37edo: Difference between revisions

Revision as of 16:14, 22 February 2011

IMPORTED REVISION FROM WIKISPACES

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This revision was by author Andrew_Heathwaite and made on 2011-02-22 16:14:17 UTC.

The original revision id was 204112484.

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Original Wikitext content:

37edo is the scale derived from dividing the octave into 37 equal steps of approximately 32.43 cents each. It offers close approximations to [[OverToneSeries|harmonics]] 5, 7, 11, and 13:

12\37 = 389.2 cents
30\37 = 973.0 cents
17\37 = 551.4 cents
26\37 = 843.2 cents

However, the just [[perfect fifth]] of frequency ratio 3:2 is not well-approximated, and falls between two intervals in 37edo:

21\37 = 681.1 cents
22\37 = 713.5 cents

37edo thus has the distinction of being the first [[edo]] which occupies two spaces on the syntonic spectrum.

21\37 generates an anti-diatonic, or mavila, scale: 5 5 6 5 5 5 6
"minor third" = 10\37 = 324.3 cents
"major third" = 11\37 = 356.8 cents

22\37 generates an extreme superpythagorean scale: 7 7 1 7 7 7 1
"minor third" = 8\37 = 259.5 cents
"major third" = 14\37 = 454.1 cents

37edo has great potential as a xenharmonic system, which high-prime chords such as 8:10:11:13:14 with no perfect fifths available for common terrestrial progressions.

==Intervals== 

|| degrees of 37edo || cents value ||
|| 0 || 0.00 ||
|| 1 || 32.43 ||
|| 2 || 64.86 ||
|| 3 || 97.30 ||
|| 4 || 129.73 ||
|| 5 || 162.16 ||
|| 6 || 194.59 ||
|| 7 || 227.03 ||
|| 8 || 259.46 ||
|| 9 || 291.89 ||
|| 10 || 324.32 ||
|| 11 || 356.76 ||
|| 12 || 389.19 ||
|| 13 || 421.62 ||
|| 14 || 454.05 ||
|| 15 || 486.49 ||
|| 16 || 518.92 ||
|| 17 || 551.35 ||
|| 18 || 583.78 ||
|| 19 || 616.22 ||
|| 20 || 648.65 ||
|| 21 || 681.08 ||
|| 22 || 713.51 ||
|| 23 || 745.95 ||
|| 24 || 778.38 ||
|| 25 || 810.81 ||
|| 26 || 843.24 ||
|| 27 || 875.68 ||
|| 28 || 908.11 ||
|| 29 || 940.54 ||
|| 30 || 972.97 ||
|| 31 || 1005.41 ||
|| 32 || 1037.84 ||
|| 33 || 1070.27 ||
|| 34 || 1102.70 ||
|| 35 || 1135.14 ||
|| 36 || 1167.57 ||

Original HTML content:

<html><head><title>37edo</title></head><body>37edo is the scale derived from dividing the octave into 37 equal steps of approximately 32.43 cents each. It offers close approximations to <a class="wiki_link" href="/OverToneSeries">harmonics</a> 5, 7, 11, and 13:<br />
<br />
12\37 = 389.2 cents<br />
30\37 = 973.0 cents<br />
17\37 = 551.4 cents<br />
26\37 = 843.2 cents<br />
<br />
However, the just <a class="wiki_link" href="/perfect%20fifth">perfect fifth</a> of frequency ratio 3:2 is not well-approximated, and falls between two intervals in 37edo:<br />
<br />
21\37 = 681.1 cents<br />
22\37 = 713.5 cents<br />
<br />
37edo thus has the distinction of being the first <a class="wiki_link" href="/edo">edo</a> which occupies two spaces on the syntonic spectrum.<br />
<br />
21\37 generates an anti-diatonic, or mavila, scale: 5 5 6 5 5 5 6<br />
&quot;minor third&quot; = 10\37 = 324.3 cents<br />
&quot;major third&quot; = 11\37 = 356.8 cents<br />
<br />
22\37 generates an extreme superpythagorean scale: 7 7 1 7 7 7 1<br />
&quot;minor third&quot; = 8\37 = 259.5 cents<br />
&quot;major third&quot; = 14\37 = 454.1 cents<br />
<br />
37edo has great potential as a xenharmonic system, which high-prime chords such as 8:10:11:13:14 with no perfect fifths available for common terrestrial progressions.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intervals</h2>
 <br />


<table class="wiki_table">
    <tr>
        <td>degrees of 37edo<br />
</td>
        <td>cents value<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0.00<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>32.43<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>64.86<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>97.30<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>129.73<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>162.16<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>194.59<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>227.03<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>259.46<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>291.89<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>324.32<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>356.76<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>389.19<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>421.62<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>454.05<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>486.49<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>518.92<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>551.35<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>583.78<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>616.22<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>648.65<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>681.08<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>713.51<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>745.95<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>778.38<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>810.81<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>843.24<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>875.68<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>908.11<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>940.54<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>972.97<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>1005.41<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>1037.84<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>1070.27<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>1102.70<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>1135.14<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>1167.57<br />
</td>
    </tr>
</table>

</body></html>

37edo: Difference between revisions

Revision as of 16:14, 22 February 2011

IMPORTED REVISION FROM WIKISPACES

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