11ed7: Difference between revisions
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{{Mathematical interest}} | |||
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Latest revision as of 22:15, 10 August 2025
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This page presents a topic of primarily mathematical interest.
While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown. |
| ← 10ed7 | 11ed7 | 12ed7 → |
(semiconvergent)
11 equal divisions of the 7th harmonic (abbreviated 11ed7) is a nonoctave tuning system that divides the interval of 7/1 into 11 equal parts of about 306 ¢ each. Each step represents a frequency ratio of 71/11, or the 11th root of 7.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +25 | -64 | +50 | -30 | -39 | +0 | +75 | -129 | -5 | +136 | -14 |
| Relative (%) | +8.2 | -21.0 | +16.3 | -9.8 | -12.9 | +0.0 | +24.5 | -42.1 | -1.6 | +44.5 | -4.7 | |
| Steps (reduced) |
4 (4) |
6 (6) |
8 (8) |
9 (9) |
10 (10) |
11 (0) |
12 (1) |
12 (1) |
13 (2) |
14 (3) |
14 (3) | |