21edt: Difference between revisions

Revision as of 14:31, 16 August 2011

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This revision was by author Sarzadoce and made on 2011-08-16 14:31:35 UTC.

The original revision id was 246279673.

The revision comment was:

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Original Wikitext content:

=21 Equal Divisions of the Tritave= 

|| Degrees || Cents || Approximate Ratio ||
|| 0 || 0 || [[1_1|1/1]] ||
|| 1 || 90.569 || [[21_20|21/20]], [[135_128|135/128]] ||
|| 2 || 181.139 || [[10_9|10/9]] ||
|| 3 || 271.708 || [[7_6|7/6]] ||
|| 4 || 362.277 || [[16_13|16/13]] ||
|| 5 || 452.846 || [[13_10|13/10]] ||
|| 6 || 543.416 || [[15_11|15/11]], [[11_8|11/8]] ||
|| 7 || 633.985 || [[13_9|13/9]] ||
|| 8 || 724.554 || 35/23 ||
|| 9 || 815.124 || [[8_5|8/5]] ||
|| 10 || 905.693 || 27/16 ||
|| 11 || 996.262 || 16/9 ||
|| 12 || 1086.831 || [[15_8|15/8]] ||
|| 13 || 1177.401 || 69/35 ||
|| 14 || 1267.970 || 27/13 ||
|| 15 || 1358.539 || 11/5 ([[11_10|11/10]] plus an octave) ||
|| 16 || 1449.109 || 30/13 ([[15_13|15/13]] plus an octave) ||
|| 17 || 1539.678 || 39/16 ||
|| 18 || 1630.247 || 18/7 ([[9_7|9/7]] plus an octave) ||
|| 19 || 1720.816 || 27/10 ||
|| 20 || 1811.386 || 20/7 ||
|| 21 || 1901.955 || 3/1 ||


21edt contains 6 intervals from [[7edt]] and 2 intervals from [[3edt]], meaning that it introduces 12 new intervals not available in lower edt's. These new intervals allow for construction of strange chords like 9:10:13:16:22:27:30...

21edt contains a 7L7s MOS similar to Whitewood, which I call Ivory. It has a period of 1/7 of the tritave and the generator is one step. The major scale is LsLsLsLsLsLsLs, and the minor scale is sLsLsLsLsLsLsL.


21edt also contains a 4L5s MOS similar to [[BP]], with a 4:1 ratio of large to small; quite exaggerated from the optimal 2:1. Not the best approximations but all within 20 cents, it has 5th (+20c), 7th(-16c), 10th (+2c), 11th (+15c), 13th (-3c), 17th (-14c), 19th (-24 c), 23rd (+6 c), and 37th (-2c) harmonics. For a lower division of the tritave that's quite a constellation! The chord is a little out of tune but it works, you can really sink into it.

Original HTML content:

<html><head><title>21edt</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x21 Equal Divisions of the Tritave"></a><!-- ws:end:WikiTextHeadingRule:0 -->21 Equal Divisions of the Tritave</h1>
 <br />


<table class="wiki_table">
    <tr>
        <td>Degrees<br />
</td>
        <td>Cents<br />
</td>
        <td>Approximate Ratio<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
</td>
        <td><a class="wiki_link" href="/1_1">1/1</a><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>90.569<br />
</td>
        <td><a class="wiki_link" href="/21_20">21/20</a>, <a class="wiki_link" href="/135_128">135/128</a><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>181.139<br />
</td>
        <td><a class="wiki_link" href="/10_9">10/9</a><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>271.708<br />
</td>
        <td><a class="wiki_link" href="/7_6">7/6</a><br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>362.277<br />
</td>
        <td><a class="wiki_link" href="/16_13">16/13</a><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>452.846<br />
</td>
        <td><a class="wiki_link" href="/13_10">13/10</a><br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>543.416<br />
</td>
        <td><a class="wiki_link" href="/15_11">15/11</a>, <a class="wiki_link" href="/11_8">11/8</a><br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>633.985<br />
</td>
        <td><a class="wiki_link" href="/13_9">13/9</a><br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>724.554<br />
</td>
        <td>35/23<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>815.124<br />
</td>
        <td><a class="wiki_link" href="/8_5">8/5</a><br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>905.693<br />
</td>
        <td>27/16<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>996.262<br />
</td>
        <td>16/9<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>1086.831<br />
</td>
        <td><a class="wiki_link" href="/15_8">15/8</a><br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>1177.401<br />
</td>
        <td>69/35<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>1267.970<br />
</td>
        <td>27/13<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>1358.539<br />
</td>
        <td>11/5 (<a class="wiki_link" href="/11_10">11/10</a> plus an octave)<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>1449.109<br />
</td>
        <td>30/13 (<a class="wiki_link" href="/15_13">15/13</a> plus an octave)<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>1539.678<br />
</td>
        <td>39/16<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>1630.247<br />
</td>
        <td>18/7 (<a class="wiki_link" href="/9_7">9/7</a> plus an octave)<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>1720.816<br />
</td>
        <td>27/10<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>1811.386<br />
</td>
        <td>20/7<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>1901.955<br />
</td>
        <td>3/1<br />
</td>
    </tr>
</table>

<br />
<br />
21edt contains 6 intervals from <a class="wiki_link" href="/7edt">7edt</a> and 2 intervals from <a class="wiki_link" href="/3edt">3edt</a>, meaning that it introduces 12 new intervals not available in lower edt's. These new intervals allow for construction of strange chords like 9:10:13:16:22:27:30...<br />
<br />
21edt contains a 7L7s MOS similar to Whitewood, which I call Ivory. It has a period of 1/7 of the tritave and the generator is one step. The major scale is LsLsLsLsLsLsLs, and the minor scale is sLsLsLsLsLsLsL.<br />
<br />
<br />
21edt also contains a 4L5s MOS similar to <a class="wiki_link" href="/BP">BP</a>, with a 4:1 ratio of large to small; quite exaggerated from the optimal 2:1. Not the best approximations but all within 20 cents, it has 5th (+20c), 7th(-16c), 10th (+2c), 11th (+15c), 13th (-3c), 17th (-14c), 19th (-24 c), 23rd (+6 c), and 37th (-2c) harmonics. For a lower division of the tritave that's quite a constellation! The chord is a little out of tune but it works, you can really sink into it.</body></html>

21edt: Difference between revisions

Revision as of 14:31, 16 August 2011

IMPORTED REVISION FROM WIKISPACES

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