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 JosephRuhf and made on 2015-01-27 16:15:33 UTC.
- The original revision id was 538741912.
- 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 [[Modal UDP Notation]] and nicknames coined by [[Andrew Heathwaite]]) are:
||= **Mode** ||= **UDP** ||= **Nickname** ||
|| s L s L s L s ||= 3|3 || bish ||
|| L s L s L s s ||= 6|0 || dril ||
|| s L s L s s L ||= 2|4 || fish ||
|| L s L s s L s ||= 5|1 || gil ||
|| s L s s L s L ||= 1|5 || jwl ||
|| L s s L s L s ||= 4|2 || kleeth ||
|| s s L s L s L ||= 0|6 || 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.
||~ ||~ ||~ ||~ ||~ g ||~ 2g ||~ 3g ||~ 4g (-1200) ||~ comments ||
|| 1\3 || || || || 400.000 || 800.000 || 1200.000 || 400.000 ||= ||
|| || 15\46 || || || 391.304 || 782.609 || 1173.913 || 365.217 ||= ||
|| || 14\43 || || || 390.698 || 781.395 || 1172.093 || 362.791 ||= ||
|| || 13\40 || || || 390.000 || 780.000 || 1170.000 || 360.000 ||= ||
|| || 12\37 || || || 389.189 || 778.378 || 1167.568 || 356.757 ||= ||
|| || 11\34 || || || 388.235 || 776.471 || 1164.706 || 352.941 ||= ||
|| || 10\31 || || || 387.097 || 774.194 || 1161.290 || 348.387 ||= <span style="text-align: center;">[[xenharmonic/Würschmidt family|Würschmidt]]</span><span style="text-align: center;"> is around here</span> ||
|| || || 19\59 || || 386.441 || 772.881 || 1159.322 || 345.763 ||= ||
|| || 9\28 || || || 385.714 || 771.429 || 1157.143 || 342.857 ||= ||
|| || 8\25 || || || 384.000 || 768.000 || 1152.000 || 336.000 ||= ||
|| || || 23\72 || || 383.333 || 766.667 || 1150.000 || 333.333 ||= ||
|| || || 15\47 || || 382.988 || 765.957 || 1148.936 || 331.915 ||= ||
|| || 7\22 || || || 381.818 || 763.636 || 1145.455 || 327.273 ||= ||
|| || || 13\41 || || 380.488 || 760.976 || 1141.463 || 321.951 ||= <span style="text-align: center;">Magic is around here</span> ||
|| || || 19\60 || || 380.000 || 760.000 || 1140.000 || 320.000 ||= ||
|| || || 25\79 || || 379.747 || 759.494 || 1139.2405 || 318.987 ||= ||
|| || 6\19 || || || 378.947 || 757.895 || 1136.842 || 315.789 ||= ||
|| || || 11\35 || || 377.143 || 754.286 || 1131.429 || 308.571 ||= ||
|| || || 16\51 || || 376.471 || 752.941 || 1129.412 || 305.882 ||= ||
|| || 5\16 || || || 375.000 || 750.000 || 1125.000 || 300.000 ||= <span style="text-align: center;">L/s = 4</span> ||
|| || || 24\77 || || 374.026 || 748.052 || 1122.078 || 296.104 ||= ||
|| || || 19\61 || || 373.7705 || 747.541 || 1121.3115 || 295.082 ||= ||
|| || || 14\45 || || 373.333 || 746.667 || 1120.000 || 293.333 ||= ||
|| || || 9\29 || || 372.414 || 744.828 || 1117.241 || 289.655 ||= ||
|| || || 13\42 || || 371.429 || 742.857 || 1114.286 || 285.714 ||= ||
|| || || || 17\55 || 370.909 || 741.818 || 1112.727 || 283.636 ||= ||
|| || 4\13 || || || 369.231 || 738.462 || 1107.692 || 276.923 ||= <span style="text-align: center;">L/s = 3</span> ||
|| || || 19\62 || || 367.742 || 735.484 || 1103.226 || 270.968 ||= ||
|| || || 15\49 || || 367.347 || 734.694 || 1102.041 || 269.388 ||= ||
|| || || 11\36 || || 366.667 || 733.333 || 1100.000 || 266.667 ||= ||
|| || || 7\23 || || 365.217 || 730.435 || 1095.652 || 260.870 ||= <span style="text-align: center;">Modi Sephiratorum (Kosmorsky)</span> ||
|| || || 17\56 || || 364.286 || 728.571 || 1092.857 || 257.143 ||= ||
|| || || 10\33 || || 363.636 || 727.272 || 1090.909 || 254.545 ||= ||
|| || || 13\43 || || 362.791 || 725.581 || 1088.372 || 251.163 ||= ||
|| || || 16\53 || || 362.264 || 724.528 || 1086.7925 || 249.057 ||= ||
|| || || 19\63 || || 361.905 || 723.8095 || 1085.714 || 247.619 ||= ||
|| || 3\10 || || || 360.000 || 720.000 || 1080.000 || 240.000 ||= <span style="text-align: center;">Boundary of propriety </span>
<span style="text-align: center;">(generators smaller than this are proper)</span> ||
|| || || 38\127 || || 359.055 || 718.110 || 1077.165 || 236.2205 ||= ||
|| || || 35\117 || || 358.974 || 717.949 || 1076.923 || 235.898 ||= ||
|| || || 32\107 || || 358.8785 || 717.757 || 1076.6355 || 235.514 ||= ||
|| || || 29\97 || || 358.763 || 717.526 || 1076.289 || 235.0515 ||= ||
|| || || 26\87 || || 358.621 || 717.241 || 1075.862 || 234.483 ||= ||
|| || || 23\77 || || 358.442 || 716.883 || 1075.325 || 233.767 ||= ||
|| || || 20\67 || || 358.209 || 716.418 || 1074.627 || 232.836 ||= ||
|| || || 17\57 || || 357.895 || 715.7895 || 1073.684 || 231.579 ||= ||
|| || || 14\47 || || 357.447 || 714.894 || 1072.340 || 229.787 ||= ||
|| || || 11\37 || || 356.757 || 713.514 || 1070.270 || 227.027 ||= ||
|| || || 8\27 || || 355.556 || 711.111 || 1066.667 || 222.222 ||= <span style="text-align: center;">Beatles is around here</span> ||
|| || || || 34\115 || 354.930 || 709.859 || 1064.789 || 219.718 ||= <span style="display: block; text-align: center;">Golden neutral thirds scale</span> ||
|| || || 21\71 || || 354.783 || 709.565 || 1064.348 || 219.13 ||= ||
|| || || 13\44 || || 354.545 || 709.091 || 1063.636 || 218.182 ||= ||
|| || 5\17 || || || 352.941 || 705.882 || 1058.824 || 211.765 ||= <span style="text-align: center;">Optimum rank range (L/s=3/2)</span> ||
|| || || 12\41 || || 351.220 || 702.439 || 1053.659 || 204.878 ||= <span style="text-align: center;">2.3.11 neutral thirds scale is around here</span> ||
|| || 7\24 || || || 350.000 || 700.000 || 1050.000 || 200.000 ||= ||
|| || || 16\55 || || 349.091 || 698.182 || 1047.273 || 196.364 || ||
|| || 9\31 || || || 348.387 || 696.774 || 1045.161 || 193.548 ||= <span style="text-align: center;">Mohajira/dicot is around here</span> ||
|| || 11\38 || || || 347.368 || 694.737 || 1042.105 || 189.474 || ||
|| 2\7 || || || || 342.857 || 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 <a class="wiki_link" href="/Modal%20UDP%20Notation">Modal UDP Notation</a> and nicknames coined by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a>) are:<br />
<br />
<table class="wiki_table">
<tr>
<td style="text-align: center;"><strong>Mode</strong><br />
</td>
<td style="text-align: center;"><strong>UDP</strong><br />
</td>
<td style="text-align: center;"><strong>Nickname</strong><br />
</td>
</tr>
<tr>
<td>s L s L s L s<br />
</td>
<td style="text-align: center;">3|3<br />
</td>
<td>bish<br />
</td>
</tr>
<tr>
<td>L s L s L s s<br />
</td>
<td style="text-align: center;">6|0<br />
</td>
<td>dril<br />
</td>
</tr>
<tr>
<td>s L s L s s L<br />
</td>
<td style="text-align: center;">2|4<br />
</td>
<td>fish<br />
</td>
</tr>
<tr>
<td>L s L s s L s<br />
</td>
<td style="text-align: center;">5|1<br />
</td>
<td>gil<br />
</td>
</tr>
<tr>
<td>s L s s L s L<br />
</td>
<td style="text-align: center;">1|5<br />
</td>
<td>jwl<br />
</td>
</tr>
<tr>
<td>L s s L s L s<br />
</td>
<td style="text-align: center;">4|2<br />
</td>
<td>kleeth<br />
</td>
</tr>
<tr>
<td>s s L s L s L<br />
</td>
<td style="text-align: center;">0|6<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><br />
</th>
<th><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>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>15\46<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>391.304<br />
</td>
<td>782.609<br />
</td>
<td>1173.913<br />
</td>
<td>365.217<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>14\43<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>390.698<br />
</td>
<td>781.395<br />
</td>
<td>1172.093<br />
</td>
<td>362.791<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>13\40<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>390.000<br />
</td>
<td>780.000<br />
</td>
<td>1170.000<br />
</td>
<td>360.000<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>12\37<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>389.189<br />
</td>
<td>778.378<br />
</td>
<td>1167.568<br />
</td>
<td>356.757<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>11\34<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>388.235<br />
</td>
<td>776.471<br />
</td>
<td>1164.706<br />
</td>
<td>352.941<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>10\31<br />
</td>
<td><br />
</td>
<td><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;"><span style="text-align: center;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/W%C3%BCrschmidt%20family">Würschmidt</a></span><span style="text-align: center;"> is around here</span><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>19\59<br />
</td>
<td><br />
</td>
<td>386.441<br />
</td>
<td>772.881<br />
</td>
<td>1159.322<br />
</td>
<td>345.763<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>9\28<br />
</td>
<td><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 style="text-align: center;"><br />
</td>
</tr>
<tr>
<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 style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>23\72<br />
</td>
<td><br />
</td>
<td>383.333<br />
</td>
<td>766.667<br />
</td>
<td>1150.000<br />
</td>
<td>333.333<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>15\47<br />
</td>
<td><br />
</td>
<td>382.988<br />
</td>
<td>765.957<br />
</td>
<td>1148.936<br />
</td>
<td>331.915<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>7\22<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>13\41<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;"><span style="text-align: center;">Magic is around here</span><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>19\60<br />
</td>
<td><br />
</td>
<td>380.000<br />
</td>
<td>760.000<br />
</td>
<td>1140.000<br />
</td>
<td>320.000<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>25\79<br />
</td>
<td><br />
</td>
<td>379.747<br />
</td>
<td>759.494<br />
</td>
<td>1139.2405<br />
</td>
<td>318.987<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<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>11\35<br />
</td>
<td><br />
</td>
<td>377.143<br />
</td>
<td>754.286<br />
</td>
<td>1131.429<br />
</td>
<td>308.571<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>16\51<br />
</td>
<td><br />
</td>
<td>376.471<br />
</td>
<td>752.941<br />
</td>
<td>1129.412<br />
</td>
<td>305.882<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>375.000<br />
</td>
<td>750.000<br />
</td>
<td>1125.000<br />
</td>
<td>300.000<br />
</td>
<td style="text-align: center;"><span style="text-align: center;">L/s = 4</span><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>24\77<br />
</td>
<td><br />
</td>
<td>374.026<br />
</td>
<td>748.052<br />
</td>
<td>1122.078<br />
</td>
<td>296.104<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>19\61<br />
</td>
<td><br />
</td>
<td>373.7705<br />
</td>
<td>747.541<br />
</td>
<td>1121.3115<br />
</td>
<td>295.082<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>14\45<br />
</td>
<td><br />
</td>
<td>373.333<br />
</td>
<td>746.667<br />
</td>
<td>1120.000<br />
</td>
<td>293.333<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>9\29<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>13\42<br />
</td>
<td><br />
</td>
<td>371.429<br />
</td>
<td>742.857<br />
</td>
<td>1114.286<br />
</td>
<td>285.714<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>17\55<br />
</td>
<td>370.909<br />
</td>
<td>741.818<br />
</td>
<td>1112.727<br />
</td>
<td>283.636<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<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 style="text-align: center;"><span style="text-align: center;">L/s = 3</span><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>19\62<br />
</td>
<td><br />
</td>
<td>367.742<br />
</td>
<td>735.484<br />
</td>
<td>1103.226<br />
</td>
<td>270.968<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>15\49<br />
</td>
<td><br />
</td>
<td>367.347<br />
</td>
<td>734.694<br />
</td>
<td>1102.041<br />
</td>
<td>269.388<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>11\36<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>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 style="text-align: center;"><span style="text-align: center;">Modi Sephiratorum (Kosmorsky)</span><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>17\56<br />
</td>
<td><br />
</td>
<td>364.286<br />
</td>
<td>728.571<br />
</td>
<td>1092.857<br />
</td>
<td>257.143<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>10\33<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><br />
</td>
<td>13\43<br />
</td>
<td><br />
</td>
<td>362.791<br />
</td>
<td>725.581<br />
</td>
<td>1088.372<br />
</td>
<td>251.163<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>16\53<br />
</td>
<td><br />
</td>
<td>362.264<br />
</td>
<td>724.528<br />
</td>
<td>1086.7925<br />
</td>
<td>249.057<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>19\63<br />
</td>
<td><br />
</td>
<td>361.905<br />
</td>
<td>723.8095<br />
</td>
<td>1085.714<br />
</td>
<td>247.619<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>360.000<br />
</td>
<td>720.000<br />
</td>
<td>1080.000<br />
</td>
<td>240.000<br />
</td>
<td style="text-align: center;"><span style="text-align: center;">Boundary of propriety </span><br />
<span style="text-align: center;">(generators smaller than this are proper)</span><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>38\127<br />
</td>
<td><br />
</td>
<td>359.055<br />
</td>
<td>718.110<br />
</td>
<td>1077.165<br />
</td>
<td>236.2205<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>35\117<br />
</td>
<td><br />
</td>
<td>358.974<br />
</td>
<td>717.949<br />
</td>
<td>1076.923<br />
</td>
<td>235.898<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>32\107<br />
</td>
<td><br />
</td>
<td>358.8785<br />
</td>
<td>717.757<br />
</td>
<td>1076.6355<br />
</td>
<td>235.514<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>29\97<br />
</td>
<td><br />
</td>
<td>358.763<br />
</td>
<td>717.526<br />
</td>
<td>1076.289<br />
</td>
<td>235.0515<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>26\87<br />
</td>
<td><br />
</td>
<td>358.621<br />
</td>
<td>717.241<br />
</td>
<td>1075.862<br />
</td>
<td>234.483<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>23\77<br />
</td>
<td><br />
</td>
<td>358.442<br />
</td>
<td>716.883<br />
</td>
<td>1075.325<br />
</td>
<td>233.767<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>20\67<br />
</td>
<td><br />
</td>
<td>358.209<br />
</td>
<td>716.418<br />
</td>
<td>1074.627<br />
</td>
<td>232.836<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>17\57<br />
</td>
<td><br />
</td>
<td>357.895<br />
</td>
<td>715.7895<br />
</td>
<td>1073.684<br />
</td>
<td>231.579<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>14\47<br />
</td>
<td><br />
</td>
<td>357.447<br />
</td>
<td>714.894<br />
</td>
<td>1072.340<br />
</td>
<td>229.787<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>11\37<br />
</td>
<td><br />
</td>
<td>356.757<br />
</td>
<td>713.514<br />
</td>
<td>1070.270<br />
</td>
<td>227.027<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<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 style="text-align: center;"><span style="text-align: center;">Beatles is around here</span><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>34\115<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;"><span style="display: block; text-align: center;">Golden neutral thirds scale</span><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>21\71<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;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>13\44<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>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 style="text-align: center;"><span style="text-align: center;">Optimum rank range (L/s=3/2)</span><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>12\41<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;"><span style="text-align: center;">2.3.11 neutral thirds scale is around here</span><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>7\24<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>16\55<br />
</td>
<td><br />
</td>
<td>349.091<br />
</td>
<td>698.182<br />
</td>
<td>1047.273<br />
</td>
<td>196.364<br />
</td>
<td><br />
</td>
</tr>
<tr>
<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;"><span style="text-align: center;">Mohajira/dicot is around here</span><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>11\38<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>347.368<br />
</td>
<td>694.737<br />
</td>
<td>1042.105<br />
</td>
<td>189.474<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>2\7<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>342.857<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>