17ed9/4
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Prime factorization
17 (prime)
Step size
82.5829¢
Octave
15\17ed9/4 (1238.74¢)
Twelfth
23\17ed9/4 (1899.41¢)
(convergent)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 15ed9/4 | 17ed9/4 | 19ed9/4 → |
(convergent)
17 equal divisions of 9/4 (abbreviated 17ed9/4) is a nonoctave tuning system that divides the interval of 9/4 into 17 equal parts of about 82.6 ¢ each. Each step represents a frequency ratio of (9/4)1/17, or the 17th root of 9/4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 82.583 | 19/18, 22/21, 23/22 |
| 2 | 165.166 | 21/19, 23/21 |
| 3 | 247.749 | 7/6, 15/13, 22/19 |
| 4 | 330.332 | 6/5, 11/9, 23/19 |
| 5 | 412.915 | 19/15, 23/18 |
| 6 | 495.498 | |
| 7 | 578.081 | 7/5, 18/13 |
| 8 | 660.664 | 19/13, 22/15 |
| 9 | 743.246 | 17/11, 23/15 |
| 10 | 825.829 | 21/13 |
| 11 | 908.412 | 22/13 |
| 12 | 990.995 | 23/13 |
| 13 | 1073.578 | 13/7 |
| 14 | 1156.161 | |
| 15 | 1238.744 | |
| 16 | 1321.327 | 13/6, 15/7 |
| 17 | 1403.91 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +38.7 | -2.5 | -5.1 | +21.5 | +36.2 | +17.1 | +33.6 | -5.1 | -22.3 | -22.2 | -7.6 |
| Relative (%) | +46.9 | -3.1 | -6.2 | +26.0 | +43.8 | +20.7 | +40.7 | -6.2 | -27.0 | -26.8 | -9.3 | |
| Steps (reduced) |
15 (15) |
23 (6) |
29 (12) |
34 (0) |
38 (4) |
41 (7) |
44 (10) |
46 (12) |
48 (14) |
50 (16) |
52 (1) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +19.0 | -26.8 | +19.0 | -10.2 | -32.6 | +33.6 | +22.6 | +16.4 | +14.5 | +16.6 | +22.2 |
| Relative (%) | +22.9 | -32.4 | +23.0 | -12.3 | -39.4 | +40.7 | +27.4 | +19.9 | +17.6 | +20.1 | +26.9 | |
| Steps (reduced) |
54 (3) |
55 (4) |
57 (6) |
58 (7) |
59 (8) |
61 (10) |
62 (11) |
63 (12) |
64 (13) |
65 (14) |
66 (15) | |