17ed5

Revision as of 21:40, 31 December 2011 by Wikispaces>guest (**Imported revision 288945041 - Original comment: **)

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This revision was by author guest and made on 2011-12-31 21:40:59 UTC.
The original revision id was 288945041.
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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:&lt;h1&gt; --><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>