8edt
| ← 7edt | 8edt | 9edt → |
(convergent)
8 equal divisions of the tritave (8edt) is the nonoctave tuning system derived by dividing the tritave (3/1) into 13 equal steps of 237.744 cents each, or the eighth root of 3. It is best known as the equal-tempered version of the Bohlen-Pierce scale. As the double of 4edt, harmonically, it is the analog of 10edo for Lambda-based systems. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in 5edo.
What it does introduce are flat pseudooctaves and sharp 3:2's, making it related to 5edo melodically.
Interval table
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 237.7 | 162.5 | 7/6, 8/7, 9/8, 15/13, 17/15, 20/17, 22/19 |
| 2 | 475.5 | 325 | 4/3, 9/7, 13/10, 17/13, 21/16 |
| 3 | 713.2 | 487.5 | 3/2, 20/13 |
| 4 | 951 | 650 | 7/4, 12/7, 17/10, 19/11 |
| 5 | 1188.7 | 812.5 | 2/1 |
| 6 | 1426.5 | 975 | 7/3, 9/4, 16/7, 20/9 |
| 7 | 1664.2 | 1137.5 | 8/3, 13/5, 18/7, 21/8 |
| 8 | 1902 | 1300 | 3/1 |
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11 | +0 | +67 | -40 | -110 | +77 | +88 | -105 | +40 | +114 | -1 |
| Relative (%) | -4.7 | +0.0 | +28.0 | -17.0 | -46.1 | +32.2 | +36.9 | -44.1 | +16.8 | +48.0 | -0.6 | |
| Steps (reduced) |
5 (5) |
8 (0) |
12 (4) |
14 (6) |
17 (1) |
19 (3) |
21 (5) |
21 (5) |
23 (7) |
25 (1) |
25 (1) | |