17ed5/4
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Prime factorization
17 (prime)
Step size
22.7243¢
Octave
53\17ed5/4 (1204.39¢)
Twelfth
84\17ed5/4 (1908.84¢)
Consistency limit
6
Distinct consistency limit
4
 |
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| ← 16ed5/4 | 17ed5/4 | 18ed5/4 → |
17 equal divisions of 5/4 (abbreviated 17ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 17 equal parts of about 22.7 ¢ each. Each step represents a frequency ratio of (5/4)1/17, or the 17th root of 5/4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 22.7 | |
| 2 | 45.4 | |
| 3 | 68.2 | 21/20, 23/22 |
| 4 | 90.9 | 17/16, 22/21, 24/23 |
| 5 | 113.6 | 16/15, 18/17 |
| 6 | 136.3 | 14/13, 15/14 |
| 7 | 159.1 | 11/10, 12/11, 23/21 |
| 8 | 181.8 | 10/9, 19/17, 21/19 |
| 9 | 204.5 | 9/8, 17/15 |
| 10 | 227.2 | 23/20 |
| 11 | 250 | 7/6, 8/7 |
| 12 | 272.7 | 13/11, 22/19 |
| 13 | 295.4 | 20/17 |
| 14 | 318.1 | 6/5 |
| 15 | 340.9 | 11/9, 17/14, 23/19 |
| 16 | 363.6 | 21/17 |
| 17 | 386.3 | 5/4 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +4.39 | +6.89 | +8.78 | +8.78 | +11.28 | -5.62 | -9.55 | -8.95 | -9.55 | +7.24 | -7.06 |
| Relative (%) | +19.3 | +30.3 | +38.6 | +38.6 | +49.6 | -24.7 | -42.0 | -39.4 | -42.0 | +31.8 | -31.0 | |
| Steps (reduced) |
53 (2) |
84 (16) |
106 (4) |
123 (4) |
137 (1) |
148 (12) |
158 (5) |
167 (14) |
175 (5) |
183 (13) |
189 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -9.28 | -1.23 | -7.06 | -5.17 | +3.50 | -4.56 | -7.26 | -5.17 | +1.27 | -11.10 | +2.84 |
| Relative (%) | -40.8 | -5.4 | -31.0 | -22.7 | +15.4 | -20.0 | -32.0 | -22.7 | +5.6 | -48.8 | +12.5 | |
| Steps (reduced) |
195 (8) |
201 (14) |
206 (2) |
211 (7) |
216 (12) |
220 (16) |
224 (3) |
228 (7) |
232 (11) |
235 (14) |
239 (1) | |