5L 3s
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author JosephRuhf and made on 2015-11-05 11:45:02 UTC.
- The original revision id was 565323793.
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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 1 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.
Original HTML content:
<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 />
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<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 1 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.</body></html>