5L 3s: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

5L 3s refers to the structure of moment of symmetry scales with generators ranging from 2\5 (two degrees of [[5edo|5edo]] = 480¢) to 3\8 (three degrees of [[8edo|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:

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

~~: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-29 11:30:16 UTC</tt>. ~~

~~: The original revision id was <tt>602894250</tt>. ~~

~~: The revision comment was: <tt>removed tel links</tt> ~~

~~The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it. ~~

~~<h4>Original Wikitext 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;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 ||= ||

|| 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 ||= ||~~

~~|| 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 ||= 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 ||

~~|| || || || || ||= e 1 e ||= 465.535 ||= 931.069 ||= 196.604 ||= 662.139 ||= 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 ||= 465 ||= 930 ||= 195 ||= 660 || ||~~

~~|| || 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 ||= ||~~

~~|| || || || || ||= √3 1 √3 ||= 459.417 ||= 918.8345 ||= 178.252 ||= 637.669 || ||~~

~~|| || 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 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 ||= 457.883 ||= 915.777 ||= 173.665 ||= 631.553 || ||~~

|| 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 ||= ||~~

~~|| 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.

~~By a weird coincidence, the other~~ generator ~~for this MOS will generate the same pattern within a tritave equivalence~~. ~~By yet another weird coincidence, this MOS belongs to a temperament which has [[Bohlen~~-~~Pierce]] as its index~~-~~2 subtemperament~~. ~~In addition to being harmonious, this tuning of the MOS gives an~~ L/s ~~ratio between~~ 3/1 ~~and~~ 3/2~~, 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~~.

{| class="wikitable"

|-

! colspan="5" | generator

! | tetrachord

! | g in cents

! | 2g

! | 3g

! | 4g

! | Comments

|-

| | 2\5

| |

| style="text-align:center;" | 1 0 1

| style="text-align:center;" | 480.000

| style="text-align:center;" | 960.000

| style="text-align:center;" | 240.00

| style="text-align:center;" | 720.000

| style="text-align:center;" |

|-

| | 21\53

| |

| style="text-align:center;" | 10 1 10

| style="text-align:center;" | 475.472

| style="text-align:center;" | 950.943

| style="text-align:center;" | 226.415

| style="text-align:center;" | 701.887

| style="text-align:center;" | Vulture/Buzzard is around here

|-

| | 19\48

| |

| style="text-align:center;" | 9 1 9

| style="text-align:center;" | 475

| style="text-align:center;" | 950

| style="text-align:center;" | 225

| style="text-align:center;" | 700

| style="text-align:center;" |

|-

| | 17\43

| |

| style="text-align:center;" | 8 1 8

| style="text-align:center;" | 474.419

| style="text-align:center;" | 948.837

| style="text-align:center;" | 223.256

| style="text-align:center;" | 697.674

| style="text-align:center;" |

|-

| | 15\38

| |

| style="text-align:center;" | 7 1 7

| style="text-align:center;" | 473.684

| style="text-align:center;" | 947.368

| style="text-align:center;" | 221.053

| style="text-align:center;" | 694.737

| style="text-align:center;" |

|-

| | 13\33

| |

| style="text-align:center;" | 6 1 6

| style="text-align:center;" | 472.727

| style="text-align:center;" | 945.455

| style="text-align:center;" | 218.181

| style="text-align:center;" | 690.909

| style="text-align:center;" |

|-

| | 11\28

| |

| style="text-align:center;" | 5 1 5

| style="text-align:center;" | 471.429

| style="text-align:center;" | 942.857

| style="text-align:center;" | 214.286

| style="text-align:center;" | 685.714

| style="text-align:center;" |

|-

| | 9\23

| |

| style="text-align:center;" | 4 1 4

| style="text-align:center;" | 469.565

| style="text-align:center;" | 939.130

| style="text-align:center;" | 208.696

| style="text-align:center;" | 678.261

| style="text-align:center;" | L/s = 4

|-

| |

| style="text-align:center;" | pi 1 pi

| style="text-align:center;" | 467.171

| style="text-align:center;" | 934.3425

| style="text-align:center;" | 201.514

| style="text-align:center;" | 668.685

| style="text-align:center;" | L/s = pi

|-

| | 7\18

| |

| style="text-align:center;" | 3 1 3

| style="text-align:center;" | 466.667

| style="text-align:center;" | 933.333

| style="text-align:center;" | 200.000

| style="text-align:center;" | 666.667

| style="text-align:center;" | L/s = 3

|-

| |

| style="text-align:center;" | e 1 e

| style="text-align:center;" | 465.535

| style="text-align:center;" | 931.069

| style="text-align:center;" | 196.604

| style="text-align:center;" | 662.139

| style="text-align:center;" | L/s = e

|-

| |

| | 19\49

| |

| style="text-align:center;" | 8 3 8

| style="text-align:center;" | 465.306

| style="text-align:center;" | 930.612

| style="text-align:center;" | 195.918

| style="text-align:center;" | 661.2245

| |

|-

| |

| | 50\129

| |

| style="text-align:center;" | 21 8 21

| style="text-align:center;" | 465.116

| style="text-align:center;" | 930.233

| style="text-align:center;" | 195.349

| style="text-align:center;" | 660.465

| |

|-

| |

| | 131\338

| |

| style="text-align:center;" | 55 21 55

| style="text-align:center;" | 465.089

| style="text-align:center;" | 930.1775

| style="text-align:center;" | 195.266

| style="text-align:center;" | 660.335

| |

|-

| |

| | 212\547

| style="text-align:center;" | 89 34 89

| style="text-align:center;" | 465.082

| style="text-align:center;" | 930.1645

| style="text-align:center;" | 195.247

| style="text-align:center;" | 660.329

| |

|-

| |

| | 81\209

| |

| style="text-align:center;" | 34 13 34

| style="text-align:center;" | 465.072

| style="text-align:center;" | 930.1435

| style="text-align:center;" | 195.215

| style="text-align:center;" | 660.287

| |

|-

| |

| | 31\80

| |

| style="text-align:center;" | 13 5 13

| style="text-align:center;" | 465

| style="text-align:center;" | 930

| style="text-align:center;" | 195

| style="text-align:center;" | 660

| |

|-

| |

| | 12\31

| |

| style="text-align:center;" | 5 2 5

| style="text-align:center;" | 464.516

| style="text-align:center;" | 929.032

| style="text-align:center;" | 193.549

| style="text-align:center;" | 658.065

| style="text-align:center;" |

|-

| | 5\13

| |

| style="text-align:center;" | 2 1 2

| style="text-align:center;" | 461.538

| style="text-align:center;" | 923.077

| style="text-align:center;" | 184.615

| style="text-align:center;" | 646.154

| style="text-align:center;" |

|-

| |

| style="text-align:center;" | √3 1 √3

| style="text-align:center;" | 459.417

| style="text-align:center;" | 918.8345

| style="text-align:center;" | 178.252

| style="text-align:center;" | 637.669

| |

|-

| |

| | 13\34

| |

| style="text-align:center;" | 5 3 5

| style="text-align:center;" | 458.824

| style="text-align:center;" | 917.647

| style="text-align:center;" | 176.471

| style="text-align:center;" | 635.294

| style="text-align:center;" |

|-

| |

| | 34\89

| |

| style="text-align:center;" | 13 8 13

| style="text-align:center;" | 458.427

| style="text-align:center;" | 916.854

| style="text-align:center;" | 175.281

| style="text-align:center;" | 633.708

| style="text-align:center;" |

|-

| |

| | 89\233

| |

| style="text-align:center;" | 34 21 34

| style="text-align:center;" | 458.369

| style="text-align:center;" | 916.738

| style="text-align:center;" | 175.107

| style="text-align:center;" | 633.473

| style="text-align:center;" |

|-

| |

| | 233\610

| style="text-align:center;" | 89 55 89

| style="text-align:center;" | 458.361

| style="text-align:center;" | 916.721

| style="text-align:center;" | 175.082

| style="text-align:center;" | 633.443

| style="text-align:center;" | Golden father

|-

| |

| | 144\377

| |

| style="text-align:center;" | 55 34 55

| style="text-align:center;" | 458.355

| style="text-align:center;" | 916.711

| style="text-align:center;" | 175.066

| style="text-align:center;" | 633.422

| style="text-align:center;" |

|-

| |

| | 55\144

| |

| style="text-align:center;" | 21 13 21

| style="text-align:center;" | 458.333

| style="text-align:center;" | 916.666

| style="text-align:center;" | 175

| style="text-align:center;" | 633.333

| style="text-align:center;" |

|-

| |

| | 21\55

| |

| style="text-align:center;" | 8 5 8

| style="text-align:center;" | 458.182

| style="text-align:center;" | 916.364

| style="text-align:center;" | 174.545

| style="text-align:center;" | 632.727

| style="text-align:center;" |

|-

| |

| style="text-align:center;" | pi 2 pi

| style="text-align:center;" | 457.883

| style="text-align:center;" | 915.777

| style="text-align:center;" | 173.665

| style="text-align:center;" | 631.553

| |

|-

| | 8\21

| |

| style="text-align:center;" | 3 2 3

| style="text-align:center;" | 457.143

| style="text-align:center;" | 914.286

| style="text-align:center;" | 171.429

| style="text-align:center;" | 628.571

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

|-

| | 11\29

| |

| style="text-align:center;" | 4 3 4

| style="text-align:center;" | 455.172

| style="text-align:center;" | 910.345

| style="text-align:center;" | 165.517

| style="text-align:center;" | 620.690

| style="text-align:center;" |

|-

| | 14\37

| |

| style="text-align:center;" | 5 4 5

| style="text-align:center;" | 454.054

| style="text-align:center;" | 908.108

| style="text-align:center;" | 162.162

| style="text-align:center;" | 616.216

| |

|-

| | 17\45

| |

| style="text-align:center;" | 6 5 6

| style="text-align:center;" | 453.333

| style="text-align:center;" | 906.667

| style="text-align:center;" | 160

| style="text-align:center;" | 613.333

| |

|-

| | 20\53

| |

| style="text-align:center;" | 7 6 7

| style="text-align:center;" | 452.83

| style="text-align:center;" | 905.66

| style="text-align:center;" | 158.491

| style="text-align:center;" | 611.321

| |

|-

| | 23\61

| |

| style="text-align:center;" | 8 7 8

| style="text-align:center;" | 452.459

| style="text-align:center;" | 904.918

| style="text-align:center;" | 157.377

| style="text-align:center;" | 609.836

| |

|-

| | 26\69

| |

| style="text-align:center;" | 9 8 9

| style="text-align:center;" | 452.174

| style="text-align:center;" | 904.348

| style="text-align:center;" | 156.522

| style="text-align:center;" | 608.696

| |

|-

| | 29\77

| |

| style="text-align:center;" | 10 9 10

| style="text-align:center;" | 451.948

| style="text-align:center;" | 903.896

| style="text-align:center;" | 155.844

| style="text-align:center;" | 607.792

| |

|-

| | 3\8

| |

| style="text-align:center;" | 1 1 1

| style="text-align:center;" | 450.000

| style="text-align:center;" | 900.000

| style="text-align:center;" | 150.000

| style="text-align:center;" | 600.000

| style="text-align:center;" |

|}

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.

~~||||||||||~~~ generator ~~||~ tetrachord ||~ g in cents ||~ 2g ||~ 3g ||~ 4g ||~ Comments ||~~

By a weird coincidence, the other generator for this MOS will generate the same pattern within a tritave equivalence. By yet another weird coincidence, this MOS belongs to a temperament which has [[Bohlen-Pierce|Bohlen-Pierce]] as its index-2 subtemperament. In addition to being harmonious, this tuning of the MOS gives an L/s ratio between 3/1 and 3/2, 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.

~~||= 2\5 ||= ||= ||= ||= ||= 1 0 1 ||= 760~~.~~782 ||= 1521.564 ||= 380.391 ||= 1141.173 ||= ||~~

~~||= 27\68 ||= ||= ||= ||= ||= 13 1 13 ||= 755.188 ||= 1510.376 ||= 363.609 ||= 1118.797 ||= ||~~

~~||= ||= ||= ||= ||= ||= ~6626 515 6626 ||= 755.132 ||= 1510.265 ||= 363.442 ||= 1118.574 ||= 2g=12/5 minus quarter comma ||~~

~~||= 25\63 ||= ||= ||= ||= ||= 12 1 12 ||= 754.744 ||= 1509.488 ||= 362.277 ||= 1117.021 ||= ||~~

~~||= 23\58 ||= ||= ||= ||= ||= 11 1 11 ||= 754.2235 ||= 1508.447 ||= 360.716 ||= 1114.939 ||= ||~~

~~||= 21\53 ||= ||= ||= ||= ||= 10 1 10 ||= 753.605 ||= 1507.21 ||= 358.859 ||= 1112.464 ||= ||~~

~~||= 19\48 ||= ||= ||= ||= ||= 9 1 9 ||= 752.857 ||= 1505.714 ||= 356.617 ||= 1109.474 ||= ||~~

~~||= 17\43 ||= ||= ||= ||= ||= 8 1 8 ||= 751.936 ||= 1503.871 ||= 353.852 ||= 1105.788 ||= ||~~

~~||= 15\38 ||= ||= ||= ||= ||= 7 1 7 ||= 750.771 ||= 1501.543 ||= 350.36 ||= 1101.132 ||= ||~~

~~||= ||= 28/71 ||= ||= ||= ||= 13 2 13 ||= 750.067 ||= 1500.1335 ||= 348.245 ||= 1098.312 ||= ||~~

~~||= ||= 41\104 ||= ||= ||= ||= 19 3 19 ||= 749.809 ||= 1466.618 ||= 347.4725 ||= 1097.282 ||= 3g=11/3 near here ||~~

~~||= 13\33 ||= ||= ||= ||= ||= 6 1 6 ||= 749.255 ||= 1498.51 ||= 345.81 ||= 1095.065 ||= ||~~

~~||= ||= 24\61 ||= ||= ||= ||= 11 2 11 ||= 748.31 ||= 1496.62 ||= 342.976 ||= 1091.286 ||= ||~~

~~||= ||= 35\89 ||= ||= ||= ||= 16 3 16 ||= 747.96 ||= 1495.92 ||= 341.924 ||= 1089.884 ||= ||~~

~~||= ||= 46\117 ||= ||= ||= ||= 21 4 21 ||= 747.777 ||= 1495.554 ||= 341.377 ||= 1089.154 ||= ||~~

~~||= ||= 57\145 ||= ||= ||= ||= 26 5 26 ||= 747.665 |~~|~~= 1495.33 ||= 341.04 ||= 1088.705 ||= ||~~

~~||= ||= ||= ||= ||= ||= 5+√29 2 5+√29 ||= 747.648 ||= 1495.297 ||= 340.99 ||= 1088.638 ||= ||~~

~~||= ||= 68\173 ||= ||= ||= ||= 31 6 31 ||= 747.589 ||= 1495.178 ||= 340.813 ||= 1088.402 ||= ||~~

~~||= ||= ||= 147\374 ||= ||= ||= 67 13 67 ||= 747.56 ||= 1495.12 ||= 340.725 ||= 1088.285 ||= 4g=45/8 near here ||~~

~~||= ||= 79\201 ||= ||= ||= ||= 36 7 36 ||= 747.535 ||= 1495.069 ||= 340.649 ||= 1088.183 ||= ||~~

~~||= 11\28 ||= ||= ||= ||= ||= 5 1 5 ||= 747.197 ||= 1494.393 ||= 339.635 ||= 1086.831 ||= ||~~

~~||= ||= 20\51 ||= ||= ||= ||= 9 2 9 ||= 745.865 ||= 1491.729 ||= 335.639 ||= 1081.50 ||= ||~~

~~||= ||= 29\74 ||= ||= ||= ||= 13 3 13 ||= 745.361 ||= 1490.721 ||= 334.127 ||= 1079.488 ||= ||~~

~~||= ||= 38/97 ||= ||= ||= ||= 17 4 17 ||= 745.096 ||= 1490.192 ||= 333.332 ||= 1078.428 ||= ||~~

~~||= ||= ||= ||= ||= ||= 2+√5 1 ~~2~~+√5 ||= 754~~.~~051 ||= 1490.101 ||= 333.197 ||= 1078.247 ||= ||~~

~~||= ||= 47\120 ||= ||= ||= ||= 21 5 21 ||= 744.932 ||= 1489.865 ||= 332.842 ||= 1077.7745 ||= ||~~

~~||= 9\23 ||= ||= ||= ||= ||= 4 1 4 ||= 744.243 ||= 1488.487 ||= 330.775 ||= 1075.018 ||= L/s = 4 ||~~

~~||= ||= 43\110 ||= ||= ||= ||= 19 5 19 ||= 743.4915 ||= 1486.983 ||= 328.5195 ||= 1072.011 ||= ||~~

~~||= ||= ||= 77\197 ||= ||= ||= 34 9 34 ||= 743.404 ||= 1486.807 ||= 328.256 ||= 1071.66 ||= 4g=39/7 near here ||~~

~~||= ||= 34\87 ||= ||= ||= ||= 15 4 15 ||= 743.293 ||= 1486.586 ||= 327.923 ||= 1071.216 ||= ||~~

~~||= ||= 25\64 ||= ||= ||= ||= 11 3 11 ||= 742.951 ||= 1485.902 ||= 326.899 ||= 1069.85 ||= ||~~

~~||= ||= 16\41 ||= ||= ||= ||= 7 2 7 ||= 742.226 ||= 1484.453 ||= 324.724 ||= 1066.95 ||= ||~~

~~||= ||= 23\59 ||= ||= ||= ||= 10 3 10 ||= 741.44 ||= 1482.88 ||= 322.365 ||= 1063.805 ||= ||~~

~~||= ||= ||= ||= ||= ||= 3+√13 2 3+√13 ||= 741.289 ||= 1482.577 ||= 321.911 ||= 1063.20 ||= ||~~

~~||= ||= 30\77 ||= ||= ||= ||= 13 4 13 ||= 741.021 ||= 1482.043 ||= 321.109 ||= 1062.131 ||= ||~~

~~||= ||= ||= ||= ||= ||= pi 1 pi ||= 740.449 ||= 1480.898 ||= 319.392 ||= 1056.841 ||= L/s = pi ||~~

~~||= 7\18 ||= ||= ||= ||= ||= 3 1 3 ||= 739.649 ||= 1479.298 ||= 316.992 ||= 1056.642 ||=~~ L/s = 3 ||

~~||= ||= 89\229 ||= ||= ||= ||= 38 13 38 ||= 739.188 ||= 1478.376 ||= 315.608 ||= 1054.796 ||= 3g=18/5 near here ||~~

~~||= ||= 82\211 ||= ||= ||= ||= 35 12 35 ||= 739.148 ||= 1478.297 ||= 315.49 ||= 1054.639 ||= ||~~

~~||= ||= 75\193 ||= ||= ||= ||= 32 11 32 ||= 739.102 ||= 1478.203 ||= 315.35 ||= 1054.452 ||= ||~~

~~||= ||= 68\175 ||= ||= ||= ||= 29 10 29 ||= 739.045 ||= 1478.091 ||= 315.181 ||= 1054.227 ||= ||~~

~~||= ||= 61~~/~~157 ||= ||= ||= ||= 26 9 26 ||= 738.976 ||= 1477.952 ||= 314.973 ||= 1053.949 ||= ||~~

~~||= ||= 54\139 ||= ||= ||= ||= 23 8 23 ||= 738.889 ||= 1477.778 ||= 314.712 ||= 1053.601 ||= ||~~

~~||= ||= 47\121 ||= ||= ||= ||= 20 7 20 ||= 738.776 ||= 1477.552 ||= 314.373 ||= 1053.149 ||= ||~~

~~||= ||= 40\103 ||= ||= ||= ||= 17 6 17 ||= 738.623 ||= 1477.247 ||= 313.915 ||= 1052.538 ||= ||~~

~~||= ||= 33\85 ||= ||= ||= ||= 14 5 14 ||= 738.406 ||= 1476.812 ||= 313.263 ||= 1051.669 ||= ||~~

~~||= ||= 26\67 ||= ||= ||= ||= 11 4 11 ||= 738.072 ||= 1476.144 ||= 312.261 ||= 1050.333 ||= ||~~

~~||= ||= ||= ||= ||= ||= e~~ 1 ~~e ||= 737.855 ||= 1478.71 ||= 311.61 ||= 1049.465 ||= L/s = e ||~~

~~||= ||= 19\49 ||= ||= ||= ||= 8~~ 3 ~~8 ||= 737.493 ||= 1474.986 ||= 310.523 ||= 1048.016 ||= ||~~

~~||= ||= ||= ||= 164\423 ||= ||= 69 26 69 ||= 737.401 ||= 1474.802 ||= 310.248 ||= 1047.649 ||= 3g=18~~/~~5 minus quarter comma near here ||~~

~~||= ||= ||= ||= 145\374 ||= ||= 61 23 61 ||= 737.389 ||= 1474.778 ||= 310.212 ||= 1047.601 ||= ||~~

~~||= ||= ||= ||= 126\325 ||= ||= 53 20 53 ||= 737.373 ||= 1474.747 ||= 310.165 ||= 1047.538 ||= ||~~

~~||= ||= ||= ||= 107\276 ||= ||= 45 17 45 ||= 737.352 ||= 1474.704 ||= 310.101 ||= 1047.453 ||= ||~~

~~||= ||= ||= ||= 88\227 ||= ||= 37 14 37 ||= 737.322 ||= 1474.644 ||= 310.01 ||= 1047.332 ||= ||~~

~~||= ||= ||= ||= 69\178 ||= ||= 29 11 29 ||= 737.275 ||= 1474.549 ||= 309.869 ||= 1047.144 ||= ||~~

~~||= ||= ||= 50\129 ||= ||= ||= 21 8 21 ||= 737.192 ||= 1474.384 ||= 309.621 ||= 1046.812 ||= ||~~

~~||= ||= ||= ||= 131\338 ||= ||= 55 21 55 ||= 737.148 ||= 1474.296 ||= 309.49 ||= 1046.638 ||= ||~~

~~||= ||= ||= ||= ||= 212\547 ||= 89 34 89 ||= 737.138 ||= 1474.276 ||= 309.459 ||= 1046.597 ||= ||~~

~~||= ||= ||= ||= 81\209 ||= ||= 34 13 34 ||= 737.121 ||= 1474.243 ||= 309.409 ||= 1046.53 ||= ||~~

~~||= ||= ||= 31\80 ||= ||= ||= 13 5 13 ||= 737.008 ||= 1474.015 ||= 309.068 ||= 1046.075 ||= ||~~

~~||= ||= 12\31 ||= ||= ||= ||= 5~~ 2 ~~5 ||= 736.241 ||= 1472.481 ||= 306.767 ||= 1043.007 ||= ||~~

~~||= ||= ||= ||= ||= ||= 1+√2 1 1+√2 ||= 735.542 ||= 1471.084 ||= 304.6715 ||= 1040.214 ||= Silver false father ||~~

~~||= ||= 17\44 ||= ||= ||= ||= 7 3 7 ||= 734.846 ||= 1469.693 ||= 302.584 ||= 1037.41 ||= ||~~

~~||= ||= 22\57 ||= ||= ||= ||= 9 4 9 ||= 734.088 ||= 1468.176 ||= 300.309 ||= 1034.397 ||= ||~~

~~||= ||= 27\70 ||= ||= ||= ||= 11 5 11 ||= 733.611 ||= 1467.222 ||= 298.879 ||= 1032.49 ||= ||~~

~~||= ||= ||= 59\153 ||= ||= ||= 24 11 24 ||= 733.434 ||= 1466.867 ||= 298.346 ||= 1031.779 ||= ||~~

~~||= ||= 32\83 ||= ||= ||= ||= 13 6 13 ||= 733.284 ||= 1466.568 ||= 297.897 ||= 1031.181 ||= 2g=7/3 near here ||~~

~~||= 5\13 ||= ||= ||= ||= ||= 2 1 2 ||= 731.521 ||= 1463.042 ||= 292.609 ||= 1024.13 ||= ||~~

~~||= ||= 53\138 ||= ||= ||= ||= 21 11 21 ||= 730.461 ||= 1460.922 ||= 289.428 ||= 1018.889 ||= ||~~

~~||= ||= ||= 101\263 ||= ||= ||= 40 21 40 ||= 730.409 ||= 1460.817 ||= 289.271 ||= 1019.679 ||= 3g=39/11 near here ||~~

~~||= ||= 48\125 ||= ||= ||= ||= 19 10 19 ||= 730.35 ||= 1460.701 ||= 289.097 ||= 1019.448 ||= ||~~

~~||= ||= 43\112 ||= ||= ||= ||= 17 9 17 ||= 730.215 ||= 1460.43 ||= 288.69 ||= 1018.905 ||= ||~~

~~||= ||= 38\99 ||= ||= ||= ||= 15 8 15 ||= 730.043 ||= 1460.087 ||= 288.175 ||= 1018.218 ||= ||~~

~~||= ||= ||= 71\185 ||= ||= ||= 28 15 28 ||= 729.9395 ||= 1459.879 ||= 287.8635 ||= 1017.803 ||= ||~~

~~||= ||= ||= 104\271 ||= ||= ||= 41 22 41 ||= 729.902 ||= 1459.803 ||= 287.75 ||= 1017.651 ||= 4g=27/5 near here ||~~

~~||= ||= 33\86 ||= ||= ||= ||= 13 7 13 ||= 729.82 ||= 1459.64 ||= 287.505 ||= 1017.325 ||= ||~~

~~||= ||= 28\73 ||= ||= ||= ||= 11 6 11 ||= 729.547 ||= 1459.034 ||= 286.596 ||= 1016.113 ||= ||~~

~~||= ||= 23\60 ||= ||= ||= ||= 9 5 9 ||= 729.083 ||= 1458.1655 ||= 285.293 ||= 1014.376 ||= ||~~

~~||= ||= ||= 41\107 ||= ||= ||= 16 9 16 ||= 728.7865 ||= 1457.573 ||= 284.4045 ||= 1013.191 ||= 3g=99/28 near here ||~~

~~||= ||= ||= 59\154 ||= ||= ||= 23 13 23 ||= 728.671 ||= 1457.342 ||= 284.058 ||= 1012.729 ||= ||~~

~~||= ||= ||= 77\201 ||= ||= ||= 30 17 30 ||= 728.61 ||= 1457.219 ||= 283.874 ||= 1012.483 ||= ||~~

~~||= ||= ||= 95\248 ||= ||= ||= 37 21 37 ||= 728.5715 ||= 1457.143 ||= 283.7595 ||= 1012.331 ||= Golden BP~~ is ~~index-2 near here ||~~

~~||= ||= 18\47 ||= ||= ||= ||= 7 4 7 ||= 728.408 ||= 1456.817 ||= 283.27 ||= 1011.678 ||= ||~~

~~||= ||= ||= ||= ||= ||= √3 1 √3 ||= 728.159 ||= 1456.318 ||= 282.522 ||= 1010.6815 ||= ||~~

~~||= ||= ||= 49\128 ||= ||= ||= 19 11 19 ||= 728.092 ||= 1456.184 ||= 282.321 ||= 1010.413 ||= 4g=27/5 minus third comma near here ||~~

~~||= ||= ||= 31\81 ||= ||= ||= 12 7 12 ||= 727.909 ||= 1455.817 ||= 281.771 ||= 1009.68 ||= ||~~

~~||= ||= 13\34 ||= ||= ||= ||= 5 3 5 ||= 727.218 ||= 1454.436 ||= 279.699 ||= 1006.917 ||= ||~~

~~||= ||= ||= 34\89 ||= ||= ||= 13 8 13 ||= 726.59 ||= 1453.179 ||= 277.814 ||= 1004.403 ||= ||~~

~~||= ||= ||= ||= 89\233 ||= ||= 34 21 34 ||= 726.498 ||= 1452.996 ||= 277.538 ||= 1004.036 ||= ||~~

~~||= ||= ||= ||= ||= 233\610 ||= 89 55 89 ||= 726.4845 ||= 1452.969 ||= 277.4985 ||= 1003.983 ||= Golden false father ||~~

~~||= ||= ||= ||= 144\377 ||= ||= 55 34 55 ||= 726.476 ||= 1452.952 ||= 277.473 ||= 1003.95 ||= ||~~

~~||= ||= ||= 55\144 ||= ||= ||= 21 13 21 ||= 726.441 ||= 1452.882 ||= 277.368 ||= 1003.809 ||= ||~~

~~||= ||= 21\55 ||= ||= ||= ||= 8 5 8 ||= 726.201 ||= 1452.402 ||= 276.468 ||= 1002.849 ||= ||~~

~~||= ||= ||= ||= ||= ||= pi 2 pi ||= 725.736 ||= 1451.472 ||= 275.252 ||= 1000.988 ||= ||~~

~~||= 8\21 ||= ||= ||= ||= ||= 3 2 3 ||= 724.554 ||= 1449.109 ||= 271.708 ||= 996.226 ||= Optimum rank range (L/s=3/2) false father ||~~

~~||= ||= ||= ||= ||= ||= ~543 361 543 ||= 724.511 ||= 1449.022 ||= 271.579 ||= 996.09 ||= 4g=16/3 ||~~

~~||= ||= 27\71 ||= ||= ||= ||= 10 7 10 ||= 723.279 ||= 1446.557 ||= 267.881 ||= 991.16 ||= ||~~

~~||= ||= ||= 46\121 ||= ||= ||= 17 12 17 ||= 723.057 ||= 1446.115 ||= 267.217 ||= 990.274 ||= ||~~

~~||= ||= ||= 65\171 ||= ||= ||= 24 17 24 ||= 722.965 ||= 1445.931 ||= 266.941 ||= 989.907 ||= 3g=7/2 near here ||~~

~~||= ||= 19\50 ||= ||= ||= ||= 7 5 7 ||= 722.743 ||= 1445.486 ||= 266.274 ||= 989.017 ||= ||~~

~~||= 11\29 ||= ||= ||= ||= ||= 4 3 4 ||= 721.431 ||= 1442.862 ||= 262.338 ||= 983.77 ||= ||~~

~~||= ||= 25\66 ||= ||= ||= ||= 9 7 9 ||= 720.4375 ||= 1440.875 ||= 259.3575 ||= 979.795 ||= ||~~

~~||= ||= ||= 64\169 ||= ||= ||= 23 18 23 ||= 720.267 ||= 1440.534 ||= 258.848 ||= 979.113 ||= ||~~

~~||= ||= ||= ||= 167\441 ||= ||= 60 47 60 ||= 720.2415 ||= 1440.483 ||= 258.7965 ||= 979.001 ||= ||~~

~~||= ||= ||= ||= ||= 437\1154 ||= 157 123 157 ||= 720.238 ||= 1440.475 ||= 258.758 ||= 978.996 ||= ||~~

~~||= ||= ||= ||= 270\713 ||= ||= 97 76 97 ||= 720.235 ||= 1440.471 ||= 258.751 ||= 978.987 ||= ||~~

~~||= ||= ||= 103\272 ||= ||= ||= 37 29 37 ||= 720.226 ||= 1440.451 ||= 258.722 ||= 978.947 ||= ||~~

~~||= ||= 39\103 ||= ||= ||= ||= 14 11 14 ||= 720.158 ||= 1440.315 ||= 258.518 ||= 978.676 ||= ||~~

~~||= 14\37 ||= ||= ||= ||= ||= 5 4 5 ||= 719.659 ||= 1439.317 ||= 257.021 ||= 976.679 ||= ||~~

~~||= ||= 31\82 ||= ||= ||= ||= 11 9 11 ||= 719.032 ||= 1438.064 ||= 255.14 ||= 974.172 ||= ||~~

~~||= ||= ||= 79\209 ||= ||= ||= 28 23 28 ||= 718.921 ||= 1437.842 ||= 254.807 ||= 973.728 ||= ||~~

~~||= ||= ||= ||= 206\545 ||= ||= 73 60 73 ||= 718.904 ||= 1437.808 ||= 254.757 ||= 973.661 ||= ||~~

~~||= ||= ||= ||= ||= 539\1426 ||= 191 117 191 ||= 718.902 ||= 1437.803 ||= 254.75 ||= 973.652 ||= ||~~

~~||= ||= ||= ||= 333\881 ||= ||= 118 97 118 ||= 718.90 ||= 1437.80 ||= 254.745 ||= 973.6455 ||= ||~~

~~||= ||= ||= 127\336 ||= ||= ||= 45 37 45 ||= 718.893 ||= 1437.787 ||= 254.726 ||= 973.619 ||= ||~~

~~||= ||= 48\127 ||= ||= ||= ||= 17 14 17 ||= 718.849 ||= 1437.698 ||= 254.592 ||= 973.441 ||= ||~~

~~||= 17\45 ||= ||= ||= ||= ||= 6 5 6 ||= 718.516 ||= 1437.032 ||= 253.549 ||= 972.11 ||= ||~~

~~||= 20\53 ||= ||= ||= ||= ||= 7 6 7 ||= 717.719 ||= 1435.438 ||= 251.202 ||= 968.9205 ||= ||~~

~~||= ||= ||= ||= ||= ||= ~401 344 401 ||= 717.695 ||= 1435.3905 ||= 251.131 ||= 968.826 ||= 4g=21/4 ||~~

~~||= 23\61 ||= ||= ||= ||= ||= 8 7 8 ||= 717.131 ||= 1434.261 ||= 249.437 ||= 966.567 ||= ||~~

~~||= ||= ||= ||= ||= ||= ~6682 5875 6682 ||= 716.9925 ||= 1433.985 ||= 249.0225 ||= 966.015 ||= 6g=12 ||~~

~~||= 26\69 ||= ||= ||= ||= ||= 9 8 9 ||= 716.679 ||= 1433.357 ||= 248.081 ||= 964.76 ||= ||~~

~~||= 29\77 ||= ||= ||= ||= ||= 10 9 10 ||= 716.321 ||= 1432.641 ||= 247.007 ||= 963.328 ||= ||~~

~~||= 32\85 ||= ||= ||= ||= ||= 11 10 11 ||= 716.03 ||= 1432.06 ||= 246.135 ||= 962.1655 ||= ||~~

~~||= 35\93 ||= ||= ||= ||= ||= 12 11 12 ||= 715.7895 ||= 1431.759 ||= 245.4135 ||= 961.203 ||= ||~~

~~||= 38/101 ||= ||= ||= ||= ||= 13 12 13 ||= 715.587 ||= 1431.174 ||= 244.806 ||= 960.393 ||= 2g=16\7 near here ||~~

~~||= 3\8 ||= ||= ||= ||= ||= 1 1 1 ||= 713.233 ||= 1426.466 ||= 237.744 ||= 950.9775 ||= ||~~

~~.</pre></div>~~

~~<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: ~~

{| class="wikitable"

~~<table class="wiki_table">~~

|-

~~<tr>~~

! colspan="5" | generator

~~<th colspan="5">generator ~~

! | tetrachord

~~</th>~~

! | g in cents

~~<th>tetrachord ~~

! | 2g

~~</th>~~

! | 3g

~~<th>g in cents ~~

! | 4g

~~</th>~~

! | Comments

~~<th>2g ~~

|-

~~</th>~~

| style="text-align:center;" | 2\5

~~<th>3g ~~

| style="text-align:center;" |

~~</th>~~

| style="text-align:center;" |

~~<th>4g ~~

| style="text-align:center;" |

~~</th>~~

| style="text-align:center;" |

~~<th>Comments ~~

| style="text-align:center;" | 1 0 1

~~</th>~~

| style="text-align:center;" | 760.782

~~</tr>~~

| style="text-align:center;" | 1521.564

~~<tr>~~

| style="text-align:center;" | 380.391

~~<td>2\5 ~~

| style="text-align:center;" | 1141.173

~~</td>~~

| style="text-align:center;" |

~~<td> ~~

|-

~~</td>~~

| style="text-align:center;" | 27\68

~~<td> ~~

| style="text-align:center;" |

~~</td>~~

| style="text-align:center;" |

~~<td> ~~

| style="text-align:center;" |

~~</td>~~

| style="text-align:center;" |

~~<td> ~~

| style="text-align:center;" | 13 1 13

~~</td>~~

| style="text-align:center;" | 755.188

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

| style="text-align:center;" | 1510.376

~~</td>~~

| style="text-align:center;" | 363.609

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

| style="text-align:center;" | 1118.797

~~</td>~~

| style="text-align:center;" |

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

|-

~~</td>~~

| style="text-align:center;" |

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

| style="text-align:center;" |

~~</td>~~

| style="text-align:center;" |

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

| style="text-align:center;" |

~~</td>~~

| style="text-align:center;" |

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

| style="text-align:center;" | ~6626 515 6626

~~</td>~~

| style="text-align:center;" | 755.132

~~</tr>~~

| style="text-align:center;" | 1510.265

~~<tr>~~

| style="text-align:center;" | 363.442

~~<td>21\53 ~~

| style="text-align:center;" | 1118.574

~~</td>~~

| style="text-align:center;" | 2g=12/5 minus quarter comma

~~<td> ~~

|-

~~</td>~~

| style="text-align:center;" | 25\63

~~<td> ~~

| style="text-align:center;" |

~~</td>~~

| style="text-align:center;" |

~~<td> ~~

| style="text-align:center;" |

~~</td>~~

| style="text-align:center;" |

~~<td> ~~

| style="text-align:center;" | 12 1 12

~~</td>~~

| style="text-align:center;" | 754.744

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

| style="text-align:center;" | 1509.488

~~</td>~~

| style="text-align:center;" | 362.277

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

| style="text-align:center;" | 1117.021

~~</td>~~

| style="text-align:center;" |

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

|-

~~</td>~~

| style="text-align:center;" | 23\58

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

| style="text-align:center;" |

~~</td>~~

| style="text-align:center;" |

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

| style="text-align:center;" |

~~</td>~~

| style="text-align:center;" |

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

| style="text-align:center;" | 11 1 11

~~</td>~~

| style="text-align:center;" | 754.2235

~~</tr>~~

| style="text-align:center;" | 1508.447

~~<tr>~~

| style="text-align:center;" | 360.716

~~<td>19\48 ~~

| style="text-align:center;" | 1114.939

~~</td>~~

| style="text-align:center;" |

~~<td> ~~

|-

~~</td>~~

| style="text-align:center;" | 21\53

~~<td> ~~

| style="text-align:center;" |

~~</td>~~

| style="text-align:center;" |

~~<td> ~~

| style="text-align:center;" |

~~</td>~~

| style="text-align:center;" |

~~<td> ~~

| style="text-align:center;" | 10 1 10

~~</td>~~

| style="text-align:center;" | 753.605

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

| style="text-align:center;" | 1507.21

~~</td>~~

| style="text-align:center;" | 358.859

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

| style="text-align:center;" | 1112.464

~~</td>~~

| style="text-align:center;" |

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

|-

~~</td>~~

| style="text-align:center;" | 19\48

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

| style="text-align:center;" |

~~</td>~~

| style="text-align:center;" |

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

| style="text-align:center;" |

~~</td>~~

| style="text-align:center;" |

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

| style="text-align:center;" | 9 1 9

~~</td>~~

| style="text-align:center;" | 752.857

~~</tr>~~

| style="text-align:center;" | 1505.714

~~<tr>~~

| style="text-align:center;" | 356.617

~~<td>17\43 ~~

| style="text-align:center;" | 1109.474

~~</td>~~

| style="text-align:center;" |

~~<td> ~~

|-

~~</td>~~

| style="text-align:center;" | 17\43

~~<td> ~~

| style="text-align:center;" |

~~</td>~~

| style="text-align:center;" |

~~<td> ~~

| style="text-align:center;" |

~~</td>~~

| style="text-align:center;" |

~~<td> ~~

| style="text-align:center;" | 8 1 8

~~</td>~~

| style="text-align:center;" | 751.936

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

| style="text-align:center;" | 1503.871

~~</td>~~

| style="text-align:center;" | 353.852

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

| style="text-align:center;" | 1105.788

~~</td>~~

| style="text-align:center;" |

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

|-

~~</td>~~

| style="text-align:center;" | 15\38

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

| style="text-align:center;" |

~~</td>~~

| style="text-align:center;" |

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

| style="text-align:center;" |

~~</td>~~

| style="text-align:center;" |

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

| style="text-align:center;" | 7 1 7

~~</td>~~

| style="text-align:center;" | 750.771

~~</tr>~~

| style="text-align:center;" | 1501.543

~~<tr>~~

| style="text-align:center;" | 350.36

~~<td>15\38 ~~

| style="text-align:center;" | 1101.132

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

~~</tr>~~

~~<tr>~~

~~<td>13\33 ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

~~</tr>~~

~~<tr>~~

~~<td>11\28 ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

~~</tr>~~

~~<tr>~~

~~<td>9\23 ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

~~</tr>~~

~~<tr>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

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

~~</td>~~

~~<td style="text-align: center;"&gt~~

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+L 3s refers to the structure of moment of symmetry scales with generators ranging from 2\5 (two degrees of [[5edo|5edo]] = 480¢) to 3\8 (three degrees of [[8edo|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:
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-29 11:30:16 UTC</tt>.<br>
-: The original revision id was <tt>602894250</tt>.<br>
-: The revision comment was: <tt>removed tel links</tt><br>
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
-<h4>Original Wikitext 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;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; ||=   ||
-|| 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 ||=   ||
-|| 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 ||=   ||
-|| 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 ||=   ||
-|| 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; ||
-||   ||   ||   ||   ||   ||= 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; ||
-||   ||   ||   ||   ||   ||= 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; ||
-||   || 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 ||   ||   ||   ||= &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 ||=   ||
-||   ||   ||   ||   ||   ||= &lt;span style="background-color: #ffffff;"&gt;√3 1 √3&lt;/span&gt; ||= 459.417 ||= 918.8345 ||= 178.252 ||= 637.669 ||   ||
-||   || 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 ||=   ||
-||   ||   ||   || 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; ||
-||   ||   ||   || 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 ||=   ||
-||   || 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 ||=   ||
-||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;pi 2 pi&lt;/span&gt; ||= 457.883 ||= 915.777 ||= 173.665 ||= 631.553 ||   ||
-|| 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 ||=   ||
-|| 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.
-By a weird coincidence, the other generator for this MOS will generate the same pattern within a tritave equivalence. By yet another weird coincidence, this MOS belongs to a temperament which has [[Bohlen-Pierce]] as its index-2 subtemperament. In addition to being harmonious, this tuning of the MOS gives an L/s ratio between 3/1 and 3/2, 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.
+{| class="wikitable"
+|-
+! colspan="5" | 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
+| |
+| |
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">1 0 1</span>
+| style="text-align:center;" | 480.000
+| style="text-align:center;" | 960.000
+| style="text-align:center;" | 240.00
+| style="text-align:center;" | <span style="line-height: 15.6000003814697px;">720.000</span>
+| style="text-align:center;" |
+|-
+| | 21\53
+| |
+| |
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">10 1 10</span>
+| style="text-align:center;" | 475.472
+| style="text-align:center;" | 950.943
+| style="text-align:center;" | 226.415
+| style="text-align:center;" | 701.887
+| style="text-align:center;" | <span style="display: block; text-align: center;">Vulture/Buzzard is around here</span>
+|-
+| | 19\48
+| |
+| |
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">9 1 9</span>
+| style="text-align:center;" | 475
+| style="text-align:center;" | 950
+| style="text-align:center;" | 225
+| style="text-align:center;" | 700
+| style="text-align:center;" |
+|-
+| | 17\43
+| |
+| |
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">8 1 8</span>
+| style="text-align:center;" | 474.419
+| style="text-align:center;" | 948.837
+| style="text-align:center;" | 223.256
+| style="text-align:center;" | 697.674
+| style="text-align:center;" |
+|-
+| | 15\38
+| |
+| |
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">7 1 7</span>
+| style="text-align:center;" | 473.684
+| style="text-align:center;" | 947.368
+| style="text-align:center;" | 221.053
+| style="text-align:center;" | 694.737
+| style="text-align:center;" |
+|-
+| | 13\33
+| |
+| |
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">6 1 6</span>
+| style="text-align:center;" | 472.727
+| style="text-align:center;" | 945.455
+| style="text-align:center;" | 218.181
+| style="text-align:center;" | 690.909
+| style="text-align:center;" |
+|-
+| | 11\28
+| |
+| |
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">5 1 5</span>
+| style="text-align:center;" | 471.429
+| style="text-align:center;" | 942.857
+| style="text-align:center;" | 214.286
+| style="text-align:center;" | 685.714
+| style="text-align:center;" |
+|-
+| | 9\23
+| |
+| |
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">4 1 4</span>
+| style="text-align:center;" | 469.565
+| style="text-align:center;" | 939.130
+| style="text-align:center;" | 208.696
+| style="text-align:center;" | 678.261
+| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = 4</span>
+|-
+| |
+| |
+| |
+| |
+| |
+| style="text-align:center;" | pi 1 pi
+| style="text-align:center;" | 467.171
+| style="text-align:center;" | 934.3425
+| style="text-align:center;" | 201.514
+| style="text-align:center;" | 668.685
+| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
+|-
+| | 7\18
+| |
+| |
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">3 1 3</span>
+| style="text-align:center;" | 466.667
+| style="text-align:center;" | 933.333
+| style="text-align:center;" | 200.000
+| style="text-align:center;" | 666.667
+| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = 3</span>
+|-
+| |
+| |
+| |
+| |
+| |
+| style="text-align:center;" | e 1 e
+| style="text-align:center;" | 465.535
+| style="text-align:center;" | 931.069
+| style="text-align:center;" | 196.604
+| style="text-align:center;" | 662.139
+| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span>
+|-
+| |
+| | 19\49
+| |
+| |
+| |
+| style="text-align:center;" | 8 3 8
+| style="text-align:center;" | 465.306
+| style="text-align:center;" | 930.612
+| style="text-align:center;" | 195.918
+| style="text-align:center;" | 661.2245
+| |
+|-
+| |
+| |
+| | 50\129
+| |
+| |
+| style="text-align:center;" | 21 8 21
+| style="text-align:center;" | 465.116
+| style="text-align:center;" | 930.233
+| style="text-align:center;" | 195.349
+| style="text-align:center;" | 660.465
+| |
+|-
+| |
+| |
+| |
+| | 131\338
+| |
+| style="text-align:center;" | 55 21 55
+| style="text-align:center;" | 465.089
+| style="text-align:center;" | 930.1775
+| style="text-align:center;" | 195.266
+| style="text-align:center;" | 660.335
+| |
+|-
+| |
+| |
+| |
+| |
+| | 212\547
+| style="text-align:center;" | 89 34 89
+| style="text-align:center;" | 465.082
+| style="text-align:center;" | 930.1645
+| style="text-align:center;" | 195.247
+| style="text-align:center;" | 660.329
+| |
+|-
+| |
+| |
+| |
+| | 81\209
+| |
+| style="text-align:center;" | 34 13 34
+| style="text-align:center;" | 465.072
+| style="text-align:center;" | 930.1435
+| style="text-align:center;" | 195.215
+| style="text-align:center;" | 660.287
+| |
+|-
+| |
+| |
+| | 31\80
+| |
+| |
+| style="text-align:center;" | 13 5 13
+| style="text-align:center;" | 465
+| style="text-align:center;" | 930
+| style="text-align:center;" | 195
+| style="text-align:center;" | 660
+| |
+|-
+| |
+| | 12\31
+| |
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">5 2 5</span>
+| style="text-align:center;" | 464.516
+| style="text-align:center;" | 929.032
+| style="text-align:center;" | 193.549
+| style="text-align:center;" | 658.065
+| style="text-align:center;" |
+|-
+| | 5\13
+| |
+| |
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">2 1 2</span>
+| style="text-align:center;" | 461.538
+| style="text-align:center;" | 923.077
+| style="text-align:center;" | 184.615
+| style="text-align:center;" | 646.154
+| style="text-align:center;" |
+|-
+| |
+| |
+| |
+| |
+| |
+| style="text-align:center;" | <span style="background-color: #ffffff;">√3 1 √3</span>
+| style="text-align:center;" | 459.417
+| style="text-align:center;" | 918.8345
+| style="text-align:center;" | 178.252
+| style="text-align:center;" | 637.669
+| |
+|-
+| |
+| | 13\34
+| |
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">5 3 5</span>
+| style="text-align:center;" | 458.824
+| style="text-align:center;" | 917.647
+| style="text-align:center;" | 176.471
+| style="text-align:center;" | 635.294
+| style="text-align:center;" |
+|-
+| |
+| |
+| | 34\89
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">13 8 13</span>
+| style="text-align:center;" | 458.427
+| style="text-align:center;" | 916.854
+| style="text-align:center;" | 175.281
+| style="text-align:center;" | 633.708
+| style="text-align:center;" |
+|-
+| |
+| |
+| |
+| | 89\233
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">34 21 34</span>
+| style="text-align:center;" | <span style="line-height: 15.6000003814697px;">458.369</span>
+| style="text-align:center;" | <span style="display: block; text-align: center;">916.738</span>
+| style="text-align:center;" | 175.107
+| style="text-align:center;" | <span style="line-height: 15.6000003814697px;">633.473</span>
+| style="text-align:center;" |
+|-
+| |
+| |
+| |
+| |
+| | 233\610
+| style="text-align:center;" | <span style="display: block; text-align: center;">89 55 89</span>
+| style="text-align:center;" | 458.361
+| style="text-align:center;" | 916.721
+| style="text-align:center;" | 175.082
+| style="text-align:center;" | 633.443
+| style="text-align:center;" | <span style="display: block; text-align: center;">Golden father</span>
+|-
+| |
+| |
+| |
+| | 144\377
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">55 34 55</span>
+| style="text-align:center;" | 458.355
+| style="text-align:center;" | 916.711
+| style="text-align:center;" | 175.066
+| style="text-align:center;" | 633.422
+| style="text-align:center;" |
+|-
+| |
+| |
+| | 55\144
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">21 13 21</span>
+| style="text-align:center;" | 458.333
+| style="text-align:center;" | 916.666
+| style="text-align:center;" | 175
+| style="text-align:center;" | 633.333
+| style="text-align:center;" |
+|-
+| |
+| | 21\55
+| |
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">8 5 8</span>
+| style="text-align:center;" | 458.182
+| style="text-align:center;" | 916.364
+| style="text-align:center;" | 174.545
+| style="text-align:center;" | 632.727
+| style="text-align:center;" |
+|-
+| |
+| |
+| |
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">pi 2 pi</span>
+| style="text-align:center;" | 457.883
+| style="text-align:center;" | 915.777
+| style="text-align:center;" | 173.665
+| style="text-align:center;" | 631.553
+| |
+|-
+| | 8\21
+| |
+| |
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">3 2 3</span>
+| style="text-align:center;" | 457.143
+| style="text-align:center;" | 914.286
+| style="text-align:center;" | 171.429
+| style="text-align:center;" | 628.571
+| style="text-align:center;" | <span style="display: block; text-align: center;">Optimum rank range (L/s=3/2) father</span>
+|-
+| | 11\29
+| |
+| |
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">4 3 4</span>
+| style="text-align:center;" | 455.172
+| style="text-align:center;" | 910.345
+| style="text-align:center;" | 165.517
+| style="text-align:center;" | 620.690
+| style="text-align:center;" |
+|-
+| | 14\37
+| |
+| |
+| |
+| |
+| style="text-align:center;" | 5 4 5
+| style="text-align:center;" | 454.054
+| style="text-align:center;" | 908.108
+| style="text-align:center;" | 162.162
+| style="text-align:center;" | 616.216
+| |
+|-
+| | 17\45
+| |
+| |
+| |
+| |
+| style="text-align:center;" | 6 5 6
+| style="text-align:center;" | 453.333
+| style="text-align:center;" | 906.667
+| style="text-align:center;" | 160
+| style="text-align:center;" | 613.333
+| |
+|-
+| | 20\53
+| |
+| |
+| |
+| |
+| style="text-align:center;" | 7 6 7
+| style="text-align:center;" | 452.83
+| style="text-align:center;" | 905.66
+| style="text-align:center;" | 158.491
+| style="text-align:center;" | 611.321
+| |
+|-
+| | 23\61
+| |
+| |
+| |
+| |
+| style="text-align:center;" | 8 7 8
+| style="text-align:center;" | 452.459
+| style="text-align:center;" | 904.918
+| style="text-align:center;" | 157.377
+| style="text-align:center;" | 609.836
+| |
+|-
+| | 26\69
+| |
+| |
+| |
+| |
+| style="text-align:center;" | 9 8 9
+| style="text-align:center;" | 452.174
+| style="text-align:center;" | 904.348
+| style="text-align:center;" | 156.522
+| style="text-align:center;" | 608.696
+| |
+|-
+| | 29\77
+| |
+| |
+| |
+| |
+| style="text-align:center;" | 10 9 10
+| style="text-align:center;" | 451.948
+| style="text-align:center;" | 903.896
+| style="text-align:center;" | 155.844
+| style="text-align:center;" | 607.792
+| |
+|-
+| | 3\8
+| |
+| |
+| |
+| |
+| style="text-align:center;" | <span style="display: block; text-align: center;">1 1 1</span>
+| style="text-align:center;" | 450.000
+| style="text-align:center;" | 900.000
+| style="text-align:center;" | 150.000
+| style="text-align:center;" | 600.000
+| style="text-align:center;" |
+|}
+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.
-||||||||||~ generator ||~ tetrachord ||~ g in cents ||~ 2g ||~ 3g ||~ 4g ||~ Comments ||
+By a weird coincidence, the other generator for this MOS will generate the same pattern within a tritave equivalence. By yet another weird coincidence, this MOS belongs to a temperament which has [[Bohlen-Pierce|Bohlen-Pierce]] as its index-2 subtemperament. In addition to being harmonious, this tuning of the MOS gives an L/s ratio between 3/1 and 3/2, 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.
-||= 2\5 ||=   ||=   ||=   ||=   ||= 1 0 1 ||= 760.782 ||= 1521.564 ||= 380.391 ||= 1141.173 ||=   ||
-||= 27\68 ||=   ||=   ||=   ||=   ||= 13 1 13 ||= 755.188 ||= 1510.376 ||= 363.609 ||= 1118.797 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= ~6626 515 6626 ||= 755.132 ||= 1510.265 ||= 363.442 ||= 1118.574 ||= &lt;span style="display: block; text-align: center;"&gt;2g=12/5 minus quarter comma&lt;/span&gt; ||
-||= 25\63 ||=   ||=   ||=   ||=   ||= 12 1 12 ||= 754.744 ||= 1509.488 ||= 362.277 ||= 1117.021 ||=   ||
-||= 23\58 ||=   ||=   ||=   ||=   ||= 11 1 11 ||= 754.2235 ||= 1508.447 ||= 360.716 ||= 1114.939 ||=   ||
-||= 21\53 ||=   ||=   ||=   ||=   ||= 10 1 10 ||= 753.605 ||= 1507.21 ||= 358.859 ||= 1112.464 ||=   ||
-||= 19\48 ||=   ||=   ||=   ||=   ||= 9 1 9 ||= 752.857 ||= 1505.714 ||= 356.617 ||= 1109.474 ||=   ||
-||= 17\43 ||=   ||=   ||=   ||=   ||= 8 1 8 ||= 751.936 ||= 1503.871 ||= 353.852 ||= 1105.788 ||=   ||
-||= 15\38 ||=   ||=   ||=   ||=   ||= 7 1 7 ||= 750.771 ||= 1501.543 ||= 350.36 ||= 1101.132 ||=   ||
-||=   ||= 28/71 ||=   ||=   ||=   ||= 13 2 13 ||= 750.067 ||= 1500.1335 ||= 348.245 ||= 1098.312 ||=   ||
-||=   ||= 41\104 ||=   ||=   ||=   ||= 19 3 19 ||= 749.809 ||= 1466.618 ||= 347.4725 ||= 1097.282 ||= 3g=11/3 near here ||
-||= 13\33 ||=   ||=   ||=   ||=   ||= 6 1 6 ||= 749.255 ||= 1498.51 ||= 345.81 ||= 1095.065 ||=   ||
-||=   ||= 24\61 ||=   ||=   ||=   ||= 11 2 11 ||= 748.31 ||= 1496.62 ||= 342.976 ||= 1091.286 ||=   ||
-||=   ||= 35\89 ||=   ||=   ||=   ||= 16 3 16 ||= 747.96 ||= 1495.92 ||= 341.924 ||= 1089.884 ||=   ||
-||=   ||= 46\117 ||=   ||=   ||=   ||= 21 4 21 ||= 747.777 ||= 1495.554 ||= 341.377 ||= 1089.154 ||=   ||
-||=   ||= 57\145 ||=   ||=   ||=   ||= 26 5 26 ||= 747.665 ||= 1495.33 ||= 341.04 ||= 1088.705 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= 5+&lt;span style="background-color: #ffffff;"&gt;√29 2 5+√29&lt;/span&gt; ||= 747.648 ||= 1495.297 ||= 340.99 ||= 1088.638 ||=   ||
-||=   ||= 68\173 ||=   ||=   ||=   ||= 31 6 31 ||= 747.589 ||= 1495.178 ||= 340.813 ||= 1088.402 ||=   ||
-||=   ||=   ||= 147\374 ||=   ||=   ||= 67 13 67 ||= 747.56 ||= 1495.12 ||= 340.725 ||= 1088.285 ||= 4g=45/8 near here ||
-||=   ||= 79\201 ||=   ||=   ||=   ||= 36 7 36 ||= 747.535 ||= 1495.069 ||= 340.649 ||= 1088.183 ||=   ||
-||= 11\28 ||=   ||=   ||=   ||=   ||= 5 1 5 ||= 747.197 ||= 1494.393 ||= 339.635 ||= 1086.831 ||=   ||
-||=   ||= 20\51 ||=   ||=   ||=   ||= 9 2 9 ||= 745.865 ||= 1491.729 ||= 335.639 ||= 1081.50 ||=   ||
-||=   ||= 29\74 ||=   ||=   ||=   ||= 13 3 13 ||= 745.361 ||= 1490.721 ||= 334.127 ||= 1079.488 ||=   ||
-||=   ||= 38/97 ||=   ||=   ||=   ||= 17 4 17 ||= 745.096 ||= 1490.192 ||= 333.332 ||= 1078.428 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= 2+&lt;span style="background-color: #ffffff;"&gt;√5 1 &lt;/span&gt;2+&lt;span style="background-color: #ffffff;"&gt;√5&lt;/span&gt; ||= 754.051 ||= 1490.101 ||= 333.197 ||= 1078.247 ||=   ||
-||=   ||= 47\120 ||=   ||=   ||=   ||= 21 5 21 ||= 744.932 ||= 1489.865 ||= 332.842 ||= 1077.7745 ||=   ||
-||= 9\23 ||=   ||=   ||=   ||=   ||= 4 1 4 ||= 744.243 ||= 1488.487 ||= 330.775 ||= 1075.018 ||= L/s = 4 ||
-||=   ||= 43\110 ||=   ||=   ||=   ||= 19 5 19 ||= 743.4915 ||= 1486.983 ||= 328.5195 ||= 1072.011 ||=   ||
-||=   ||=   ||= 77\197 ||=   ||=   ||= 34 9 34 ||= 743.404 ||= 1486.807 ||= 328.256 ||= 1071.66 ||= 4g=39/7 near here ||
-||=   ||= 34\87 ||=   ||=   ||=   ||= 15 4 15 ||= 743.293 ||= 1486.586 ||= 327.923 ||= 1071.216 ||=   ||
-||=   ||= 25\64 ||=   ||=   ||=   ||= 11 3 11 ||= 742.951 ||= 1485.902 ||= 326.899 ||= 1069.85 ||=   ||
-||=   ||= 16\41 ||=   ||=   ||=   ||= 7 2 7 ||= 742.226 ||= 1484.453 ||= 324.724 ||= 1066.95 ||=   ||
-||=   ||= 23\59 ||=   ||=   ||=   ||= 10 3 10 ||= 741.44 ||= 1482.88 ||= 322.365 ||= 1063.805 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= 3+&lt;span style="background-color: #ffffff;"&gt;√13 2 3+√13&lt;/span&gt; ||= 741.289 ||= 1482.577 ||= 321.911 ||= 1063.20 ||=   ||
-||=   ||= 30\77 ||=   ||=   ||=   ||= 13 4 13 ||= 741.021 ||= 1482.043 ||= 321.109 ||= 1062.131 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= pi 1 pi ||= 740.449 ||= 1480.898 ||= 319.392 ||= 1056.841 ||= L/s = pi ||
-||= 7\18 ||=   ||=   ||=   ||=   ||= 3 1 3 ||= 739.649 ||= 1479.298 ||= 316.992 ||= 1056.642 ||= L/s = 3 ||
-||=   ||= 89\229 ||=   ||=   ||=   ||= 38 13 38 ||= 739.188 ||= 1478.376 ||= 315.608 ||= 1054.796 ||= 3g=18/5 near here ||
-||=   ||= 82\211 ||=   ||=   ||=   ||= 35 12 35 ||= 739.148 ||= 1478.297 ||= 315.49 ||= 1054.639 ||=   ||
-||=   ||= 75\193 ||=   ||=   ||=   ||= 32 11 32 ||= 739.102 ||= 1478.203 ||= 315.35 ||= 1054.452 ||=   ||
-||=   ||= 68\175 ||=   ||=   ||=   ||= 29 10 29 ||= 739.045 ||= 1478.091 ||= 315.181 ||= 1054.227 ||=   ||
-||=   ||= 61/157 ||=   ||=   ||=   ||= 26 9 26 ||= 738.976 ||= 1477.952 ||= 314.973 ||= 1053.949 ||=   ||
-||=   ||= 54\139 ||=   ||=   ||=   ||= 23 8 23 ||= 738.889 ||= 1477.778 ||= 314.712 ||= 1053.601 ||=   ||
-||=   ||= 47\121 ||=   ||=   ||=   ||= 20 7 20 ||= 738.776 ||= 1477.552 ||= 314.373 ||= 1053.149 ||=   ||
-||=   ||= 40\103 ||=   ||=   ||=   ||= 17 6 17 ||= 738.623 ||= 1477.247 ||= 313.915 ||= 1052.538 ||=   ||
-||=   ||= 33\85 ||=   ||=   ||=   ||= 14 5 14 ||= 738.406 ||= 1476.812 ||= 313.263 ||= 1051.669 ||=   ||
-||=   ||= 26\67 ||=   ||=   ||=   ||= 11 4 11 ||= 738.072 ||= 1476.144 ||= 312.261 ||= 1050.333 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= e 1 e ||= 737.855 ||= 1478.71 ||= 311.61 ||= 1049.465 ||= L/s = e ||
-||=   ||= 19\49 ||=   ||=   ||=   ||= 8 3 8 ||= 737.493 ||= 1474.986 ||= 310.523 ||= 1048.016 ||=   ||
-||=   ||=   ||=   ||= 164\423 ||=   ||= 69 26 69 ||= 737.401 ||= 1474.802 ||= 310.248 ||= 1047.649 ||= 3g=18/5 minus quarter comma near here ||
-||=   ||=   ||=   ||= 145\374 ||=   ||= 61 23 61 ||= 737.389 ||= 1474.778 ||= 310.212 ||= 1047.601 ||=   ||
-||=   ||=   ||=   ||= 126\325 ||=   ||= 53 20 53 ||= 737.373 ||= 1474.747 ||= 310.165 ||= 1047.538 ||=   ||
-||=   ||=   ||=   ||= 107\276 ||=   ||= 45 17 45 ||= 737.352 ||= 1474.704 ||= 310.101 ||= 1047.453 ||=   ||
-||=   ||=   ||=   ||= 88\227 ||=   ||= 37 14 37 ||= 737.322 ||= 1474.644 ||= 310.01 ||= 1047.332 ||=   ||
-||=   ||=   ||=   ||= 69\178 ||=   ||= 29 11 29 ||= 737.275 ||= 1474.549 ||= 309.869 ||= 1047.144 ||=   ||
-||=   ||=   ||= 50\129 ||=   ||=   ||= 21 8 21 ||= 737.192 ||= 1474.384 ||= 309.621 ||= 1046.812 ||=   ||
-||=   ||=   ||=   ||= 131\338 ||=   ||= 55 21 55 ||= 737.148 ||= 1474.296 ||= 309.49 ||= 1046.638 ||=   ||
-||=   ||=   ||=   ||=   ||= 212\547 ||= 89 34 89 ||= 737.138 ||= 1474.276 ||= 309.459 ||= 1046.597 ||=   ||
-||=   ||=   ||=   ||= 81\209 ||=   ||= 34 13 34 ||= 737.121 ||= 1474.243 ||= 309.409 ||= 1046.53 ||=   ||
-||=   ||=   ||= 31\80 ||=   ||=   ||= 13 5 13 ||= 737.008 ||= 1474.015 ||= 309.068 ||= 1046.075 ||=   ||
-||=   ||= 12\31 ||=   ||=   ||=   ||= 5 2 5 ||= 736.241 ||= 1472.481 ||= 306.767 ||= 1043.007 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= &lt;span style="background-color: #ffffff;"&gt;1+√2 1 1+√2&lt;/span&gt; ||= 735.542 ||= 1471.084 ||= 304.6715 ||= 1040.214 ||= Silver false father ||
-||=   ||= 17\44 ||=   ||=   ||=   ||= 7 3 7 ||= 734.846 ||= 1469.693 ||= 302.584 ||= 1037.41 ||=   ||
-||=   ||= 22\57 ||=   ||=   ||=   ||= 9 4 9 ||= 734.088 ||= 1468.176 ||= 300.309 ||= 1034.397 ||=   ||
-||=   ||= 27\70 ||=   ||=   ||=   ||= 11 5 11 ||= 733.611 ||= 1467.222 ||= 298.879 ||= 1032.49 ||=   ||
-||=   ||=   ||= 59\153 ||=   ||=   ||= 24 11 24 ||= 733.434 ||= 1466.867 ||= 298.346 ||= 1031.779 ||=   ||
-||=   ||= 32\83 ||=   ||=   ||=   ||= 13 6 13 ||= 733.284 ||= 1466.568 ||= 297.897 ||= 1031.181 ||= 2g=7/3 near here ||
-||= 5\13 ||=   ||=   ||=   ||=   ||= 2 1 2 ||= 731.521 ||= 1463.042 ||= 292.609 ||= 1024.13 ||=   ||
-||=   ||= 53\138 ||=   ||=   ||=   ||= 21 11 21 ||= 730.461 ||= 1460.922 ||= 289.428 ||= 1018.889 ||=   ||
-||=   ||=   ||= 101\263 ||=   ||=   ||= 40 21 40 ||= 730.409 ||= 1460.817 ||= 289.271 ||= 1019.679 ||= 3g=39/11 near here ||
-||=   ||= 48\125 ||=   ||=   ||=   ||= 19 10 19 ||= 730.35 ||= 1460.701 ||= 289.097 ||= 1019.448 ||=   ||
-||=   ||= 43\112 ||=   ||=   ||=   ||= 17 9 17 ||= 730.215 ||= 1460.43 ||= 288.69 ||= 1018.905 ||=   ||
-||=   ||= 38\99 ||=   ||=   ||=   ||= 15 8 15 ||= 730.043 ||= 1460.087 ||= 288.175 ||= 1018.218 ||=   ||
-||=   ||=   ||= 71\185 ||=   ||=   ||= 28 15 28 ||= 729.9395 ||= 1459.879 ||= 287.8635 ||= 1017.803 ||=   ||
-||=   ||=   ||= 104\271 ||=   ||=   ||= 41 22 41 ||= 729.902 ||= 1459.803 ||= 287.75 ||= 1017.651 ||= 4g=27/5 near here ||
-||=   ||= 33\86 ||=   ||=   ||=   ||= 13 7 13 ||= 729.82 ||= 1459.64 ||= 287.505 ||= 1017.325 ||=   ||
-||=   ||= 28\73 ||=   ||=   ||=   ||= 11 6 11 ||= 729.547 ||= 1459.034 ||= 286.596 ||= 1016.113 ||=   ||
-||=   ||= 23\60 ||=   ||=   ||=   ||= 9 5 9 ||= 729.083 ||= 1458.1655 ||= 285.293 ||= 1014.376 ||=   ||
-||=   ||=   ||= 41\107 ||=   ||=   ||= 16 9 16 ||= 728.7865 ||= 1457.573 ||= 284.4045 ||= 1013.191 ||= 3g=99/28 near here ||
-||=   ||=   ||= 59\154 ||=   ||=   ||= 23 13 23 ||= 728.671 ||= 1457.342 ||= 284.058 ||= 1012.729 ||=   ||
-||=   ||=   ||= 77\201 ||=   ||=   ||= 30 17 30 ||= 728.61 ||= 1457.219 ||= 283.874 ||= 1012.483 ||=   ||
-||=   ||=   ||= 95\248 ||=   ||=   ||= 37 21 37 ||= 728.5715 ||= 1457.143 ||= 283.7595 ||= 1012.331 ||= Golden BP is index-2 near here ||
-||=   ||= 18\47 ||=   ||=   ||=   ||= 7 4 7 ||= 728.408 ||= 1456.817 ||= 283.27 ||= 1011.678 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= &lt;span style="background-color: #ffffff;"&gt;√3 1 √3&lt;/span&gt; ||= 728.159 ||= 1456.318 ||= 282.522 ||= 1010.6815 ||=   ||
-||=   ||=   ||= 49\128 ||=   ||=   ||= 19 11 19 ||= 728.092 ||= 1456.184 ||= 282.321 ||= 1010.413 ||= 4g=27/5 minus third comma near here ||
-||=   ||=   ||= 31\81 ||=   ||=   ||= 12 7 12 ||= 727.909 ||= 1455.817 ||= 281.771 ||= 1009.68 ||=   ||
-||=   ||= 13\34 ||=   ||=   ||=   ||= 5 3 5 ||= 727.218 ||= 1454.436 ||= 279.699 ||= 1006.917 ||=   ||
-||=   ||=   ||= 34\89 ||=   ||=   ||= 13 8 13 ||= 726.59 ||= 1453.179 ||= 277.814 ||= 1004.403 ||=   ||
-||=   ||=   ||=   ||= 89\233 ||=   ||= 34 21 34 ||= 726.498 ||= 1452.996 ||= 277.538 ||= 1004.036 ||=   ||
-||=   ||=   ||=   ||=   ||= 233\610 ||= 89 55 89 ||= 726.4845 ||= 1452.969 ||= 277.4985 ||= 1003.983 ||= Golden false father ||
-||=   ||=   ||=   ||= 144\377 ||=   ||= 55 34 55 ||= 726.476 ||= 1452.952 ||= 277.473 ||= 1003.95 ||=   ||
-||=   ||=   ||= 55\144 ||=   ||=   ||= 21 13 21 ||= 726.441 ||= 1452.882 ||= 277.368 ||= 1003.809 ||=   ||
-||=   ||= 21\55 ||=   ||=   ||=   ||= 8 5 8 ||= 726.201 ||= 1452.402 ||= 276.468 ||= 1002.849 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= pi 2 pi ||= 725.736 ||= 1451.472 ||= 275.252 ||= 1000.988 ||=   ||
-||= 8\21 ||=   ||=   ||=   ||=   ||= 3 2 3 ||= 724.554 ||= 1449.109 ||= 271.708 ||= 996.226 ||= Optimum rank range (L/s=3/2) false father ||
-||=   ||=   ||=   ||=   ||=   ||= ~543 361 543 ||= 724.511 ||= 1449.022 ||= 271.579 ||= 996.09 ||= 4g=16/3 ||
-||=   ||= 27\71 ||=   ||=   ||=   ||= 10 7 10 ||= 723.279 ||= 1446.557 ||= 267.881 ||= 991.16 ||=   ||
-||=   ||=   ||= 46\121 ||=   ||=   ||= 17 12 17 ||= 723.057 ||= 1446.115 ||= 267.217 ||= 990.274 ||=   ||
-||=   ||=   ||= 65\171 ||=   ||=   ||= 24 17 24 ||= 722.965 ||= 1445.931 ||= 266.941 ||= 989.907 ||= 3g=7/2 near here ||
-||=   ||= 19\50 ||=   ||=   ||=   ||= 7 5 7 ||= 722.743 ||= 1445.486 ||= 266.274 ||= 989.017 ||=   ||
-||= 11\29 ||=   ||=   ||=   ||=   ||= 4 3 4 ||= 721.431 ||= 1442.862 ||= 262.338 ||= 983.77 ||=   ||
-||=   ||= 25\66 ||=   ||=   ||=   ||= 9 7 9 ||= 720.4375 ||= 1440.875 ||= 259.3575 ||= 979.795 ||=   ||
-||=   ||=   ||= 64\169 ||=   ||=   ||= 23 18 23 ||= 720.267 ||= 1440.534 ||= 258.848 ||= 979.113 ||=   ||
-||=   ||=   ||=   ||= 167\441 ||=   ||= 60 47 60 ||= 720.2415 ||= 1440.483 ||= 258.7965 ||= 979.001 ||=   ||
-||=   ||=   ||=   ||=   ||= 437\1154 ||= 157 123 157 ||= 720.238 ||= 1440.475 ||= 258.758 ||= 978.996 ||=   ||
-||=   ||=   ||=   ||= 270\713 ||=   ||= 97 76 97 ||= 720.235 ||= 1440.471 ||= 258.751 ||= 978.987 ||=   ||
-||=   ||=   ||= 103\272 ||=   ||=   ||= 37 29 37 ||= 720.226 ||= 1440.451 ||= 258.722 ||= 978.947 ||=   ||
-||=   ||= 39\103 ||=   ||=   ||=   ||= 14 11 14 ||= 720.158 ||= 1440.315 ||= 258.518 ||= 978.676 ||=   ||
-||= 14\37 ||=   ||=   ||=   ||=   ||= 5 4 5 ||= 719.659 ||= 1439.317 ||= 257.021 ||= 976.679 ||=   ||
-||=   ||= 31\82 ||=   ||=   ||=   ||= 11 9 11 ||= 719.032 ||= 1438.064 ||= 255.14 ||= 974.172 ||=   ||
-||=   ||=   ||= 79\209 ||=   ||=   ||= 28 23 28 ||= 718.921 ||= 1437.842 ||= 254.807 ||= 973.728 ||=   ||
-||=   ||=   ||=   ||= 206\545 ||=   ||= 73 60 73 ||= 718.904 ||= 1437.808 ||= 254.757 ||= 973.661 ||=   ||
-||=   ||=   ||=   ||=   ||= 539\1426 ||= 191 117 191 ||= 718.902 ||= 1437.803 ||= 254.75 ||= 973.652 ||=   ||
-||=   ||=   ||=   ||= 333\881 ||=   ||= 118 97 118 ||= 718.90 ||= 1437.80 ||= 254.745 ||= 973.6455 ||=   ||
-||=   ||=   ||= 127\336 ||=   ||=   ||= 45 37 45 ||= 718.893 ||= 1437.787 ||= 254.726 ||= 973.619 ||=   ||
-||=   ||= 48\127 ||=   ||=   ||=   ||= 17 14 17 ||= 718.849 ||= 1437.698 ||= 254.592 ||= 973.441 ||=   ||
-||= 17\45 ||=   ||=   ||=   ||=   ||= 6 5 6 ||= 718.516 ||= 1437.032 ||= 253.549 ||= 972.11 ||=   ||
-||= 20\53 ||=   ||=   ||=   ||=   ||= 7 6 7 ||= 717.719 ||= 1435.438 ||= 251.202 ||= 968.9205 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= ~401 344 401 ||= 717.695 ||= 1435.3905 ||= 251.131 ||= 968.826 ||= 4g=21/4 ||
-||= 23\61 ||=   ||=   ||=   ||=   ||= 8 7 8 ||= 717.131 ||= 1434.261 ||= 249.437 ||= 966.567 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= ~6682 5875 6682 ||= 716.9925 ||= 1433.985 ||= 249.0225 ||= 966.015 ||= 6g=12 ||
-||= 26\69 ||=   ||=   ||=   ||=   ||= 9 8 9 ||= 716.679 ||= 1433.357 ||= 248.081 ||= 964.76 ||=   ||
-||= 29\77 ||=   ||=   ||=   ||=   ||= 10 9 10 ||= 716.321 ||= 1432.641 ||= 247.007 ||= 963.328 ||=   ||
-||= 32\85 ||=   ||=   ||=   ||=   ||= 11 10 11 ||= 716.03 ||= 1432.06 ||= 246.135 ||= 962.1655 ||=   ||
-||= 35\93 ||=   ||=   ||=   ||=   ||= 12 11 12 ||= 715.7895 ||= 1431.759 ||= 245.4135 ||= 961.203 ||=   ||
-||= 38/101 ||=   ||=   ||=   ||=   ||= 13 12 13 ||= 715.587 ||= 1431.174 ||= 244.806 ||= 960.393 ||= 2g=16\7 near here ||
-||= 3\8 ||=   ||=   ||=   ||=   ||= 1 1 1 ||= 713.233 ||= 1426.466 ||= 237.744 ||= 950.9775 ||=   ||
-.</pre></div>
-<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;5L 3s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;5L 3s refers to the structure of moment of symmetry scales with generators ranging from 2\5 (two degrees of &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt; = 480¢) to 3\8 (three degrees of &lt;a class="wiki_link" href="/8edo"&gt;8edo&lt;/a&gt; = 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:&lt;br /&gt;
+{| class="wikitable"
-&lt;table class="wiki_table"&gt;
+|-
-    &lt;tr&gt;
+! colspan="5" | generator
-        &lt;th colspan="5"&gt;generator&lt;br /&gt;
+! | tetrachord
-&lt;/th&gt;
+! | g in cents
-        &lt;th&gt;&lt;span style="display: block; text-align: center;"&gt;tetrachord&lt;/span&gt;&lt;br /&gt;
+! | 2g
-&lt;/th&gt;
+! | 3g
-        &lt;th&gt;&lt;span style="display: block; text-align: center;"&gt;g in cents&lt;/span&gt;&lt;br /&gt;
+! | 4g
-&lt;/th&gt;
+! | Comments
-        &lt;th&gt;&lt;span style="display: block; text-align: center;"&gt;2g&lt;/span&gt;&lt;br /&gt;
+|-
-&lt;/th&gt;
+| style="text-align:center;" | 2\5
-        &lt;th&gt;&lt;span style="display: block; text-align: center;"&gt;3g&lt;/span&gt;&lt;br /&gt;
+| style="text-align:center;" |
-&lt;/th&gt;
+| style="text-align:center;" |
-        &lt;th&gt;&lt;span style="display: block; text-align: center;"&gt;4g&lt;/span&gt;&lt;br /&gt;
+| style="text-align:center;" |
-&lt;/th&gt;
+| style="text-align:center;" |
-        &lt;th&gt;&lt;span style="display: block; text-align: center;"&gt;Comments&lt;/span&gt;&lt;br /&gt;
+| style="text-align:center;" | 1 0 1
-&lt;/th&gt;
+| style="text-align:center;" | 760.782
-    &lt;/tr&gt;
+| style="text-align:center;" | 1521.564
-    &lt;tr&gt;
+| style="text-align:center;" | 380.391
-        &lt;td&gt;2\5&lt;br /&gt;
+| style="text-align:center;" | 1141.173
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td&gt;&lt;br /&gt;
+|-
-&lt;/td&gt;
+| style="text-align:center;" | 27\68
-        &lt;td&gt;&lt;br /&gt;
+| style="text-align:center;" |
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td&gt;&lt;br /&gt;
+| style="text-align:center;" |
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td&gt;&lt;br /&gt;
+| style="text-align:center;" | 13 1 13
-&lt;/td&gt;
+| style="text-align:center;" | 755.188
-        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;1 0 1&lt;/span&gt;&lt;br /&gt;
+| style="text-align:center;" | 1510.376
-&lt;/td&gt;
+| style="text-align:center;" | 363.609
-        &lt;td style="text-align: center;"&gt;480.000&lt;br /&gt;
+| style="text-align:center;" | 1118.797
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td style="text-align: center;"&gt;960.000&lt;br /&gt;
+|-
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td style="text-align: center;"&gt;240.00&lt;br /&gt;
+| style="text-align:center;" |
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td style="text-align: center;"&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;720.000&lt;/span&gt;&lt;br /&gt;
+| style="text-align:center;" |
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+| style="text-align:center;" | ~6626 515 6626
-&lt;/td&gt;
+| style="text-align:center;" | 755.132
-    &lt;/tr&gt;
+| style="text-align:center;" | 1510.265
-    &lt;tr&gt;
+| style="text-align:center;" | 363.442
-        &lt;td&gt;21\53&lt;br /&gt;
+| style="text-align:center;" | 1118.574
-&lt;/td&gt;
+| style="text-align:center;" | <span style="display: block; text-align: center;">2g=12/5 minus quarter comma</span>
-        &lt;td&gt;&lt;br /&gt;
+|-
-&lt;/td&gt;
+| style="text-align:center;" | 25\63
-        &lt;td&gt;&lt;br /&gt;
+| style="text-align:center;" |
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td&gt;&lt;br /&gt;
+| style="text-align:center;" |
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td&gt;&lt;br /&gt;
+| style="text-align:center;" | 12 1 12
-&lt;/td&gt;
+| style="text-align:center;" | 754.744
-        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;10 1 10&lt;/span&gt;&lt;br /&gt;
+| style="text-align:center;" | 1509.488
-&lt;/td&gt;
+| style="text-align:center;" | 362.277
-        &lt;td style="text-align: center;"&gt;475.472&lt;br /&gt;
+| style="text-align:center;" | 1117.021
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td style="text-align: center;"&gt;950.943&lt;br /&gt;
+|-
-&lt;/td&gt;
+| style="text-align:center;" | 23\58
-        &lt;td style="text-align: center;"&gt;226.415&lt;br /&gt;
+| style="text-align:center;" |
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td style="text-align: center;"&gt;701.887&lt;br /&gt;
+| style="text-align:center;" |
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Vulture/Buzzard is around here&lt;/span&gt;&lt;br /&gt;
+| style="text-align:center;" | 11 1 11
-&lt;/td&gt;
+| style="text-align:center;" | 754.2235
-    &lt;/tr&gt;
+| style="text-align:center;" | 1508.447
-    &lt;tr&gt;
+| style="text-align:center;" | 360.716
-        &lt;td&gt;19\48&lt;br /&gt;
+| style="text-align:center;" | 1114.939
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td&gt;&lt;br /&gt;
+|-
-&lt;/td&gt;
+| style="text-align:center;" | 21\53
-        &lt;td&gt;&lt;br /&gt;
+| style="text-align:center;" |
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td&gt;&lt;br /&gt;
+| style="text-align:center;" |
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td&gt;&lt;br /&gt;
+| style="text-align:center;" | 10 1 10
-&lt;/td&gt;
+| style="text-align:center;" | 753.605
-        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;9 1 9&lt;/span&gt;&lt;br /&gt;
+| style="text-align:center;" | 1507.21
-&lt;/td&gt;
+| style="text-align:center;" | 358.859
-        &lt;td style="text-align: center;"&gt;475&lt;br /&gt;
+| style="text-align:center;" | 1112.464
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td style="text-align: center;"&gt;950&lt;br /&gt;
+|-
-&lt;/td&gt;
+| style="text-align:center;" | 19\48
-        &lt;td style="text-align: center;"&gt;225&lt;br /&gt;
+| style="text-align:center;" |
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td style="text-align: center;"&gt;700&lt;br /&gt;
+| style="text-align:center;" |
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+| style="text-align:center;" | 9 1 9
-&lt;/td&gt;
+| style="text-align:center;" | 752.857
-    &lt;/tr&gt;
+| style="text-align:center;" | 1505.714
-    &lt;tr&gt;
+| style="text-align:center;" | 356.617
-        &lt;td&gt;17\43&lt;br /&gt;
+| style="text-align:center;" | 1109.474
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td&gt;&lt;br /&gt;
+|-
-&lt;/td&gt;
+| style="text-align:center;" | 17\43
-        &lt;td&gt;&lt;br /&gt;
+| style="text-align:center;" |
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td&gt;&lt;br /&gt;
+| style="text-align:center;" |
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td&gt;&lt;br /&gt;
+| style="text-align:center;" | 8 1 8
-&lt;/td&gt;
+| style="text-align:center;" | 751.936
-        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;8 1 8&lt;/span&gt;&lt;br /&gt;
+| style="text-align:center;" | 1503.871
-&lt;/td&gt;
+| style="text-align:center;" | 353.852
-        &lt;td style="text-align: center;"&gt;474.419&lt;br /&gt;
+| style="text-align:center;" | 1105.788
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td style="text-align: center;"&gt;948.837&lt;br /&gt;
+|-
-&lt;/td&gt;
+| style="text-align:center;" | 15\38
-        &lt;td style="text-align: center;"&gt;223.256&lt;br /&gt;
+| style="text-align:center;" |
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td style="text-align: center;"&gt;697.674&lt;br /&gt;
+| style="text-align:center;" |
-&lt;/td&gt;
+| style="text-align:center;" |
-        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+| style="text-align:center;" | 7 1 7
-&lt;/td&gt;
+| style="text-align:center;" | 750.771
-    &lt;/tr&gt;
+| style="text-align:center;" | 1501.543
-    &lt;tr&gt;
+| style="text-align:center;" | 350.36
-        &lt;td&gt;15\38&lt;br /&gt;
+| style="text-align:center;" | 1101.132
-&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;&lt;span style="display: block; text-align: center;"&gt;7 1 7&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;473.684&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;947.368&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;221.053&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;694.737&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;13\33&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;&lt;span style="display: block; text-align: center;"&gt;6 1 6&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;472.727&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;945.455&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;218.181&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;690.909&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;11\28&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;&lt;span style="display: block; text-align: center;"&gt;5 1 5&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;471.429&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;942.857&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;214.286&lt;br /&gt;
-&lt;/td&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;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;9\23&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;&lt;span style="display: block; text-align: center;"&gt;4 1 4&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;469.565&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;939.130&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;208.696&lt;br /&gt;
-&lt;/td&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;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&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;pi 1 pi&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt