3L 10s

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Revision as of 02:42, 5 October 2012 by Wikispaces>keenanpepper (**Imported revision 370452530 - Original comment: **)
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This revision was by author keenanpepper and made on 2012-10-05 02:42:25 UTC.
The original revision id was 370452530.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

"3L 10s" is a [[MOSScales|MOS]] scale pattern with 3 large steps and 10 small steps. Some notable temperaments that form a MOS with this pattern are [[magic]] and [[würschmidt]].

Of course, magic[13] is still slightly improper and würschmidt[13] is almost totally lopsided (L:s = 6:1 to 8:1). Even so, the excellence of magic temperament as a fit for 13 tone per octave melodic scales and its close affinity to strongly harmonic fifth temperaments make up for the roughness of the major third that 13 tone circles favor multiple times over.

|| 1\3 ||   ||   ||   ||   ||   ||   ||   ||   || 400 ||=   ||
||   ||   ||   ||   ||   ||   ||   || 11\34 ||   || 388.235 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   || 21\65 || 387.692 ||   ||
||   ||   ||   ||   ||   ||   || 10\31 ||   ||   || 387.097 ||= Würschimdt is around here ||
||   ||   ||   ||   ||   || 9\28 ||   ||   ||   || 385.714 ||=   ||
||   ||   ||   ||   || 8\25 ||   ||   ||   ||   || 384 ||=   ||
||   ||   ||   || 7\22 ||   ||   ||   ||   ||   || 381.818 ||=   ||
||   ||   ||   ||   ||   || 20\63 ||   ||   ||   || 380.952 ||=   ||
||   ||   ||   ||   ||   ||   || 33\104 ||   ||   || 380.769 ||= Optimal patent val for 11-limit magic ||
||   ||   ||   ||   || 13\41 ||   ||   ||   ||   || 380.488 ||=   ||
||   ||   ||   ||   ||   || 19\60 ||   ||   ||   || 380 ||= Optimal patent val for 5-limit magic ||
||   ||   || 6\19 ||   ||   ||   ||   ||   ||   || 378.947 ||=   ||
||   ||   ||   || 11\35 ||   ||   ||   ||   ||   || 377.143 ||=   ||
||   || 5\16 ||   ||   ||   ||   ||   ||   ||   || 375 ||= Boundary of propriety
(Smaller generators are proper) ||
||   ||   ||   || 14\45 ||   ||   ||   ||   ||   || 373.333 ||=   ||
||   ||   || 9\29 ||   ||   ||   ||   ||   ||   || 372.414 ||=   ||
||   ||   ||   || 13\42 ||   ||   ||   ||   ||   || 371.429 ||=   ||
|| 4\13 ||   ||   ||   ||   ||   ||   ||   ||   || 369.231 ||=   ||

Original HTML content:

<html><head><title>3L 10s</title></head><body>&quot;3L 10s&quot; is a <a class="wiki_link" href="/MOSScales">MOS</a> scale pattern with 3 large steps and 10 small steps. Some notable temperaments that form a MOS with this pattern are <a class="wiki_link" href="/magic">magic</a> and <a class="wiki_link" href="/w%C3%BCrschmidt">würschmidt</a>.<br />
<br />
Of course, magic[13] is still slightly improper and würschmidt[13] is almost totally lopsided (L:s = 6:1 to 8:1). Even so, the excellence of magic temperament as a fit for 13 tone per octave melodic scales and its close affinity to strongly harmonic fifth temperaments make up for the roughness of the major third that 13 tone circles favor multiple times over.<br />
<br />


<table class="wiki_table">
    <tr>
        <td>1\3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>400<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>11\34<br />
</td>
        <td><br />
</td>
        <td>388.235<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>21\65<br />
</td>
        <td>387.692<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>10\31<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>387.097<br />
</td>
        <td style="text-align: center;">Würschimdt is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>9\28<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>385.714<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>8\25<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>384<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7\22<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>381.818<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>20\63<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>380.952<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>33\104<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>380.769<br />
</td>
        <td style="text-align: center;">Optimal patent val for 11-limit magic<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>13\41<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>380.488<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>19\60<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>380<br />
</td>
        <td style="text-align: center;">Optimal patent val for 5-limit magic<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>6\19<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>378.947<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>11\35<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>377.143<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>5\16<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>375<br />
</td>
        <td style="text-align: center;">Boundary of propriety<br />
(Smaller generators are proper)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>14\45<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>373.333<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>9\29<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>372.414<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>13\42<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>371.429<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>4\13<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>369.231<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

</body></html>
Retrieved from "https://en.xen.wiki/index.php?title=3L_10s&oldid=8542"