17ed5
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author guest and made on 2011-12-31 21:40:59 UTC.
- The original revision id was 288945041.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
=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. || 0: 0.000 cents || 1/1 || || || 1: 163.901 || || || || 2: 327.802 || || || || 3: 491.702 || || || || 4: 655.603 || || || || 5: 819.504 || || || || 6: 983.405 || 9/5, 16/9, 7/4 || 1017 || || 7: 1147.306 || || || || 8: 1311.206 || || || || 9: 1475.107 || || || || 10: 1639.008 || 13/5 || 1654 || || 11: 1802.909 || || || || 12: 1966.810 || || || || 13: 2130.710 || 17/5 || 2118 || || 14: 2294.611 || || || || 15: 2458.512 || (21/5) || 2486 || || 16: 2622.413 || || || || 17: 2786.314 || 5/1 || ||
Original HTML content:
<html><head><title>17ed5</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Division of the 5/1 into 17 tones"></a><!-- ws:end:WikiTextHeadingRule:0 -->Division of the 5/1 into 17 tones</h1>
<br />
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.<br />
<br />
But wait, an interesting pattern emerges:<br />
<br />
22ed5 focuses on 9/5<br />
27ed5 focuses on 13/5<br />
29ed5 focuses on 17/5<br />
(and 34=17*2)<br />
<br />
so: 22+27+29=78=39*2<br />
and behold, of the lot, 39ed5 offers the best balance between those intervals.<br />
<br />
<table class="wiki_table">
<tr>
<td>0: 0.000 cents<br />
</td>
<td>1/1<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>1: 163.901<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>2: 327.802<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>3: 491.702<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>4: 655.603<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>5: 819.504<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>6: 983.405<br />
</td>
<td>9/5, 16/9, 7/4<br />
</td>
<td>1017<br />
</td>
</tr>
<tr>
<td>7: 1147.306<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>8: 1311.206<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>9: 1475.107<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>10: 1639.008<br />
</td>
<td>13/5<br />
</td>
<td>1654<br />
</td>
</tr>
<tr>
<td>11: 1802.909<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>12: 1966.810<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>13: 2130.710<br />
</td>
<td>17/5<br />
</td>
<td>2118<br />
</td>
</tr>
<tr>
<td>14: 2294.611<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>15: 2458.512<br />
</td>
<td>(21/5)<br />
</td>
<td>2486<br />
</td>
</tr>
<tr>
<td>16: 2622.413<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>17: 2786.314<br />
</td>
<td>5/1<br />
</td>
<td><br />
</td>
</tr>
</table>
</body></html>