Augene: Difference between revisions

Revision as of 17:40, 15 August 2014

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This revision was by author genewardsmith and made on 2014-08-15 17:40:36 UTC.

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Augene is a regular temperament of the [[augmented family#x-Augene]], which means that 128/125 is tempered out and three 5/4s make a 2/1. Augene is distinguished from its relative [[august]] by tempering out 64/63, which means that tunings in which the fifth is larger than 7\12 (700 cents) are optimal. Therefore the MOS sequence of augene goes 12, 15, 27... in constrast to august's which goes 9, 12, 21...

The first few augene MOSes are [[3L 3s]], [[3L 6s]], [[3L 9s]], [[12L 3s]]... and the first EDOs that reasonably support augene are [[12edo]], [[15edo]], and especially [[27edo]].

=Spectrum of Augene Tunings by Eigenmonzos= 
||~ Eigenmonzo ||~ Fifth ||
|| 14/13 || 671.702 ||
|| 12\28 || 685.714 ||
|| 16/15 || 688.269 ||
|| 13/11 || 689.210 ||
|| 7\12 || 700.000 ||
|| 31\53 || 701.887 ||
|| 4/3 || 701.955 ||
|| 30\51 || 705.882 ||
|| 15/14 || 706.481 ||
|| 23\39 || 707.692 ||
|| 7/5 || 708.744 ||
|| 9/7 || 708.771 ||
|| 10/9 || 708.798 (9 limit minimax) ||
|| 39\66 || 709.091 ||
|| 7/6 || 711.043 ||
|| 16\27 || 711.111 ||
|| 15/11 || 712.317 ||
|| 11/9 || 713.148 (11 limit minimax) ||
|| 25\42 || 714.286 ||
|| 8/7 || 715.587 (7, 13 and 15 limit minimax) ||
|| 34\57 || 715.789 ||
|| 6/5 || 715.641 (5 limit minimax) ||
|| 25\72 || 716.667 ||
|| 12/11 || 716.879 ||
|| 11/10 || 717.498 ||
|| 9\15 || 720.000 ||
|| 18/13 || 721.127 ||
|| 15/13 || 723.871 ||
|| 11/8 || 724.341 ||
|| 13/12 || 730.714 ||
|| 13/10 || 745.786 ||
|| 16/13 || 759.472 ||

=Music= 
//[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3|Sad Like Winter Leaves]]// by [[http://soundcloud.com/cityoftheasleep/sad-like-winter-trees|Igliashon Jones]] in Augene[12] tuned to 27edo
//[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3|Galticeran Sonatina]]// by [[http://soundcloud.com/joelgranttaylor/galticeran_sonatina|Joel Grant Taylor]] in Augene[12] tuned to 27edo

Original HTML content:

<html><head><title>Augene</title></head><body>Augene is a regular temperament of the <a class="wiki_link" href="/augmented%20family#x-Augene">augmented family</a>, which means that 128/125 is tempered out and three 5/4s make a 2/1. Augene is distinguished from its relative <a class="wiki_link" href="/august">august</a> by tempering out 64/63, which means that tunings in which the fifth is larger than 7\12 (700 cents) are optimal. Therefore the MOS sequence of augene goes 12, 15, 27... in constrast to august's which goes 9, 12, 21...<br />
<br />
The first few augene MOSes are <a class="wiki_link" href="/3L%203s">3L 3s</a>, <a class="wiki_link" href="/3L%206s">3L 6s</a>, <a class="wiki_link" href="/3L%209s">3L 9s</a>, <a class="wiki_link" href="/12L%203s">12L 3s</a>... and the first EDOs that reasonably support augene are <a class="wiki_link" href="/12edo">12edo</a>, <a class="wiki_link" href="/15edo">15edo</a>, and especially <a class="wiki_link" href="/27edo">27edo</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Spectrum of Augene Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:0 -->Spectrum of Augene Tunings by Eigenmonzos</h1>
 

<table class="wiki_table">
    <tr>
        <th>Eigenmonzo<br />
</th>
        <th>Fifth<br />
</th>
    </tr>
    <tr>
        <td>14/13<br />
</td>
        <td>671.702<br />
</td>
    </tr>
    <tr>
        <td>12\28<br />
</td>
        <td>685.714<br />
</td>
    </tr>
    <tr>
        <td>16/15<br />
</td>
        <td>688.269<br />
</td>
    </tr>
    <tr>
        <td>13/11<br />
</td>
        <td>689.210<br />
</td>
    </tr>
    <tr>
        <td>7\12<br />
</td>
        <td>700.000<br />
</td>
    </tr>
    <tr>
        <td>31\53<br />
</td>
        <td>701.887<br />
</td>
    </tr>
    <tr>
        <td>4/3<br />
</td>
        <td>701.955<br />
</td>
    </tr>
    <tr>
        <td>30\51<br />
</td>
        <td>705.882<br />
</td>
    </tr>
    <tr>
        <td>15/14<br />
</td>
        <td>706.481<br />
</td>
    </tr>
    <tr>
        <td>23\39<br />
</td>
        <td>707.692<br />
</td>
    </tr>
    <tr>
        <td>7/5<br />
</td>
        <td>708.744<br />
</td>
    </tr>
    <tr>
        <td>9/7<br />
</td>
        <td>708.771<br />
</td>
    </tr>
    <tr>
        <td>10/9<br />
</td>
        <td>708.798 (9 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>39\66<br />
</td>
        <td>709.091<br />
</td>
    </tr>
    <tr>
        <td>7/6<br />
</td>
        <td>711.043<br />
</td>
    </tr>
    <tr>
        <td>16\27<br />
</td>
        <td>711.111<br />
</td>
    </tr>
    <tr>
        <td>15/11<br />
</td>
        <td>712.317<br />
</td>
    </tr>
    <tr>
        <td>11/9<br />
</td>
        <td>713.148 (11 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>25\42<br />
</td>
        <td>714.286<br />
</td>
    </tr>
    <tr>
        <td>8/7<br />
</td>
        <td>715.587 (7, 13 and 15 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>34\57<br />
</td>
        <td>715.789<br />
</td>
    </tr>
    <tr>
        <td>6/5<br />
</td>
        <td>715.641 (5 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>25\72<br />
</td>
        <td>716.667<br />
</td>
    </tr>
    <tr>
        <td>12/11<br />
</td>
        <td>716.879<br />
</td>
    </tr>
    <tr>
        <td>11/10<br />
</td>
        <td>717.498<br />
</td>
    </tr>
    <tr>
        <td>9\15<br />
</td>
        <td>720.000<br />
</td>
    </tr>
    <tr>
        <td>18/13<br />
</td>
        <td>721.127<br />
</td>
    </tr>
    <tr>
        <td>15/13<br />
</td>
        <td>723.871<br />
</td>
    </tr>
    <tr>
        <td>11/8<br />
</td>
        <td>724.341<br />
</td>
    </tr>
    <tr>
        <td>13/12<br />
</td>
        <td>730.714<br />
</td>
    </tr>
    <tr>
        <td>13/10<br />
</td>
        <td>745.786<br />
</td>
    </tr>
    <tr>
        <td>16/13<br />
</td>
        <td>759.472<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:2 -->Music</h1>
 <em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3" rel="nofollow">Sad Like Winter Leaves</a></em> by <a class="wiki_link_ext" href="http://soundcloud.com/cityoftheasleep/sad-like-winter-trees" rel="nofollow">Igliashon Jones</a> in Augene[12] tuned to 27edo<br />
<em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3" rel="nofollow">Galticeran Sonatina</a></em> by <a class="wiki_link_ext" href="http://soundcloud.com/joelgranttaylor/galticeran_sonatina" rel="nofollow">Joel Grant Taylor</a> in Augene[12] tuned to 27edo</body></html>

Augene: Difference between revisions

Revision as of 17:40, 15 August 2014

IMPORTED REVISION FROM WIKISPACES

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