13ed11/5: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
For its size, 13ed11/5 has decent approximations of the 3rd and 4th harmonics, and a great approximation of the 7th harmonic. | |||
It completely misses the 5th harmonic, however it nails the 10th harmonic almost exactly. | |||
Given this, it could be approached as a 3.4.7 subgroup tuning, or even as a 3.4.7.10 tuning, which is quite the quirky combination. | |||
When playing by ear, the [[4/1]] approximation, roughly 2415 cents, tends to sound like an equivalence or a tonal centre. This makes 13ed11/5 sound similar to [[23ed4]], or every second note of [[46edo]]. | |||
== Integer harmonics == | |||
{{Harmonics in equal | |||
| steps = 13 | |||
| num = 11 | |||
| denom = 5 | |||
| columns = 16 | |||
}} | |||
Revision as of 12:20, 8 May 2023
| ← 12ed11/5 | 13ed11/5 | 14ed11/5 → |
(semiconvergent)
For its size, 13ed11/5 has decent approximations of the 3rd and 4th harmonics, and a great approximation of the 7th harmonic.
It completely misses the 5th harmonic, however it nails the 10th harmonic almost exactly.
Given this, it could be approached as a 3.4.7 subgroup tuning, or even as a 3.4.7.10 tuning, which is quite the quirky combination.
When playing by ear, the 4/1 approximation, roughly 2415 cents, tends to sound like an equivalence or a tonal centre. This makes 13ed11/5 sound similar to 23ed4, or every second note of 46edo.
Integer harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -45.0 | -11.9 | +15.0 | +48.7 | +48.1 | -8.8 | -30.0 | -23.9 | +3.7 | +48.7 | +3.1 | -30.5 | +51.2 | +36.7 | +30.0 | +30.1 |
| Relative (%) | -42.9 | -11.4 | +14.3 | +46.4 | +45.8 | -8.4 | -28.6 | -22.8 | +3.5 | +46.4 | +2.9 | -29.1 | +48.8 | +35.0 | +28.6 | +28.6 | |
| Steps (reduced) |
11 (11) |
18 (5) |
23 (10) |
27 (1) |
30 (4) |
32 (6) |
34 (8) |
36 (10) |
38 (12) |
40 (1) |
41 (2) |
42 (3) |
44 (5) |
45 (6) |
46 (7) |
47 (8) | |