User:MisterShafXen/31ed8/7
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Prime factorization
31 (prime)
Step size
7.45723 ¢
Octave
161\31ed8/7 (1200.61 ¢)
Twelfth
255\31ed8/7 (1901.59 ¢)
Consistency limit
9
Distinct consistency limit
9
| ← 30ed8/7 | 31ed8/7 | 32ed8/7 → |
31 equal divisions of 8/7 (abbreviated 31ed8/7) is a nonoctave tuning system that divides the interval of 8/7 into 31 equal parts of about 7.46 ¢ each. Each step represents a frequency ratio of (8/7)1/31, or the 31st root of 8/7.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 7.5 | |
| 2 | 14.9 | |
| 3 | 22.4 | |
| 4 | 29.8 | |
| 5 | 37.3 | |
| 6 | 44.7 | |
| 7 | 52.2 | |
| 8 | 59.7 | 26/25 |
| 9 | 67.1 | 27/26 |
| 10 | 74.6 | 23/22, 24/23, 25/24 |
| 11 | 82 | 21/20, 22/21 |
| 12 | 89.5 | 20/19 |
| 13 | 96.9 | 18/17, 19/18 |
| 14 | 104.4 | 17/16 |
| 15 | 111.9 | 16/15 |
| 16 | 119.3 | 15/14 |
| 17 | 126.8 | 27/25 |
| 18 | 134.2 | 13/12, 14/13 |
| 19 | 141.7 | |
| 20 | 149.1 | 12/11, 25/23 |
| 21 | 156.6 | 23/21 |
| 22 | 164.1 | 11/10 |
| 23 | 171.5 | 21/19 |
| 24 | 179 | |
| 25 | 186.4 | 10/9 |
| 26 | 193.9 | 19/17 |
| 27 | 201.3 | 9/8 |
| 28 | 208.8 | 26/23 |
| 29 | 216.3 | 17/15 |
| 30 | 223.7 | 25/22 |
| 31 | 231.2 | 8/7 |