10ed5
| ← 9ed5 | 10ed5 | 11ed5 → |
(semiconvergent)
In general, 10ed5 is simply a smashing tuning. The relatively large small steps, about the size of a minor third or an orwell generator, actually work for melodies, and it's harmonies while strange have no lack of impact. It can be used such that the fifth harmonic is equivalent, but of course, doesn't have to.
It is especially important as a structural framework for the 5.7.11.13 subgroup.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -85 | +48 | +108 | +0 | -37 | -25 | +22 | +97 | -85 | +28 | -122 |
| Relative (%) | -30.7 | +17.4 | +38.6 | +0.0 | -13.3 | -9.1 | +8.0 | +34.8 | -30.7 | +10.1 | -44.0 | |
| Steps (reduced) |
4 (4) |
7 (7) |
9 (9) |
10 (0) |
11 (1) |
12 (2) |
13 (3) |
14 (4) |
14 (4) |
15 (5) |
15 (5) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +18 | -111 | +48 | -63 | +110 | +11 | -82 | +108 | +23 | -57 | -134 |
| Relative (%) | +6.3 | -39.7 | +17.4 | -22.7 | +39.6 | +4.1 | -29.5 | +38.6 | +8.3 | -20.6 | -48.2 | |
| Steps (reduced) |
16 (6) |
16 (6) |
17 (7) |
17 (7) |
18 (8) |
18 (8) |
18 (8) |
19 (9) |
19 (9) |
19 (9) |
19 (9) | |
Intervals
| Degree | Cents | 5.7.11.13 intervals |
|---|---|---|
| 0 | 0.000 | 1/1 |
| 1 | 278.631 | 13/11, 55/49 |
| 2 | 557.263 | 7/5 |
| 3 | 835.894 | 11/7 |
| 4 | 1114.525 | 13/7, 25/13 |
| 5 | 1393.157 | 11/5, 25/11 |
| 6 | 1671.788 | 13/5, 35/13 |
| 7 | 1950.420 | 35/11 |
| 8 | 2229.051 | 49/13 |
| 9 | 2507.682 | 49/11 |
| 10 | 2786.314 | 5/1 |
Subsets and supersets
Half of 20ed5.
As 5ed5 is the simplest hyperpyth tuning (analogous to 5edo and 4edt in their own spheres) this, its double, can be compared structurally to 10edo. While its approximations of 9/5, 17/5 and 21/5 are quite far off, these are still categorically important intervals.
Octaves can be added by dividing the step in three to get 13edo with octaves 7 cents sharp. If octaves are instead made just, prime 7 becomes very flat, as well as prime 5 to a lesser extent. Alternatively, the step can be divided in ten to get 43edo.
Music
Weird Blues -- Kosmorsky