10ed5: Difference between revisions
interval table, reorganization |
interval table, reorganization |
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{{Infobox ET}} | {{Infobox ET}} | ||
In general, 10ed5 is simply a smashing tuning. The relatively large 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. | 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]]. | It is especially important as a structural framework for the [[5.7.11.13 subgroup]]. | ||
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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. | 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 relates this tuning to 13edo, which divides the step in three | Adding octaves relates this tuning to [[13edo]], which divides the step in three. | ||
== Music == | == Music == | ||
Revision as of 01:59, 10 April 2026
| ← 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.
Adding octaves relates this tuning to 13edo, which divides the step in three.
Music
Weird Blues -- Kosmorsky