17ed8/3
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(convergent)
(semiconvergent)
17 equal divisions of 8/3 (abbreviated 17ed8/3) is a nonoctave tuning system that divides the interval of 8/3 into 17 equal parts of about 99.9 ¢ each. Each step represents a frequency ratio of (8/3)1/17, or the 17th root of 8/3.
Theory
17ed8/3 is not a truly xenharmonic tuning; it is a slightly compressed version (with an octave of 1198.6 cents) of the normal 12-tone scale.
Interval table
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 99.9 | 16/15, 17/16, 18/17, 19/18, 20/19, 21/20 |
| 2 | 199.8 | 9/8, 10/9, 17/15, 19/17 |
| 3 | 299.7 | 6/5, 19/16, 20/17 |
| 4 | 399.5 | 5/4, 14/11, 19/15, 24/19 |
| 5 | 499.4 | 4/3 |
| 6 | 599.3 | 7/5, 10/7, 17/12, 24/17 |
| 7 | 699.2 | 3/2 |
| 8 | 799.1 | 8/5, 11/7, 19/12 |
| 9 | 899 | 5/3 |
| 10 | 998.8 | 9/5, 16/9, 23/13 |
| 11 | 1098.7 | 15/8, 17/9, 19/10 |
| 12 | 1198.6 | 2/1 |
| 13 | 1298.5 | 17/8, 19/9, 21/10 |
| 14 | 1398.4 | 9/4, 20/9 |
| 15 | 1498.3 | 12/5, 19/8 |
| 16 | 1598.2 | 5/2 |
| 17 | 1698 | 8/3 |