3L 10s

Revision as of 16:23, 11 November 2015 by Wikispaces>JosephRuhf (**Imported revision 566098373 - Original comment: **)

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This revision was by author JosephRuhf and made on 2015-11-11 16:23:21 UTC.
The original revision id was 566098373.
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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 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   || 13\40 || 390 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   || 12\37 ||   || 389.189 ||   ||
||   ||   ||   ||   ||   ||   ||   || 11\34 ||   ||   || 388.235 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   || 32\99 || 387.879 ||= Whirrschmidt ||
||   ||   ||   ||   ||   ||   ||   ||   || 21\65 ||   || 387.692 ||= Worschmidt ||
||   ||   ||   ||   ||   ||   ||   ||   ||   || 31\96 || 387.5 ||= Würschimdt ||
||   ||   ||   ||   ||   ||   || 10\31 ||   ||   ||   || 387.097 ||= Würschimdt ||
||   ||   ||   ||   ||   ||   ||   || 19\59 ||   ||   || 386.441 ||= Sulis ||
||   ||   ||   ||   ||   || 9\28 ||   ||   ||   ||   || 385.714 ||=   ||
||   ||   ||   ||   || 8\25 ||   ||   ||   ||   ||   || 384 ||= Marveltri ||
||   ||   ||   || 7\22 ||   ||   ||   ||   ||   ||   || 381.818 ||= Sorcery ||
||   ||   ||   ||   ||   || 20\63 ||   ||   ||   ||   || 380.952 ||=   ||
||   ||   ||   ||   ||   ||   || 33\104 ||   ||   ||   || 380.769 ||= Optimal patent val for 11-limit magic ||
||   ||   ||   ||   || 13\41 ||   ||   ||   ||   ||   || 380.488 ||= Optimal patent val for 13-limit magic ||
||   ||   ||   ||   ||   || 19\60 ||   ||   ||   ||   || 380 ||= Optimal patent val for 5-limit magic ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 379.408 ||   ||
||   ||   || 6\19 ||   ||   ||   ||   ||   ||   ||   || 378.947 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 377.967 ||   ||
||   ||   ||   ||   || 17\54 ||   ||   ||   ||   ||   || 377.778 ||   ||
||   ||   ||   ||   ||   ||   || 45\143 ||   ||   ||   || 377.622 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   || 118\375 ||   || 377.6 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   || 191\607 || 377.595 ||   ||
||   ||   ||   ||   ||   ||   ||   || 73\232 ||   ||   || 377.586 ||   ||
||   ||   ||   ||   ||   || 28\89 ||   ||   ||   ||   || 377.528 ||   ||
||   ||   ||   || 11\35 ||   ||   ||   ||   ||   ||   || 377.143 ||=   ||
||   || 5\16 ||   ||   ||   ||   ||   ||   ||   ||   || 375 ||= Boundary of propriety
(Smaller generators are proper) ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 373.6775 ||   ||
||   ||   ||   || 14\45 ||   ||   ||   ||   ||   ||   || 373.333 ||=   ||
||   ||   ||   ||   ||   || 37\119 ||   ||   ||   ||   || 373.109 ||   ||
||   ||   ||   ||   ||   ||   ||   || 97\312 ||   ||   || 373.077 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   || 254\817 || 373.072 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   || 157\505 ||   || 373.069 ||   ||
||   ||   ||   ||   ||   ||   || 60/193 ||   ||   ||   || 373.057 ||   ||
||   ||   ||   ||   || 23\74 ||   ||   ||   ||   ||   || 372.973 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 372.812 ||   ||
||   ||   || 9\29 ||   ||   ||   ||   ||   ||   ||   || 372.414 ||=   ||
||   ||   ||   || 13\42 ||   ||   ||   ||   ||   ||   || 371.429 ||=   ||
||   ||   ||   ||   || 17\55 ||   ||   ||   ||   ||   || 370.909 ||   ||
||   ||   ||   ||   ||   || 21\68 ||   ||   ||   ||   || 370.588 ||   ||
||   ||   ||   ||   ||   ||   || 25\81 ||   ||   ||   || 370.37 ||   ||
||   ||   ||   ||   ||   ||   ||   || 29\94 ||   ||   || 370.213 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   || 33\107 ||   || [[tel/370.0935|370.0935]] ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   || 37\120 || 370 ||   ||
|| 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><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><br />
</td>
        <td><br />
</td>
        <td>13\40<br />
</td>
        <td>390<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><br />
</td>
        <td><br />
</td>
        <td>12\37<br />
</td>
        <td><br />
</td>
        <td>389.189<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><br />
</td>
        <td>11\34<br />
</td>
        <td><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><br />
</td>
        <td>32\99<br />
</td>
        <td>387.879<br />
</td>
        <td style="text-align: center;">Whirrschmidt<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><br />
</td>
        <td>387.692<br />
</td>
        <td style="text-align: center;">Worschmidt<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><br />
</td>
        <td>31\96<br />
</td>
        <td>387.5<br />
</td>
        <td style="text-align: center;">Würschimdt<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><br />
</td>
        <td>387.097<br />
</td>
        <td style="text-align: center;">Würschimdt<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>19\59<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>386.441<br />
</td>
        <td style="text-align: center;">Sulis<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><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><br />
</td>
        <td>384<br />
</td>
        <td style="text-align: center;">Marveltri<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><br />
</td>
        <td>381.818<br />
</td>
        <td style="text-align: center;">Sorcery<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><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><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><br />
</td>
        <td>380.488<br />
</td>
        <td style="text-align: center;">Optimal patent val for 13-limit magic<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><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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>379.408<br />
</td>
        <td><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><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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>377.967<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>17\54<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>377.778<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>45\143<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>377.622<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><br />
</td>
        <td><br />
</td>
        <td>118\375<br />
</td>
        <td><br />
</td>
        <td>377.6<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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>191\607<br />
</td>
        <td>377.595<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><br />
</td>
        <td>73\232<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>377.586<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>28\89<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>377.528<br />
</td>
        <td><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><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><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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>373.6775<br />
</td>
        <td><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><br />
</td>
        <td>373.333<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>37\119<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>373.109<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><br />
</td>
        <td>97\312<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>373.077<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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>254\817<br />
</td>
        <td>373.072<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><br />
</td>
        <td><br />
</td>
        <td>157\505<br />
</td>
        <td><br />
</td>
        <td>373.069<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>60/193<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>373.057<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>23\74<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>372.973<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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>372.812<br />
</td>
        <td><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><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><br />
</td>
        <td>371.429<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>17\55<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>370.909<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>21\68<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>370.588<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>25\81<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>370.37<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><br />
</td>
        <td>29\94<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>370.213<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><br />
</td>
        <td><br />
</td>
        <td>33\107<br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/370.0935">370.0935</a><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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>37\120<br />
</td>
        <td>370<br />
</td>
        <td><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><br />
</td>
        <td>369.231<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

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