User:MisterShafXen/18ed7/5
| ← 17ed7/5 | 18ed7/5 | 19ed7/5 → |
18 equal divisions of 7/5 (abbreviated 18ed7/5) is a nonoctave tuning system that divides the interval of 7/5 into 18 equal parts of about 32.4 ¢ each. Each step represents a frequency ratio of (7/5)1/18, or the 18th root of 7/5.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 32.4 | |
| 2 | 64.7 | 22/21, 24/23 |
| 3 | 97.1 | 16/15, 18/17, 19/18, 21/20 |
| 4 | 129.4 | 13/12, 14/13, 15/14 |
| 5 | 161.8 | 11/10, 12/11, 21/19, 23/21 |
| 6 | 194.2 | 19/17 |
| 7 | 226.5 | 8/7, 17/15 |
| 8 | 258.9 | 7/6, 15/13, 23/20 |
| 9 | 291.3 | 13/11 |
| 10 | 323.6 | 6/5, 23/19 |
| 11 | 356 | 16/13, 21/17 |
| 12 | 388.3 | 5/4, 24/19 |
| 13 | 420.7 | 14/11, 19/15, 23/18 |
| 14 | 453.1 | 9/7, 13/10 |
| 15 | 485.4 | 4/3, 21/16 |
| 16 | 517.8 | 23/17 |
| 17 | 550.2 | 11/8, 15/11 |
| 18 | 582.5 | 7/5, 24/17 |
Commas
This tuning tempers out 64/63 in the 7-limit, 55/54 in the 11-limit, 52/51 in the 17-limit, 77/76 in the 19-limit, 70/69 in the 23-limit, 58/57 in the 29-limit, 82/81 in the 41-limit, 86/85 in the 43-limit, and many more.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.6 | +7.4 | -3.2 | -3.2 | -9.0 | -7.0 | +14.0 | +15.6 | +8.5 | -4.5 |
| Relative (%) | -8.1 | +22.8 | -9.9 | -9.9 | -27.8 | -21.5 | +43.4 | +48.4 | +26.3 | -13.8 | |
| Steps (reduced) |
37 (1) |
59 (5) |
86 (14) |
104 (14) |
128 (2) |
137 (11) |
152 (8) |
158 (14) |
168 (6) |
180 (0) | |
| Harmonic | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +9.5 | -5.5 | +10.9 | -6.8 | +1.0 | -12.8 | -4.3 | +2.7 | +2.1 | -1.2 |
| Relative (%) | +29.5 | -17.1 | +33.8 | -21.0 | +3.2 | -39.6 | -13.3 | +8.4 | +6.5 | -3.7 | |
| Steps (reduced) |
184 (4) |
193 (13) |
199 (1) |
201 (3) |
206 (8) |
212 (14) |
218 (2) |
220 (4) |
225 (9) |
228 (12) | |