8ed6: Difference between revisions
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| Line 15: | Line 15: | ||
| 1 | | 1 | ||
| 387.744 | | 387.744 | ||
| 5/4 | | 5/4 | ||
|- | |- | ||
| 2 | | 2 | ||
| 775.489 | | 775.489 | ||
| | | 25/16, 11/7 | ||
|- | |- | ||
| 3 | | 3 | ||
| 1163.233 | | 1163.233 | ||
| | | | ||
|- | |- | ||
| 4 | | 4 | ||
| 1550.978 | | 1550.978 | ||
| | | 22/9 | ||
|- | |- | ||
| 5 | | 5 | ||
| 1938.722 | | 1938.722 | ||
| | | 64/21, 49/16 | ||
|- | |- | ||
| 6 | | 6 | ||
| 2326.466 | | 2326.466 | ||
| | | | ||
|- | |- | ||
| 7 | | 7 | ||
| 2714.211 | | 2714.211 | ||
| 5 | | 24/5 | ||
|- | |- | ||
| 8 | | 8 | ||
Revision as of 17:35, 15 July 2025
| ← 7ed6 | 8ed6 | 9ed6 → |
(semiconvergent)
(semiconvergent)
8 equal divisions of the 6th harmonic (abbreviated 8ed6) is a nonoctave tuning system that divides the interval of 6/1 into 8 equal parts of about 388 ¢ each. Each step represents a frequency ratio of 61/8, or the 8th root of 6.
Intervals
| # | Cents | Approximate JI ratio(s) |
|---|---|---|
| 0 | 0.000 | exact 1/1 |
| 1 | 387.744 | 5/4 |
| 2 | 775.489 | 25/16, 11/7 |
| 3 | 1163.233 | |
| 4 | 1550.978 | 22/9 |
| 5 | 1938.722 | 64/21, 49/16 |
| 6 | 2326.466 | |
| 7 | 2714.211 | 24/5 |
| 8 | 3101.955 | exact 6/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -37 | +37 | -74 | -72 | +0 | +121 | -110 | +74 | -109 | +114 | -37 |
| Relative (%) | -9.5 | +9.5 | -19.0 | -18.6 | +0.0 | +31.2 | -28.4 | +19.0 | -28.1 | +29.4 | -9.5 | |
| Steps (reduced) |
3 (3) |
5 (5) |
6 (6) |
7 (7) |
8 (0) |
9 (1) |
9 (1) |
10 (2) |
10 (2) |
11 (3) |
11 (3) | |