User:MisterShafXen/6ed31/9
6 equal divisions of 31/9 (abbreviated 6ed31/9) is a nonoctave tuning system that divides the interval of 31/9 into 6 equal parts of about 357 ¢ each. Each step represents a frequency ratio of (31/9)1/6, or the 6th root of 31/9.
Intervals
| # | Cents | Approximate JI ratios (direct) | Approximate JI ratios (val) |
|---|---|---|---|
| 1 | 356.9 | 16/13 | 5/4, 6/5, 8/7, 9/8, 7/5, 11/10 |
| 2 | 713.7 | 3/2 | 3/2, 4/3 |
| 3 | 1070.6 | 13/7 | 5/3 |
| 4 | 1427.4 | 16/7 | 2/1 |
| 5 | 1784.3 | 14/5 | 5/2 |
| 6 | 2141.1 | exact 31/9 | 3/1, 7/2, 11/3 |
Harmonics
| x | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Absolute error (cents) | -129 | -118 | 98 | 69 | 110 | -157 | -31 | 121 | -61 | 131 | -20 |
| Steps | 3 | 5 | 7 | 8 | 9 | 9 | 10 | 11 | 11 | 12 | 12 |
| Steps (reduced) | 3 | 5 | 1 | 2 | 3 | 3 | 4 | 5 | 5 | 0 | 0 |