User:MisterShafXen/23ed8/7
| ← 22ed8/7 | 23ed8/7 | 24ed8/7 → |
23 equal divisions of 8/7 (abbreviated 23ed8/7) is a nonoctave tuning system that divides the interval of 8/7 into 23 equal parts of about 10.1 ¢ each. Each step represents a frequency ratio of (8/7)1/23, or the 23rd root of 8/7. This tuning is almost exactly every 5th step of 597edo.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.93 | -2.31 | +2.20 | -2.17 | +3.82 | -1.72 | -1.72 | -4.61 | +3.95 | -0.24 | -0.11 |
| Relative (%) | -39.1 | -23.0 | +21.9 | -21.6 | +38.0 | -17.2 | -17.2 | -45.9 | +39.3 | -2.3 | -1.1 | |
| Steps (reduced) |
119 (4) |
189 (5) |
239 (9) |
277 (1) |
309 (10) |
335 (13) |
358 (13) |
378 (10) |
397 (6) |
413 (22) |
428 (14) | |
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 10.1 | |
| 2 | 20.1 | |
| 3 | 30.2 | |
| 4 | 40.2 | |
| 5 | 50.3 | |
| 6 | 60.3 | 24/23 |
| 7 | 70.4 | |
| 8 | 80.4 | 20/19, 22/21, 23/22, 25/24 |
| 9 | 90.5 | 18/17, 21/20 |
| 10 | 100.5 | 16/15, 19/18 |
| 11 | 110.6 | |
| 12 | 120.6 | 14/13, 15/14 |
| 13 | 130.7 | |
| 14 | 140.7 | 12/11, 25/23 |
| 15 | 150.8 | 13/12 |
| 16 | 160.8 | 23/21 |
| 17 | 170.9 | 11/10, 21/19 |
| 18 | 180.9 | 10/9 |
| 19 | 191 | 19/17 |
| 20 | 201 | |
| 21 | 211.1 | 9/8 |
| 22 | 221.1 | 8/7, 17/15, 25/22 |
| 23 | 231.2 |