17ed5: Difference between revisions
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{{Infobox ET}} | |||
'''[[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, | == 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 17: | ||
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" | ||
|- | |- | ||
| | 0 | ! | degree | ||
| | 1/1 | ! | cents value | ||
! | corresponding <br>JI intervals | |||
! | comments | |||
|- | |||
| | 0 | |||
| | 0.000 | |||
| | '''exact [[1/1]]''' | |||
| | | | | | ||
|- | |- | ||
| | 1 | | | 1 | ||
| | 163.901 | |||
| | [[11/10]] | |||
| | | | | | ||
|- | |||
| | 2 | |||
| | 327.802 | |||
| | [[6/5]] | |||
| | | | | | ||
|- | |- | ||
| | | | | 3 | ||
| | 491.702 | |||
| | [[4/3]] | |||
| | | | | | ||
|- | |||
| | 4 | |||
| | 655.603 | |||
| | [[16/11]], [[19/13]], <br>[[22/15]] | |||
| | | | | | ||
|- | |- | ||
| | | | | 5 | ||
| | 819.504 | |||
| | [[8/5]] | |||
| | | | | | ||
|- | |||
| | 6 | |||
| | 983.405 | |||
| | [[7/4]], [[9/5]], [[16/9]] | |||
| | | | | | ||
|- | |- | ||
| | | | | 7 | ||
| | 1147.306 | |||
| | [[25/13]], [[27/14]], <br>[[35/18]], [[64/33]] | |||
| | | | | | ||
|- | |||
| | 8 | |||
| | 1311.206 | |||
| | [[16/15|32/15]] | |||
| | | | | | ||
|- | |- | ||
| | | | | 9 | ||
| | | | | 1475.107 | ||
| | [[75/64|75/32]] | |||
| | | | | | ||
|- | |- | ||
| | | | | 10 | ||
| | | | | 1639.008 | ||
| | [[13/5]], [[9/7|18/7]] | |||
| | | | | | ||
|- | |- | ||
| | | | | 11 | ||
| | | | | 1802.909 | ||
| | [[17/12|17/6]] | |||
| | | | | | ||
|- | |- | ||
| | | | | 12 | ||
| | | | | 1966.810 | ||
| | [[14/9|28/9]] | |||
| | | | | | ||
|- | |- | ||
| | 13 | |||
| | 13 | | | 2130.710 | ||
| | | | | [[17/10|17/5]], [[12/7|24/7]] | ||
| | | |||
| | | |||
| | | | | | ||
|- | |- | ||
| | | | | 14 | ||
| | | | | 2294.611 | ||
| | [[19/10|19/5]], [[32/17|64/17]] | |||
| | | | | | ||
|- | |- | ||
| | | | | 15 | ||
| | | | | 2458.512 | ||
| | | | | [[21/20|21/5]], [[25/24|25/6]], <br>[[33/32|33/8]] | ||
| | |||
| | | |||
| | | | | | ||
|- | |- | ||
| | | | | 16 | ||
| | 2622.413 | |||
| | [[17/15|68/15]] | |||
| | |||
| | |||
| | | |||
| | | | | | ||
|- | |- | ||
| | 17 | | | 17 | ||
| | 5/1 | | | 2786.314 | ||
| | | | | '''exact [[5/1]]''' | ||
| | just major third plus two octaves | |||
|} | |} | ||
[[Category: | == Harmonics == | ||
[[Category: | {{Harmonics in equal | ||
| steps = 17 | |||
| num = 5 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 17 | |||
| num = 5 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
[[Category:Hyperpyth]] | |||
[[Category:Todo:add sound example]] | |||