3L 4s

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author keenanpepper and made on 2011-04-25 05:07:08 UTC.

The original revision id was 222633306.

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 4s - "mosh"= 

MOS scales of this form are built from a generator that falls between 1\3 (one degree of [[3edo]] - 400 cents) and 2\7 (two degrees of [[7edo]] - 343 cents.

It has the form s L s L s L s and its various "modes" (with nicknames coined by [[Andrew Heathwaite]]) are:

|| s L s L s L s || bish ||
|| L s L s L s s || dril ||
|| s L s L s s L || fish ||
|| L s L s s L s || gil ||
|| s L s s L s L || jwl ||
|| L s s L s L s || kleeth ||
|| s s L s L s L || led ||
The two notable harmonic entropy minima with this pattern are neutral third scales ("dicot" / "hemififth" / "mohajira") where two generators make a 3/2, and [[Magic family|magic]], where the generator is a 5/4 but five of them make a 3/1.
||||||||||||||~ generator ||~ g ||~ 2g ||~ 3g ||~ 4g (-1200) ||~ comments ||
|| 1\3 ||   ||   ||   ||   ||   ||   || 400.000 || 800.000 || 1200.000 || 400.000 ||=   ||
||   ||   ||   ||   ||   || 7\22 ||   || 381.818 ||   ||   ||   ||=   ||
||   ||   ||   ||   ||   ||   || 13\41 || 380.488 ||   ||   ||   ||= Magic is around here ||
||   ||   ||   ||   || 6\19 ||   ||   || 378.947 || 757.895 || 1136.842 || 315.789 ||=   ||
||   ||   ||   || 5\16 ||   ||   ||   || 375.000 || 750.000 || 1125.000 || 300.000 ||=   ||
||   ||   ||   ||   || 9\29 ||   ||   || 372.414 || 744.828 || 1117.241 || 289.655 ||=   ||
||   ||   || 4\13 ||   ||   ||   ||   || 369.231 || 738.462 || 1107.692 || 276.923 ||=   ||
||   ||   ||   ||   || 11\36 ||   ||   || 366.667 || 733.333 || 1100.000 || 266.667 ||=   ||
||   ||   ||   || 7\23 ||   ||   ||   || 365.217 || 730.435 || 1095.652 || 260.870 ||=   ||
||   ||   ||   ||   || 10\33 ||   ||   || 363.636 || 727.272 || 1090.909 || 254.545 ||=   ||
||   || 3\10 ||   ||   ||   ||   ||   || 360.000 || 720.000 || 1080.000 || 240.000 ||= Boundary of propriety (generators
smaller than this are proper) ||
||   ||   ||   ||   || 11\37 ||   ||   || 356.757 || 713.514 || 1080.270 || 227.027 ||=   ||
||   ||   ||   || 8\27 ||   ||   ||   || 355.556 || 711.111 || 1066.667 || 222.222 ||=   ||
||   ||   ||   ||   || 13\44 ||   ||   || 354.545 || 709.091 || 1063.636 || 218.182 ||=   ||
||   ||   || 5\17 ||   ||   ||   ||   || 352.941 || 705.882 || 1058.824 || 211.765 ||=   ||
||   ||   ||   ||   || 12\41 ||   ||   || 351.220 || 702.439 || 1053.659 || 204.878 ||= Neutral thirds scale /
Mohajira is around here ||
||   ||   ||   || 7\24 ||   ||   ||   || 350.000 || 700.000 || 1050.000 || 200.000 ||=   ||
||   ||   ||   ||   || 9\31 ||   ||   || 348.387 || 696.774 || 1045.161 || 193.548 ||=   ||
|| 2\7 ||   ||   ||   ||   ||   ||   || 342.847 || 685.714 || 1028.571 || 171.429 ||=   ||

3\10 on this chart represents a dividing line between "neutral third scales" on the bottom (eg. [[17edo neutral scale]]), and something else I don't have a name for yet on the top, with [[10edo]] standing in between. (What do you call this region, dear reader?) Of course, magic is in the top half, but it's a pretty specific scale and doesn't describe the whole range. MOS-wise, the neutral third scales, after three more generations, make MOS [[7L 3s]] ("unfair mosh"); the other scales make MOS [[3L 7s]] ("fair mosh").

In "neural third scale territory," the generators are all "neutral thirds," and two of them make an approximation of the "perfect fifth." Additionally, the L of the scale is somewhere around a "whole tone" and the s of the scale is somewhere around a "neutral tone".

In the as-yet unnamed northern territory, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a "supermajor second" to a "major third" and s is a "semitone" or smaller.

Original HTML content:

<html><head><title>3L 4s</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x3L 4s - &quot;mosh&quot;"></a><!-- ws:end:WikiTextHeadingRule:0 -->3L 4s - &quot;mosh&quot;</h1>
 <br />
MOS scales of this form are built from a generator that falls between 1\3 (one degree of <a class="wiki_link" href="/3edo">3edo</a> - 400 cents) and 2\7 (two degrees of <a class="wiki_link" href="/7edo">7edo</a> - 343 cents.<br />
<br />
It has the form s L s L s L s and its various &quot;modes&quot; (with nicknames coined by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a>) are:<br />
<br />


<table class="wiki_table">
    <tr>
        <td>s L s L s L s<br />
</td>
        <td>bish<br />
</td>
    </tr>
    <tr>
        <td>L s L s L s s<br />
</td>
        <td>dril<br />
</td>
    </tr>
    <tr>
        <td>s L s L s s L<br />
</td>
        <td>fish<br />
</td>
    </tr>
    <tr>
        <td>L s L s s L s<br />
</td>
        <td>gil<br />
</td>
    </tr>
    <tr>
        <td>s L s s L s L<br />
</td>
        <td>jwl<br />
</td>
    </tr>
    <tr>
        <td>L s s L s L s<br />
</td>
        <td>kleeth<br />
</td>
    </tr>
    <tr>
        <td>s s L s L s L<br />
</td>
        <td>led<br />
</td>
    </tr>
</table>

The two notable harmonic entropy minima with this pattern are neutral third scales (&quot;dicot&quot; / &quot;hemififth&quot; / &quot;mohajira&quot;) where two generators make a 3/2, and <a class="wiki_link" href="/Magic%20family">magic</a>, where the generator is a 5/4 but five of them make a 3/1.<br />


<table class="wiki_table">
    <tr>
        <th colspan="7">generator<br />
</th>
        <th>g<br />
</th>
        <th>2g<br />
</th>
        <th>3g<br />
</th>
        <th>4g (-1200)<br />
</th>
        <th>comments<br />
</th>
    </tr>
    <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>400.000<br />
</td>
        <td>800.000<br />
</td>
        <td>1200.000<br />
</td>
        <td>400.000<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>7\22<br />
</td>
        <td><br />
</td>
        <td>381.818<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><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>13\41<br />
</td>
        <td>380.488<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">Magic is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>6\19<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>378.947<br />
</td>
        <td>757.895<br />
</td>
        <td>1136.842<br />
</td>
        <td>315.789<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\16<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>375.000<br />
</td>
        <td>750.000<br />
</td>
        <td>1125.000<br />
</td>
        <td>300.000<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>9\29<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>372.414<br />
</td>
        <td>744.828<br />
</td>
        <td>1117.241<br />
</td>
        <td>289.655<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>4\13<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>369.231<br />
</td>
        <td>738.462<br />
</td>
        <td>1107.692<br />
</td>
        <td>276.923<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>11\36<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>366.667<br />
</td>
        <td>733.333<br />
</td>
        <td>1100.000<br />
</td>
        <td>266.667<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7\23<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>365.217<br />
</td>
        <td>730.435<br />
</td>
        <td>1095.652<br />
</td>
        <td>260.870<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>10\33<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>363.636<br />
</td>
        <td>727.272<br />
</td>
        <td>1090.909<br />
</td>
        <td>254.545<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>3\10<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>360.000<br />
</td>
        <td>720.000<br />
</td>
        <td>1080.000<br />
</td>
        <td>240.000<br />
</td>
        <td style="text-align: center;">Boundary of propriety (generators<br />
smaller than this are proper)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>11\37<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>356.757<br />
</td>
        <td>713.514<br />
</td>
        <td>1080.270<br />
</td>
        <td>227.027<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>8\27<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>355.556<br />
</td>
        <td>711.111<br />
</td>
        <td>1066.667<br />
</td>
        <td>222.222<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>13\44<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>354.545<br />
</td>
        <td>709.091<br />
</td>
        <td>1063.636<br />
</td>
        <td>218.182<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\17<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>352.941<br />
</td>
        <td>705.882<br />
</td>
        <td>1058.824<br />
</td>
        <td>211.765<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>12\41<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>351.220<br />
</td>
        <td>702.439<br />
</td>
        <td>1053.659<br />
</td>
        <td>204.878<br />
</td>
        <td style="text-align: center;">Neutral thirds scale<br />
Mohajira is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7\24<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>350.000<br />
</td>
        <td>700.000<br />
</td>
        <td>1050.000<br />
</td>
        <td>200.000<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>9\31<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>348.387<br />
</td>
        <td>696.774<br />
</td>
        <td>1045.161<br />
</td>
        <td>193.548<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>2\7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>342.847<br />
</td>
        <td>685.714<br />
</td>
        <td>1028.571<br />
</td>
        <td>171.429<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

<br />
3\10 on this chart represents a dividing line between &quot;neutral third scales&quot; on the bottom (eg. <a class="wiki_link" href="/17edo%20neutral%20scale">17edo neutral scale</a>), and something else I don't have a name for yet on the top, with <a class="wiki_link" href="/10edo">10edo</a> standing in between. (What do you call this region, dear reader?) Of course, magic is in the top half, but it's a pretty specific scale and doesn't describe the whole range. MOS-wise, the neutral third scales, after three more generations, make MOS <a class="wiki_link" href="/7L%203s">7L 3s</a> (&quot;unfair mosh&quot;); the other scales make MOS <a class="wiki_link" href="/3L%207s">3L 7s</a> (&quot;fair mosh&quot;).<br />
<br />
In &quot;neural third scale territory,&quot; the generators are all &quot;neutral thirds,&quot; and two of them make an approximation of the &quot;perfect fifth.&quot; Additionally, the L of the scale is somewhere around a &quot;whole tone&quot; and the s of the scale is somewhere around a &quot;neutral tone&quot;.<br />
<br />
In the as-yet unnamed northern territory, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a &quot;supermajor second&quot; to a &quot;major third&quot; and s is a &quot;semitone&quot; or smaller.</body></html>