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 Andrew_Heathwaite and made on 2009-11-08 22:28:05 UTC.
- The original revision id was 101164205.
- The revision comment was: added 3g & 4g
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" are:
s L s L s L s
L s L s L s s
s L s L s s L
L s L s s L s
s L s s L s L
L s s L s L s
s s L s L s L
One can build a continuum of equal-tempered scales between 1\3 and 2\7 by taking "freshman sums," adding together the numerators, then adding together the denominators.
<span style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; border-collapse: collapse;">
</span>
||||||||||~ generator || g || 2g || 3g || 4g (-1200) ||
|| 1\3 || || || || || 400.000 || 800.000 || 1200.000 || 400.000 || ||
|| || || || || 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 || ||
|| || || || || 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 || ||
|| || || || 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 what I call "neutral 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. MOS-wise, the neutral scales, after three more generations, make MOS [[7L 3s]] ("unfair mosh"); the other scales make MOS [[3L 7s]] ("fair mosh").
In "neural 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:<h1> --><h1 id="toc0"><a name="x3L 4s - "mosh""></a><!-- ws:end:WikiTextHeadingRule:0 -->3L 4s - "mosh"</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 "modes" are:<br />
<br />
s L s L s L s<br />
L s L s L s s<br />
s L s L s s L<br />
L s L s s L s<br />
s L s s L s L<br />
L s s L s L s<br />
s s L s L s L<br />
<br />
One can build a continuum of equal-tempered scales between 1\3 and 2\7 by taking "freshman sums," adding together the numerators, then adding together the denominators.<br />
<br />
<span style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; border-collapse: collapse;"><br />
</span><br />
<table class="wiki_table">
<tr>
<th colspan="5">generator<br />
</th>
<td>g<br />
</td>
<td>2g<br />
</td>
<td>3g<br />
</td>
<td>4g (-1200)<br />
</td>
</tr>
<tr>
<td>1\3<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><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>6\19<br />
</td>
<td>378.947<br />
</td>
<td>757.895<br />
</td>
<td>1136.842<br />
</td>
<td>315.789<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>5\16<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><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>9\29<br />
</td>
<td>372.414<br />
</td>
<td>744.828<br />
</td>
<td>1117.241<br />
</td>
<td>289.655<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>4\13<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><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>11\36<br />
</td>
<td>366.667<br />
</td>
<td>733.333<br />
</td>
<td>1100.000<br />
</td>
<td>266.667<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>7\23<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><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>10\33<br />
</td>
<td>363.636<br />
</td>
<td>727.272<br />
</td>
<td>1090.909<br />
</td>
<td>254.545<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>3\10<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><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>11\37<br />
</td>
<td>356.757<br />
</td>
<td>713.514<br />
</td>
<td>1080.270<br />
</td>
<td>227.027<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>8\27<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><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>13\44<br />
</td>
<td>354.545<br />
</td>
<td>709.091<br />
</td>
<td>1063.636<br />
</td>
<td>218.182<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>5\17<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><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>12\41<br />
</td>
<td>351.220<br />
</td>
<td>702.439<br />
</td>
<td>1053.659<br />
</td>
<td>204.878<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>7\24<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><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>9\31<br />
</td>
<td>348.387<br />
</td>
<td>696.774<br />
</td>
<td>1045.161<br />
</td>
<td>193.548<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>2\7<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><br />
</td>
</tr>
</table>
<br />
3\10 on this chart represents a dividing line between what I call "neutral scales" 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. MOS-wise, the neutral scales, after three more generations, make MOS <a class="wiki_link" href="/7L%203s">7L 3s</a> ("unfair mosh"); the other scales make MOS <a class="wiki_link" href="/3L%207s">3L 7s</a> ("fair mosh").<br />
<br />
In "neural 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".<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 "supermajor second" to a "major third" and s is a "semitone" or smaller.</body></html>