User:Jdood/4ed6/5: Difference between revisions
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Latest revision as of 18:32, 27 December 2025
4 equal divisions of 6/5 (abbreviated 4ed6/5) is a nonoctave tuning system that divides the interval of 6/5 into 4 equal parts of about 78.9 ¢ each. Each step represents a frequency ratio of (6/5)1/4, or the 4th root of 6/5.
Theory
Commas
4ed6/5 tempers out the comma 585640/583443 if you take one step to be an approximation of 22/21.
Approximation of harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -8.1 | -24.5 | +24.3 | -16.2 | +30.9 | -21.5 | -32.6 | -12.5 | +31.7 | +16.2 | +16.5 | +30.0 | -24.3 |
| Relative (%) | -10.3 | -31.0 | +30.8 | -20.5 | +39.2 | -27.3 | -41.3 | -15.9 | +40.1 | +20.5 | +21.0 | +38.0 | -30.8 | |
| Steps (reduced) |
24 (0) |
35 (3) |
43 (3) |
48 (0) |
53 (1) |
56 (0) |
59 (3) |
62 (2) |
65 (1) |
67 (3) |
69 (1) |
71 (3) |
72 (0) | |
Subsets and supersets
4ed6/5 contains 2ed6/5.