User:MisterShafXen/24ed9/2
Jump to navigation
Jump to search
Prime factorization
23 × 3 (highly composite)
Step size
108.496 ¢
Octave
11\24ed9/2 (1193.46 ¢)
(semiconvergent)
Twelfth
18\24ed9/2 (1952.93 ¢) (→ 3\4ed9/2)
Consistency limit
2
Distinct consistency limit
2
| ← 23ed9/2 | 24ed9/2 | 25ed9/2 → |
(semiconvergent)
24 equal divisions of 9/2 (abbreviated 24ed9/2) is a nonoctave tuning system that divides the interval of 9/2 into 24 equal parts of about 108 ¢ each. Each step represents a frequency ratio of (9/2)1/24, or the 24th root of 9/2.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 108.5 | 17/16 |
| 2 | 217 | 26/23 |
| 3 | 325.5 | 6/5, 17/14, 23/19 |
| 4 | 434 | 22/17 |
| 5 | 542.5 | 11/8, 26/19 |
| 6 | 651 | 16/11, 19/13 |
| 7 | 759.5 | 17/11 |
| 8 | 868 | 23/14 |
| 9 | 976.5 | 7/4, 23/13 |
| 10 | 1085 | |
| 11 | 1193.5 | 2/1 |
| 12 | 1302 | 17/8 |
| 13 | 1410.5 | |
| 14 | 1518.9 | 12/5 |
| 15 | 1627.4 | |
| 16 | 1735.9 | 19/7 |
| 17 | 1844.4 | |
| 18 | 1952.9 | |
| 19 | 2061.4 | 23/7 |
| 20 | 2169.9 | 7/2 |
| 21 | 2278.4 | 26/7 |
| 22 | 2386.9 | |
| 23 | 2495.4 | 17/4, 21/5 |
| 24 | 2603.9 |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -6.5 | +51.0 | +34.6 | -5.4 | -28.5 | +7.8 | -22.6 | +1.8 | -3.5 | +29.2 | +22.3 |
| Relative (%) | -6.0 | +47.0 | +31.9 | -5.0 | -26.2 | +7.2 | -20.9 | +1.7 | -3.2 | +26.9 | +20.5 | |
| Steps (reduced) |
11 (11) |
18 (18) |
26 (2) |
31 (7) |
38 (14) |
41 (17) |
45 (21) |
47 (23) |
50 (2) |
54 (6) |
55 (7) | |