18ed7/3
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Prime factorization
2 × 32
Step size
81.4928 ¢
Octave
15\18ed7/3 (1222.39 ¢) (→ 5\6ed7/3)
Twelfth
23\18ed7/3 (1874.34 ¢)
Consistency limit
2
Distinct consistency limit
2
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| ← 17ed7/3 | 18ed7/3 | 19ed7/3 → |
18 equal divisions of 7/3 (abbreviated 18ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 18 equal parts of about 81.5 ¢ each. Each step represents a frequency ratio of (7/3)1/18, or the 18th root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 81.5 | 18/17, 20/19, 23/22, 24/23 |
| 2 | 163 | 11/10, 12/11 |
| 3 | 244.5 | 15/13, 22/19, 23/20 |
| 4 | 326 | 6/5, 17/14, 23/19 |
| 5 | 407.5 | 14/11, 24/19 |
| 6 | 489 | |
| 7 | 570.4 | 7/5, 18/13 |
| 8 | 651.9 | 13/9 |
| 9 | 733.4 | |
| 10 | 814.9 | 21/13 |
| 11 | 896.4 | 5/3 |
| 12 | 977.9 | |
| 13 | 1059.4 | 11/6, 13/7 |
| 14 | 1140.9 | 23/12 |
| 15 | 1222.4 | |
| 16 | 1303.9 | 15/7 |
| 17 | 1385.4 | |
| 18 | 1466.9 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +22.4 | -27.6 | -36.7 | -15.6 | -5.2 | -27.6 | -14.3 | +26.3 | +6.8 | +4.8 | +17.2 |
| Relative (%) | +27.5 | -33.9 | -45.0 | -19.1 | -6.4 | -33.9 | -17.6 | +32.2 | +8.4 | +5.9 | +21.1 | |
| Steps (reduced) |
15 (15) |
23 (5) |
29 (11) |
34 (16) |
38 (2) |
41 (5) |
44 (8) |
47 (11) |
49 (13) |
51 (15) |
53 (17) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -39.9 | -5.2 | +38.3 | +8.1 | -15.4 | -32.8 | +36.5 | +29.2 | +26.3 | +27.2 | +31.7 |
| Relative (%) | -49.0 | -6.4 | +47.0 | +9.9 | -18.9 | -40.3 | +44.8 | +35.9 | +32.2 | +33.4 | +39.0 | |
| Steps (reduced) |
54 (0) |
56 (2) |
58 (4) |
59 (5) |
60 (6) |
61 (7) |
63 (9) |
64 (10) |
65 (11) |
66 (12) |
67 (13) | |