Xenharmonic Wiki

46edo

Revision as of 14:49, 11 February 2011 by Wikispaces>Andrew_Heathwaite (**Imported revision 200994036 - Original comment: **)

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=<span style="color: #300094; font-size: 111%;">46 tone equal temperament</span>= 

The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the octave into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 cents, an interval close in size to 66/65, the interval from 13/11 to 6/5.

46et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. Rank two temperaments it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The 11-limit [[Target tunings|minimax]] tuning for [[Starling family|valentine temperament]], (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the 13-limit, though others award that distinction to [[41edo]].

The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the just fifth and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.

46edo can be treated as two [[23edo]]'s separated by an interval of 26.09 cents.

==46edo srutis== 
[[Magic22 as srutis#shrutar22assrutis|Shrutar22 as srutis]] describes a possible use of 46edo for [[Indian]] music.

==Intervals== 
|| degrees of 46edo || cents value ||
|| 0 || 0.00 ||
|| 1 || 26.09 ||
|| 2 || 52.17 ||
|| 3 || 78.26 ||
|| 4 || 104.35 ||
|| 5 || 130.43 ||
|| 6 || 156.52 ||
|| 7 || 182.61 ||
|| 8 || 208.70 ||
|| 9 || 234.78 ||
|| 10 || 260.87 ||
|| 11 || 286.96 ||
|| 12 || 313.04 ||
|| 13 || 339.13 ||
|| 14 || 365.22 ||
|| 15 || 391.30 ||
|| 16 || 417.39 ||
|| 17 || 443.48 ||
|| 18 || 469.57 ||
|| 19 || 495.65 ||
|| 20 || 521.74 ||
|| 21 || 547.83 ||
|| 22 || 573.91 ||
|| 23 || 600.00 ||
|| 24 || 626.09 ||
|| 25 || 652.17 ||
|| 26 || 628.26 ||
|| 27 || 704.35 ||
|| 28 || 730.43 ||
|| 29 || 756.52 ||
|| 30 || 782.61 ||
|| 31 || 808.70 ||
|| 32 || 834.78 ||
|| 33 || 860.87 ||
|| 34 || 886.96 ||
|| 35 || 913.04 ||
|| 36 || 939.13 ||
|| 37 || 965.22 ||
|| 38 || 991.30 ||
|| 39 || 1017.39 ||
|| 40 || 1043.48 ||
|| 41 || 1069.56 ||
|| 42 || 1095.65 ||
|| 43 || 1121.74 ||
|| 44 || 1147.83 ||
|| 45 || 1173.91 ||


==Music== 
[[http://www.archive.org/details/Chromosounds|Chromosounds]]
[[http://www.archive.org/details/MusicForYourEars|Music For Your Ears]]

Original HTML content:

<html><head><title>46edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x46 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #300094; font-size: 111%;">46 tone equal temperament</span></h1>
 <br />
The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the octave into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 cents, an interval close in size to 66/65, the interval from 13/11 to 6/5.<br />
<br />
46et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. Rank two temperaments it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The 11-limit <a class="wiki_link" href="/Target%20tunings">minimax</a> tuning for <a class="wiki_link" href="/Starling%20family">valentine temperament</a>, (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the 13-limit, though others award that distinction to <a class="wiki_link" href="/41edo">41edo</a>.<br />
<br />
The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the just fifth and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.<br />
<br />
46edo can be treated as two <a class="wiki_link" href="/23edo">23edo</a>'s separated by an interval of 26.09 cents.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x46 tone equal temperament-46edo srutis"></a><!-- ws:end:WikiTextHeadingRule:2 -->46edo srutis</h2>
 <a class="wiki_link" href="/Magic22%20as%20srutis#shrutar22assrutis">Shrutar22 as srutis</a> describes a possible use of 46edo for <a class="wiki_link" href="/Indian">Indian</a> music.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x46 tone equal temperament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h2>
 

<table class="wiki_table">
    <tr>
        <td>degrees of 46edo<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>26.09<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>52.17<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>78.26<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>104.35<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>130.43<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>156.52<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>182.61<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>208.70<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>234.78<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>260.87<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>286.96<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>313.04<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>339.13<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>365.22<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>391.30<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>417.39<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>443.48<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>469.57<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>495.65<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>521.74<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>547.83<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>573.91<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>600.00<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>626.09<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>652.17<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>628.26<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>704.35<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>730.43<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>756.52<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>782.61<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>808.70<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>834.78<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>860.87<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>886.96<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>913.04<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>939.13<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>965.22<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>991.30<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>1017.39<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>1043.48<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>1069.56<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>1095.65<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>1121.74<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>1147.83<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>1173.91<br />
</td>
    </tr>
</table>

<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x46 tone equal temperament-Music"></a><!-- ws:end:WikiTextHeadingRule:6 -->Music</h2>
 <a class="wiki_link_ext" href="http://www.archive.org/details/Chromosounds" rel="nofollow">Chromosounds</a><br />
<a class="wiki_link_ext" href="http://www.archive.org/details/MusicForYourEars" rel="nofollow">Music For Your Ears</a></body></html>
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