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Wikispaces>JosephRuhf **Imported revision 595579778 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 595677806 - Original comment: ** |
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<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:JosephRuhf|JosephRuhf]] and made on <tt>2016-10- | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-17 21:05:46 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>595677806</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> | ||
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The only notable harmonic entropy minimum is Vulture/[[Hemifamity temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes. | The only notable harmonic entropy minimum is Vulture/[[Hemifamity temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes. | ||
By a weird coincidence, the other generator for this MOS will generate the same pattern within a tritave equivalence. By yet another weird coincidence, this MOS belongs to a temperament which has | By a weird coincidence, the other generator for this MOS will generate the same pattern within a tritave equivalence. By yet another weird coincidence, this MOS belongs to a temperament which has [[Bohlen-Pierce]] as its index-2 subtemperament. In addition to being harmonious, this tuning of the MOS gives an L/s ratio between 3 and 5/3, which is squarely in the middle of the range, being thus neither too exaggerated nor too equalized to be recognizable as such, unlike in octaves, where the only notable harmonic entropy minimum is near a greatly exaggerated 10/1 L/s ratio. | ||
||||||||||~ generator ||~ tetrachord ||~ g in cents ||~ 2g ||~ 3g ||~ 4g ||~ Comments || | |||
|| 2\5 || || || || | ||= 2\5 ||= ||= ||= ||= ||= 1 0 1 ||= 760.782 ||= 1521.564 ||= 380.391 ||= 1141.173 ||= || | ||
|| 21\53 || || || || | ||= 21\53 ||= ||= ||= ||= ||= 10 1 10 ||= 753.605 ||= 1507.21 ||= 358.859 ||= 1112.464 ||= || | ||
|| 19\48 || || || || | ||= 19\48 ||= ||= ||= ||= ||= 9 1 9 ||= 752.857 ||= 1505.714 ||= 356.617 ||= 1109.474 ||= || | ||
|| 17\43 || || || || | ||= 17\43 ||= ||= ||= ||= ||= 8 1 8 ||= 751.936 ||= 1503.871 ||= 353.852 ||= 1105.788 ||= || | ||
|| 15\38 || || || || | ||= 15\38 ||= ||= ||= ||= ||= 7 1 7 ||= 750.771 ||= 1501.543 ||= 350.36 ||= 1101.132 ||= || | ||
|| 13\33 || || || || | ||= 13\33 ||= ||= ||= ||= ||= 6 1 6 ||= 749.255 ||= 1498.51 ||= 345.81 ||= 1095.065 ||= || | ||
|| | ||= ||= 24\61 ||= ||= ||= ||= 11 2 11 ||= 748.31 ||= 1496.62 ||= 342.976 ||= 1091.286 ||= || | ||
|| | ||= ||= 35\89 ||= ||= ||= ||= 16 3 16 ||= 747.96 ||= 1495.92 ||= 341.924 ||= 1089.884 ||= || | ||
|| || | ||= ||= 46\117 ||= ||= ||= ||= 21 4 21 ||= 747.777 ||= 1495.554 ||= 341.377 ||= 1089.154 ||= || | ||
|| | ||= ||= 57\145 ||= ||= ||= ||= 26 5 26 ||= 747.665 ||= 1495.33 ||= 341.04 ||= 1088.705 ||= || | ||
|| || || || || || | ||= ||= ||= ||= ||= ||= 5+<span style="background-color: #ffffff;">√29 2 5+√29</span> ||= 747.648 ||= 1495.297 ||= 340.99 ||= 1088.638 ||= || | ||
||= ||= 68\173 ||= ||= ||= ||= 31 6 31 ||= 747.589 ||= 1495.178 ||= 340.813 ||= 1088.402 ||= || | |||
|| || || || || | ||= ||= ||= 147\374 ||= ||= ||= 67 13 67 ||= 747.56 ||= 1495.12 ||= 340.725 ||= 1088.285 ||= 4g=45/8 near here || | ||
|| || | ||= ||= 79\201 ||= ||= ||= ||= 36 7 36 ||= 747.535 ||= 1495.069 ||= 340.649 ||= 1088.183 ||= || | ||
|| | ||= 11\28 ||= ||= ||= ||= ||= 5 1 5 ||= 747.197 ||= 1494.393 ||= 339.635 ||= 1086.831 ||= || | ||
|| || | ||= ||= 20\51 ||= ||= ||= ||= 9 2 9 ||= 745.865 ||= 1491.729 ||= 335.639 ||= 1081.50 ||= || | ||
|| || || || | ||= ||= 29\74 ||= ||= ||= ||= 13 3 13 ||= 745.361 ||= 1490.721 ||= 334.127 ||= 1079.488 ||= || | ||
|| || | ||= ||= 38/97 ||= ||= ||= ||= 17 4 17 ||= 745.096 ||= 1490.192 ||= 333.332 ||= 1078.428 ||= || | ||
|| | ||= ||= ||= ||= ||= ||= 2+<span style="background-color: #ffffff;">√5 1 </span>2+<span style="background-color: #ffffff;">√5</span> ||= 754.051 ||= 1490.101 ||= 333.197 ||= 1078.247 ||= || | ||
|| || || || || || | ||= ||= 47\120 ||= ||= ||= ||= 21 5 21 ||= 744.932 ||= 1489.865 ||= 332.842 ||= 1077.7745 ||= || | ||
|| || | ||= 9\23 ||= ||= ||= ||= ||= 4 1 4 ||= 744.243 ||= 1488.487 ||= 330.775 ||= 1075.018 ||= L/s = 4 || | ||
|| || || | ||= ||= 43\110 ||= ||= ||= ||= 19 5 19 ||= 743.4915 ||= 1486.983 ||= 328.5195 ||= 1072.011 ||= || | ||
|| || | ||= ||= ||= 77\197 ||= ||= ||= 34 9 34 ||= 743.404 ||= 1486.807 ||= 328.256 ||= 1071.66 ||= 4g=39/7 near here || | ||
|| || | ||= ||= 34\87 ||= ||= ||= ||= 15 4 15 ||= 743.293 ||= 1486.586 ||= 327.923 ||= 1071.216 ||= || | ||
|| || | ||= ||= 25\64 ||= ||= ||= ||= 11 3 11 ||= 742.951 ||= 1485.902 ||= 326.899 ||= 1069.85 ||= || | ||
|| || | ||= ||= 16\41 ||= ||= ||= ||= 7 2 7 ||= 742.226 ||= 1484.453 ||= 324.724 ||= 1066.95 ||= || | ||
|| || || | ||= ||= 23\59 ||= ||= ||= ||= 10 3 10 ||= 741.44 ||= 1482.88 ||= 322.365 ||= 1063.805 ||= || | ||
|| || | ||= ||= ||= ||= ||= ||= 3+<span style="background-color: #ffffff;">√13 2 3+√13</span> ||= 741.289 ||= 1482.577 ||= 321.911 ||= 1063.20 ||= || | ||
|| | ||= ||= 30\77 ||= ||= ||= ||= 13 4 13 ||= 741.021 ||= 1482.043 ||= 321.109 ||= 1062.131 ||= || | ||
|| | ||= ||= ||= ||= ||= ||= pi 1 pi ||= 740.449 ||= 1480.898 ||= 319.392 ||= 1056.841 ||= L/s = pi || | ||
|| | ||= 7\18 ||= ||= ||= ||= ||= 3 1 3 ||= 739.649 ||= 1479.298 ||= 316.992 ||= 1056.642 ||= L/s = 3 || | ||
|| | ||= ||= 89\229 ||= ||= ||= ||= 38 13 38 ||= 739.188 ||= 1478.376 ||= 315.608 ||= 1054.796 ||= 3g=18/5 near here || | ||
|| | ||= ||= 82\211 ||= ||= ||= ||= 35 12 35 ||= 739.148 ||= 1478.297 ||= 315.49 ||= 1054.639 ||= || | ||
|| | ||= ||= 75\193 ||= ||= ||= ||= 32 11 32 ||= 739.102 ||= 1478.203 ||= 315.35 ||= 1054.452 ||= || | ||
|| | ||= ||= 68\175 ||= ||= ||= ||= 29 10 29 ||= 739.045 ||= 1478.091 ||= 315.181 ||= 1054.227 ||= || | ||
|| | ||= ||= 61/157 ||= ||= ||= ||= 26 9 26 ||= 738.976 ||= 1477.952 ||= 314.973 ||= 1053.949 ||= || | ||
|| 3\8 || || || || | ||= ||= 54\139 ||= ||= ||= ||= 23 8 23 ||= 738.889 ||= 1477.778 ||= 314.712 ||= 1053.601 ||= || | ||
||= ||= 47\121 ||= ||= ||= ||= 20 7 20 ||= 738.776 ||= 1477.552 ||= 314.373 ||= 1053.149 ||= || | |||
||= ||= 40\103 ||= ||= ||= ||= 17 6 17 ||= 738.623 ||= 1477.247 ||= 313.915 ||= 1052.538 ||= || | |||
||= ||= 33\85 ||= ||= ||= ||= 14 5 14 ||= 738.406 ||= 1476.812 ||= 313.263 ||= 1051.669 ||= || | |||
||= ||= 26\67 ||= ||= ||= ||= 11 4 11 ||= 738.072 ||= 1476.144 ||= 312.261 ||= 1050.333 ||= || | |||
||= ||= ||= ||= ||= ||= e 1 e ||= 737.855 ||= 1478.71 ||= 311.61 ||= 1049.465 ||= L/s = e || | |||
||= ||= 19\49 ||= ||= ||= ||= 8 3 8 ||= 465.306 ||= 930.612 ||= 195.918 ||= 661.2245 ||= || | |||
||= ||= ||= 50\129 ||= ||= ||= 21 8 21 ||= 465.116 ||= 930.233 ||= 195.349 ||= 660.465 ||= || | |||
||= ||= ||= ||= 131\338 ||= ||= 55 21 55 ||= 465.089 ||= 930.1775 ||= 195.266 ||= 660.335 ||= || | |||
||= ||= ||= ||= ||= 212\547 ||= 89 34 89 ||= 465.082 ||= 930.1645 ||= 195.247 ||= 660.329 ||= || | |||
||= ||= ||= ||= 81\209 ||= ||= 34 13 34 ||= 465.072 ||= 930.1435 ||= 195.215 ||= 660.287 ||= || | |||
||= ||= ||= 31\80 ||= ||= ||= 13 5 13 ||= 737.008 ||= 1474.015 ||= 309.068 ||= 1046.075 ||= || | |||
||= ||= 12\31 ||= ||= ||= ||= 5 2 5 ||= 464.516 ||= 929.032 ||= 193.549 ||= 658.065 ||= || | |||
||= 5\13 ||= ||= ||= ||= ||= 2 1 2 ||= 461.538 ||= 923.077 ||= 184.615 ||= 646.154 ||= || | |||
||= ||= ||= ||= ||= ||= <span style="background-color: #ffffff;">√3 1 √3</span> ||= 728.159 ||= 1456.318 ||= 282.522 ||= 1010.6815 ||= || | |||
||= ||= 13\34 ||= ||= ||= ||= 5 3 5 ||= 458.824 ||= 917.647 ||= 176.471 ||= 635.294 ||= || | |||
||= ||= ||= 34\89 ||= ||= ||= 13 8 13 ||= 458.427 ||= 916.854 ||= 175.281 ||= 633.708 ||= || | |||
||= ||= ||= ||= 89\233 ||= ||= 34 21 34 ||= 458.369 ||= 916.738 ||= 175.107 ||= 633.473 ||= || | |||
||= ||= ||= ||= ||= 233\610 ||= 89 55 89 ||= 458.361 ||= 916.721 ||= 175.082 ||= 633.443 ||= Golden false father || | |||
||= ||= ||= ||= 144\377 ||= ||= 55 34 55 ||= 458.355 ||= 916.711 ||= 175.066 ||= 633.422 ||= || | |||
||= ||= ||= 55\144 ||= ||= ||= 21 13 21 ||= 458.333 ||= 916.666 ||= 175 ||= 633.333 ||= || | |||
||= ||= 21\55 ||= ||= ||= ||= 8 5 8 ||= 458.182 ||= 916.364 ||= 174.545 ||= 632.727 ||= || | |||
||= ||= ||= ||= ||= ||= pi 2 pi ||= 725.736 ||= 1451.472 ||= 275.252 ||= 1000.988 ||= || | |||
||= 8\21 ||= ||= ||= ||= ||= 3 2 3 ||= 457.143 ||= 914.286 ||= 171.429 ||= 628.571 ||= Optimum rank range (L/s=3/2) false father || | |||
||= 11\29 ||= ||= ||= ||= ||= 4 3 4 ||= 455.172 ||= 910.345 ||= 165.517 ||= 620.690 ||= || | |||
||= 14\37 ||= ||= ||= ||= ||= 5 4 5 ||= 454.054 ||= 908.108 ||= 162.162 ||= 616.216 ||= || | |||
||= 17\45 ||= ||= ||= ||= ||= 6 5 6 ||= 453.333 ||= 906.667 ||= 160 ||= 613.333 ||= || | |||
||= 20\53 ||= ||= ||= ||= ||= 7 6 7 ||= 452.83 ||= 905.66 ||= 158.491 ||= 611.321 ||= || | |||
||= 23\61 ||= ||= ||= ||= ||= 8 7 8 ||= 452.459 ||= 904.918 ||= 157.377 ||= 609.836 ||= || | |||
||= 26\69 ||= ||= ||= ||= ||= 9 8 9 ||= 452.174 ||= 904.348 ||= 156.522 ||= 608.696 ||= || | |||
||= 29\77 ||= ||= ||= ||= ||= 10 9 10 ||= 451.948 ||= 903.896 ||= 155.844 ||= 607.792 ||= || | |||
||= 3\8 ||= ||= ||= ||= ||= 1 1 1 ||= 713.233 ||= 1426.466 ||= 237.744 ||= 950.9775 ||= || | |||
.</pre></div> | .</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
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The only notable harmonic entropy minimum is Vulture/<a class="wiki_link" href="/Hemifamity%20temperaments">Buzzard</a>, in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes.<br /> | The only notable harmonic entropy minimum is Vulture/<a class="wiki_link" href="/Hemifamity%20temperaments">Buzzard</a>, in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes.<br /> | ||
<br /> | <br /> | ||
By a weird coincidence, the other generator for this MOS will generate the same pattern within a tritave equivalence. By yet another weird coincidence, this MOS belongs to a temperament which has | By a weird coincidence, the other generator for this MOS will generate the same pattern within a tritave equivalence. By yet another weird coincidence, this MOS belongs to a temperament which has <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> as its index-2 subtemperament. In addition to being harmonious, this tuning of the MOS gives an L/s ratio between 3 and 5/3, which is squarely in the middle of the range, being thus neither too exaggerated nor too equalized to be recognizable as such, unlike in octaves, where the only notable harmonic entropy minimum is near a greatly exaggerated 10/1 L/s ratio.<br /> | ||
<br /> | <br /> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<th colspan=" | <th colspan="5">generator<br /> | ||
</th> | </th> | ||
<th>tetrachord<br /> | <th>tetrachord<br /> | ||
Line 1,245: | Line 1,276: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>2\5<br /> | <td style="text-align: center;">2\5<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1 0 1<br /> | <td style="text-align: center;">1 0 1<br /> | ||
Line 1,275: | Line 1,300: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>21\53<br /> | <td style="text-align: center;">21\53<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">10 1 10<br /> | <td style="text-align: center;">10 1 10<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">753.605<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1507.21<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">358.859<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1112.464<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
Line 1,305: | Line 1,324: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>19\48<br /> | <td style="text-align: center;">19\48<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">9 1 9<br /> | <td style="text-align: center;">9 1 9<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">752.857<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1505.714<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">356.617<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1109.474<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
Line 1,335: | Line 1,348: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>17\43<br /> | <td style="text-align: center;">17\43<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">8 1 8<br /> | <td style="text-align: center;">8 1 8<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">751.936<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1503.871<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">353.852<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1105.788<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
Line 1,365: | Line 1,372: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>15\38<br /> | <td style="text-align: center;">15\38<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">7 1 7<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">750.771<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1501.543<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">350.36<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1101.132<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
Line 1,395: | Line 1,396: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>13\33<br /> | <td style="text-align: center;">13\33<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">6 1 6<br /> | <td style="text-align: center;">6 1 6<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">749.255<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1498.51<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">345.81<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1095.065<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
Line 1,425: | Line 1,420: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">24\61<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">11 2 11<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">748.31<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1496.62<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">342.976<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1091.286<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
Line 1,455: | Line 1,444: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">35\89<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">16 3 16<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">747.96<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1495.92<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">341.924<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1089.884<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | </tr> | ||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">46\117<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">21 4 21<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">747.777<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1495.554<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">341.377<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1089.154<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | </tr> | ||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">57\145<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">26 5 26<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">747.665<br /> | |||
<td> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1495.33<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">341.04<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1088.705<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">5+<span style="background-color: #ffffff;">√29 2 5+√29</span><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">747.648<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1495.297<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">340.99<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1088.638<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">68\173<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">31 6 31<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">747.589<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1495.178<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">340.813<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1088.402<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">147\374<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">67 13 67<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">747.56<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1495.12<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">340.725<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1088.285<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">4g=45/8 near here<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | </tr> | ||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">79\201<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">36 7 36<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">747.535<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">1495.069<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">340.649<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1088.183<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | </tr> | ||
<tr> | |||
<td style="text-align: center;">11\28<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">5 1 5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">747.197<br /> | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1494.393<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">339.635<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1086.831<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | </tr> | ||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">20\51<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">9 2 9<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">745.865<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1491.729<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">335.639<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1081.50<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">29\74<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">13 3 13<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">745.361<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">1490.721<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">334.127<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1079.488<br /> | ||
</td> | </td> | ||
<td style="text-align: center;" | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">38/97<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">17 4 17<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">745.096<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1490.192<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">333.332<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1078.428<br /> | ||
</td> | </td> | ||
<td style="text-align: center;" | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">2+<span style="background-color: #ffffff;">√5 1 </span>2+<span style="background-color: #ffffff;">√5</span><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">754.051<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1490.101<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">333.197<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1078.247<br /> | ||
</td> | </td> | ||
<td style="text-align: center;" | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">47\120<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">21 5 21<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">744.932<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1489.865<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">332.842<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1077.7745<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
Line 1,785: | Line 1,756: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">9\23<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">4 1 4<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">744.243<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1488.487<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">330.775<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1075.018<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">L/s = 4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | </tr> | ||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">43\110<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">19 5 19<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">743.4915<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1486.983<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">328.5195<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1072.011<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">77\197<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">34 9 34<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">743.404<br /> | |||
<td><br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">1486.807<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">328.256<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1071.66<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">4g=39/7 near here<br /> | ||
</td> | </td> | ||
<td><br /> | </tr> | ||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">34\87<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">15 4 15<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">743.293<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1486.586<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">327.923<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1071.216<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
Line 1,875: | Line 1,852: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">25\64<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">11 3 11<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">742.951<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1485.902<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">326.899<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1069.85<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
Line 1,905: | Line 1,876: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">16\41<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">7 2 7<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">742.226<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1484.453<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">324.724<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1066.95<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
Line 1,935: | Line 1,900: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">23\59<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">10 3 10<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">741.44<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">1482.88<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">322.365<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1063.805<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">3+<span style="background-color: #ffffff;">√13 2 3+√13</span><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">741.289<br /> | |||
<td style="text-align: center;"> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1482.577<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">321.911<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1063.20<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
Line 1,995: | Line 1,948: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">30\77<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">13 4 13<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">741.021<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1482.043<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">321.109<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1062.131<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
Line 2,025: | Line 1,972: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">pi 1 pi<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">740.449<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1480.898<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">319.392<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1056.841<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">L/s = pi<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | </tr> | ||
<tr> | |||
<td style="text-align: center;">7\18<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">3 1 3<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">739.649<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1479.298<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">316.992<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1056.642<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">L/s = 3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | </tr> | ||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">89\229<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">38 13 38<br /> | ||
</td> | |||
<td style="text-align: center;">739.188<br /> | |||
</td> | |||
<td style="text-align: center;">1478.376<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">315.608<br /> | |||
<td> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1054.796<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">3g=18/5 near here<br /> | ||
</td> | </td> | ||
<td><br /> | </tr> | ||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">82\211<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">35 12 35<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">739.148<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1478.297<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">315.49<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1054.639<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">75\193<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">32 11 32<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">739.102<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1478.203<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">315.35<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1054.452<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
Line 2,145: | Line 2,092: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">68\175<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">29 10 29<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">739.045<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1478.091<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">315.181<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1054.227<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | </tr> | ||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">61/157<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | |||
<td> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">26 9 26<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">738.976<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1477.952<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">314.973<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1053.949<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | </tr> | ||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">54\139<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">23 8 23<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">738.889<br /> | |||
<td> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1477.778<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">314.712<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1053.601<br /> | ||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">47\121<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">7 | <td style="text-align: center;">20 7 20<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">738.776<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1477.552<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">314.373<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1053.149<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">40\103<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">17 6 17<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">738.623<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1477.247<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">313.915<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1052.538<br /> | ||
</td> | </td> | ||
<td style="text-align: center;" | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">33\85<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">14 5 14<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">738.406<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1476.812<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">313.263<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1051.669<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | </tr> | ||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">26\67<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | |||
<td> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">11 4 11<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">738.072<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1476.144<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">312.261<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1050.333<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | </tr> | ||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">e 1 e<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">737.855<br /> | |||
<td> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1478.71<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">311.61<br /> | ||
</td> | |||
<td style="text-align: center;">1049.465<br /> | |||
</td> | |||
<td style="text-align: center;">L/s = e<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">19\49<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">8 3 8<br /> | |||
</td> | |||
<td style="text-align: center;">465.306<br /> | |||
</td> | |||
<td style="text-align: center;">930.612<br /> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">195.918<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">661.2245<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | </tr> | ||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | |||
<td style="text-align: center;">50\129<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">21 8 21<br /> | |||
</td> | |||
<td style="text-align: center;">465.116<br /> | |||
</td> | |||
<td style="text-align: center;">930.233<br /> | |||
</td> | |||
<td style="text-align: center;">195.349<br /> | |||
</td> | |||
<td style="text-align: center;">660.465<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">131\338<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">55 21 55<br /> | |||
</td> | |||
<td style="text-align: center;">465.089<br /> | |||
</td> | |||
<td style="text-align: center;">930.1775<br /> | |||
</td> | |||
<td style="text-align: center;">195.266<br /> | |||
</td> | |||
<td style="text-align: center;">660.335<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">212\547<br /> | |||
</td> | |||
<td style="text-align: center;">89 34 89<br /> | |||
</td> | |||
<td style="text-align: center;">465.082<br /> | |||
</td> | |||
<td style="text-align: center;">930.1645<br /> | |||
</td> | |||
<td style="text-align: center;">195.247<br /> | |||
</td> | |||
<td style="text-align: center;">660.329<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">81\209<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">34 13 34<br /> | |||
</td> | |||
<td style="text-align: center;">465.072<br /> | |||
</td> | |||
<td style="text-align: center;">930.1435<br /> | |||
</td> | |||
<td style="text-align: center;">195.215<br /> | |||
</td> | |||
<td style="text-align: center;">660.287<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">31\80<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">13 5 13<br /> | |||
</td> | |||
<td style="text-align: center;">737.008<br /> | |||
</td> | |||
<td style="text-align: center;">1474.015<br /> | |||
</td> | |||
<td style="text-align: center;">309.068<br /> | |||
</td> | |||
<td style="text-align: center;">1046.075<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">12\31<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">5 2 5<br /> | |||
</td> | |||
<td style="text-align: center;">464.516<br /> | |||
</td> | |||
<td style="text-align: center;">929.032<br /> | |||
</td> | |||
<td style="text-align: center;">193.549<br /> | |||
</td> | |||
<td style="text-align: center;">658.065<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">5\13<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">2 1 2<br /> | |||
</td> | |||
<td style="text-align: center;">461.538<br /> | |||
</td> | |||
<td style="text-align: center;">923.077<br /> | |||
</td> | |||
<td style="text-align: center;">184.615<br /> | |||
</td> | |||
<td style="text-align: center;">646.154<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><span style="background-color: #ffffff;">√3 1 √3</span><br /> | |||
</td> | |||
<td style="text-align: center;">728.159<br /> | |||
</td> | |||
<td style="text-align: center;">1456.318<br /> | |||
</td> | |||
<td style="text-align: center;">282.522<br /> | |||
</td> | |||
<td style="text-align: center;">1010.6815<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">13\34<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">5 3 5<br /> | |||
</td> | |||
<td style="text-align: center;">458.824<br /> | |||
</td> | |||
<td style="text-align: center;">917.647<br /> | |||
</td> | |||
<td style="text-align: center;">176.471<br /> | |||
</td> | |||
<td style="text-align: center;">635.294<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">34\89<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">13 8 13<br /> | |||
</td> | |||
<td style="text-align: center;">458.427<br /> | |||
</td> | |||
<td style="text-align: center;">916.854<br /> | |||
</td> | |||
<td style="text-align: center;">175.281<br /> | |||
</td> | |||
<td style="text-align: center;">633.708<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">89\233<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">34 21 34<br /> | |||
</td> | |||
<td style="text-align: center;">458.369<br /> | |||
</td> | |||
<td style="text-align: center;">916.738<br /> | |||
</td> | |||
<td style="text-align: center;">175.107<br /> | |||
</td> | |||
<td style="text-align: center;">633.473<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">233\610<br /> | |||
</td> | |||
<td style="text-align: center;">89 55 89<br /> | |||
</td> | |||
<td style="text-align: center;">458.361<br /> | |||
</td> | |||
<td style="text-align: center;">916.721<br /> | |||
</td> | |||
<td style="text-align: center;">175.082<br /> | |||
</td> | |||
<td style="text-align: center;">633.443<br /> | |||
</td> | |||
<td style="text-align: center;">Golden false father<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">144\377<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">55 34 55<br /> | |||
</td> | |||
<td style="text-align: center;">458.355<br /> | |||
</td> | |||
<td style="text-align: center;">916.711<br /> | |||
</td> | |||
<td style="text-align: center;">175.066<br /> | |||
</td> | |||
<td style="text-align: center;">633.422<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">55\144<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">21 13 21<br /> | |||
</td> | |||
<td style="text-align: center;">458.333<br /> | |||
</td> | |||
<td style="text-align: center;">916.666<br /> | |||
</td> | |||
<td style="text-align: center;">175<br /> | |||
</td> | |||
<td style="text-align: center;">633.333<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">21\55<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">8 5 8<br /> | |||
</td> | |||
<td style="text-align: center;">458.182<br /> | |||
</td> | |||
<td style="text-align: center;">916.364<br /> | |||
</td> | |||
<td style="text-align: center;">174.545<br /> | |||
</td> | |||
<td style="text-align: center;">632.727<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">pi 2 pi<br /> | |||
</td> | |||
<td style="text-align: center;">725.736<br /> | |||
</td> | |||
<td style="text-align: center;">1451.472<br /> | |||
</td> | |||
<td style="text-align: center;">275.252<br /> | |||
</td> | |||
<td style="text-align: center;">1000.988<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">8\21<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">3 2 3<br /> | |||
</td> | |||
<td style="text-align: center;">457.143<br /> | |||
</td> | |||
<td style="text-align: center;">914.286<br /> | |||
</td> | |||
<td style="text-align: center;">171.429<br /> | |||
</td> | |||
<td style="text-align: center;">628.571<br /> | |||
</td> | |||
<td style="text-align: center;">Optimum rank range (L/s=3/2) false father<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">11\29<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">4 3 4<br /> | |||
</td> | |||
<td style="text-align: center;">455.172<br /> | |||
</td> | |||
<td style="text-align: center;">910.345<br /> | |||
</td> | |||
<td style="text-align: center;">165.517<br /> | |||
</td> | |||
<td style="text-align: center;">620.690<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">14\37<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">5 4 5<br /> | |||
</td> | |||
<td style="text-align: center;">454.054<br /> | |||
</td> | |||
<td style="text-align: center;">908.108<br /> | |||
</td> | |||
<td style="text-align: center;">162.162<br /> | |||
</td> | |||
<td style="text-align: center;">616.216<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">17\45<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">6 5 6<br /> | |||
</td> | |||
<td style="text-align: center;">453.333<br /> | |||
</td> | |||
<td style="text-align: center;">906.667<br /> | |||
</td> | |||
<td style="text-align: center;">160<br /> | |||
</td> | |||
<td style="text-align: center;">613.333<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">20\53<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">7 6 7<br /> | |||
</td> | |||
<td style="text-align: center;">452.83<br /> | |||
</td> | |||
<td style="text-align: center;">905.66<br /> | |||
</td> | |||
<td style="text-align: center;">158.491<br /> | |||
</td> | |||
<td style="text-align: center;">611.321<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">23\61<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">8 7 8<br /> | |||
</td> | |||
<td style="text-align: center;">452.459<br /> | |||
</td> | |||
<td style="text-align: center;">904.918<br /> | |||
</td> | |||
<td style="text-align: center;">157.377<br /> | |||
</td> | |||
<td style="text-align: center;">609.836<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">26\69<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">9 8 9<br /> | |||
</td> | |||
<td style="text-align: center;">452.174<br /> | |||
</td> | |||
<td style="text-align: center;">904.348<br /> | |||
</td> | |||
<td style="text-align: center;">156.522<br /> | |||
</td> | |||
<td style="text-align: center;">608.696<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">29\77<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">10 9 10<br /> | |||
</td> | |||
<td style="text-align: center;">451.948<br /> | |||
</td> | |||
<td style="text-align: center;">903.896<br /> | |||
</td> | |||
<td style="text-align: center;">155.844<br /> | |||
</td> | |||
<td style="text-align: center;">607.792<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">3\8<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">1 1 1<br /> | <td style="text-align: center;">1 1 1<br /> |
Revision as of 21:05, 17 October 2016
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 2016-10-17 21:05:46 UTC.
- The original revision id was 595677806.
- 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:
5L 3s refers to the structure of moment of symmetry scales with generators ranging from 2\5 (two degrees of [[5edo]] = 480¢) to 3\8 (three degrees of [[8edo]] = 450¢). In the case of 8edo, L and s are the same size; in the case of 5edo, s becomes so small it disappears (and all that remains are the five equal L's). The spectrum looks like this: ||||||||||||||||~ generator ||~ <span style="display: block; text-align: center;">tetrachord</span> ||~ <span style="display: block; text-align: center;">g in cents</span> ||~ <span style="display: block; text-align: center;">2g</span> ||~ <span style="display: block; text-align: center;">3g</span> ||~ <span style="display: block; text-align: center;">4g</span> ||~ <span style="display: block; text-align: center;">Comments</span> || || 2\5 || || || || || || || ||= <span style="display: block; text-align: center;">1 0 1</span> ||= 480.000 ||= 960.000 ||= 240.00 ||= <span style="line-height: 15.6000003814697px;">720.000</span> ||= || || 21\53 || || || || || || || ||= <span style="display: block; text-align: center;">10 1 10</span> ||= 475.472 ||= 950.943 ||= 226.415 ||= 701.887 ||= <span style="display: block; text-align: center;">Vulture/Buzzard is around here</span> || || 19\48 || || || || || || || ||= <span style="display: block; text-align: center;">9 1 9</span> ||= 475 ||= 950 ||= 225 ||= 700 ||= || || 17\43 || || || || || || || ||= <span style="display: block; text-align: center;">8 1 8</span> ||= 474.419 ||= 948.837 ||= 223.256 ||= 697.674 ||= || || 15\38 || || || || || || || ||= <span style="display: block; text-align: center;">7 1 7</span> ||= 473.684 ||= 947.368 ||= 221.053 ||= 694.737 ||= || || 13\33 || || || || || || || ||= <span style="display: block; text-align: center;">6 1 6</span> ||= 472.727 ||= 945.455 ||= 218.181 ||= 690.909 ||= || || 11\28 || || || || || || || ||= <span style="display: block; text-align: center;">5 1 5</span> ||= 471.429 ||= 942.857 ||= 214.286 ||= 685.714 ||= || || 9\23 || || || || || || || ||= <span style="display: block; text-align: center;">4 1 4</span> ||= 469.565 ||= 939.130 ||= 208.696 ||= 678.261 ||= <span style="display: block; text-align: center;">L/s = 4</span> || || || || || || || || || ||= pi 1 pi ||= 467.171 ||= 934.3425 ||= 201.514 ||= 668.685 ||= <span style="display: block; text-align: center;">L/s = pi</span> || || 7\18 || || || || || || || ||= <span style="display: block; text-align: center;">3 1 3</span> ||= 466.667 ||= 933.333 ||= 200.000 ||= 666.667 ||= <span style="display: block; text-align: center;">L/s = 3</span> || || || || || || || || || ||= e 1 e ||= 465.535 ||= 931.069 ||= 196.604 ||= 662.139 ||= <span style="display: block; text-align: center;">L/s = e</span> || || || || 19\49 || || || || || ||= 8 3 8 ||= 465.306 ||= 930.612 ||= 195.918 ||= 661.2245 || || || || || || || 50\129 || || || ||= 21 8 21 ||= 465.116 ||= 930.233 ||= 195.349 ||= 660.465 || || || || || || || || || 131\338 || ||= 55 21 55 ||= 465.089 ||= 930.1775 ||= 195.266 ||= 660.335 || || || || || || || || || || 212\547 ||= 89 34 89 ||= 465.082 ||= 930.1645 ||= 195.247 ||= 660.329 || || || || || || || || 81\209 || || ||= 34 13 34 ||= 465.072 ||= 930.1435 ||= 195.215 ||= 660.287 || || || || || || 31\80 || || || || ||= 13 5 13 ||= 465 ||= 930 ||= 195 ||= 660 || || || || 12\31 || || || || || || ||= <span style="display: block; text-align: center;">5 2 5</span> ||= 464.516 ||= 929.032 ||= 193.549 ||= 658.065 ||= || || 5\13 || || || || || || || ||= <span style="display: block; text-align: center;">2 1 2</span> ||= 461.538 ||= 923.077 ||= 184.615 ||= 646.154 ||= || || || || || || || || || ||= <span style="background-color: #ffffff;">√3 1 √3</span> ||= 459.417 ||= 918.8345 ||= 178.252 ||= 637.669 || || || || 13\34 || || || || || || ||= <span style="display: block; text-align: center;">5 3 5</span> ||= 458.824 ||= 917.647 ||= 176.471 ||= 635.294 ||= || || || || || 34\89 || || || || ||= <span style="display: block; text-align: center;">13 8 13</span> ||= 458.427 ||= 916.854 ||= 175.281 ||= 633.708 ||= || || || || || || || 89\233 || || ||= <span style="display: block; text-align: center;">34 21 34</span> ||= <span style="line-height: 15.6000003814697px;">458.369</span> ||= <span style="display: block; text-align: center;">916.738</span> ||= 175.107 ||= <span style="line-height: 15.6000003814697px;">633.473</span> ||= || || || || || || || || || 233\610 ||= <span style="display: block; text-align: center;">89 55 89</span> ||= 458.361 ||= 916.721 ||= 175.082 ||= 633.443 ||= <span style="display: block; text-align: center;">Golden father</span> || || || || || || || || 144\377 || ||= <span style="display: block; text-align: center;">55 34 55</span> ||= 458.355 ||= 916.711 ||= 175.066 ||= 633.422 ||= || || || || || || 55\144 || || || ||= <span style="display: block; text-align: center;">21 13 21</span> ||= 458.333 ||= 916.666 ||= 175 ||= 633.333 ||= || || || || 21\55 || || || || || ||= <span style="display: block; text-align: center;">8 5 8</span> ||= 458.182 ||= 916.364 ||= 174.545 ||= 632.727 ||= || || || || || || || || || ||= <span style="display: block; text-align: center;">pi 2 pi</span> ||= 457.883 ||= 915.777 ||= 173.665 ||= 631.553 || || || 8\21 || || || || || || || ||= <span style="display: block; text-align: center;">3 2 3</span> ||= 457.143 ||= 914.286 ||= 171.429 ||= 628.571 ||= <span style="display: block; text-align: center;">Optimum rank range (L/s=3/2) father</span> || || 11\29 || || || || || || || ||= <span style="display: block; text-align: center;">4 3 4</span> ||= 455.172 ||= 910.345 ||= 165.517 ||= 620.690 ||= || || 14\37 || || || || || || || ||= 5 4 5 ||= 454.054 ||= 908.108 ||= 162.162 ||= 616.216 || || || 17\45 || || || || || || || ||= 6 5 6 ||= 453.333 ||= 906.667 ||= 160 ||= 613.333 || || || 20\53 || || || || || || || ||= 7 6 7 ||= 452.83 ||= 905.66 ||= 158.491 ||= 611.321 || || || 23\61 || || || || || || || ||= 8 7 8 ||= 452.459 ||= 904.918 ||= 157.377 ||= 609.836 || || || 26\69 || || || || || || || ||= 9 8 9 ||= 452.174 ||= 904.348 ||= 156.522 ||= 608.696 || || || 29\77 || || || || || || || ||= 10 9 10 ||= 451.948 ||= 903.896 ||= 155.844 ||= 607.792 || || || 3\8 || || || || || || || ||= <span style="display: block; text-align: center;">1 1 1</span> ||= 450.000 ||= 900.000 ||= 150.000 ||= 600.000 ||= || The only notable harmonic entropy minimum is Vulture/[[Hemifamity temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes. By a weird coincidence, the other generator for this MOS will generate the same pattern within a tritave equivalence. By yet another weird coincidence, this MOS belongs to a temperament which has [[Bohlen-Pierce]] as its index-2 subtemperament. In addition to being harmonious, this tuning of the MOS gives an L/s ratio between 3 and 5/3, which is squarely in the middle of the range, being thus neither too exaggerated nor too equalized to be recognizable as such, unlike in octaves, where the only notable harmonic entropy minimum is near a greatly exaggerated 10/1 L/s ratio. ||||||||||~ generator ||~ tetrachord ||~ g in cents ||~ 2g ||~ 3g ||~ 4g ||~ Comments || ||= 2\5 ||= ||= ||= ||= ||= 1 0 1 ||= 760.782 ||= 1521.564 ||= 380.391 ||= 1141.173 ||= || ||= 21\53 ||= ||= ||= ||= ||= 10 1 10 ||= 753.605 ||= 1507.21 ||= 358.859 ||= 1112.464 ||= || ||= 19\48 ||= ||= ||= ||= ||= 9 1 9 ||= 752.857 ||= 1505.714 ||= 356.617 ||= 1109.474 ||= || ||= 17\43 ||= ||= ||= ||= ||= 8 1 8 ||= 751.936 ||= 1503.871 ||= 353.852 ||= 1105.788 ||= || ||= 15\38 ||= ||= ||= ||= ||= 7 1 7 ||= 750.771 ||= 1501.543 ||= 350.36 ||= 1101.132 ||= || ||= 13\33 ||= ||= ||= ||= ||= 6 1 6 ||= 749.255 ||= 1498.51 ||= 345.81 ||= 1095.065 ||= || ||= ||= 24\61 ||= ||= ||= ||= 11 2 11 ||= 748.31 ||= 1496.62 ||= 342.976 ||= 1091.286 ||= || ||= ||= 35\89 ||= ||= ||= ||= 16 3 16 ||= 747.96 ||= 1495.92 ||= 341.924 ||= 1089.884 ||= || ||= ||= 46\117 ||= ||= ||= ||= 21 4 21 ||= 747.777 ||= 1495.554 ||= 341.377 ||= 1089.154 ||= || ||= ||= 57\145 ||= ||= ||= ||= 26 5 26 ||= 747.665 ||= 1495.33 ||= 341.04 ||= 1088.705 ||= || ||= ||= ||= ||= ||= ||= 5+<span style="background-color: #ffffff;">√29 2 5+√29</span> ||= 747.648 ||= 1495.297 ||= 340.99 ||= 1088.638 ||= || ||= ||= 68\173 ||= ||= ||= ||= 31 6 31 ||= 747.589 ||= 1495.178 ||= 340.813 ||= 1088.402 ||= || ||= ||= ||= 147\374 ||= ||= ||= 67 13 67 ||= 747.56 ||= 1495.12 ||= 340.725 ||= 1088.285 ||= 4g=45/8 near here || ||= ||= 79\201 ||= ||= ||= ||= 36 7 36 ||= 747.535 ||= 1495.069 ||= 340.649 ||= 1088.183 ||= || ||= 11\28 ||= ||= ||= ||= ||= 5 1 5 ||= 747.197 ||= 1494.393 ||= 339.635 ||= 1086.831 ||= || ||= ||= 20\51 ||= ||= ||= ||= 9 2 9 ||= 745.865 ||= 1491.729 ||= 335.639 ||= 1081.50 ||= || ||= ||= 29\74 ||= ||= ||= ||= 13 3 13 ||= 745.361 ||= 1490.721 ||= 334.127 ||= 1079.488 ||= || ||= ||= 38/97 ||= ||= ||= ||= 17 4 17 ||= 745.096 ||= 1490.192 ||= 333.332 ||= 1078.428 ||= || ||= ||= ||= ||= ||= ||= 2+<span style="background-color: #ffffff;">√5 1 </span>2+<span style="background-color: #ffffff;">√5</span> ||= 754.051 ||= 1490.101 ||= 333.197 ||= 1078.247 ||= || ||= ||= 47\120 ||= ||= ||= ||= 21 5 21 ||= 744.932 ||= 1489.865 ||= 332.842 ||= 1077.7745 ||= || ||= 9\23 ||= ||= ||= ||= ||= 4 1 4 ||= 744.243 ||= 1488.487 ||= 330.775 ||= 1075.018 ||= L/s = 4 || ||= ||= 43\110 ||= ||= ||= ||= 19 5 19 ||= 743.4915 ||= 1486.983 ||= 328.5195 ||= 1072.011 ||= || ||= ||= ||= 77\197 ||= ||= ||= 34 9 34 ||= 743.404 ||= 1486.807 ||= 328.256 ||= 1071.66 ||= 4g=39/7 near here || ||= ||= 34\87 ||= ||= ||= ||= 15 4 15 ||= 743.293 ||= 1486.586 ||= 327.923 ||= 1071.216 ||= || ||= ||= 25\64 ||= ||= ||= ||= 11 3 11 ||= 742.951 ||= 1485.902 ||= 326.899 ||= 1069.85 ||= || ||= ||= 16\41 ||= ||= ||= ||= 7 2 7 ||= 742.226 ||= 1484.453 ||= 324.724 ||= 1066.95 ||= || ||= ||= 23\59 ||= ||= ||= ||= 10 3 10 ||= 741.44 ||= 1482.88 ||= 322.365 ||= 1063.805 ||= || ||= ||= ||= ||= ||= ||= 3+<span style="background-color: #ffffff;">√13 2 3+√13</span> ||= 741.289 ||= 1482.577 ||= 321.911 ||= 1063.20 ||= || ||= ||= 30\77 ||= ||= ||= ||= 13 4 13 ||= 741.021 ||= 1482.043 ||= 321.109 ||= 1062.131 ||= || ||= ||= ||= ||= ||= ||= pi 1 pi ||= 740.449 ||= 1480.898 ||= 319.392 ||= 1056.841 ||= L/s = pi || ||= 7\18 ||= ||= ||= ||= ||= 3 1 3 ||= 739.649 ||= 1479.298 ||= 316.992 ||= 1056.642 ||= L/s = 3 || ||= ||= 89\229 ||= ||= ||= ||= 38 13 38 ||= 739.188 ||= 1478.376 ||= 315.608 ||= 1054.796 ||= 3g=18/5 near here || ||= ||= 82\211 ||= ||= ||= ||= 35 12 35 ||= 739.148 ||= 1478.297 ||= 315.49 ||= 1054.639 ||= || ||= ||= 75\193 ||= ||= ||= ||= 32 11 32 ||= 739.102 ||= 1478.203 ||= 315.35 ||= 1054.452 ||= || ||= ||= 68\175 ||= ||= ||= ||= 29 10 29 ||= 739.045 ||= 1478.091 ||= 315.181 ||= 1054.227 ||= || ||= ||= 61/157 ||= ||= ||= ||= 26 9 26 ||= 738.976 ||= 1477.952 ||= 314.973 ||= 1053.949 ||= || ||= ||= 54\139 ||= ||= ||= ||= 23 8 23 ||= 738.889 ||= 1477.778 ||= 314.712 ||= 1053.601 ||= || ||= ||= 47\121 ||= ||= ||= ||= 20 7 20 ||= 738.776 ||= 1477.552 ||= 314.373 ||= 1053.149 ||= || ||= ||= 40\103 ||= ||= ||= ||= 17 6 17 ||= 738.623 ||= 1477.247 ||= 313.915 ||= 1052.538 ||= || ||= ||= 33\85 ||= ||= ||= ||= 14 5 14 ||= 738.406 ||= 1476.812 ||= 313.263 ||= 1051.669 ||= || ||= ||= 26\67 ||= ||= ||= ||= 11 4 11 ||= 738.072 ||= 1476.144 ||= 312.261 ||= 1050.333 ||= || ||= ||= ||= ||= ||= ||= e 1 e ||= 737.855 ||= 1478.71 ||= 311.61 ||= 1049.465 ||= L/s = e || ||= ||= 19\49 ||= ||= ||= ||= 8 3 8 ||= 465.306 ||= 930.612 ||= 195.918 ||= 661.2245 ||= || ||= ||= ||= 50\129 ||= ||= ||= 21 8 21 ||= 465.116 ||= 930.233 ||= 195.349 ||= 660.465 ||= || ||= ||= ||= ||= 131\338 ||= ||= 55 21 55 ||= 465.089 ||= 930.1775 ||= 195.266 ||= 660.335 ||= || ||= ||= ||= ||= ||= 212\547 ||= 89 34 89 ||= 465.082 ||= 930.1645 ||= 195.247 ||= 660.329 ||= || ||= ||= ||= ||= 81\209 ||= ||= 34 13 34 ||= 465.072 ||= 930.1435 ||= 195.215 ||= 660.287 ||= || ||= ||= ||= 31\80 ||= ||= ||= 13 5 13 ||= 737.008 ||= 1474.015 ||= 309.068 ||= 1046.075 ||= || ||= ||= 12\31 ||= ||= ||= ||= 5 2 5 ||= 464.516 ||= 929.032 ||= 193.549 ||= 658.065 ||= || ||= 5\13 ||= ||= ||= ||= ||= 2 1 2 ||= 461.538 ||= 923.077 ||= 184.615 ||= 646.154 ||= || ||= ||= ||= ||= ||= ||= <span style="background-color: #ffffff;">√3 1 √3</span> ||= 728.159 ||= 1456.318 ||= 282.522 ||= 1010.6815 ||= || ||= ||= 13\34 ||= ||= ||= ||= 5 3 5 ||= 458.824 ||= 917.647 ||= 176.471 ||= 635.294 ||= || ||= ||= ||= 34\89 ||= ||= ||= 13 8 13 ||= 458.427 ||= 916.854 ||= 175.281 ||= 633.708 ||= || ||= ||= ||= ||= 89\233 ||= ||= 34 21 34 ||= 458.369 ||= 916.738 ||= 175.107 ||= 633.473 ||= || ||= ||= ||= ||= ||= 233\610 ||= 89 55 89 ||= 458.361 ||= 916.721 ||= 175.082 ||= 633.443 ||= Golden false father || ||= ||= ||= ||= 144\377 ||= ||= 55 34 55 ||= 458.355 ||= 916.711 ||= 175.066 ||= 633.422 ||= || ||= ||= ||= 55\144 ||= ||= ||= 21 13 21 ||= 458.333 ||= 916.666 ||= 175 ||= 633.333 ||= || ||= ||= 21\55 ||= ||= ||= ||= 8 5 8 ||= 458.182 ||= 916.364 ||= 174.545 ||= 632.727 ||= || ||= ||= ||= ||= ||= ||= pi 2 pi ||= 725.736 ||= 1451.472 ||= 275.252 ||= 1000.988 ||= || ||= 8\21 ||= ||= ||= ||= ||= 3 2 3 ||= 457.143 ||= 914.286 ||= 171.429 ||= 628.571 ||= Optimum rank range (L/s=3/2) false father || ||= 11\29 ||= ||= ||= ||= ||= 4 3 4 ||= 455.172 ||= 910.345 ||= 165.517 ||= 620.690 ||= || ||= 14\37 ||= ||= ||= ||= ||= 5 4 5 ||= 454.054 ||= 908.108 ||= 162.162 ||= 616.216 ||= || ||= 17\45 ||= ||= ||= ||= ||= 6 5 6 ||= 453.333 ||= 906.667 ||= 160 ||= 613.333 ||= || ||= 20\53 ||= ||= ||= ||= ||= 7 6 7 ||= 452.83 ||= 905.66 ||= 158.491 ||= 611.321 ||= || ||= 23\61 ||= ||= ||= ||= ||= 8 7 8 ||= 452.459 ||= 904.918 ||= 157.377 ||= 609.836 ||= || ||= 26\69 ||= ||= ||= ||= ||= 9 8 9 ||= 452.174 ||= 904.348 ||= 156.522 ||= 608.696 ||= || ||= 29\77 ||= ||= ||= ||= ||= 10 9 10 ||= 451.948 ||= 903.896 ||= 155.844 ||= 607.792 ||= || ||= 3\8 ||= ||= ||= ||= ||= 1 1 1 ||= 713.233 ||= 1426.466 ||= 237.744 ||= 950.9775 ||= || .
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<html><head><title>5L 3s</title></head><body>5L 3s refers to the structure of moment of symmetry scales with generators ranging from 2\5 (two degrees of <a class="wiki_link" href="/5edo">5edo</a> = 480¢) to 3\8 (three degrees of <a class="wiki_link" href="/8edo">8edo</a> = 450¢). In the case of 8edo, L and s are the same size; in the case of 5edo, s becomes so small it disappears (and all that remains are the five equal L's). The spectrum looks like this:<br /> <table class="wiki_table"> <tr> <th colspan="8">generator<br /> </th> <th><span style="display: block; text-align: center;">tetrachord</span><br /> </th> <th><span style="display: block; text-align: center;">g in cents</span><br /> </th> <th><span style="display: block; text-align: center;">2g</span><br /> </th> <th><span style="display: block; text-align: center;">3g</span><br /> </th> <th><span style="display: block; text-align: center;">4g</span><br /> </th> <th><span style="display: block; text-align: center;">Comments</span><br /> </th> </tr> <tr> <td>2\5<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">1 0 1</span><br /> </td> <td style="text-align: center;">480.000<br /> </td> <td style="text-align: center;">960.000<br /> </td> <td style="text-align: center;">240.00<br /> </td> <td style="text-align: center;"><span style="line-height: 15.6000003814697px;">720.000</span><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td>21\53<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">10 1 10</span><br /> </td> <td style="text-align: center;">475.472<br /> </td> <td style="text-align: center;">950.943<br /> </td> <td style="text-align: center;">226.415<br /> </td> <td style="text-align: center;">701.887<br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">Vulture/Buzzard is around here</span><br /> </td> </tr> <tr> <td>19\48<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">9 1 9</span><br /> </td> <td style="text-align: center;">475<br /> </td> <td style="text-align: center;">950<br /> </td> <td style="text-align: center;">225<br /> </td> <td style="text-align: center;">700<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td>17\43<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">8 1 8</span><br /> </td> <td style="text-align: center;">474.419<br /> </td> <td style="text-align: center;">948.837<br /> </td> <td style="text-align: center;">223.256<br /> </td> <td style="text-align: center;">697.674<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td>15\38<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">7 1 7</span><br /> </td> <td style="text-align: center;">473.684<br /> </td> <td style="text-align: center;">947.368<br /> </td> <td style="text-align: center;">221.053<br /> </td> <td style="text-align: center;">694.737<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td>13\33<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">6 1 6</span><br /> </td> <td style="text-align: center;">472.727<br /> </td> <td style="text-align: center;">945.455<br /> </td> <td style="text-align: center;">218.181<br /> </td> <td style="text-align: center;">690.909<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td>11\28<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">5 1 5</span><br /> </td> <td style="text-align: center;">471.429<br /> </td> <td style="text-align: center;">942.857<br /> </td> <td style="text-align: center;">214.286<br /> </td> <td style="text-align: center;">685.714<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td>9\23<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">4 1 4</span><br /> </td> <td style="text-align: center;">469.565<br /> </td> <td style="text-align: center;">939.130<br /> </td> <td style="text-align: center;">208.696<br /> </td> <td style="text-align: center;">678.261<br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 4</span><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 style="text-align: center;">pi 1 pi<br /> </td> <td style="text-align: center;">467.171<br /> </td> <td style="text-align: center;">934.3425<br /> </td> <td style="text-align: center;">201.514<br /> </td> <td style="text-align: center;">668.685<br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = pi</span><br /> </td> </tr> <tr> <td>7\18<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">3 1 3</span><br /> </td> <td style="text-align: center;">466.667<br /> </td> <td style="text-align: center;">933.333<br /> </td> <td style="text-align: center;">200.000<br /> </td> <td style="text-align: center;">666.667<br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3</span><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 style="text-align: center;">e 1 e<br /> </td> <td style="text-align: center;">465.535<br /> </td> <td style="text-align: center;">931.069<br /> </td> <td style="text-align: center;">196.604<br /> </td> <td style="text-align: center;">662.139<br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = e</span><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td>19\49<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;">8 3 8<br /> </td> <td style="text-align: center;">465.306<br /> </td> <td style="text-align: center;">930.612<br /> </td> <td style="text-align: center;">195.918<br /> </td> <td style="text-align: center;">661.2245<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>50\129<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;">21 8 21<br /> </td> <td style="text-align: center;">465.116<br /> </td> <td style="text-align: center;">930.233<br /> </td> <td style="text-align: center;">195.349<br /> </td> <td style="text-align: center;">660.465<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>131\338<br /> </td> <td><br /> </td> <td style="text-align: center;">55 21 55<br /> </td> <td style="text-align: center;">465.089<br /> </td> <td style="text-align: center;">930.1775<br /> </td> <td style="text-align: center;">195.266<br /> </td> <td style="text-align: center;">660.335<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><br /> </td> <td>212\547<br /> </td> <td style="text-align: center;">89 34 89<br /> </td> <td style="text-align: center;">465.082<br /> </td> <td style="text-align: center;">930.1645<br /> </td> <td style="text-align: center;">195.247<br /> </td> <td style="text-align: center;">660.329<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>81\209<br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;">34 13 34<br /> </td> <td style="text-align: center;">465.072<br /> </td> <td style="text-align: center;">930.1435<br /> </td> <td style="text-align: center;">195.215<br /> </td> <td style="text-align: center;">660.287<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>31\80<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;">13 5 13<br /> </td> <td style="text-align: center;">465<br /> </td> <td style="text-align: center;">930<br /> </td> <td style="text-align: center;">195<br /> </td> <td style="text-align: center;">660<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td>12\31<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">5 2 5</span><br /> </td> <td style="text-align: center;">464.516<br /> </td> <td style="text-align: center;">929.032<br /> </td> <td style="text-align: center;">193.549<br /> </td> <td style="text-align: center;">658.065<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td>5\13<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">2 1 2</span><br /> </td> <td style="text-align: center;">461.538<br /> </td> <td style="text-align: center;">923.077<br /> </td> <td style="text-align: center;">184.615<br /> </td> <td style="text-align: center;">646.154<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 style="text-align: center;"><span style="background-color: #ffffff;">√3 1 √3</span><br /> </td> <td style="text-align: center;">459.417<br /> </td> <td style="text-align: center;">918.8345<br /> </td> <td style="text-align: center;">178.252<br /> </td> <td style="text-align: center;">637.669<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td>13\34<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">5 3 5</span><br /> </td> <td style="text-align: center;">458.824<br /> </td> <td style="text-align: center;">917.647<br /> </td> <td style="text-align: center;">176.471<br /> </td> <td style="text-align: center;">635.294<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>34\89<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">13 8 13</span><br /> </td> <td style="text-align: center;">458.427<br /> </td> <td style="text-align: center;">916.854<br /> </td> <td style="text-align: center;">175.281<br /> </td> <td style="text-align: center;">633.708<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>89\233<br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">34 21 34</span><br /> </td> <td style="text-align: center;"><span style="line-height: 15.6000003814697px;">458.369</span><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">916.738</span><br /> </td> <td style="text-align: center;">175.107<br /> </td> <td style="text-align: center;"><span style="line-height: 15.6000003814697px;">633.473</span><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>233\610<br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">89 55 89</span><br /> </td> <td style="text-align: center;">458.361<br /> </td> <td style="text-align: center;">916.721<br /> </td> <td style="text-align: center;">175.082<br /> </td> <td style="text-align: center;">633.443<br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">Golden father</span><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>144\377<br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">55 34 55</span><br /> </td> <td style="text-align: center;">458.355<br /> </td> <td style="text-align: center;">916.711<br /> </td> <td style="text-align: center;">175.066<br /> </td> <td style="text-align: center;">633.422<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>55\144<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">21 13 21</span><br /> </td> <td style="text-align: center;">458.333<br /> </td> <td style="text-align: center;">916.666<br /> </td> <td style="text-align: center;">175<br /> </td> <td style="text-align: center;">633.333<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td>21\55<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">8 5 8</span><br /> </td> <td style="text-align: center;">458.182<br /> </td> <td style="text-align: center;">916.364<br /> </td> <td style="text-align: center;">174.545<br /> </td> <td style="text-align: center;">632.727<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 style="text-align: center;"><span style="display: block; text-align: center;">pi 2 pi</span><br /> </td> <td style="text-align: center;">457.883<br /> </td> <td style="text-align: center;">915.777<br /> </td> <td style="text-align: center;">173.665<br /> </td> <td style="text-align: center;">631.553<br /> </td> <td><br /> </td> </tr> <tr> <td>8\21<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">3 2 3</span><br /> </td> <td style="text-align: center;">457.143<br /> </td> <td style="text-align: center;">914.286<br /> </td> <td style="text-align: center;">171.429<br /> </td> <td style="text-align: center;">628.571<br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">Optimum rank range (L/s=3/2) father</span><br /> </td> </tr> <tr> <td>11\29<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">4 3 4</span><br /> </td> <td style="text-align: center;">455.172<br /> </td> <td style="text-align: center;">910.345<br /> </td> <td style="text-align: center;">165.517<br /> </td> <td style="text-align: center;">620.690<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td>14\37<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;">5 4 5<br /> </td> <td style="text-align: center;">454.054<br /> </td> <td style="text-align: center;">908.108<br /> </td> <td style="text-align: center;">162.162<br /> </td> <td style="text-align: center;">616.216<br /> </td> <td><br /> </td> </tr> <tr> <td>17\45<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;">6 5 6<br /> </td> <td style="text-align: center;">453.333<br /> </td> <td style="text-align: center;">906.667<br /> </td> <td style="text-align: center;">160<br /> </td> <td style="text-align: center;">613.333<br /> </td> <td><br /> </td> </tr> <tr> <td>20\53<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;">7 6 7<br /> </td> <td style="text-align: center;">452.83<br /> </td> <td style="text-align: center;">905.66<br /> </td> <td style="text-align: center;">158.491<br /> </td> <td style="text-align: center;">611.321<br /> </td> <td><br /> </td> </tr> <tr> <td>23\61<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;">8 7 8<br /> </td> <td style="text-align: center;">452.459<br /> </td> <td style="text-align: center;">904.918<br /> </td> <td style="text-align: center;">157.377<br /> </td> <td style="text-align: center;">609.836<br /> </td> <td><br /> </td> </tr> <tr> <td>26\69<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;">9 8 9<br /> </td> <td style="text-align: center;">452.174<br /> </td> <td style="text-align: center;">904.348<br /> </td> <td style="text-align: center;">156.522<br /> </td> <td style="text-align: center;">608.696<br /> </td> <td><br /> </td> </tr> <tr> <td>29\77<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;">10 9 10<br /> </td> <td style="text-align: center;">451.948<br /> </td> <td style="text-align: center;">903.896<br /> </td> <td style="text-align: center;">155.844<br /> </td> <td style="text-align: center;">607.792<br /> </td> <td><br /> </td> </tr> <tr> <td>3\8<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">1 1 1</span><br /> </td> <td style="text-align: center;">450.000<br /> </td> <td style="text-align: center;">900.000<br /> </td> <td style="text-align: center;">150.000<br /> </td> <td style="text-align: center;">600.000<br /> </td> <td style="text-align: center;"><br /> </td> </tr> </table> The only notable harmonic entropy minimum is Vulture/<a class="wiki_link" href="/Hemifamity%20temperaments">Buzzard</a>, in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes.<br /> <br /> By a weird coincidence, the other generator for this MOS will generate the same pattern within a tritave equivalence. By yet another weird coincidence, this MOS belongs to a temperament which has <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> as its index-2 subtemperament. In addition to being harmonious, this tuning of the MOS gives an L/s ratio between 3 and 5/3, which is squarely in the middle of the range, being thus neither too exaggerated nor too equalized to be recognizable as such, unlike in octaves, where the only notable harmonic entropy minimum is near a greatly exaggerated 10/1 L/s ratio.<br /> <br /> <table class="wiki_table"> <tr> <th colspan="5">generator<br /> </th> <th>tetrachord<br /> </th> <th>g in cents<br /> </th> <th>2g<br /> </th> <th>3g<br /> </th> <th>4g<br /> </th> <th>Comments<br /> </th> </tr> <tr> <td style="text-align: center;">2\5<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">1 0 1<br /> </td> <td style="text-align: center;">760.782<br /> </td> <td style="text-align: center;">1521.564<br /> </td> <td style="text-align: center;">380.391<br /> </td> <td style="text-align: center;">1141.173<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">21\53<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">10 1 10<br /> </td> <td style="text-align: center;">753.605<br /> </td> <td style="text-align: center;">1507.21<br /> </td> <td style="text-align: center;">358.859<br /> </td> <td style="text-align: center;">1112.464<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">19\48<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">9 1 9<br /> </td> <td style="text-align: center;">752.857<br /> </td> <td style="text-align: center;">1505.714<br /> </td> <td style="text-align: center;">356.617<br /> </td> <td style="text-align: center;">1109.474<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">17\43<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">8 1 8<br /> </td> <td style="text-align: center;">751.936<br /> </td> <td style="text-align: center;">1503.871<br /> </td> <td style="text-align: center;">353.852<br /> </td> <td style="text-align: center;">1105.788<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">15\38<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">7 1 7<br /> </td> <td style="text-align: center;">750.771<br /> </td> <td style="text-align: center;">1501.543<br /> </td> <td style="text-align: center;">350.36<br /> </td> <td style="text-align: center;">1101.132<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">13\33<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">6 1 6<br /> </td> <td style="text-align: center;">749.255<br /> </td> <td style="text-align: center;">1498.51<br /> </td> <td style="text-align: center;">345.81<br /> </td> <td style="text-align: center;">1095.065<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">24\61<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">11 2 11<br /> </td> <td style="text-align: center;">748.31<br /> </td> <td style="text-align: center;">1496.62<br /> </td> <td style="text-align: center;">342.976<br /> </td> <td style="text-align: center;">1091.286<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">35\89<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">16 3 16<br /> </td> <td style="text-align: center;">747.96<br /> </td> <td style="text-align: center;">1495.92<br /> </td> <td style="text-align: center;">341.924<br /> </td> <td style="text-align: center;">1089.884<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">46\117<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">21 4 21<br /> </td> <td style="text-align: center;">747.777<br /> </td> <td style="text-align: center;">1495.554<br /> </td> <td style="text-align: center;">341.377<br /> </td> <td style="text-align: center;">1089.154<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">57\145<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">26 5 26<br /> </td> <td style="text-align: center;">747.665<br /> </td> <td style="text-align: center;">1495.33<br /> </td> <td style="text-align: center;">341.04<br /> </td> <td style="text-align: center;">1088.705<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">5+<span style="background-color: #ffffff;">√29 2 5+√29</span><br /> </td> <td style="text-align: center;">747.648<br /> </td> <td style="text-align: center;">1495.297<br /> </td> <td style="text-align: center;">340.99<br /> </td> <td style="text-align: center;">1088.638<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">68\173<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">31 6 31<br /> </td> <td style="text-align: center;">747.589<br /> </td> <td style="text-align: center;">1495.178<br /> </td> <td style="text-align: center;">340.813<br /> </td> <td style="text-align: center;">1088.402<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">147\374<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">67 13 67<br /> </td> <td style="text-align: center;">747.56<br /> </td> <td style="text-align: center;">1495.12<br /> </td> <td style="text-align: center;">340.725<br /> </td> <td style="text-align: center;">1088.285<br /> </td> <td style="text-align: center;">4g=45/8 near here<br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">79\201<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">36 7 36<br /> </td> <td style="text-align: center;">747.535<br /> </td> <td style="text-align: center;">1495.069<br /> </td> <td style="text-align: center;">340.649<br /> </td> <td style="text-align: center;">1088.183<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">11\28<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">5 1 5<br /> </td> <td style="text-align: center;">747.197<br /> </td> <td style="text-align: center;">1494.393<br /> </td> <td style="text-align: center;">339.635<br /> </td> <td style="text-align: center;">1086.831<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">20\51<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">9 2 9<br /> </td> <td style="text-align: center;">745.865<br /> </td> <td style="text-align: center;">1491.729<br /> </td> <td style="text-align: center;">335.639<br /> </td> <td style="text-align: center;">1081.50<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">29\74<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">13 3 13<br /> </td> <td style="text-align: center;">745.361<br /> </td> <td style="text-align: center;">1490.721<br /> </td> <td style="text-align: center;">334.127<br /> </td> <td style="text-align: center;">1079.488<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">38/97<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">17 4 17<br /> </td> <td style="text-align: center;">745.096<br /> </td> <td style="text-align: center;">1490.192<br /> </td> <td style="text-align: center;">333.332<br /> </td> <td style="text-align: center;">1078.428<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">2+<span style="background-color: #ffffff;">√5 1 </span>2+<span style="background-color: #ffffff;">√5</span><br /> </td> <td style="text-align: center;">754.051<br /> </td> <td style="text-align: center;">1490.101<br /> </td> <td style="text-align: center;">333.197<br /> </td> <td style="text-align: center;">1078.247<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">47\120<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">21 5 21<br /> </td> <td style="text-align: center;">744.932<br /> </td> <td style="text-align: center;">1489.865<br /> </td> <td style="text-align: center;">332.842<br /> </td> <td style="text-align: center;">1077.7745<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">9\23<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">4 1 4<br /> </td> <td style="text-align: center;">744.243<br /> </td> <td style="text-align: center;">1488.487<br /> </td> <td style="text-align: center;">330.775<br /> </td> <td style="text-align: center;">1075.018<br /> </td> <td style="text-align: center;">L/s = 4<br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">43\110<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">19 5 19<br /> </td> <td style="text-align: center;">743.4915<br /> </td> <td style="text-align: center;">1486.983<br /> </td> <td style="text-align: center;">328.5195<br /> </td> <td style="text-align: center;">1072.011<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">77\197<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">34 9 34<br /> </td> <td style="text-align: center;">743.404<br /> </td> <td style="text-align: center;">1486.807<br /> </td> <td style="text-align: center;">328.256<br /> </td> <td style="text-align: center;">1071.66<br /> </td> <td style="text-align: center;">4g=39/7 near here<br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">34\87<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">15 4 15<br /> </td> <td style="text-align: center;">743.293<br /> </td> <td style="text-align: center;">1486.586<br /> </td> <td style="text-align: center;">327.923<br /> </td> <td style="text-align: center;">1071.216<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">25\64<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">11 3 11<br /> </td> <td style="text-align: center;">742.951<br /> </td> <td style="text-align: center;">1485.902<br /> </td> <td style="text-align: center;">326.899<br /> </td> <td style="text-align: center;">1069.85<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">16\41<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">7 2 7<br /> </td> <td style="text-align: center;">742.226<br /> </td> <td style="text-align: center;">1484.453<br /> </td> <td style="text-align: center;">324.724<br /> </td> <td style="text-align: center;">1066.95<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">23\59<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">10 3 10<br /> </td> <td style="text-align: center;">741.44<br /> </td> <td style="text-align: center;">1482.88<br /> </td> <td style="text-align: center;">322.365<br /> </td> <td style="text-align: center;">1063.805<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">3+<span style="background-color: #ffffff;">√13 2 3+√13</span><br /> </td> <td style="text-align: center;">741.289<br /> </td> <td style="text-align: center;">1482.577<br /> </td> <td style="text-align: center;">321.911<br /> </td> <td style="text-align: center;">1063.20<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">30\77<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">13 4 13<br /> </td> <td style="text-align: center;">741.021<br /> </td> <td style="text-align: center;">1482.043<br /> </td> <td style="text-align: center;">321.109<br /> </td> <td style="text-align: center;">1062.131<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">pi 1 pi<br /> </td> <td style="text-align: center;">740.449<br /> </td> <td style="text-align: center;">1480.898<br /> </td> <td style="text-align: center;">319.392<br /> </td> <td style="text-align: center;">1056.841<br /> </td> <td style="text-align: center;">L/s = pi<br /> </td> </tr> <tr> <td style="text-align: center;">7\18<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">3 1 3<br /> </td> <td style="text-align: center;">739.649<br /> </td> <td style="text-align: center;">1479.298<br /> </td> <td style="text-align: center;">316.992<br /> </td> <td style="text-align: center;">1056.642<br /> </td> <td style="text-align: center;">L/s = 3<br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">89\229<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">38 13 38<br /> </td> <td style="text-align: center;">739.188<br /> </td> <td style="text-align: center;">1478.376<br /> </td> <td style="text-align: center;">315.608<br /> </td> <td style="text-align: center;">1054.796<br /> </td> <td style="text-align: center;">3g=18/5 near here<br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">82\211<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">35 12 35<br /> </td> <td style="text-align: center;">739.148<br /> </td> <td style="text-align: center;">1478.297<br /> </td> <td style="text-align: center;">315.49<br /> </td> <td style="text-align: center;">1054.639<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">75\193<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">32 11 32<br /> </td> <td style="text-align: center;">739.102<br /> </td> <td style="text-align: center;">1478.203<br /> </td> <td style="text-align: center;">315.35<br /> </td> <td style="text-align: center;">1054.452<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">68\175<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">29 10 29<br /> </td> <td style="text-align: center;">739.045<br /> </td> <td style="text-align: center;">1478.091<br /> </td> <td style="text-align: center;">315.181<br /> </td> <td style="text-align: center;">1054.227<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">61/157<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">26 9 26<br /> </td> <td style="text-align: center;">738.976<br /> </td> <td style="text-align: center;">1477.952<br /> </td> <td style="text-align: center;">314.973<br /> </td> <td style="text-align: center;">1053.949<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">54\139<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">23 8 23<br /> </td> <td style="text-align: center;">738.889<br /> </td> <td style="text-align: center;">1477.778<br /> </td> <td style="text-align: center;">314.712<br /> </td> <td style="text-align: center;">1053.601<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">47\121<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">20 7 20<br /> </td> <td style="text-align: center;">738.776<br /> </td> <td style="text-align: center;">1477.552<br /> </td> <td style="text-align: center;">314.373<br /> </td> <td style="text-align: center;">1053.149<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">40\103<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">17 6 17<br /> </td> <td style="text-align: center;">738.623<br /> </td> <td style="text-align: center;">1477.247<br /> </td> <td style="text-align: center;">313.915<br /> </td> <td style="text-align: center;">1052.538<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">33\85<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">14 5 14<br /> </td> <td style="text-align: center;">738.406<br /> </td> <td style="text-align: center;">1476.812<br /> </td> <td style="text-align: center;">313.263<br /> </td> <td style="text-align: center;">1051.669<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">26\67<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">11 4 11<br /> </td> <td style="text-align: center;">738.072<br /> </td> <td style="text-align: center;">1476.144<br /> </td> <td style="text-align: center;">312.261<br /> </td> <td style="text-align: center;">1050.333<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">e 1 e<br /> </td> <td style="text-align: center;">737.855<br /> </td> <td style="text-align: center;">1478.71<br /> </td> <td style="text-align: center;">311.61<br /> </td> <td style="text-align: center;">1049.465<br /> </td> <td style="text-align: center;">L/s = e<br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">19\49<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">8 3 8<br /> </td> <td style="text-align: center;">465.306<br /> </td> <td style="text-align: center;">930.612<br /> </td> <td style="text-align: center;">195.918<br /> </td> <td style="text-align: center;">661.2245<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">50\129<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">21 8 21<br /> </td> <td style="text-align: center;">465.116<br /> </td> <td style="text-align: center;">930.233<br /> </td> <td style="text-align: center;">195.349<br /> </td> <td style="text-align: center;">660.465<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">131\338<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">55 21 55<br /> </td> <td style="text-align: center;">465.089<br /> </td> <td style="text-align: center;">930.1775<br /> </td> <td style="text-align: center;">195.266<br /> </td> <td style="text-align: center;">660.335<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">212\547<br /> </td> <td style="text-align: center;">89 34 89<br /> </td> <td style="text-align: center;">465.082<br /> </td> <td style="text-align: center;">930.1645<br /> </td> <td style="text-align: center;">195.247<br /> </td> <td style="text-align: center;">660.329<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">81\209<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">34 13 34<br /> </td> <td style="text-align: center;">465.072<br /> </td> <td style="text-align: center;">930.1435<br /> </td> <td style="text-align: center;">195.215<br /> </td> <td style="text-align: center;">660.287<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">31\80<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">13 5 13<br /> </td> <td style="text-align: center;">737.008<br /> </td> <td style="text-align: center;">1474.015<br /> </td> <td style="text-align: center;">309.068<br /> </td> <td style="text-align: center;">1046.075<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">12\31<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">5 2 5<br /> </td> <td style="text-align: center;">464.516<br /> </td> <td style="text-align: center;">929.032<br /> </td> <td style="text-align: center;">193.549<br /> </td> <td style="text-align: center;">658.065<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">5\13<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">2 1 2<br /> </td> <td style="text-align: center;">461.538<br /> </td> <td style="text-align: center;">923.077<br /> </td> <td style="text-align: center;">184.615<br /> </td> <td style="text-align: center;">646.154<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><span style="background-color: #ffffff;">√3 1 √3</span><br /> </td> <td style="text-align: center;">728.159<br /> </td> <td style="text-align: center;">1456.318<br /> </td> <td style="text-align: center;">282.522<br /> </td> <td style="text-align: center;">1010.6815<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">13\34<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">5 3 5<br /> </td> <td style="text-align: center;">458.824<br /> </td> <td style="text-align: center;">917.647<br /> </td> <td style="text-align: center;">176.471<br /> </td> <td style="text-align: center;">635.294<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">34\89<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">13 8 13<br /> </td> <td style="text-align: center;">458.427<br /> </td> <td style="text-align: center;">916.854<br /> </td> <td style="text-align: center;">175.281<br /> </td> <td style="text-align: center;">633.708<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">89\233<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">34 21 34<br /> </td> <td style="text-align: center;">458.369<br /> </td> <td style="text-align: center;">916.738<br /> </td> <td style="text-align: center;">175.107<br /> </td> <td style="text-align: center;">633.473<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">233\610<br /> </td> <td style="text-align: center;">89 55 89<br /> </td> <td style="text-align: center;">458.361<br /> </td> <td style="text-align: center;">916.721<br /> </td> <td style="text-align: center;">175.082<br /> </td> <td style="text-align: center;">633.443<br /> </td> <td style="text-align: center;">Golden false father<br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">144\377<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">55 34 55<br /> </td> <td style="text-align: center;">458.355<br /> </td> <td style="text-align: center;">916.711<br /> </td> <td style="text-align: center;">175.066<br /> </td> <td style="text-align: center;">633.422<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">55\144<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">21 13 21<br /> </td> <td style="text-align: center;">458.333<br /> </td> <td style="text-align: center;">916.666<br /> </td> <td style="text-align: center;">175<br /> </td> <td style="text-align: center;">633.333<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">21\55<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">8 5 8<br /> </td> <td style="text-align: center;">458.182<br /> </td> <td style="text-align: center;">916.364<br /> </td> <td style="text-align: center;">174.545<br /> </td> <td style="text-align: center;">632.727<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">pi 2 pi<br /> </td> <td style="text-align: center;">725.736<br /> </td> <td style="text-align: center;">1451.472<br /> </td> <td style="text-align: center;">275.252<br /> </td> <td style="text-align: center;">1000.988<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">8\21<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">3 2 3<br /> </td> <td style="text-align: center;">457.143<br /> </td> <td style="text-align: center;">914.286<br /> </td> <td style="text-align: center;">171.429<br /> </td> <td style="text-align: center;">628.571<br /> </td> <td style="text-align: center;">Optimum rank range (L/s=3/2) false father<br /> </td> </tr> <tr> <td style="text-align: center;">11\29<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">4 3 4<br /> </td> <td style="text-align: center;">455.172<br /> </td> <td style="text-align: center;">910.345<br /> </td> <td style="text-align: center;">165.517<br /> </td> <td style="text-align: center;">620.690<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">14\37<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">5 4 5<br /> </td> <td style="text-align: center;">454.054<br /> </td> <td style="text-align: center;">908.108<br /> </td> <td style="text-align: center;">162.162<br /> </td> <td style="text-align: center;">616.216<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">17\45<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">6 5 6<br /> </td> <td style="text-align: center;">453.333<br /> </td> <td style="text-align: center;">906.667<br /> </td> <td style="text-align: center;">160<br /> </td> <td style="text-align: center;">613.333<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">20\53<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">7 6 7<br /> </td> <td style="text-align: center;">452.83<br /> </td> <td style="text-align: center;">905.66<br /> </td> <td style="text-align: center;">158.491<br /> </td> <td style="text-align: center;">611.321<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">23\61<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">8 7 8<br /> </td> <td style="text-align: center;">452.459<br /> </td> <td style="text-align: center;">904.918<br /> </td> <td style="text-align: center;">157.377<br /> </td> <td style="text-align: center;">609.836<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">26\69<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">9 8 9<br /> </td> <td style="text-align: center;">452.174<br /> </td> <td style="text-align: center;">904.348<br /> </td> <td style="text-align: center;">156.522<br /> </td> <td style="text-align: center;">608.696<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">29\77<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">10 9 10<br /> </td> <td style="text-align: center;">451.948<br /> </td> <td style="text-align: center;">903.896<br /> </td> <td style="text-align: center;">155.844<br /> </td> <td style="text-align: center;">607.792<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">3\8<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;">1 1 1<br /> </td> <td style="text-align: center;">713.233<br /> </td> <td style="text-align: center;">1426.466<br /> </td> <td style="text-align: center;">237.744<br /> </td> <td style="text-align: center;">950.9775<br /> </td> <td style="text-align: center;"><br /> </td> </tr> </table> .</body></html>