11ed5/4
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Prime factorization
11 (prime)
Step size
35.1194¢
Octave
34\11ed5/4 (1194.06¢)
Twelfth
54\11ed5/4 (1896.45¢)
(semiconvergent)
Consistency limit
7
Distinct consistency limit
2
 |
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| ← 10ed5/4 | 11ed5/4 | 12ed5/4 → |
(semiconvergent)
11 equal divisions of 5/4 (abbreviated 11ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 11 equal parts of about 35.1 ¢ each. Each step represents a frequency ratio of (5/4)1/11, or the 11th root of 5/4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 35.1 | |
| 2 | 70.2 | 18/17, 20/19, 22/21 |
| 3 | 105.4 | 15/14, 16/15, 19/18, 21/20 |
| 4 | 140.5 | 12/11, 13/12, 14/13 |
| 5 | 175.6 | 10/9, 11/10, 19/17, 21/19 |
| 6 | 210.7 | 8/7, 9/8 |
| 7 | 245.8 | 15/13, 17/15, 22/19 |
| 8 | 281 | 7/6, 13/11 |
| 9 | 316.1 | 6/5, 19/16 |
| 10 | 351.2 | 11/9, 16/13, 17/14, 21/17 |
| 11 | 386.3 | 5/4 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -5.9 | -5.5 | -11.9 | -11.9 | -11.4 | +2.6 | +17.3 | -11.0 | +17.3 | -7.2 | -17.4 |
| Relative (%) | -16.9 | -15.7 | -33.8 | -33.8 | -32.6 | +7.5 | +49.3 | -31.4 | +49.3 | -20.6 | -49.5 | |
| Steps (reduced) |
34 (1) |
54 (10) |
68 (2) |
79 (2) |
88 (0) |
96 (8) |
103 (4) |
108 (9) |
114 (4) |
118 (8) |
122 (1) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -15.5 | -3.3 | -17.4 | +11.4 | +11.8 | -17.0 | -5.2 | +11.4 | -2.9 | -13.2 | +15.2 |
| Relative (%) | -44.1 | -9.4 | -49.5 | +32.4 | +33.5 | -48.3 | -14.8 | +32.4 | -8.2 | -37.5 | +43.4 | |
| Steps (reduced) |
126 (5) |
130 (9) |
133 (1) |
137 (5) |
140 (8) |
142 (10) |
145 (2) |
148 (5) |
150 (7) |
152 (9) |
155 (1) | |