3L 4s: Difference between revisions
Wikispaces>Ninly **Imported revision 394233146 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 538741912 - Original comment: ** |
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| Line 1: | Line 1: | ||
<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-01-27 16:15:33 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>538741912</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
| Line 21: | Line 21: | ||
|| s s L s L s L ||= 0|6 || led || | || 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. | 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 | || 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"). | 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"). | ||
| Line 135: | Line 168: | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<th | <th><br /> | ||
</th> | |||
<th><br /> | |||
</th> | </th> | ||
<th><br /> | <th><br /> | ||
| Line 161: | Line 196: | ||
<td><br /> | <td><br /> | ||
</td> | </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><br /> | ||
</td> | |||
<td>15\46<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <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> | ||
<td><br /> | <td><br /> | ||
| Line 171: | Line 236: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>390.698<br /> | ||
</td> | </td> | ||
<td> | <td>781.395<br /> | ||
</td> | </td> | ||
<td> | <td>1172.093<br /> | ||
</td> | </td> | ||
<td> | <td>362.791<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 184: | Line 249: | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>13\40<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 189: | Line 256: | ||
<td><br /> | <td><br /> | ||
</td> | </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><br /> | ||
</td> | |||
<td>12\37<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <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> | ||
<td><br /> | <td><br /> | ||
</td> | </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><br /> | ||
</td> | </td> | ||
<td>10\31<br /> | <td>10\31<br /> | ||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td>387.097<br /> | <td>387.097<br /> | ||
| Line 209: | Line 324: | ||
<td>348.387<br /> | <td>348.387<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/W%C3%BCrschmidt%20family">Würschmidt</a> is around here<br /> | <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> | </td> | ||
</tr> | </tr> | ||
| Line 216: | Line 331: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>19\59<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>386.441<br /> | ||
</td> | |||
<td>772.881<br /> | |||
</td> | |||
<td>1159.322<br /> | |||
</td> | </td> | ||
<td><br /> | <td>345.763<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | |||
<tr> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>9\28<br /> | <td>9\28<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 239: | Line 364: | ||
<td>342.857<br /> | <td>342.857<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 269: | Line 384: | ||
<td>336.000<br /> | <td>336.000<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 276: | Line 391: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>23\72<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>383.333<br /> | ||
</td> | |||
<td>766.667<br /> | |||
</td> | |||
<td>1150.000<br /> | |||
</td> | </td> | ||
<td><br /> | <td>333.333<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | |||
<tr> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>15\47<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>382.988<br /> | ||
</td> | </td> | ||
<td> | <td>765.957<br /> | ||
</td> | </td> | ||
<td> | <td>1148.936<br /> | ||
</td> | </td> | ||
<td> | <td>331.915<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 304: | Line 429: | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>7\22<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 309: | Line 436: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <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> | </td> | ||
</tr> | |||
<tr> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 316: | Line 453: | ||
</td> | </td> | ||
<td>13\41<br /> | <td>13\41<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 329: | Line 464: | ||
<td>321.951<br /> | <td>321.951<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Magic is around here<br /> | <td style="text-align: center;"><span style="text-align: center;">Magic is around here</span><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 337: | Line 472: | ||
<td><br /> | <td><br /> | ||
</td> | </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><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>25\79<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </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><br /> | ||
</td> | |||
<td>6\19<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 366: | Line 531: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>11\35<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<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> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>16\51<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </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><br /> | ||
</td> | |||
<td>5\16<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 389: | Line 584: | ||
<td>300.000<br /> | <td>300.000<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">L/s = 4<br /> | <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> | </td> | ||
</tr> | </tr> | ||
| Line 396: | Line 611: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>19\61<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </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><br /> | ||
</td> | </td> | ||
<td> | <td><br /> | ||
</td> | |||
<td>14\45<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </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><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>9\29<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 427: | Line 672: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<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> | </td> | ||
</tr> | |||
<tr> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 435: | Line 694: | ||
<td><br /> | <td><br /> | ||
</td> | </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><br /> | ||
</td> | |||
<td>4\13<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 449: | Line 724: | ||
<td>276.923<br /> | <td>276.923<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">L/s = 3<br /> | <td style="text-align: center;"><span style="text-align: center;">L/s = 3</span><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 456: | Line 731: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>19\62<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>367.742<br /> | ||
</td> | |||
<td>735.484<br /> | |||
</td> | |||
<td>1103.226<br /> | |||
</td> | |||
<td>270.968<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | |||
<tr> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>15\49<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>367.347<br /> | ||
</td> | </td> | ||
<td> | <td>734.694<br /> | ||
</td> | </td> | ||
<td> | <td>1102.041<br /> | ||
</td> | </td> | ||
<td> | <td>269.388<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 486: | Line 771: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>11\36<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>366.667<br /> | ||
</td> | |||
<td>733.333<br /> | |||
</td> | |||
<td>1100.000<br /> | |||
</td> | |||
<td>266.667<br /> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | |||
<tr> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>7\23<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 509: | Line 804: | ||
<td>260.870<br /> | <td>260.870<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Modi Sephiratorum (Kosmorsky)<br /> | <td style="text-align: center;"><span style="text-align: center;">Modi Sephiratorum (Kosmorsky)</span><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 516: | Line 811: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>17\56<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>364.286<br /> | ||
</td> | |||
<td>728.571<br /> | |||
</td> | |||
<td>1092.857<br /> | |||
</td> | |||
<td>257.143<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | |||
<tr> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>10\33<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 545: | Line 850: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<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> | </td> | ||
</tr> | |||
<tr> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>16\53<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </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><br /> | ||
</td> | </td> | ||
<td><br /> | <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> | ||
<td><br /> | <td><br /> | ||
| Line 569: | Line 924: | ||
<td>240.000<br /> | <td>240.000<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Boundary of propriety | <td style="text-align: center;"><span style="text-align: center;">Boundary of propriety </span><br /> | ||
smaller than this are proper)<br /> | <span style="text-align: center;">(generators smaller than this are proper)</span><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 577: | Line 932: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>38\127<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>359.055<br /> | ||
</td> | |||
<td>718.110<br /> | |||
</td> | |||
<td>1077.165<br /> | |||
</td> | |||
<td>236.2205<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | |||
<tr> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>35\117<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>358.974<br /> | ||
</td> | </td> | ||
<td> | <td>717.949<br /> | ||
</td> | </td> | ||
<td> | <td>1076.923<br /> | ||
</td> | </td> | ||
<td> | <td>235.898<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 607: | Line 972: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>32\107<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>358.8785<br /> | ||
</td> | |||
<td>717.757<br /> | |||
</td> | |||
<td>1076.6355<br /> | |||
</td> | |||
<td>235.514<br /> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | |||
<tr> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>29\97<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>358.763<br /> | ||
</td> | </td> | ||
<td> | <td>717.526<br /> | ||
</td> | </td> | ||
<td> | <td>1076.289<br /> | ||
</td> | </td> | ||
<td> | <td>235.0515<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 637: | Line 1,012: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>26\87<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>358.621<br /> | ||
</td> | |||
<td>717.241<br /> | |||
</td> | |||
<td>1075.862<br /> | |||
</td> | </td> | ||
<td><br /> | <td>234.483<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | |||
<tr> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>23\77<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>358.442<br /> | ||
</td> | </td> | ||
<td> | <td>716.883<br /> | ||
</td> | </td> | ||
<td> | <td>1075.325<br /> | ||
</td> | </td> | ||
<td> | <td>233.767<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 667: | Line 1,052: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>20\67<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <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> | </td> | ||
</tr> | |||
<tr> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>17\57<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>357.895<br /> | ||
</td> | </td> | ||
<td> | <td>715.7895<br /> | ||
</td> | </td> | ||
<td> | <td>1073.684<br /> | ||
</td> | </td> | ||
<td> | <td>231.579<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | |||
<td style="text-align: center;"> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 697: | Line 1,092: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>14\47<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>357.447<br /> | ||
</td> | |||
<td>714.894<br /> | |||
</td> | |||
<td>1072.340<br /> | |||
</td> | |||
<td>229.787<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | |||
<tr> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>11\37<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>356.757<br /> | ||
</td> | </td> | ||
<td> | <td>713.514<br /> | ||
</td> | </td> | ||
<td> | <td>1070.270<br /> | ||
</td> | </td> | ||
<td> | <td>227.027<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 728: | Line 1,133: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<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> | </td> | ||
</tr> | |||
<tr> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 736: | Line 1,155: | ||
<td><br /> | <td><br /> | ||
</td> | </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><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>21\71<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>354.783<br /> | ||
</td> | </td> | ||
<td> | <td>709.565<br /> | ||
</td> | </td> | ||
<td> | <td>1064.348<br /> | ||
</td> | </td> | ||
<td> | <td>219.13<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 757: | Line 1,192: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>13\44<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>354.545<br /> | ||
</td> | |||
<td>709.091<br /> | |||
</td> | |||
<td>1063.636<br /> | |||
</td> | |||
<td>218.182<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | |||
<tr> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>5\17<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 772: | Line 1,217: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>352.941<br /> | ||
</td> | </td> | ||
<td> | <td>705.882<br /> | ||
</td> | </td> | ||
<td> | <td>1058.824<br /> | ||
</td> | </td> | ||
<td> | <td>211.765<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">2 | <td style="text-align: center;"><span style="text-align: center;">Optimum rank range (L/s=3/2)</span><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 788: | Line 1,232: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>12\41<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>351.220<br /> | ||
</td> | |||
<td>702.439<br /> | |||
</td> | |||
<td>1053.659<br /> | |||
</td> | |||
<td>204.878<br /> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><span style="text-align: center;">2.3.11 neutral thirds scale is around here</span><br /> | ||
</td> | </td> | ||
</tr> | |||
<tr> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>7\24<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 818: | Line 1,272: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>16\55<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>349.091<br /> | ||
</td> | |||
<td>698.182<br /> | |||
</td> | |||
<td>1047.273<br /> | |||
</td> | </td> | ||
<td> | <td>196.364<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
</tr> | |||
<tr> | |||
<td><br /> | <td><br /> | ||
</td> | |||
<td>9\31<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 841: | Line 1,305: | ||
<td>193.548<br /> | <td>193.548<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Mohajira/dicot is around here<br /> | <td style="text-align: center;"><span style="text-align: center;">Mohajira/dicot is around here</span><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td><br /> | ||
</td> | |||
<td>11\38<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 851: | Line 1,317: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>347.368<br /> | ||
</td> | |||
<td>694.737<br /> | |||
</td> | |||
<td>1042.105<br /> | |||
</td> | |||
<td>189.474<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | </tr> | ||
<tr> | |||
<td>2\7<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 863: | Line 1,337: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>342. | <td>342.857<br /> | ||
</td> | </td> | ||
<td>685.714<br /> | <td>685.714<br /> | ||