17ed5

From Xenharmonic Wiki
Jump to navigation Jump to search

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