3L 10s: Difference between revisions

Revision as of 20:03, 23 May 2015

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author JosephRuhf and made on 2015-05-23 20:03:58 UTC.

The original revision id was 551981980.

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 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   || 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 ||   ||
||   ||   ||   || 11\35 ||   ||   ||   ||   ||   ||   || 377.143 ||=   ||
||   || 5\16 ||   ||   ||   ||   ||   ||   ||   ||   || 375 ||= Boundary of propriety
(Smaller generators are proper) ||
||   ||   ||   || 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 ||   ||
||   ||   || 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 ||   || 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>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>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>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>370.0935<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>

</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-12 11:55:46 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-23 20:03:58 UTC</tt>.<br>
-: The original revision id was <tt>540767670</tt>.<br>
+: The original revision id was <tt>551981980</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 26: / Line 26: @@
 ||   ||   ||   ||   || 13\41 ||   ||   ||   ||   ||   || 380.488 ||= Optimal patent val for 13-limit magic ||
 ||   ||   ||   ||   ||   || 19\60 ||   ||   ||   ||   || 380 ||= Optimal patent val for 5-limit magic ||
-||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 379.040 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 379.408 ||   ||
 ||   ||   || 6\19 ||   ||   ||   ||   ||   ||   ||   || 378.947 ||=   ||
-||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 378.855 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 377.967 ||   ||
 ||   ||   ||   || 11\35 ||   ||   ||   ||   ||   ||   || 377.143 ||=   ||
 ||   || 5\16 ||   ||   ||   ||   ||   ||   ||   ||   || 375 ||= Boundary of propriety
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          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;379.040&lt;br /&gt;
+         &lt;td&gt;379.408&lt;br /&gt;
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          &lt;td&gt;&lt;br /&gt;
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          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;378.855&lt;br /&gt;
+         &lt;td&gt;377.967&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;

3L 10s: Difference between revisions

Revision as of 20:03, 23 May 2015

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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