42ed7/4
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Prime factorization
2 × 3 × 7
Step size
23.0673¢
Octave
52\42ed7/4 (1199.5¢) (→26\21ed7/4)
Twelfth
82\42ed7/4 (1891.52¢) (→41\21ed7/4)
Consistency limit
4
Distinct consistency limit
3
 |
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| ← 41ed7/4 | 42ed7/4 | 43ed7/4 → |
42 equal divisions of 7/4 (abbreviated 42ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 42 equal parts of about 23.1⁠ ⁠¢ each. Each step represents a frequency ratio of (7/4)1/42, or the 42nd root of 7/4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 23.1 | |
| 2 | 46.1 | |
| 3 | 69.2 | 24/23, 26/25 |
| 4 | 92.3 | 20/19 |
| 5 | 115.3 | 15/14, 16/15 |
| 6 | 138.4 | |
| 7 | 161.5 | 11/10, 23/21 |
| 8 | 184.5 | 29/26 |
| 9 | 207.6 | |
| 10 | 230.7 | 8/7 |
| 11 | 253.7 | 22/19, 29/25 |
| 12 | 276.8 | 20/17 |
| 13 | 299.9 | 19/16 |
| 14 | 322.9 | |
| 15 | 346 | 28/23 |
| 16 | 369.1 | |
| 17 | 392.1 | 5/4 |
| 18 | 415.2 | 14/11, 19/15 |
| 19 | 438.3 | |
| 20 | 461.3 | 17/13, 30/23 |
| 21 | 484.4 | 29/22 |
| 22 | 507.5 | |
| 23 | 530.5 | 15/11, 19/14 |
| 24 | 553.6 | 11/8 |
| 25 | 576.7 | 7/5 |
| 26 | 599.7 | |
| 27 | 622.8 | 10/7, 23/16 |
| 28 | 645.9 | 16/11, 29/20 |
| 29 | 669 | 22/15, 25/17, 28/19 |
| 30 | 692 | |
| 31 | 715.1 | |
| 32 | 738.2 | 23/15, 26/17, 29/19 |
| 33 | 761.2 | |
| 34 | 784.3 | 11/7, 30/19 |
| 35 | 807.4 | 8/5 |
| 36 | 830.4 | |
| 37 | 853.5 | 23/14 |
| 38 | 876.6 | |
| 39 | 899.6 | |
| 40 | 922.7 | 17/10, 29/17 |
| 41 | 945.8 | 19/11 |
| 42 | 968.8 | 7/4 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.5 | -10.4 | -1.0 | +4.8 | -10.9 | -1.0 | -1.5 | +2.2 | +4.3 | +0.8 | -11.4 |
| Relative (%) | -2.2 | -45.2 | -4.3 | +20.9 | -47.4 | -4.3 | -6.5 | +9.5 | +18.8 | +3.4 | -49.6 | |
| Steps (reduced) |
52 (10) |
82 (40) |
104 (20) |
121 (37) |
134 (8) |
146 (20) |
156 (30) |
165 (39) |
173 (5) |
180 (12) |
186 (18) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +11.5 | -1.5 | -5.6 | -2.0 | +8.4 | +1.7 | +0.4 | +3.8 | -11.4 | +0.3 | -7.5 |
| Relative (%) | +49.7 | -6.5 | -24.3 | -8.7 | +36.3 | +7.3 | +1.5 | +16.6 | -49.6 | +1.3 | -32.4 | |
| Steps (reduced) |
193 (25) |
198 (30) |
203 (35) |
208 (40) |
213 (3) |
217 (7) |
221 (11) |
225 (15) |
228 (18) |
232 (22) |
235 (25) | |