5L 3s: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-~~11 14~~:17:20 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-23 15:16:06 UTC</tt>.

: The original revision id was <tt>~~540641992~~</tt>.

: The original revision id was <tt>551971290</tt>.

: The revision comment was: <tt></tt>

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<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;white-space: pre-wrap ! important" class="old-revision-html">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 ||~ tetrachord ||~ g in cents ||~ 2g ||~ 3g ||~ 4g ||~ Comments ||

|| 2\5 || || || || || || || || 1 0 1 || 480.000 || 960.000 || 240.00 || 720.000 ||= ||

|| 2\5 || || || || || || || ||= 1 0 1 ||= 480.000 ||= 960.000 ||= 240.00 ||= 720.000 ||= ||

|| 21\53 || || || || || || || || 10 1 10 || 475.472 || 950.943 || 226.415 || 701.887 ||= Vulture/Buzzard is around here ||

|| 21\53 || || || || || || || ||= 10 1 10 ||= 475.472 ||= 950.943 ||= 226.415 ||= 701.887 ||= Vulture/Buzzard is around here ||

|| 19\48 || || || || || || || || 9 1 9 || 475 || 950 || 225 || 700 ||= ||

|| 19\48 || || || || || || || ||= 9 1 9 ||= 475 ||= 950 ||= 225 ||= 700 ||= ||

|| 17\43 || || || || || || || || 8 1 8 || 474.419 || 948.837 || 223.256 || 697.674 ||= ||

|| 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 ||= ||

|| 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 ||= ||

|| 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 ||= ||

|| 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 ||

|| 9\23 || || || || || || || ||= 4 1 4 ||= 469.565 ||= 939.130 ||= 208.696 ||= 678.261 ||= L/s = 4 ||

|| || || || || || || || || ~~3.03~~ 1 ~~3.03~~ || ~~466~~.~~769~~ || ~~933~~.~~538~~ || ~~200~~.~~307~~ || ~~667~~.~~076~~ ||= L/s = ~~3*2^(1/75)~~ ||

|| || || || || || || || ||= pi 1 pi ||= 467.171 ||= 934.3425 ||= 201.514 ||= 668.685 ||= L/s = pi ||

|| 7\18 || || || || || || || || 3 1 3 || 466.667 || 933.333 || 200.000 || 666.667 ||= L/s = 3 ||

|| 7\18 || || || || || || || ||= 3 1 3 ||= 466.667 ||= 933.333 ||= 200.000 ||= 666.667 ||= L/s = 3 ||

|| || || || || || || || || ~~2.97~~ 1 ~~2.97~~ || ~~466~~.~~564~~ || ~~933~~.~~127~~ || ~~199~~.~~691~~ || ~~666~~.~~255~~ ||= L/s = ~~3/2^(1/75)~~ ||

|| || || || || || || || ||= e 1 e ||= 465.535 ||= 931.069 ||= 196.604 ||= 662.139 ||= L/s = e ||

|| || 12\31 || || || || || || || 5 2 5 || 464.516 || 929.032 || 193.549 || 658.065 ||= ||

|| || 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 ||= ||

|| 5\13 || || || || || || || ||= 2 1 2 ||= 461.538 ||= 923.077 ||= 184.615 ||= 646.154 ||= ||

|| || 13\34 || || || || || || || 5 3 5 || 458.824 || 917.647 || 176.471 || 635.294 ||= ||

|| || 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 ||= ||

|| || || || 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 ||= ||

|| || || || || || 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 father ||

|| || || || || || || || 233\610 ||= 89 55 89 ||= 458.361 ||= 916.721 ||= 175.082 ||= 633.443 ||= Golden father ||

|| || || || || || || 144\377 || || 55 34 55 || 458.355 || 916.711 || 175.066 || 633.422 ||= ||

|| || || || || || || 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 ||= ||

|| || || || || 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 ||= ||

|| || || 21\55 || || || || || ||= 8 5 8 ||= 458.182 ||= 916.364 ||= 174.545 ||= 632.727 ||= ||

|| 8\21 || || || || || || || || 3 2 3 || 457.143 || 914.286 || 171.429 || 628.571 ||= Optimum rank range (L/s=3/2) father ||

|| 8\21 || || || || || || || ||= 3 2 3 ||= 457.143 ||= 914.286 ||= 171.429 ||= 628.571 ||= Optimum rank range (L/s=3/2) father ||

|| 11\29 || || || || || || || || 4 3 4 || 455.172 || 910.345 || 165.517 || 620.690 ||= ||

|| 11\29 || || || || || || || ||= 4 3 4 ||= 455.172 ||= 910.345 ||= 165.517 ||= 620.690 ||= ||

|| 3\8 || || || || || || || || ~~1 1 1~~ || ~~450~~.~~000~~ || ~~900~~.~~000~~ || ~~150.000~~ || 600.000 ||= ||

|| 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 ||= 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>

<h4>Original HTML content:</h4>

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<td>

</td>

<td>1 0 1

<td style="text-align: center;">1 0 1

</td>

<td>480.000

<td style="text-align: center;">480.000

</td>

<td>960.000

<td style="text-align: center;">960.000

</td>

<td>240.00

<td style="text-align: center;">240.00

</td>

<td>720.000

<td style="text-align: center;">720.000

</td>

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<td>

</td>

<td>10 1 10

<td style="text-align: center;">10 1 10

</td>

<td>475.472

<td style="text-align: center;">475.472

</td>

<td>950.943

<td style="text-align: center;">950.943

</td>

<td>226.415

<td style="text-align: center;">226.415

</td>

<td>701.887

<td style="text-align: center;">701.887

</td>

<td style="text-align: center;">Vulture/Buzzard is around here

Line 130:

Line 136:

<td>

</td>

<td>9 1 9

<td style="text-align: center;">9 1 9

</td>

<td>475

<td style="text-align: center;">475

</td>

<td>950

<td style="text-align: center;">950

</td>

<td>225

<td style="text-align: center;">225

</td>

<td>700

<td style="text-align: center;">700

</td>

Line 160:

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<td>

</td>

<td>8 1 8

<td style="text-align: center;">8 1 8

</td>

<td>474.419

<td style="text-align: center;">474.419

</td>

<td>948.837

<td style="text-align: center;">948.837

</td>

<td>223.256

<td style="text-align: center;">223.256

</td>

<td>697.674

<td style="text-align: center;">697.674

</td>

Line 190:

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<td>

</td>

<td>7 1 7

<td style="text-align: center;">7 1 7

</td>

<td>473.684

<td style="text-align: center;">473.684

</td>

<td>947.368

<td style="text-align: center;">947.368

</td>

<td>221.053

<td style="text-align: center;">221.053

</td>

<td>694.737

<td style="text-align: center;">694.737

</td>

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<td>

</td>

<td>6 1 6

<td style="text-align: center;">6 1 6

</td>

<td>472.727

<td style="text-align: center;">472.727

</td>

<td>945.455

<td style="text-align: center;">945.455

</td>

<td>218.181

<td style="text-align: center;">218.181

</td>

<td>690.909

<td style="text-align: center;">690.909

</td>

Line 250:

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<td>

</td>

<td>5 1 5

<td style="text-align: center;">5 1 5

</td>

<td>471.429

<td style="text-align: center;">471.429

</td>

<td>942.857

<td style="text-align: center;">942.857

</td>

<td>214.286

<td style="text-align: center;">214.286

</td>

<td>685.714

<td style="text-align: center;">685.714

</td>

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<td>

</td>

<td>4 1 4

<td style="text-align: center;">4 1 4

</td>

<td>469.565

<td style="text-align: center;">469.565

</td>

<td>939.130

<td style="text-align: center;">939.130

</td>

<td>208.696

<td style="text-align: center;">208.696

</td>

<td>678.261

<td style="text-align: center;">678.261

</td>

<td style="text-align: center;">L/s = 4

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<td>

</td>

<td>~~3.03~~ 1 ~~3.03~~

<td style="text-align: center;">pi 1 pi

</td>

<td>~~466~~.~~769~~

<td style="text-align: center;">467.171

</td>

<td>~~933~~.~~538~~

<td style="text-align: center;">934.3425

</td>

<td>~~200~~.~~307~~

<td style="text-align: center;">201.514

</td>

<td>~~667~~.~~076~~

<td style="text-align: center;">668.685

</td>

<td style="text-align: center;">L/s = ~~3*2^(1/75)~~

<td style="text-align: center;">L/s = pi

</td>

</tr>

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<td>

</td>

<td>3 1 3

<td style="text-align: center;">3 1 3

</td>

<td>466.667

<td style="text-align: center;">466.667

</td>

<td>933.333

<td style="text-align: center;">933.333

</td>

<td>200.000

<td style="text-align: center;">200.000

</td>

<td>666.667

<td style="text-align: center;">666.667

</td>

<td style="text-align: center;">L/s = 3

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<td>

</td>

<td>~~2.97~~ 1 ~~2.97~~

<td style="text-align: center;">e 1 e

</td>

<td>~~466~~.~~564~~

<td style="text-align: center;">465.535

</td>

<td>~~933~~.~~127~~

<td style="text-align: center;">931.069

</td>

<td>~~199~~.~~691~~

<td style="text-align: center;">196.604

</td>

<td>~~666~~.~~255~~

<td style="text-align: center;">662.139

</td>

<td style="text-align: center;">L/s = ~~3/2^(1/75)~~

<td style="text-align: center;">L/s = e

</td>

</tr>

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<td>

</td>

<td>5 2 5

<td style="text-align: center;">5 2 5

</td>

<td>464.516

<td style="text-align: center;">464.516

</td>

<td>929.032

<td style="text-align: center;">929.032

</td>

<td>193.549

<td style="text-align: center;">193.549

</td>

<td>658.065

<td style="text-align: center;">658.065

</td>

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<td>

</td>

<td>2 1 2

<td style="text-align: center;">2 1 2

</td>

<td>461.538

<td style="text-align: center;">461.538

</td>

<td>923.077

<td style="text-align: center;">923.077

</td>

<td>184.615

<td style="text-align: center;">184.615

</td>

<td>646.154

<td style="text-align: center;">646.154

</td>

Line 460:

Line 466:

<td>

</td>

<td>5 3 5

<td style="text-align: center;">5 3 5

</td>

<td>458.824

<td style="text-align: center;">458.824

</td>

<td>917.647

<td style="text-align: center;">917.647

</td>

<td>176.471

<td style="text-align: center;">176.471

</td>

<td>635.294

<td style="text-align: center;">635.294

</td>

Line 490:

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<td>

</td>

<td>13 8 13

<td style="text-align: center;">13 8 13

</td>

<td>458.427

<td style="text-align: center;">458.427

</td>

<td>916.854

<td style="text-align: center;">916.854

</td>

<td>175.281

<td style="text-align: center;">175.281

</td>

<td>633.708

<td style="text-align: center;">633.708

</td>

Line 520:

Line 526:

<td>

</td>

<td>34 21 34

<td style="text-align: center;">34 21 34

</td>

<td>458.369

<td style="text-align: center;">458.369

</td>

<td>916.738

<td style="text-align: center;">916.738

</td>

<td>175.107

<td style="text-align: center;">175.107

</td>

<td>633.473

<td style="text-align: center;">633.473

</td>

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<td>233\610

</td>

<td>89 55 89

<td style="text-align: center;">89 55 89

</td>

<td>458.361

<td style="text-align: center;">458.361

</td>

<td>916.721

<td style="text-align: center;">916.721

</td>

<td>175.082

<td style="text-align: center;">175.082

</td>

<td>633.443

<td style="text-align: center;">633.443

</td>

<td style="text-align: center;">Golden father

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<td>

</td>

<td>55 34 55

<td style="text-align: center;">55 34 55

</td>

<td>458.355

<td style="text-align: center;">458.355

</td>

<td>916.711

<td style="text-align: center;">916.711

</td>

<td>175.066

<td style="text-align: center;">175.066

</td>

<td>633.422

<td style="text-align: center;">633.422

</td>

Line 610:

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<td>

</td>

<td>21 13 21

<td style="text-align: center;">21 13 21

</td>

<td>458.333

<td style="text-align: center;">458.333

</td>

<td>916.666

<td style="text-align: center;">916.666

</td>

<td>175

<td style="text-align: center;">175

</td>

<td>633.333

<td style="text-align: center;">633.333

</td>

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<td>

</td>

<td>8 5 8

<td style="text-align: center;">8 5 8

</td>

<td>458.182

<td style="text-align: center;">458.182

</td>

<td>916.364

<td style="text-align: center;">916.364

</td>

<td>174.545

<td style="text-align: center;">174.545

</td>

<td>632.727

<td style="text-align: center;">632.727

</td>

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Line 676:

<td>

</td>

<td>3 2 3

<td style="text-align: center;">3 2 3

</td>

<td>457.143

<td style="text-align: center;">457.143

</td>

<td>914.286

<td style="text-align: center;">914.286

</td>

<td>171.429

<td style="text-align: center;">171.429

</td>

<td>628.571

<td style="text-align: center;">628.571

</td>

<td style="text-align: center;">Optimum rank range (L/s=3/2) father

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<td>

</td>

<td>4 3 4

<td style="text-align: center;">4 3 4

</td>

<td>455.172

<td style="text-align: center;">455.172

</td>

<td>910.345

<td style="text-align: center;">910.345

</td>

<td>165.517

<td style="text-align: center;">165.517

</td>

<td>620.690

<td style="text-align: center;">620.690

</td>

</td>

</tr>

<tr>

<td>14\37

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">5 4 5

</td>

<td style="text-align: center;">454.054

</td>

<td style="text-align: center;">908.108

</td>

<td style="text-align: center;">162.162

</td>

<td style="text-align: center;">616.216

</td>

<td>

</td>

</tr>

<tr>

<td>17\45

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">6 5 6

</td>

<td style="text-align: center;">453.333

</td>

<td style="text-align: center;">906.667

</td>

<td style="text-align: center;">160

</td>

<td style="text-align: center;">613.333

</td>

<td>

</td>

</tr>

<tr>

<td>20\53

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">7 6 7

</td>

<td style="text-align: center;">452.83

</td>

<td style="text-align: center;">905.66

</td>

<td style="text-align: center;">158.491

</td>

<td style="text-align: center;">611.321

</td>

<td>

</td>

</tr>

<tr>

<td>23\61

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">8 7 8

</td>

<td style="text-align: center;">452.459

</td>

<td style="text-align: center;">904.918

</td>

<td style="text-align: center;">157.377

</td>

<td style="text-align: center;">609.836

</td>

<td>

</td>

</tr>

<tr>

<td>26\69

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">9 8 9

</td>

<td style="text-align: center;">452.174

</td>

<td style="text-align: center;">904.348

</td>

<td style="text-align: center;">156.522

</td>

<td style="text-align: center;">608.696

</td>

<td>

</td>

</tr>

<tr>

<td>29\77

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">10 9 10

</td>

<td style="text-align: center;">451.948

</td>

<td style="text-align: center;">903.896

</td>

<td style="text-align: center;">155.844

</td>

<td style="text-align: center;">607.792

</td>

<td>

</td>

</tr>

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<td>

</td>

<td>1 1 1

<td style="text-align: center;">1 1 1

</td>

<td>450.000

<td style="text-align: center;">450.000

</td>

<td>900.000

<td style="text-align: center;">900.000

</td>

<td>150.000

<td style="text-align: center;">150.000

</td>

<td>600.000

<td style="text-align: center;">600.000

</td>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2015-02-11 14:17:20 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-23 15:16:06 UTC</tt>.<br>
-: The original revision id was <tt>540641992</tt>.<br>
+: The original revision id was <tt>551971290</tt>.<br>
 : The revision comment was: <tt></tt><br>
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 <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;white-space: pre-wrap ! important" class="old-revision-html">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 ||~ &lt;span style="display: block; text-align: center;"&gt;tetrachord&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;g in cents&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;2g&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;3g&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;4g&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;Comments&lt;/span&gt; ||
-|| 2\5 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;1 0 1&lt;/span&gt; || 480.000 || 960.000 || 240.00 || &lt;span style="line-height: 15.6000003814697px;"&gt;720.000&lt;/span&gt; ||=   ||
+|| 2\5 ||   ||   ||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;1 0 1&lt;/span&gt; ||= 480.000 ||= 960.000 ||= 240.00 ||= &lt;span style="line-height: 15.6000003814697px;"&gt;720.000&lt;/span&gt; ||=   ||
-|| 21\53 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;10 1 10&lt;/span&gt; || 475.472 || 950.943 || 226.415 || 701.887 ||= &lt;span style="display: block; text-align: center;"&gt;Vulture/Buzzard is around here&lt;/span&gt; ||
+|| 21\53 ||   ||   ||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;10 1 10&lt;/span&gt; ||= 475.472 ||= 950.943 ||= 226.415 ||= 701.887 ||= &lt;span style="display: block; text-align: center;"&gt;Vulture/Buzzard is around here&lt;/span&gt; ||
-|| 19\48 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;9 1 9&lt;/span&gt; || 475 || 950 || 225 || 700 ||=   ||
+|| 19\48 ||   ||   ||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;9 1 9&lt;/span&gt; ||= 475 ||= 950 ||= 225 ||= 700 ||=   ||
-|| 17\43 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;8 1 8&lt;/span&gt; || 474.419 || 948.837 || 223.256 || 697.674 ||=   ||
+|| 17\43 ||   ||   ||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;8 1 8&lt;/span&gt; ||= 474.419 ||= 948.837 ||= 223.256 ||= 697.674 ||=   ||
-|| 15\38 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;7 1 7&lt;/span&gt; || 473.684 || 947.368 || 221.053 || 694.737 ||=   ||
+|| 15\38 ||   ||   ||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;7 1 7&lt;/span&gt; ||= 473.684 ||= 947.368 ||= 221.053 ||= 694.737 ||=   ||
-|| 13\33 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;6 1 6&lt;/span&gt; || 472.727 || 945.455 || 218.181 || 690.909 ||=   ||
+|| 13\33 ||   ||   ||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;6 1 6&lt;/span&gt; ||= 472.727 ||= 945.455 ||= 218.181 ||= 690.909 ||=   ||
-|| 11\28 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;5 1 5&lt;/span&gt; || 471.429 || 942.857 || 214.286 || 685.714 ||=   ||
+|| 11\28 ||   ||   ||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;5 1 5&lt;/span&gt; ||= 471.429 ||= 942.857 ||= 214.286 ||= 685.714 ||=   ||
-|| 9\23 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;4 1 4&lt;/span&gt; || 469.565 || 939.130 || 208.696 || 678.261 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = 4&lt;/span&gt; ||
+|| 9\23 ||   ||   ||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;4 1 4&lt;/span&gt; ||= 469.565 ||= 939.130 ||= 208.696 ||= 678.261 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = 4&lt;/span&gt; ||
-||   ||   ||   ||   ||   ||   ||   ||   || 3.03 1 3.03 || 466.769 || 933.538 || 200.307 || 667.076 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = 3*2^(1/75)&lt;/span&gt; ||
+||   ||   ||   ||   ||   ||   ||   ||   ||= pi 1 pi ||= 467.171 ||= 934.3425 ||= 201.514 ||= 668.685 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = pi&lt;/span&gt; ||
-|| 7\18 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;3 1 3&lt;/span&gt; || 466.667 || 933.333 || 200.000 || 666.667 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = 3&lt;/span&gt; ||
+|| 7\18 ||   ||   ||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;3 1 3&lt;/span&gt; ||= 466.667 ||= 933.333 ||= 200.000 ||= 666.667 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = 3&lt;/span&gt; ||
-||   ||   ||   ||   ||   ||   ||   ||   || 2.97 1 2.97 || 466.564 || 933.127 || 199.691 || 666.255 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = 3/2^(1/75)&lt;/span&gt; ||
+||   ||   ||   ||   ||   ||   ||   ||   ||= e 1 e ||= 465.535 ||= 931.069 ||= 196.604 ||= 662.139 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = e&lt;/span&gt; ||
-||   || 12\31 ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;5 2 5&lt;/span&gt; || 464.516 || 929.032 || 193.549 || 658.065 ||=   ||
+||   || 12\31 ||   ||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;5 2 5&lt;/span&gt; ||= 464.516 ||= 929.032 ||= 193.549 ||= 658.065 ||=   ||
-|| 5\13 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;2 1 2&lt;/span&gt; || 461.538 || 923.077 || 184.615 || 646.154 ||=   ||
+|| 5\13 ||   ||   ||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;2 1 2&lt;/span&gt; ||= 461.538 ||= 923.077 ||= 184.615 ||= 646.154 ||=   ||
-||   || 13\34 ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;5 3 5&lt;/span&gt; || 458.824 || 917.647 || 176.471 || 635.294 ||=   ||
+||   || 13\34 ||   ||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;5 3 5&lt;/span&gt; ||= 458.824 ||= 917.647 ||= 176.471 ||= 635.294 ||=   ||
-||   ||   ||   || 34\89 ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;13 8 13&lt;/span&gt; || 458.427 || 916.854 || 175.281 || 633.708 ||=   ||
+||   ||   ||   || 34\89 ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;13 8 13&lt;/span&gt; ||= 458.427 ||= 916.854 ||= 175.281 ||= 633.708 ||=   ||
-||   ||   ||   ||   ||   || 89\233 ||   ||   || &lt;span style="display: block; text-align: center;"&gt;34 21 34&lt;/span&gt; || &lt;span style="line-height: 15.6000003814697px;"&gt;458.369&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;916.738&lt;/span&gt; || 175.107 || &lt;span style="line-height: 15.6000003814697px;"&gt;633.473&lt;/span&gt; ||=   ||
+||   ||   ||   ||   ||   || 89\233 ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;34 21 34&lt;/span&gt; ||= &lt;span style="line-height: 15.6000003814697px;"&gt;458.369&lt;/span&gt; ||= &lt;span style="display: block; text-align: center;"&gt;916.738&lt;/span&gt; ||= 175.107 ||= &lt;span style="line-height: 15.6000003814697px;"&gt;633.473&lt;/span&gt; ||=   ||
-||   ||   ||   ||   ||   ||   ||   || 233\610 || &lt;span style="display: block; text-align: center;"&gt;89 55 89&lt;/span&gt; || 458.361 || 916.721 || 175.082 || 633.443 ||= &lt;span style="display: block; text-align: center;"&gt;Golden father&lt;/span&gt; ||
+||   ||   ||   ||   ||   ||   ||   || 233\610 ||= &lt;span style="display: block; text-align: center;"&gt;89 55 89&lt;/span&gt; ||= 458.361 ||= 916.721 ||= 175.082 ||= 633.443 ||= &lt;span style="display: block; text-align: center;"&gt;Golden father&lt;/span&gt; ||
-||   ||   ||   ||   ||   ||   || 144\377 ||   || &lt;span style="display: block; text-align: center;"&gt;55 34 55&lt;/span&gt; || 458.355 || 916.711 || 175.066 || 633.422 ||=   ||
+||   ||   ||   ||   ||   ||   || 144\377 ||   ||= &lt;span style="display: block; text-align: center;"&gt;55 34 55&lt;/span&gt; ||= 458.355 ||= 916.711 ||= 175.066 ||= 633.422 ||=   ||
-||   ||   ||   ||   || 55\144 ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;21 13 21&lt;/span&gt; || 458.333 || 916.666 || 175 || 633.333 ||=   ||
+||   ||   ||   ||   || 55\144 ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;21 13 21&lt;/span&gt; ||= 458.333 ||= 916.666 ||= 175 ||= 633.333 ||=   ||
-||   ||   || 21\55 ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;8 5 8&lt;/span&gt; || 458.182 || 916.364 || 174.545 || 632.727 ||=   ||
+||   ||   || 21\55 ||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;8 5 8&lt;/span&gt; ||= 458.182 ||= 916.364 ||= 174.545 ||= 632.727 ||=   ||
-|| 8\21 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;3 2 3&lt;/span&gt; || 457.143 || 914.286 || 171.429 || 628.571 ||= &lt;span style="display: block; text-align: center;"&gt;Optimum rank range (L/s=3/2) father&lt;/span&gt; ||
+|| 8\21 ||   ||   ||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;3 2 3&lt;/span&gt; ||= 457.143 ||= 914.286 ||= 171.429 ||= 628.571 ||= &lt;span style="display: block; text-align: center;"&gt;Optimum rank range (L/s=3/2) father&lt;/span&gt; ||
-|| 11\29 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;4 3 4&lt;/span&gt; || 455.172 || 910.345 || 165.517 || 620.690 ||=   ||
+|| 11\29 ||   ||   ||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;4 3 4&lt;/span&gt; ||= 455.172 ||= 910.345 ||= 165.517 ||= 620.690 ||=   ||
-|| 3\8 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;1 1 1&lt;/span&gt; || 450.000 || 900.000 || 150.000 || 600.000 ||=   ||
+|| 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 ||   ||   ||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;1 1 1&lt;/span&gt; ||= 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>
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-         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;5 1 5&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;5 1 5&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;471.429&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;471.429&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;942.857&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;942.857&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;214.286&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;214.286&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;685.714&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;685.714&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 280: / Line 286: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;4 1 4&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;4 1 4&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;469.565&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;469.565&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;939.130&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;939.130&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;208.696&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;208.696&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;678.261&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;678.261&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;L/s = 4&lt;/span&gt;&lt;br /&gt;
@@ Line 310: / Line 316: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;3.03 1 3.03&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;pi 1 pi&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;466.769&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;467.171&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;933.538&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;934.3425&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;200.307&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;201.514&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;667.076&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;668.685&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;L/s = 3*2^(1/75)&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;L/s = pi&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 340: / Line 346: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;3 1 3&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;3 1 3&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;466.667&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;466.667&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;933.333&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;933.333&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;200.000&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;200.000&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;666.667&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;666.667&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;L/s = 3&lt;/span&gt;&lt;br /&gt;
@@ Line 370: / Line 376: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2.97 1 2.97&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;e 1 e&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;466.564&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;465.535&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;933.127&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;931.069&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;199.691&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;196.604&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;666.255&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;662.139&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;L/s = 3/2^(1/75)&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;L/s = e&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 400: / Line 406: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;5 2 5&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;5 2 5&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;464.516&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;464.516&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;929.032&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;929.032&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;193.549&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;193.549&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;658.065&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;658.065&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 430: / Line 436: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;2 1 2&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;2 1 2&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;461.538&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;461.538&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;923.077&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;923.077&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;184.615&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;184.615&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;646.154&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;646.154&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 460: / Line 466: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;5 3 5&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;5 3 5&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;458.824&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;458.824&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;917.647&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;917.647&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;176.471&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;176.471&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;635.294&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;635.294&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 490: / Line 496: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;13 8 13&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;13 8 13&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;458.427&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;458.427&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;916.854&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;916.854&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;175.281&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;175.281&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;633.708&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;633.708&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 520: / Line 526: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;34 21 34&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;34 21 34&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;458.369&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;458.369&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;916.738&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;916.738&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;175.107&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;175.107&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;633.473&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;633.473&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 550: / Line 556: @@
          &lt;td&gt;233\610&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;89 55 89&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;89 55 89&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;458.361&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;458.361&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;916.721&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;916.721&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;175.082&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;175.082&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;633.443&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;633.443&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Golden father&lt;/span&gt;&lt;br /&gt;
@@ Line 580: / Line 586: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;55 34 55&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;55 34 55&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;458.355&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;458.355&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;916.711&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;916.711&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;175.066&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;175.066&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;633.422&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;633.422&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 610: / Line 616: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;21 13 21&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;21 13 21&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;458.333&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;458.333&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;916.666&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;916.666&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;175&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;175&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;633.333&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;633.333&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 640: / Line 646: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;8 5 8&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;8 5 8&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;458.182&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;458.182&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;916.364&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;916.364&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;174.545&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;174.545&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;632.727&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;632.727&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 670: / Line 676: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;3 2 3&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;3 2 3&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;457.143&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;457.143&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;914.286&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;914.286&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;171.429&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;171.429&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;628.571&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;628.571&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Optimum rank range (L/s=3/2) father&lt;/span&gt;&lt;br /&gt;
@@ Line 700: / Line 706: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;4 3 4&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;4 3 4&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;455.172&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;455.172&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;910.345&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;910.345&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;165.517&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;165.517&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;620.690&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;620.690&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;14\37&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;5 4 5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;454.054&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;908.108&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;162.162&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;616.216&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
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@@ Line 730: / Line 916: @@
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-         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;1 1 1&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;1 1 1&lt;/span&gt;&lt;br /&gt;
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-         &lt;td&gt;450.000&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;450.000&lt;br /&gt;
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-         &lt;td&gt;900.000&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;900.000&lt;br /&gt;
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-         &lt;td&gt;150.000&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;150.000&lt;br /&gt;
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-         &lt;td&gt;600.000&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;600.000&lt;br /&gt;
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          &lt;td style="text-align: center;"&gt;&lt;br /&gt;