43edt: Difference between revisions

Revision as of 10:18, 15 December 2016

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This revision was by author JosephRuhf and made on 2016-12-15 10:18:35 UTC.

The original revision id was 602234052.

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Original Wikitext content:

=43 EDT= 

This tuning is related to [[27edo]] having compressed octaves of 1194.251 cents, a small but significant deviation. This is particularly relevant because 27edo is a "sharp tending" system, and flattening its octaves has been suggested before as an improvement (I think by no less than Ivor Darreg, but I'll have to check that).

However, in addition to its rich octave-based harmony, the 43edt is also a fine tritave-based tuning: with a 7/3 of 1460 cents and such a near perfect 5/3, Bohlen-Pierce harmony is very clear and hearty, as well as capable of extended enharmonic distinctions that [[13edt]] is not. The 4L+5s MOS has L=7 s=3.

||~ Degrees ||~ Cents ||
|| 1 || 44.2315 ||
|| 2 || 88.463 ||
|| 3 || 132.6945/1 ||
|| 4 || 176.926 ||
|| 5 || 221.158 ||
|| 6 || 265.389 ||
|| 7 || 309.621 ||
|| 8 || 353.852 ||
|| 9 || 398.084 ||
|| 10 || 442.315 ||
|| 11 || 486.547 ||
|| 12 || 530.778 ||
|| 13 || 575.01 ||
|| 14 || 619.241 ||
|| 15 || 663.473 ||
|| 16 || 707.704 ||
|| 17 || 751.936 ||
|| 18 || 796.167 ||
|| 19 || 840.399 ||
|| 20 || 884.63 ||
|| 21 || 928.862 ||
|| 22 || 973.093 ||
|| 23 || 1017.325 ||
|| 24 || 1061.556 ||
|| 25 || 1105.788 ||
|| 26 || 1150.019 ||
|| 27 || 1194.251 ||
|| 28 || 1238.482 ||
|| 29 || 1282.713 ||
|| 30 || 1326.946 ||
|| 31 || 1371.177 ||
|| 32 || 1415.408 ||
|| 33 || 1459.64 ||
|| 34 || 1503.871 ||
|| 35 || 1548.193 ||
|| 36 || 1592.334 ||
|| 37 || 1636.566 ||
|| 38 || 1680.797 ||
|| 39 || 1725.029 ||
|| 40 || 1769.2605 ||
|| 41 || 1813.492 ||
|| 42 || 1857.7235 ||
|| 43 || 1901.955 ||

Original HTML content:

<html><head><title>43edt</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x43 EDT"></a><!-- ws:end:WikiTextHeadingRule:0 -->43 EDT</h1>
 <br />
This tuning is related to <a class="wiki_link" href="/27edo">27edo</a> having compressed octaves of 1194.251 cents, a small but significant deviation. This is particularly relevant because 27edo is a &quot;sharp tending&quot; system, and flattening its octaves has been suggested before as an improvement (I think by no less than Ivor Darreg, but I'll have to check that).<br />
<br />
However, in addition to its rich octave-based harmony, the 43edt is also a fine tritave-based tuning: with a 7/3 of 1460 cents and such a near perfect 5/3, Bohlen-Pierce harmony is very clear and hearty, as well as capable of extended enharmonic distinctions that <a class="wiki_link" href="/13edt">13edt</a> is not. The 4L+5s MOS has L=7 s=3.<br />
<br />


<table class="wiki_table">
    <tr>
        <th>Degrees<br />
</th>
        <th>Cents<br />
</th>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>44.2315<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>88.463<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>132.6945/1<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>176.926<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>221.158<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>265.389<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>309.621<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>353.852<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>398.084<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>442.315<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>486.547<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>530.778<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>575.01<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>619.241<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>663.473<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>707.704<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>751.936<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>796.167<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>840.399<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>884.63<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>928.862<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>973.093<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>1017.325<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>1061.556<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>1105.788<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>1150.019<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>1194.251<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>1238.482<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>1282.713<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>1326.946<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>1371.177<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>1415.408<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>1459.64<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>1503.871<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>1548.193<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>1592.334<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>1636.566<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>1680.797<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>1725.029<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>1769.2605<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>1813.492<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>1857.7235<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>1901.955<br />
</td>
    </tr>
</table>

</body></html>

43edt: Difference between revisions

Revision as of 10:18, 15 December 2016

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