3L 4s
IMPORTED REVISION FROM WIKISPACES
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=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 ||= ||
|| || || || || || || || || 10\31 || 387.097 || 774.194 || 1161.290 || 348.387 ||= [[Würschmidt family|Würschmidt]] is around here ||
|| || || || || || || || 9\28 || || 385.714 || 771.429 || 1157.143 || 342.857 || ||
|| || || || || || || 8\25 || || || 384.000 || 768.000 || 1152.000 || 336.000 || ||
|| || || || || || 7\22 || || || || 381.818 || 763.636 || 1145.455 || 327.273 ||= ||
|| || || || || || || 13\41 || || || 380.488 || 760.976 || 1141.463 || 321.951 ||= Magic is around here ||
|| || || || || 6\19 || || || || || 378.947 || 757.895 || 1136.842 || 315.789 ||= ||
|| || || || 5\16 || || || || || || 375.000 || 750.000 || 1125.000 || 300.000 ||= Boundary of "practicality" ends around here ||
|| || || || || 9\29 || || || || || 372.414 || 744.828 || 1117.241 || 289.655 ||= ||
|| || || 4\13 || || || || || || || 369.231 || 738.462 || 1107.692 || 276.923 ||= Boundary of "practicality" begins around here ||
|| || || || || 11\36 || || || || || 366.667 || 733.333 || 1100.000 || 266.667 ||= ||
|| || || || 7\23 || || || || || || 365.217 || 730.435 || 1095.652 || 260.870 ||= Modi Sephiratorum (Kosmorsky) ||
|| || || || || 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 ||= Beatles is around here ||
|| || || || || || 21\71 || || || || 354.930 || 709.859 || 1064.789 || 219.718 ||= ||
|| || || || || || || 34\115 || || || 354.783 || 709.565 || 1064.348 || 219.13 ||= Golden neutral thirds scale ||
|| || || || || 13\44 || || || || || 354.545 || 709.091 || 1063.636 || 218.182 ||= ||
|| || || 5\17 || || || || || || || 352.941 || 705.882 || 1058.824 || 211.765 ||= Optimum rank range (L/s=3/2) ||
|| || || || || 12\41 || || || || || 351.220 || 702.439 || 1053.659 || 204.878 ||= 2.3.11 neutral thirds scale
is around here ||
|| || || || 7\24 || || || || || || 350.000 || 700.000 || 1050.000 || 200.000 ||= ||
|| || || || || 9\31 || || || || || 348.387 || 696.774 || 1045.161 || 193.548 ||= Mohajira is around here ||
|| 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 "neutral 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:<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" (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 ("dicot" / "hemififth" / "mohajira") 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><br />
</th>
<th><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><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><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>10\31<br />
</td>
<td>387.097<br />
</td>
<td>774.194<br />
</td>
<td>1161.290<br />
</td>
<td>348.387<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/W%C3%BCrschmidt%20family">Würschmidt</a> is around here<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>9\28<br />
</td>
<td><br />
</td>
<td>385.714<br />
</td>
<td>771.429<br />
</td>
<td>1157.143<br />
</td>
<td>342.857<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>8\25<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>384.000<br />
</td>
<td>768.000<br />
</td>
<td>1152.000<br />
</td>
<td>336.000<br />
</td>
<td><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><br />
</td>
<td><br />
</td>
<td>381.818<br />
</td>
<td>763.636<br />
</td>
<td>1145.455<br />
</td>
<td>327.273<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><br />
</td>
<td><br />
</td>
<td>380.488<br />
</td>
<td>760.976<br />
</td>
<td>1141.463<br />
</td>
<td>321.951<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><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><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;">Boundary of "practicality" ends around here<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><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><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;">Boundary of "practicality" begins around here<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><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><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;">Modi Sephiratorum (Kosmorsky)<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><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><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><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><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;">Beatles is around here<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>21\71<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>354.930<br />
</td>
<td>709.859<br />
</td>
<td>1064.789<br />
</td>
<td>219.718<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>34\115<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>354.783<br />
</td>
<td>709.565<br />
</td>
<td>1064.348<br />
</td>
<td>219.13<br />
</td>
<td style="text-align: center;">Golden neutral thirds scale<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><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><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;">Optimum rank range (L/s=3/2)<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><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;">2.3.11 neutral thirds scale<br />
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><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><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;">Mohajira is around here<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><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 "neutral third 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. (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> ("unfair mosh"); the other scales make MOS <a class="wiki_link" href="/3L%207s">3L 7s</a> ("fair mosh").<br />
<br />
In "neutral 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".<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>