8edt: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
As the double of [[4edt|4edt]], harmonically, it is | '''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 [[cent]]s 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|4edt]], harmonically, it is the analog of [[10edo]] for [[4L 5s (3/1-equivalent)|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. | What it does introduce are flat pseudooctaves and sharp 3:2's, making it related to 5edo melodically. | ||
Revision as of 23:33, 26 February 2024
| ← 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.
0: 1/1 0.000 unison, perfect prime
1: 237.744 cents 237.744
2: 475.489 cents 4/3
3: 713.233 cents 713.233
4: 950.978 cents 5/3
5: 1188.722 cents 1188.722
6: 1426.466 cents 1426.466
7: 1664.211 cents 1664.211
8: 3/1 1901.955 perfect 12th
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) | |