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101edo

Revision as of 11:30, 1 August 2016 by Wikispaces>JosephRuhf (**Imported revision 588470276 - Original comment: **)

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Original Wikitext content:

**//101-EDO//** divides the [[octave]] into 101 equal parts of 11.881 [[cent]]s each. It can be used to tune the [[Schismatic family|grackle temperament]]. It is the 26th [[prime numbers|prime]] edo. The 101cd val provides an excellent tuning for [[Magic family#Witchcraft|witchcraft temperament]], falling between the 13 and 15 limit least squares tuning.

[[5-limit]] commas: 32805/32768, <5 13 -11|

[[7-limit]] commas: 126/125, 32805/32768, 2430/2401

==__Some important MOS scales:__== 

**25 13 25 25 13:** //3L2s MOS// (Pentatonic)
|| 25/101 || 297.03 ||
|| 38/101 || 451.485 ||
|| 63/101 || 748.515 ||
|| 88/101 || 1045.545 ||
**17 17 8 17 17 17 8:** //5L2s MOS// (Diatonic Pythagorean)
|| **17/101** || **201.98** ||
|| 34/101 || 403.96 ||
|| **42/101** || **499.01** ||
|| **59/101** || **700.99** ||
|| **76/101** || **902.97** ||
|| 93/101 || 1104.95 ||
**13 13 13 13 13 13 13 10:** //7L1s MOS// (Grumpy Octatonic)
|| 13/101 || 154.455 ||
|| 26/101 || 308.911 ||
|| 39/101 || 463.366 ||
|| 52/101 || 617.822 ||
|| 65/101 || 772.277 ||
|| 78/101 || 926.733 ||
|| 91/101 || 1081.188 ||
**13 13 13 5 13 13 13 13 5:** //7L2s MOS// (Superdiatonic 1/13-tone 13;5 relation)
|| **13/101** || **154.455** ||
|| **26/101** || **308.911** ||
|| 39/101 || 463.366 ||
|| **44/101** || **522.772** ||
|| **57/101** || **677.228** ||
|| **70/101** || **831.683** ||
|| **83/101** || **986.139** ||
|| 96/101 || 1045.545 ||
**10 10 7 10 10 10 7 10 10 10 7:** //8L3s MOS// (Improper Sensi-11)
|| **10/101** || **118.812** ||
|| 20/101 || 237.624 ||
|| **27/101** || **320.792** ||
|| **37/101** || **439.604** ||
|| **47/101** || **558.416** ||
|| 57/101 || 677.228 ||
|| **64/101** || **760.396** ||
|| **74/101** || **879.218** ||
|| **84/101** || **998.03** ||
|| 94/101 || 1116.842 ||
**7 7 7 8 7 7 7 7 8 7 7 7 7 8:** //3L11s MOS// (Anti-Ketradektriatoh form)

=Links= 
[[http://tech.groups.yahoo.com/group/tuning-math/message/11157|The Ellis duodene in 101-equal]]

Original HTML content:

<html><head><title>101edo</title></head><body><strong><em>101-EDO</em></strong> divides the <a class="wiki_link" href="/octave">octave</a> into 101 equal parts of 11.881 <a class="wiki_link" href="/cent">cent</a>s each. It can be used to tune the <a class="wiki_link" href="/Schismatic%20family">grackle temperament</a>. It is the 26th <a class="wiki_link" href="/prime%20numbers">prime</a> edo. The 101cd val provides an excellent tuning for <a class="wiki_link" href="/Magic%20family#Witchcraft">witchcraft temperament</a>, falling between the 13 and 15 limit least squares tuning.<br />
<br />
<a class="wiki_link" href="/5-limit">5-limit</a> commas: 32805/32768, &lt;5 13 -11|<br />
<br />
<a class="wiki_link" href="/7-limit">7-limit</a> commas: 126/125, 32805/32768, 2430/2401<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Some important MOS scales:"></a><!-- ws:end:WikiTextHeadingRule:0 --><u>Some important MOS scales:</u></h2>
 <br />
<strong>25 13 25 25 13:</strong> <em>3L2s MOS</em> (Pentatonic)<br />


<table class="wiki_table">
    <tr>
        <td>25/101<br />
</td>
        <td>297.03<br />
</td>
    </tr>
    <tr>
        <td>38/101<br />
</td>
        <td>451.485<br />
</td>
    </tr>
    <tr>
        <td>63/101<br />
</td>
        <td>748.515<br />
</td>
    </tr>
    <tr>
        <td>88/101<br />
</td>
        <td>1045.545<br />
</td>
    </tr>
</table>

<strong>17 17 8 17 17 17 8:</strong> <em>5L2s MOS</em> (Diatonic Pythagorean)<br />


<table class="wiki_table">
    <tr>
        <td><strong>17/101</strong><br />
</td>
        <td><strong>201.98</strong><br />
</td>
    </tr>
    <tr>
        <td>34/101<br />
</td>
        <td>403.96<br />
</td>
    </tr>
    <tr>
        <td><strong>42/101</strong><br />
</td>
        <td><strong>499.01</strong><br />
</td>
    </tr>
    <tr>
        <td><strong>59/101</strong><br />
</td>
        <td><strong>700.99</strong><br />
</td>
    </tr>
    <tr>
        <td><strong>76/101</strong><br />
</td>
        <td><strong>902.97</strong><br />
</td>
    </tr>
    <tr>
        <td>93/101<br />
</td>
        <td>1104.95<br />
</td>
    </tr>
</table>

<strong>13 13 13 13 13 13 13 10:</strong> <em>7L1s MOS</em> (Grumpy Octatonic)<br />


<table class="wiki_table">
    <tr>
        <td>13/101<br />
</td>
        <td>154.455<br />
</td>
    </tr>
    <tr>
        <td>26/101<br />
</td>
        <td>308.911<br />
</td>
    </tr>
    <tr>
        <td>39/101<br />
</td>
        <td>463.366<br />
</td>
    </tr>
    <tr>
        <td>52/101<br />
</td>
        <td>617.822<br />
</td>
    </tr>
    <tr>
        <td>65/101<br />
</td>
        <td>772.277<br />
</td>
    </tr>
    <tr>
        <td>78/101<br />
</td>
        <td>926.733<br />
</td>
    </tr>
    <tr>
        <td>91/101<br />
</td>
        <td>1081.188<br />
</td>
    </tr>
</table>

<strong>13 13 13 5 13 13 13 13 5:</strong> <em>7L2s MOS</em> (Superdiatonic 1/13-tone 13;5 relation)<br />


<table class="wiki_table">
    <tr>
        <td><strong>13/101</strong><br />
</td>
        <td><strong>154.455</strong><br />
</td>
    </tr>
    <tr>
        <td><strong>26/101</strong><br />
</td>
        <td><strong>308.911</strong><br />
</td>
    </tr>
    <tr>
        <td>39/101<br />
</td>
        <td>463.366<br />
</td>
    </tr>
    <tr>
        <td><strong>44/101</strong><br />
</td>
        <td><strong>522.772</strong><br />
</td>
    </tr>
    <tr>
        <td><strong>57/101</strong><br />
</td>
        <td><strong>677.228</strong><br />
</td>
    </tr>
    <tr>
        <td><strong>70/101</strong><br />
</td>
        <td><strong>831.683</strong><br />
</td>
    </tr>
    <tr>
        <td><strong>83/101</strong><br />
</td>
        <td><strong>986.139</strong><br />
</td>
    </tr>
    <tr>
        <td>96/101<br />
</td>
        <td>1045.545<br />
</td>
    </tr>
</table>

<strong>10 10 7 10 10 10 7 10 10 10 7:</strong> <em>8L3s MOS</em> (Improper Sensi-11)<br />


<table class="wiki_table">
    <tr>
        <td><strong>10/101</strong><br />
</td>
        <td><strong>118.812</strong><br />
</td>
    </tr>
    <tr>
        <td>20/101<br />
</td>
        <td>237.624<br />
</td>
    </tr>
    <tr>
        <td><strong>27/101</strong><br />
</td>
        <td><strong>320.792</strong><br />
</td>
    </tr>
    <tr>
        <td><strong>37/101</strong><br />
</td>
        <td><strong>439.604</strong><br />
</td>
    </tr>
    <tr>
        <td><strong>47/101</strong><br />
</td>
        <td><strong>558.416</strong><br />
</td>
    </tr>
    <tr>
        <td>57/101<br />
</td>
        <td>677.228<br />
</td>
    </tr>
    <tr>
        <td><strong>64/101</strong><br />
</td>
        <td><strong>760.396</strong><br />
</td>
    </tr>
    <tr>
        <td><strong>74/101</strong><br />
</td>
        <td><strong>879.218</strong><br />
</td>
    </tr>
    <tr>
        <td><strong>84/101</strong><br />
</td>
        <td><strong>998.03</strong><br />
</td>
    </tr>
    <tr>
        <td>94/101<br />
</td>
        <td>1116.842<br />
</td>
    </tr>
</table>

<strong>7 7 7 8 7 7 7 7 8 7 7 7 7 8:</strong> <em>3L11s MOS</em> (Anti-Ketradektriatoh form)<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:2 -->Links</h1>
 <a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/11157" rel="nofollow">The Ellis duodene in 101-equal</a></body></html>
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