17ed5
| ← 16ed5 | 17ed5 | 18ed5 → |
Division of the 5th harmonic into 17 equal parts (17ED5) is a good hyperpyth tuning. The step size is about 163.9008 cents, corresponding to 7.3215 EDO.
Division of the 5/1 into 17 tones
A hyperpyth tuning, 17ED5 offers a good compromise between 13/5 and 17/5, but the 9/5 of 983 cents is a little bit flat. However, in hyperpyth, 21/5 isn't necessarily represented, at least not as well. In 17ED5, the 21/5 is represented about as well as the 9/5 is, although that's not too good. Luckily, 27, 29, and 39 do a fair job of it. Nevertheless it's the simplest equal hyperpyth after 5ED5, and quite consonant. I imagine it to be the traditional tonality of the tiny creatures living on subatomic particles.
But wait, an interesting pattern emerges:
22ED5 focuses on 9/5
27ED5 focuses on 13/5
29ED5 focuses on 17/5
(and 34=17*2)
so: 22+27+29=78=39*2
and behold, of the lot, 39ED5 offers the best balance between those intervals.
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.000 | exact 1/1 | |
| 1 | 163.901 | 11/10 | |
| 2 | 327.802 | 6/5 | |
| 3 | 491.702 | 4/3 | |
| 4 | 655.603 | 16/11, 19/13, 22/15 |
|
| 5 | 819.504 | 8/5 | |
| 6 | 983.405 | 7/4, 9/5, 16/9 | |
| 7 | 1147.306 | 25/13, 27/14, 35/18, 64/33 |
|
| 8 | 1311.206 | 32/15 | |
| 9 | 1475.107 | 75/32 | |
| 10 | 1639.008 | 13/5, 18/7 | |
| 11 | 1802.909 | 17/6 | |
| 12 | 1966.810 | 28/9 | |
| 13 | 2130.710 | 17/5, 24/7 | |
| 14 | 2294.611 | 19/5, 64/17 | |
| 15 | 2458.512 | 21/5, 25/6, 33/8 |
|
| 16 | 2622.413 | 68/15 | |
| 17 | 2786.314 | exact 5/1 | just major third plus two octaves |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -52.7 | +64.9 | +58.5 | +0.0 | +12.2 | +73.1 | +5.8 | -34.2 | -52.7 | -53.8 | -40.5 |
| Relative (%) | -32.2 | +39.6 | +35.7 | +0.0 | +7.4 | +44.6 | +3.5 | -20.9 | -32.2 | -32.8 | -24.7 | |
| Steps (reduced) |
7 (7) |
12 (12) |
15 (15) |
17 (0) |
19 (2) |
21 (4) |
22 (5) |
23 (6) |
24 (7) |
25 (8) |
26 (9) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -15.2 | +20.4 | +64.9 | -46.9 | +12.1 | +77.0 | -16.6 | +58.5 | -26.0 | +57.4 | -19.5 |
| Relative (%) | -9.3 | +12.4 | +39.6 | -28.6 | +7.4 | +47.0 | -10.1 | +35.7 | -15.8 | +35.0 | -11.9 | |
| Steps (reduced) |
27 (10) |
28 (11) |
29 (12) |
29 (12) |
30 (13) |
31 (14) |
31 (14) |
32 (15) |
32 (15) |
33 (16) |
33 (16) | |