5L 3s: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 565323793 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 595579778 - 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> | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-16 23:45:26 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>595579778</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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|| || || || || 55\144 || || || ||= <span style="display: block; text-align: center;">21 13 21</span> ||= 458.333 ||= 916.666 ||= 175 ||= 633.333 ||= || | || || || || || 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 ||= || | || || || 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 | || || || || || || || || ||= <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> || | || 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 ||= || | || 11\29 || || || || || || || ||= <span style="display: block; text-align: center;">4 3 4</span> ||= 455.172 ||= 910.345 ||= 165.517 ||= 620.690 ||= || | ||
| Line 45: | Line 45: | ||
|| 29\77 || || || || || || || ||= 10 9 10 ||= 451.948 ||= 903.896 ||= 155.844 ||= 607.792 || || | || 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 ||= || | || 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.</pre></div> | 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 BP 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 ||= 475.472 ||= 950.943 ||= 226.415 ||= 701.887 ||= || | |||
|| 19\48 || || || || || || || ||= 9 1 9 ||= 475 ||= 950 ||= 225 ||= 700 ||= || | |||
|| 17\43 || || || || || || || ||= 8 1 8 ||= 474.419 ||= 948.837 ||= 223.256 ||= 697.674 ||= || | |||
|| 15\38 || || || || || || || ||= 7 1 7 ||= 473.684 ||= 947.368 ||= 221.053 ||= 694.737 ||= || | |||
|| 13\33 || || || || || || || ||= 6 1 6 ||= 472.727 ||= 945.455 ||= 218.181 ||= 690.909 ||= || | |||
|| 11\28 || || || || || || || ||= 5 1 5 ||= 471.429 ||= 942.857 ||= 214.286 ||= 685.714 ||= || | |||
|| 9\23 || || || || || || || ||= 4 1 4 ||= 469.565 ||= 939.130 ||= 208.696 ||= 678.261 ||= L/s = 4 || | |||
|| || || || || || || || ||= pi 1 pi ||= 740.449 ||= 1480.898 ||= 319.392 ||= 1056.841 ||= L/s = pi || | |||
|| 7\18 || || || || || || || ||= 3 1 3 ||= 466.667 ||= 933.333 ||= 200.000 ||= 666.667 ||= L/s = 3 || | |||
|| || || || || || || || ||= 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> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><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 /> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><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 /> | ||
| Line 894: | Line 936: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><span style="display: block; text-align: center;">pi | <td style="text-align: center;"><span style="display: block; text-align: center;">pi 2 pi</span><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">457.883<br /> | <td style="text-align: center;">457.883<br /> | ||
| Line 1,179: | Line 1,221: | ||
</table> | </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.</body></html></pre></div> | 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 BP 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="8">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>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;">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>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;">10 1 10<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;"><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;">9 1 9<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;">8 1 8<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;">7 1 7<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;">6 1 6<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;">5 1 5<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;">4 1 4<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;">L/s = 4<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;">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>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;">3 1 3<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;">L/s = 3<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;">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><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;">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><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;">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>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;">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><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;">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><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;">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><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;">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><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;">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><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;">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><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;">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><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;">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><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;">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><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 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><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;">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>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;">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>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;">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></pre></div> | |||