18ed7/4
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Prime factorization
2 × 32
Step size
53.8237¢
Octave
22\18ed7/4 (1184.12¢) (→11\9ed7/4)
Twelfth
35\18ed7/4 (1883.83¢)
(semiconvergent)
Consistency limit
3
Distinct consistency limit
3
 |
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| ← 17ed7/4 | 18ed7/4 | 19ed7/4 → |
(semiconvergent)
18 equal divisions of 7/4 (abbreviated 18ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 18 equal parts of about 53.8 ¢ each. Each step represents a frequency ratio of (7/4)1/18, or the 18th root of 7/4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 53.8 | |
| 2 | 107.6 | 15/14 |
| 3 | 161.5 | 11/10, 21/19, 23/21 |
| 4 | 215.3 | 9/8, 17/15 |
| 5 | 269.1 | 20/17 |
| 6 | 322.9 | 17/14, 23/19 |
| 7 | 376.8 | 21/17 |
| 8 | 430.6 | 14/11, 22/17 |
| 9 | 484.4 | 4/3 |
| 10 | 538.2 | 15/11, 19/14, 23/17 |
| 11 | 592.1 | 7/5 |
| 12 | 645.9 | 19/13, 22/15 |
| 13 | 699.7 | 3/2 |
| 14 | 753.5 | 17/11, 23/15 |
| 15 | 807.4 | |
| 16 | 861.2 | 23/14 |
| 17 | 915 | 17/10 |
| 18 | 968.8 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -15.9 | -18.1 | +22.1 | +12.5 | +19.8 | +22.1 | +6.2 | +17.6 | -3.4 | -6.9 | +3.9 |
| Relative (%) | -29.5 | -33.7 | +41.0 | +23.3 | +36.8 | +41.0 | +11.5 | +32.6 | -6.2 | -12.8 | +7.3 | |
| Steps (reduced) |
22 (4) |
35 (17) |
45 (9) |
52 (16) |
58 (4) |
63 (9) |
67 (13) |
71 (17) |
74 (2) |
77 (5) |
80 (8) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +26.8 | +6.2 | -5.6 | -9.7 | -7.0 | +1.7 | +15.7 | -19.2 | +3.9 | -22.8 | +7.9 |
| Relative (%) | +49.9 | +11.5 | -10.4 | -18.0 | -13.0 | +3.1 | +29.2 | -35.8 | +7.3 | -42.3 | +14.7 | |
| Steps (reduced) |
83 (11) |
85 (13) |
87 (15) |
89 (17) |
91 (1) |
93 (3) |
95 (5) |
96 (6) |
98 (8) |
99 (9) |
101 (11) | |