8ed6: Difference between revisions
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== Intervals == | == Intervals == | ||
{| class="wikitable" | {| class="wikitable right-2" | ||
|- | |- | ||
! # | ! # | ||
| Line 16: | Line 16: | ||
|- | |- | ||
| 0 | | 0 | ||
| | | 0 | ||
| | | 1/1 | ||
|- | |- | ||
| 1 | | 1 | ||
| | | 388 | ||
| 5/4 | | 5/4 | ||
|- | |- | ||
| 2 | | 2 | ||
| 775 | | 775 | ||
| 25/16 | | 11/7, 25/16 | ||
|- | |- | ||
| 3 | | 3 | ||
| 1163 | | 1163 | ||
| | | | ||
|- | |- | ||
| 4 | | 4 | ||
| | | 1551 | ||
| 22/9 | | 22/9 | ||
|- | |- | ||
| 5 | | 5 | ||
| | | 1939 | ||
| 64/21 | | 49/16, 64/21 | ||
|- | |- | ||
| 6 | | 6 | ||
| 2326 | | 2326 | ||
| | | | ||
|- | |- | ||
| 7 | | 7 | ||
| 2714 | | 2714 | ||
| 24/5 | | 24/5 | ||
|- | |- | ||
| 8 | | 8 | ||
| | | 3102 | ||
| | | 6/1 | ||
|} | |} | ||
Revision as of 17:50, 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.
Theory
8ed6 can be thought of as a subset (where the ~5/4 generator is stacked) of the 6/1-eigenmonzo tuning of würschmidt.
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) | |
Intervals
| # | Cents | Approximate JI ratio(s) |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 388 | 5/4 |
| 2 | 775 | 11/7, 25/16 |
| 3 | 1163 | |
| 4 | 1551 | 22/9 |
| 5 | 1939 | 49/16, 64/21 |
| 6 | 2326 | |
| 7 | 2714 | 24/5 |
| 8 | 3102 | 6/1 |