31 |
| 6 | 131.4 | 14/13 |
| 7 | 153.3 | 12/11 |
| 8 | 175.1 | 21/19, 31/28 |
| 9 | 197 | |
| 10 | 218.9 | 17/15 |
| 11 | 240.8 | 23/20, 31/27 |
| 12 | 262.7 | 36/31 |
| 13 | 284.6 | 20/17, 33/28 |
| 14 | 306.5 | 31/26 |
| 15 | 328.4 | 23/19, 35/29 |
| 16 | 350.3 | 11/9 |
| 17 | 372.2 | 26/21 |
| 18 | 394.1 | |
| 19 | 416 | 14/11, 33/26 |
| 20 | 437.9 | 9/7 |
| 21 | 459.8 | 30/23 |
| 22 | 481.7 | |
| 23 | 503.6 | |
| 24 | 525.4 | 19/14, 23/17 |
| 25 | 547.3 | |
| 26 | 569.2 | |
| 27 | 591.1 | 31/22 |
| 28 | 613 | |
| 29 | 634.9 | 13/9 |
| 30 | 656.8 | 19/13 |
| 31 | 678.7 | 34/23 |
| 32 | 700.6 | 3/2 |
| 33 | 722.5 | |
| 34 | 744.4 | 20/13 |
| 35 | 766.3 | 14/9 |
| 36 | 788.2 | 30/19 |
| 37 | 810.1 | |
| 38 | 832 | 21/13, 34/21 |
| 39 | 853.9 | 18/11 |
| 40 | 875.7 | |
| 41 | 897.6 | |
| 42 | 919.5 | 17/10 |
| 43 | 941.4 | 31/18 |
| 44 | 963.3 | |
| 45 | 985.2 | 23/13, 30/17 |
| 46 | 1007.1 | 34/19 |
| 47 | 1029 | |
| 48 | 1050.9 | 11/6 |
| 49 | 1072.8 | 13/7 |
| 50 | 1094.7 | |
| 51 | 1116.6 | 21/11 |
| 52 | 1138.5 | 27/14, 29/15 |
| 53 | 1160.4 | |
| 54 | 1182.3 | |
| 55 | 1204.1 | |
| 56 | 1226 | |
| 57 | 1247.9 | 35/17 |
| 58 | 1269.8 | |
| 59 | 1291.7 | 19/9 |
| 60 | 1313.6 | |
| 61 | 1335.5 | 13/6 |
| 62 | 1357.4 | |
| 63 | 1379.3 | 20/9, 31/14 |
| 64 | 1401.2 | 9/4 |
| 65 | 1423.1 | |
| 66 | 1445 | 23/10, 30/13 |
| 67 | 1466.9 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +4.15 | +2.79 | +8.30 | -5.83 | +6.94 | +2.79 | -9.45 | +5.58 | -1.68 | +8.47 | -10.81 |
| Relative (%) | +18.9 | +12.7 | +37.9 | -26.6 | +31.7 | +12.7 | -43.2 | +25.5 | -7.7 | +38.7 | -49.4 | |
| Steps (reduced) |
55 (55) |
87 (20) |
110 (43) |
127 (60) |
142 (8) |
154 (20) |
164 (30) |
174 (40) |
182 (48) |
190 (56) |
196 (62) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.87 | +6.94 | -3.04 | -5.30 | -0.79 | +9.72 | +3.69 | +2.47 | +5.58 | -9.28 | +1.34 |
| Relative (%) | +17.7 | +31.7 | -13.9 | -24.2 | -3.6 | +44.4 | +16.9 | +11.3 | +25.5 | -42.4 | +6.1 | |
| Steps (reduced) |
203 (2) |
209 (8) |
214 (13) |
219 (18) |
224 (23) |
229 (28) |
233 (32) |
237 (36) |
241 (40) |
244 (43) |
248 (47) | |