13ed9/4
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Prime factorization
13 (prime)
Step size
107.993¢
Octave
11\13ed9/4 (1187.92¢)
(semiconvergent)
Twelfth
18\13ed9/4 (1943.88¢)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 11ed9/4 | 13ed9/4 | 15ed9/4 → |
(semiconvergent)
13 equal divisions of 9/4 (abbreviated 13ed9/4) is a nonoctave tuning system that divides the interval of 9/4 into 13 equal parts of about 108 ¢ each. Each step represents a frequency ratio of (9/4)1/13, or the 13th root of 9/4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 108 | 14/13, 17/16, 20/19, 21/20 |
| 2 | 216 | 8/7, 19/17, 23/20 |
| 3 | 324 | 6/5, 17/14, 23/19 |
| 4 | 432 | 13/10, 14/11, 22/17 |
| 5 | 540 | 11/8, 19/14, 23/17 |
| 6 | 648 | 16/11, 19/13, 23/16 |
| 7 | 756 | 17/11, 20/13 |
| 8 | 863.9 | 5/3, 13/8, 23/14 |
| 9 | 971.9 | 7/4, 19/11, 23/13 |
| 10 | 1079.9 | 13/7 |
| 11 | 1187.9 | 2/1 |
| 12 | 1295.9 | 17/8, 21/10, 23/11 |
| 13 | 1403.9 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -12.1 | +41.9 | -24.2 | +21.5 | +29.8 | -21.0 | -36.2 | -24.2 | +9.4 | -47.6 | +17.8 |
| Relative (%) | -11.2 | +38.8 | -22.4 | +19.9 | +27.6 | -19.5 | -33.5 | -22.4 | +8.7 | -44.1 | +16.5 | |
| Steps (reduced) |
11 (11) |
18 (5) |
22 (9) |
26 (0) |
29 (3) |
31 (5) |
33 (7) |
35 (9) |
37 (11) |
38 (12) |
40 (1) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -12.8 | -33.1 | -44.6 | -48.3 | -45.3 | -36.2 | -21.8 | -2.6 | +20.9 | +48.3 | -28.6 |
| Relative (%) | -11.9 | -30.7 | -41.3 | -44.7 | -41.9 | -33.5 | -20.2 | -2.5 | +19.3 | +44.8 | -26.5 | |
| Steps (reduced) |
41 (2) |
42 (3) |
43 (4) |
44 (5) |
45 (6) |
46 (7) |
47 (8) |
48 (9) |
49 (10) |
50 (11) |
50 (11) | |