12ed5/4
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Prime factorization
22 × 3
Step size
32.1928¢
Octave
37\12ed5/4 (1191.13¢)
Twelfth
59\12ed5/4 (1899.38¢)
(semiconvergent)
Consistency limit
3
Distinct consistency limit
2
Special properties
 |
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| ← 11ed5/4 | 12ed5/4 | 13ed5/4 → |
(semiconvergent)
12 equal divisions of 5/4 (abbreviated 12ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 12 equal parts of about 32.2 ¢ each. Each step represents a frequency ratio of (5/4)1/12, or the 12th root of 5/4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 32.2 | |
| 2 | 64.4 | 22/21 |
| 3 | 96.6 | 18/17, 19/18, 20/19, 21/20, 23/22 |
| 4 | 128.8 | 12/11, 14/13, 15/14, 17/16 |
| 5 | 161 | 11/10, 13/12, 23/21 |
| 6 | 193.2 | 10/9, 17/15, 19/17, 21/19 |
| 7 | 225.3 | 9/8 |
| 8 | 257.5 | 15/13, 22/19, 23/20 |
| 9 | 289.7 | 6/5, 7/6, 13/11, 20/17 |
| 10 | 321.9 | 17/14, 19/16 |
| 11 | 354.1 | 11/9, 23/19 |
| 12 | 386.3 | 19/15, 21/17 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -8.9 | -2.6 | +14.5 | +14.5 | -11.4 | +11.4 | +5.6 | -5.2 | +5.6 | +1.6 | +11.9 |
| Relative (%) | -27.5 | -8.0 | +44.9 | +44.9 | -35.6 | +35.5 | +17.4 | -16.0 | +17.4 | +4.8 | +36.9 | |
| Steps (reduced) |
37 (1) |
59 (11) |
75 (3) |
87 (3) |
96 (0) |
105 (9) |
112 (4) |
118 (10) |
124 (4) |
129 (9) |
134 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.1 | +2.6 | +11.9 | -3.3 | -11.6 | -14.0 | -11.0 | -3.3 | +8.8 | -7.3 | +12.3 |
| Relative (%) | +6.5 | +7.9 | +36.9 | -10.2 | -36.2 | -43.6 | -34.3 | -10.2 | +27.5 | -22.7 | +38.2 | |
| Steps (reduced) |
138 (6) |
142 (10) |
146 (2) |
149 (5) |
152 (8) |
155 (11) |
158 (2) |
161 (5) |
164 (8) |
166 (10) |
169 (1) | |