17ed5/3
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Prime factorization
17 (prime)
Step size
52.0211¢
Octave
23\17ed5/3 (1196.49¢)
(semiconvergent)
Twelfth
37\17ed5/3 (1924.78¢)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 16ed5/3 | 17ed5/3 | 18ed5/3 → |
(semiconvergent)
17 equal divisions of 5/3 (abbreviated 17ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 17 equal parts of about 52 ¢ each. Each step represents a frequency ratio of (5/3)1/17, or the 17th root of 5/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 52 | |
| 2 | 104 | 17/16, 20/19 |
| 3 | 156.1 | 11/10, 12/11 |
| 4 | 208.1 | 19/17 |
| 5 | 260.1 | 7/6, 22/19 |
| 6 | 312.1 | 6/5, 19/16, 23/19 |
| 7 | 364.1 | 16/13 |
| 8 | 416.2 | 14/11, 24/19 |
| 9 | 468.2 | 17/13 |
| 10 | 520.2 | 19/14, 23/17 |
| 11 | 572.2 | 7/5 |
| 12 | 624.3 | 10/7, 23/16 |
| 13 | 676.3 | |
| 14 | 728.3 | |
| 15 | 780.3 | 11/7, 19/12 |
| 16 | 832.3 | 13/8 |
| 17 | 884.4 | 5/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.5 | +22.8 | -7.0 | +22.8 | +19.3 | +12.5 | -10.5 | -6.4 | +19.3 | +10.4 | +15.8 |
| Relative (%) | -6.8 | +43.9 | -13.5 | +43.9 | +37.1 | +24.1 | -20.3 | -12.2 | +37.1 | +19.9 | +30.4 | |
| Steps (reduced) |
23 (6) |
37 (3) |
46 (12) |
54 (3) |
60 (9) |
65 (14) |
69 (1) |
73 (5) |
77 (9) |
80 (12) |
83 (15) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -18.7 | +9.0 | -6.4 | -14.1 | -15.0 | -9.9 | +0.6 | +15.8 | -16.6 | +6.9 | -18.1 |
| Relative (%) | -36.0 | +17.4 | -12.2 | -27.0 | -28.8 | -19.0 | +1.1 | +30.4 | -32.0 | +13.2 | -34.8 | |
| Steps (reduced) |
85 (0) |
88 (3) |
90 (5) |
92 (7) |
94 (9) |
96 (11) |
98 (13) |
100 (15) |
101 (16) |
103 (1) |
104 (2) | |