17ed5: Difference between revisions
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'''[[Ed5|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]]. | '''[[Ed5|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]]. | ||
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 | == 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: | But wait, an interesting pattern emerges: | ||
22ED5 focuses on 9/5 | [[22ed5|22ED5]] focuses on 9/5 | ||
27ED5 focuses on 13/5 | [[27ed5|27ED5]] focuses on 13/5 | ||
29ED5 focuses on 17/5 | [[29ed5|29ED5]] focuses on 17/5 | ||
(and 34=17*2) | (and 34=17*2) | ||
| Line 15: | Line 16: | ||
so: 22+27+29=78=39*2 | so: 22+27+29=78=39*2 | ||
and behold, of the lot, 39ED5 offers the best balance between those intervals. | and behold, of the lot, [[39ed5|39ED5]] offers the best balance between those intervals. | ||
{| class="wikitable" | {| class="wikitable" | ||
Revision as of 07:43, 28 August 2021
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 |