18ed5/3
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Prime factorization
2 × 32
Step size
49.131¢
Octave
24\18ed5/3 (1179.14¢) (→4\3ed5/3)
Twelfth
39\18ed5/3 (1916.11¢) (→13\6ed5/3)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 17ed5/3 | 18ed5/3 | 19ed5/3 → |
18 equal divisions of 5/3 (abbreviated 18ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 18 equal parts of about 49.1 ¢ each. Each step represents a frequency ratio of (5/3)1/18, or the 18th root of 5/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 49.131 | |
| 2 | 98.262 | 18/17, 19/18 |
| 3 | 147.393 | 11/10, 12/11, 13/12 |
| 4 | 196.524 | 19/17 |
| 5 | 245.655 | 23/20 |
| 6 | 294.786 | 13/11 |
| 7 | 343.917 | 17/14 |
| 8 | 393.048 | 19/15 |
| 9 | 442.179 | 9/7, 13/10 |
| 10 | 491.31 | |
| 11 | 540.441 | 19/14 |
| 12 | 589.572 | 7/5 |
| 13 | 638.704 | |
| 14 | 687.835 | |
| 15 | 736.966 | 20/13 |
| 16 | 786.097 | |
| 17 | 835.228 | |
| 18 | 884.359 | 5/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -20.9 | +14.2 | +7.4 | +14.2 | -6.7 | +21.2 | -13.4 | -20.8 | -6.7 | -24.3 | +21.6 |
| Relative (%) | -42.4 | +28.8 | +15.1 | +28.8 | -13.6 | +43.2 | -27.3 | -42.4 | -13.6 | -49.5 | +43.9 | |
| Steps (reduced) |
24 (6) |
39 (3) |
49 (13) |
57 (3) |
63 (9) |
69 (15) |
73 (1) |
77 (5) |
81 (9) |
84 (12) |
88 (16) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -18.7 | +0.4 | -20.8 | +14.8 | +8.1 | +7.5 | +12.1 | +21.6 | -13.8 | +4.0 | -23.9 |
| Relative (%) | -38.1 | +0.7 | -42.4 | +30.2 | +16.6 | +15.2 | +24.7 | +43.9 | -28.0 | +8.1 | -48.6 | |
| Steps (reduced) |
90 (0) |
93 (3) |
95 (5) |
98 (8) |
100 (10) |
102 (12) |
104 (14) |
106 (16) |
107 (17) |
109 (1) |
110 (2) | |