User:MisterShafXen/5edo
| ← 4edo | 5edo | 6edo → |
(convergent)
5 equal divisions of the octave (abbreviated 5edo or 5ed2), also called 5-tone equal temperament (5tet) or 5 equal temperament (5et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 5 equal parts of exactly 240 ¢ each. Each step represents a frequency ratio of 21/5, or the 5th root of 2.
Intervals
| Steps | Cents | Approximate ratios | Ups and downs notation |
|---|---|---|---|
| 0 | 0 | 1/1 | D |
| 1 | 240 | 7/6, 8/7, 9/8, 10/9, 15/13, 19/16, 19/17, 21/19 | E, F |
| 2 | 480 | 4/3, 9/7, 11/8, 13/10, 14/11, 19/14, 21/16 | G |
| 3 | 720 | 3/2, 11/7, 14/9, 16/11, 17/11, 20/13 | A |
| 4 | 960 | 7/4, 9/5, 12/7, 16/9, 19/11 | B, C |
| 5 | 1200 | 2/1 | D |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0 | +18 | +94 | -9 | -71 | +119 | -105 | -58 | +92 | -70 | +55 |
| Relative (%) | +0.0 | +7.5 | +39.0 | -3.7 | -29.7 | +49.8 | -43.7 | -24.0 | +38.2 | -29.0 | +22.9 | |
| Steps (reduced) |
5 (0) |
8 (3) |
12 (2) |
14 (4) |
17 (2) |
19 (4) |
20 (0) |
21 (1) |
23 (3) |
24 (4) |
25 (0) | |