38edo: Difference between revisions

Revision as of 18:35, 24 June 2011

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author Osmiorisbendi and made on 2011-06-24 18:35:40 UTC.

The original revision id was 238638717.

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:

=<span style="background-color: #e1e1e1; color: #008693; font-size: 110%;">38 tone equal temperament</span>= 

//38edo// divides the octave into 38 equal parts of 31.579 cents. Since 38 = 2*19, it can be thought of as two parallel [[19edo]]s. It tempers out the same 5-limit commas as 19, namely 81/80, 3125/3072 and 15625/15552. In the 7-limit, we can add 50/49, and tempering out 81/80 and 50/49 gives [[Meantone family|injera temperament]], for which 38 is the [[optimal patent val]]. In the 11-limit, we can add 121/120 and 176/175.

===38-EDO Intervals:=== 
|| **Step** || **Size in Cents** ||
|| 0 || 0 ||
|| 1 || 31.579 ||
|| 2 || 63.158 ||
|| 3 || 94.737 ||
|| 4 || 126.316 ||
|| 5 || 157.895 ||
|| 6 || 189.474 ||
|| 7 || 221.053 ||
|| 8 || 252.632 ||
|| 9 || 284.211 ||
|| 10 || 315.789 ||
|| 11 || 347.368 ||
|| 12 || 378.947 ||
|| 13 || 410.526 ||
|| 14 || 442.105 ||
|| 15 || 473.684 ||
|| 16 || 505.263 ||
|| 17 || 536.842 ||
|| 18 || 568.421 ||
|| 19 || 600 ||
|| 20 || 631.579 ||
|| 21 || 663.158 ||
|| 22 || 694.737 ||
|| 23 || 726.316 ||
|| 24 || 757.895 ||
|| 25 || 789.474 ||
|| 26 || 821.053 ||
|| 27 || 852.632 ||
|| 28 || 884.211 ||
|| 29 || 915.789 ||
|| 30 || 947.368 ||
|| 31 || 978.947 ||
|| 32 || 1010.526 ||
|| 33 || 1042.105 ||
|| 34 || 1073.684 ||
|| 35 || 1105.263 ||
|| 36 || 1136.842 ||
|| 37 || 1168.421 ||

Original HTML content:

<html><head><title>38edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x38 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="background-color: #e1e1e1; color: #008693; font-size: 110%;">38 tone equal temperament</span></h1>
 <br />
<em>38edo</em> divides the octave into 38 equal parts of 31.579 cents. Since 38 = 2*19, it can be thought of as two parallel <a class="wiki_link" href="/19edo">19edo</a>s. It tempers out the same 5-limit commas as 19, namely 81/80, 3125/3072 and 15625/15552. In the 7-limit, we can add 50/49, and tempering out 81/80 and 50/49 gives <a class="wiki_link" href="/Meantone%20family">injera temperament</a>, for which 38 is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a>. In the 11-limit, we can add 121/120 and 176/175.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x38 tone equal temperament--38-EDO Intervals:"></a><!-- ws:end:WikiTextHeadingRule:2 -->38-EDO Intervals:</h3>
 

<table class="wiki_table">
    <tr>
        <td><strong>Step</strong><br />
</td>
        <td><strong>Size in Cents</strong><br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>31.579<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>63.158<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>94.737<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>126.316<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>157.895<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>189.474<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>221.053<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>252.632<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>284.211<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>315.789<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>347.368<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>378.947<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>410.526<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>442.105<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>473.684<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>505.263<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>536.842<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>568.421<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>600<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>631.579<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>663.158<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>694.737<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>726.316<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>757.895<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>789.474<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>821.053<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>852.632<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>884.211<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>915.789<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>947.368<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>978.947<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>1010.526<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>1042.105<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>1073.684<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>1105.263<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>1136.842<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>1168.421<br />
</td>
    </tr>
</table>

</body></html>

38edo: Difference between revisions

Revision as of 18:35, 24 June 2011

IMPORTED REVISION FROM WIKISPACES

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Original HTML content:

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