10ed5
| ← 9ed5 | 10ed5 | 11ed5 → |
(semiconvergent)
Half of 20ed5. But it has important characteristics of its own:
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.
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.
Adding octaves, strangely enough, relates this tuning to 43edo.
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
0: 1/1
1: 278.631 cents 13/11
2: 557.263 cents 7/5
3: 835.894 cents
4: 1114.525 cents "9/5"
5: 1393.157 cents 11/5
6: 1671.788 cents 13/5
7: 1950.420 cents
8: 2229.051 cents "17/5"
9: 2507.682 cents 21/5
10: 5/1
Music
Weird Blues -- Kosmorsky