23ed11/5
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Prime factorization
23 (prime)
Step size
59.348¢
Octave
20\23ed11/5 (1186.96¢)
Twelfth
32\23ed11/5 (1899.14¢)
(semiconvergent)
Consistency limit
6
Distinct consistency limit
4
 |
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| ← 22ed11/5 | 23ed11/5 | 24ed11/5 → |
(semiconvergent)
23 equal divisions of 11/5 (abbreviated 23ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 23 equal parts of about 59.3 ¢ each. Each step represents a frequency ratio of (11/5)1/23, or the 23rd root of 11/5.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 59.348 | |
| 2 | 118.696 | 14/13, 15/14 |
| 3 | 178.044 | 10/9, 11/10, 21/19 |
| 4 | 237.392 | 15/13, 23/20 |
| 5 | 296.74 | 13/11, 25/21 |
| 6 | 356.088 | 11/9, 21/17 |
| 7 | 415.436 | 14/11, 19/15, 23/18 |
| 8 | 474.784 | 17/13, 25/19 |
| 9 | 534.132 | 15/11, 19/14 |
| 10 | 593.48 | 7/5 |
| 11 | 652.828 | 19/13, 22/15 |
| 12 | 712.176 | 3/2 |
| 13 | 771.524 | 11/7, 14/9 |
| 14 | 830.872 | 21/13 |
| 15 | 890.22 | 5/3 |
| 16 | 949.568 | 19/11 |
| 17 | 1008.916 | 9/5, 25/14 |
| 18 | 1068.264 | 13/7 |
| 19 | 1127.612 | 21/11, 23/12, 25/13 |
| 20 | 1186.96 | 2/1 |
| 21 | 1246.308 | |
| 22 | 1305.656 | 19/9 |
| 23 | 1365.004 | 11/5 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -13.0 | -2.8 | -26.1 | +3.0 | -15.9 | +14.0 | +20.2 | -5.6 | -10.0 | +3.0 | -28.9 |
| Relative (%) | -22.0 | -4.7 | -43.9 | +5.1 | -26.7 | +23.6 | +34.1 | -9.5 | -16.8 | +5.1 | -48.7 | |
| Steps (reduced) |
20 (20) |
32 (9) |
40 (17) |
47 (1) |
52 (6) |
57 (11) |
61 (15) |
64 (18) |
67 (21) |
70 (1) |
72 (3) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +10.6 | +1.0 | +0.2 | +7.2 | +20.9 | -18.7 | +6.4 | -23.0 | +11.2 | -10.0 | -27.6 |
| Relative (%) | +17.8 | +1.6 | +0.4 | +12.1 | +35.3 | -31.5 | +10.8 | -38.8 | +18.9 | -16.8 | -46.5 | |
| Steps (reduced) |
75 (6) |
77 (8) |
79 (10) |
81 (12) |
83 (14) |
84 (15) |
86 (17) |
87 (18) |
89 (20) |
90 (21) |
91 (22) | |