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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Interwiki |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | en = 5L 3s |
| : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-29 11:30:16 UTC</tt>.<br>
| | | de = |
| : The original revision id was <tt>602894250</tt>.<br>
| | | es = |
| : The revision comment was: <tt>removed tel links</tt><br>
| | | ja = |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | | ko = 5L3s (Korean) |
| <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:
| | {{Infobox MOS |
| ||||||||||~ 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> || | | | Neutral = 2L 6s |
| || 2\5 || || || || ||= <span style="display: block; text-align: center;">1 0 1</span> ||= 480.000 ||= 960.000 ||= 240.00 ||= <span style="line-height: 15.6000003814697px;">720.000</span> ||= || | | }} |
| || 21\53 || || || || ||= <span style="display: block; text-align: center;">10 1 10</span> ||= 475.472 ||= 950.943 ||= 226.415 ||= 701.887 ||= <span style="display: block; text-align: center;">Vulture/Buzzard is around here</span> || | | : ''For the tritave-equivalent MOS structure with the same step pattern, see [[5L 3s (3/1-equivalent)]].'' |
| || 19\48 || || || || ||= <span style="display: block; text-align: center;">9 1 9</span> ||= 475 ||= 950 ||= 225 ||= 700 ||= || | | {{MOS intro}} |
| || 17\43 || || || || ||= <span style="display: block; text-align: center;">8 1 8</span> ||= 474.419 ||= 948.837 ||= 223.256 ||= 697.674 ||= ||
| | 5L 3s can be seen as a [[Warped diatonic|warped diatonic scale]], because it has one extra small step compared to diatonic ([[5L 2s]]). |
| || 15\38 || || || || ||= <span style="display: block; text-align: center;">7 1 7</span> ||= 473.684 ||= 947.368 ||= 221.053 ||= 694.737 ||= ||
| |
| || 13\33 || || || || ||= <span style="display: block; text-align: center;">6 1 6</span> ||= 472.727 ||= 945.455 ||= 218.181 ||= 690.909 ||= || | |
| || 11\28 || || || || ||= <span style="display: block; text-align: center;">5 1 5</span> ||= 471.429 ||= 942.857 ||= 214.286 ||= 685.714 ||= ||
| |
| || 9\23 || || || || ||= <span style="display: block; text-align: center;">4 1 4</span> ||= 469.565 ||= 939.130 ||= 208.696 ||= 678.261 ||= <span style="display: block; text-align: center;">L/s = 4</span> ||
| |
| || || || || || ||= pi 1 pi ||= 467.171 ||= 934.3425 ||= 201.514 ||= 668.685 ||= <span style="display: block; text-align: center;">L/s = pi</span> ||
| |
| || 7\18 || || || || ||= <span style="display: block; text-align: center;">3 1 3</span> ||= 466.667 ||= 933.333 ||= 200.000 ||= 666.667 ||= <span style="display: block; text-align: center;">L/s = 3</span> ||
| |
| || || || || || ||= e 1 e ||= 465.535 ||= 931.069 ||= 196.604 ||= 662.139 ||= <span style="display: block; text-align: center;">L/s = e</span> ||
| |
| || || 19\49 || || || ||= 8 3 8 ||= 465.306 ||= 930.612 ||= 195.918 ||= 661.2245 || ||
| |
| || || || 50\129 || || ||= 21 8 21 ||= 465.116 ||= 930.233 ||= 195.349 ||= 660.465 || ||
| |
| || || || || 131\338 || ||= 55 21 55 ||= 465.089 ||= 930.1775 ||= 195.266 ||= 660.335 || ||
| |
| || || || || || 212\547 ||= 89 34 89 ||= 465.082 ||= 930.1645 ||= 195.247 ||= 660.329 || ||
| |
| || || || || 81\209 || ||= 34 13 34 ||= 465.072 ||= 930.1435 ||= 195.215 ||= 660.287 || ||
| |
| || || || 31\80 || || ||= 13 5 13 ||= 465 ||= 930 ||= 195 ||= 660 || ||
| |
| || || 12\31 || || || ||= <span style="display: block; text-align: center;">5 2 5</span> ||= 464.516 ||= 929.032 ||= 193.549 ||= 658.065 ||= ||
| |
| || 5\13 || || || || ||= <span style="display: block; text-align: center;">2 1 2</span> ||= 461.538 ||= 923.077 ||= 184.615 ||= 646.154 ||= ||
| |
| || || || || || ||= <span style="background-color: #ffffff;">√3 1 √3</span> ||= 459.417 ||= 918.8345 ||= 178.252 ||= 637.669 || ||
| |
| || || 13\34 || || || ||= <span style="display: block; text-align: center;">5 3 5</span> ||= 458.824 ||= 917.647 ||= 176.471 ||= 635.294 ||= ||
| |
| || || || 34\89 || || ||= <span style="display: block; text-align: center;">13 8 13</span> ||= 458.427 ||= 916.854 ||= 175.281 ||= 633.708 ||= ||
| |
| || || || || 89\233 || ||= <span style="display: block; text-align: center;">34 21 34</span> ||= <span style="line-height: 15.6000003814697px;">458.369</span> ||= <span style="display: block; text-align: center;">916.738</span> ||= 175.107 ||= <span style="line-height: 15.6000003814697px;">633.473</span> ||= ||
| |
| || || || || || 233\610 ||= <span style="display: block; text-align: center;">89 55 89</span> ||= 458.361 ||= 916.721 ||= 175.082 ||= 633.443 ||= <span style="display: block; text-align: center;">Golden father</span> ||
| |
| || || || || 144\377 || ||= <span style="display: block; text-align: center;">55 34 55</span> ||= 458.355 ||= 916.711 ||= 175.066 ||= 633.422 ||= ||
| |
| || || || 55\144 || || ||= <span style="display: block; text-align: center;">21 13 21</span> ||= 458.333 ||= 916.666 ||= 175 ||= 633.333 ||= ||
| |
| || || 21\55 || || || ||= <span style="display: block; text-align: center;">8 5 8</span> ||= 458.182 ||= 916.364 ||= 174.545 ||= 632.727 ||= ||
| |
| || || || || || ||= <span style="display: block; text-align: center;">pi 2 pi</span> ||= 457.883 ||= 915.777 ||= 173.665 ||= 631.553 || ||
| |
| || 8\21 || || || || ||= <span style="display: block; text-align: center;">3 2 3</span> ||= 457.143 ||= 914.286 ||= 171.429 ||= 628.571 ||= <span style="display: block; text-align: center;">Optimum rank range (L/s=3/2) father</span> ||
| |
| || 11\29 || || || || ||= <span style="display: block; text-align: center;">4 3 4</span> ||= 455.172 ||= 910.345 ||= 165.517 ||= 620.690 ||= ||
| |
| || 14\37 || || || || ||= 5 4 5 ||= 454.054 ||= 908.108 ||= 162.162 ||= 616.216 || ||
| |
| || 17\45 || || || || ||= 6 5 6 ||= 453.333 ||= 906.667 ||= 160 ||= 613.333 || ||
| |
| || 20\53 || || || || ||= 7 6 7 ||= 452.83 ||= 905.66 ||= 158.491 ||= 611.321 || ||
| |
| || 23\61 || || || || ||= 8 7 8 ||= 452.459 ||= 904.918 ||= 157.377 ||= 609.836 || ||
| |
| || 26\69 || || || || ||= 9 8 9 ||= 452.174 ||= 904.348 ||= 156.522 ||= 608.696 || ||
| |
| || 29\77 || || || || ||= 10 9 10 ||= 451.948 ||= 903.896 ||= 155.844 ||= 607.792 || ||
| |
| || 3\8 || || || || ||= <span style="display: block; text-align: center;">1 1 1</span> ||= 450.000 ||= 900.000 ||= 150.000 ||= 600.000 ||= ||
| |
| The only notable harmonic entropy minimum is Vulture/[[Hemifamity temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes.
| |
|
| |
|
| By a weird coincidence, the other generator for this MOS will generate the same pattern within a tritave equivalence. By yet another weird coincidence, this MOS belongs to a temperament which has [[Bohlen-Pierce]] as its index-2 subtemperament. In addition to being harmonious, this tuning of the MOS gives an L/s ratio between 3/1 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.
| | == Name == |
| | {{TAMNAMS name}} 'Oneiro' is sometimes used as a shortened form. |
|
| |
|
| ||||||||||~ generator ||~ tetrachord ||~ g in cents ||~ 2g ||~ 3g ||~ 4g ||~ Comments ||
| | 'Father' is sometimes also used to denote 5L 3s, but it's a misnomer, as [[father]] is technically an abstract [[regular temperament]] (although a very inaccurate one), not a generator range. There are father tunings which generate 3L 5s. A more correct but still not quite correct name would be 'father[8]' or 'father octatonic'. "Father" is also vague regarding the number of notes, because optimal generators for it also generate [[3L 2s]]. |
| ||= 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 ||= <span style="display: block; text-align: center;">2g=12/5 minus quarter comma</span> ||
| |
| ||= 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+<span style="background-color: #ffffff;">√29 2 5+√29</span> ||= 747.648 ||= 1495.297 ||= 340.99 ||= 1088.638 ||= ||
| |
| ||= ||= 68\173 ||= ||= ||= ||= 31 6 31 ||= 747.589 ||= 1495.178 ||= 340.813 ||= 1088.402 ||= ||
| |
| ||= ||= ||= 147\374 ||= ||= ||= 67 13 67 ||= 747.56 ||= 1495.12 ||= 340.725 ||= 1088.285 ||= 4g=45/8 near here ||
| |
| ||= ||= 79\201 ||= ||= ||= ||= 36 7 36 ||= 747.535 ||= 1495.069 ||= 340.649 ||= 1088.183 ||= ||
| |
| ||= 11\28 ||= ||= ||= ||= ||= 5 1 5 ||= 747.197 ||= 1494.393 ||= 339.635 ||= 1086.831 ||= ||
| |
| ||= ||= 20\51 ||= ||= ||= ||= 9 2 9 ||= 745.865 ||= 1491.729 ||= 335.639 ||= 1081.50 ||= ||
| |
| ||= ||= 29\74 ||= ||= ||= ||= 13 3 13 ||= 745.361 ||= 1490.721 ||= 334.127 ||= 1079.488 ||= ||
| |
| ||= ||= 38/97 ||= ||= ||= ||= 17 4 17 ||= 745.096 ||= 1490.192 ||= 333.332 ||= 1078.428 ||= ||
| |
| ||= ||= ||= ||= ||= ||= 2+<span style="background-color: #ffffff;">√5 1 </span>2+<span style="background-color: #ffffff;">√5</span> ||= 754.051 ||= 1490.101 ||= 333.197 ||= 1078.247 ||= ||
| |
| ||= ||= 47\120 ||= ||= ||= ||= 21 5 21 ||= 744.932 ||= 1489.865 ||= 332.842 ||= 1077.7745 ||= ||
| |
| ||= 9\23 ||= ||= ||= ||= ||= 4 1 4 ||= 744.243 ||= 1488.487 ||= 330.775 ||= 1075.018 ||= L/s = 4 ||
| |
| ||= ||= 43\110 ||= ||= ||= ||= 19 5 19 ||= 743.4915 ||= 1486.983 ||= 328.5195 ||= 1072.011 ||= ||
| |
| ||= ||= ||= 77\197 ||= ||= ||= 34 9 34 ||= 743.404 ||= 1486.807 ||= 328.256 ||= 1071.66 ||= 4g=39/7 near here ||
| |
| ||= ||= 34\87 ||= ||= ||= ||= 15 4 15 ||= 743.293 ||= 1486.586 ||= 327.923 ||= 1071.216 ||= ||
| |
| ||= ||= 25\64 ||= ||= ||= ||= 11 3 11 ||= 742.951 ||= 1485.902 ||= 326.899 ||= 1069.85 ||= ||
| |
| ||= ||= 16\41 ||= ||= ||= ||= 7 2 7 ||= 742.226 ||= 1484.453 ||= 324.724 ||= 1066.95 ||= ||
| |
| ||= ||= 23\59 ||= ||= ||= ||= 10 3 10 ||= 741.44 ||= 1482.88 ||= 322.365 ||= 1063.805 ||= ||
| |
| ||= ||= ||= ||= ||= ||= 3+<span style="background-color: #ffffff;">√13 2 3+√13</span> ||= 741.289 ||= 1482.577 ||= 321.911 ||= 1063.20 ||= ||
| |
| ||= ||= 30\77 ||= ||= ||= ||= 13 4 13 ||= 741.021 ||= 1482.043 ||= 321.109 ||= 1062.131 ||= ||
| |
| ||= ||= ||= ||= ||= ||= pi 1 pi ||= 740.449 ||= 1480.898 ||= 319.392 ||= 1056.841 ||= L/s = pi ||
| |
| ||= 7\18 ||= ||= ||= ||= ||= 3 1 3 ||= 739.649 ||= 1479.298 ||= 316.992 ||= 1056.642 ||= L/s = 3 ||
| |
| ||= ||= 89\229 ||= ||= ||= ||= 38 13 38 ||= 739.188 ||= 1478.376 ||= 315.608 ||= 1054.796 ||= 3g=18/5 near here ||
| |
| ||= ||= 82\211 ||= ||= ||= ||= 35 12 35 ||= 739.148 ||= 1478.297 ||= 315.49 ||= 1054.639 ||= ||
| |
| ||= ||= 75\193 ||= ||= ||= ||= 32 11 32 ||= 739.102 ||= 1478.203 ||= 315.35 ||= 1054.452 ||= ||
| |
| ||= ||= 68\175 ||= ||= ||= ||= 29 10 29 ||= 739.045 ||= 1478.091 ||= 315.181 ||= 1054.227 ||= ||
| |
| ||= ||= 61/157 ||= ||= ||= ||= 26 9 26 ||= 738.976 ||= 1477.952 ||= 314.973 ||= 1053.949 ||= ||
| |
| ||= ||= 54\139 ||= ||= ||= ||= 23 8 23 ||= 738.889 ||= 1477.778 ||= 314.712 ||= 1053.601 ||= ||
| |
| ||= ||= 47\121 ||= ||= ||= ||= 20 7 20 ||= 738.776 ||= 1477.552 ||= 314.373 ||= 1053.149 ||= ||
| |
| ||= ||= 40\103 ||= ||= ||= ||= 17 6 17 ||= 738.623 ||= 1477.247 ||= 313.915 ||= 1052.538 ||= ||
| |
| ||= ||= 33\85 ||= ||= ||= ||= 14 5 14 ||= 738.406 ||= 1476.812 ||= 313.263 ||= 1051.669 ||= ||
| |
| ||= ||= 26\67 ||= ||= ||= ||= 11 4 11 ||= 738.072 ||= 1476.144 ||= 312.261 ||= 1050.333 ||= ||
| |
| ||= ||= ||= ||= ||= ||= e 1 e ||= 737.855 ||= 1478.71 ||= 311.61 ||= 1049.465 ||= L/s = e ||
| |
| ||= ||= 19\49 ||= ||= ||= ||= 8 3 8 ||= 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 ||= ||
| |
| ||= ||= ||= ||= ||= ||= <span style="background-color: #ffffff;">1+√2 1 1+√2</span> ||= 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 ||= ||
| |
| ||= ||= ||= ||= ||= ||= <span style="background-color: #ffffff;">√3 1 √3</span> ||= 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:<br />
| |
|
| |
|
| | == Scale properties == |
|
| |
|
| <table class="wiki_table">
| | === Intervals === |
| <tr>
| | {{MOS intervals}} |
| <th colspan="5">generator<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">tetrachord</span><br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">g in cents</span><br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">2g</span><br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">3g</span><br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">4g</span><br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Comments</span><br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>2\5<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">1 0 1</span><br />
| |
| </td>
| |
| <td style="text-align: center;">480.000<br />
| |
| </td>
| |
| <td style="text-align: center;">960.000<br />
| |
| </td>
| |
| <td style="text-align: center;">240.00<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="line-height: 15.6000003814697px;">720.000</span><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21\53<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">10 1 10</span><br />
| |
| </td>
| |
| <td style="text-align: center;">475.472<br />
| |
| </td>
| |
| <td style="text-align: center;">950.943<br />
| |
| </td>
| |
| <td style="text-align: center;">226.415<br />
| |
| </td>
| |
| <td style="text-align: center;">701.887<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">Vulture/Buzzard is around here</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19\48<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">9 1 9</span><br />
| |
| </td>
| |
| <td style="text-align: center;">475<br />
| |
| </td>
| |
| <td style="text-align: center;">950<br />
| |
| </td>
| |
| <td style="text-align: center;">225<br />
| |
| </td>
| |
| <td style="text-align: center;">700<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17\43<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">8 1 8</span><br />
| |
| </td>
| |
| <td style="text-align: center;">474.419<br />
| |
| </td>
| |
| <td style="text-align: center;">948.837<br />
| |
| </td>
| |
| <td style="text-align: center;">223.256<br />
| |
| </td>
| |
| <td style="text-align: center;">697.674<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15\38<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">7 1 7</span><br />
| |
| </td>
| |
| <td style="text-align: center;">473.684<br />
| |
| </td>
| |
| <td style="text-align: center;">947.368<br />
| |
| </td>
| |
| <td style="text-align: center;">221.053<br />
| |
| </td>
| |
| <td style="text-align: center;">694.737<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13\33<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">6 1 6</span><br />
| |
| </td>
| |
| <td style="text-align: center;">472.727<br />
| |
| </td>
| |
| <td style="text-align: center;">945.455<br />
| |
| </td>
| |
| <td style="text-align: center;">218.181<br />
| |
| </td>
| |
| <td style="text-align: center;">690.909<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11\28<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">5 1 5</span><br />
| |
| </td>
| |
| <td style="text-align: center;">471.429<br />
| |
| </td>
| |
| <td style="text-align: center;">942.857<br />
| |
| </td>
| |
| <td style="text-align: center;">214.286<br />
| |
| </td>
| |
| <td style="text-align: center;">685.714<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9\23<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">4 1 4</span><br />
| |
| </td>
| |
| <td style="text-align: center;">469.565<br />
| |
| </td>
| |
| <td style="text-align: center;">939.130<br />
| |
| </td>
| |
| <td style="text-align: center;">208.696<br />
| |
| </td>
| |
| <td style="text-align: center;">678.261<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 4</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">pi 1 pi<br />
| |
| </td>
| |
| <td style="text-align: center;">467.171<br />
| |
| </td>
| |
| <td style="text-align: center;">934.3425<br />
| |
| </td>
| |
| <td style="text-align: center;">201.514<br />
| |
| </td>
| |
| <td style="text-align: center;">668.685<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = pi</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7\18<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">3 1 3</span><br />
| |
| </td>
| |
| <td style="text-align: center;">466.667<br />
| |
| </td>
| |
| <td style="text-align: center;">933.333<br />
| |
| </td>
| |
| <td style="text-align: center;">200.000<br />
| |
| </td>
| |
| <td style="text-align: center;">666.667<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">e 1 e<br />
| |
| </td>
| |
| <td style="text-align: center;">465.535<br />
| |
| </td>
| |
| <td style="text-align: center;">931.069<br />
| |
| </td>
| |
| <td style="text-align: center;">196.604<br />
| |
| </td>
| |
| <td style="text-align: center;">662.139<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = e</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>19\49<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">8 3 8<br />
| |
| </td>
| |
| <td style="text-align: center;">465.306<br />
| |
| </td>
| |
| <td style="text-align: center;">930.612<br />
| |
| </td>
| |
| <td style="text-align: center;">195.918<br />
| |
| </td>
| |
| <td style="text-align: center;">661.2245<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>50\129<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">21 8 21<br />
| |
| </td>
| |
| <td style="text-align: center;">465.116<br />
| |
| </td>
| |
| <td style="text-align: center;">930.233<br />
| |
| </td>
| |
| <td style="text-align: center;">195.349<br />
| |
| </td>
| |
| <td style="text-align: center;">660.465<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>131\338<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">55 21 55<br />
| |
| </td>
| |
| <td style="text-align: center;">465.089<br />
| |
| </td>
| |
| <td style="text-align: center;">930.1775<br />
| |
| </td>
| |
| <td style="text-align: center;">195.266<br />
| |
| </td>
| |
| <td style="text-align: center;">660.335<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>212\547<br />
| |
| </td>
| |
| <td style="text-align: center;">89 34 89<br />
| |
| </td>
| |
| <td style="text-align: center;">465.082<br />
| |
| </td>
| |
| <td style="text-align: center;">930.1645<br />
| |
| </td>
| |
| <td style="text-align: center;">195.247<br />
| |
| </td>
| |
| <td style="text-align: center;">660.329<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>81\209<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">34 13 34<br />
| |
| </td>
| |
| <td style="text-align: center;">465.072<br />
| |
| </td>
| |
| <td style="text-align: center;">930.1435<br />
| |
| </td>
| |
| <td style="text-align: center;">195.215<br />
| |
| </td>
| |
| <td style="text-align: center;">660.287<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>31\80<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">13 5 13<br />
| |
| </td>
| |
| <td style="text-align: center;">465<br />
| |
| </td>
| |
| <td style="text-align: center;">930<br />
| |
| </td>
| |
| <td style="text-align: center;">195<br />
| |
| </td>
| |
| <td style="text-align: center;">660<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>12\31<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">5 2 5</span><br />
| |
| </td>
| |
| <td style="text-align: center;">464.516<br />
| |
| </td>
| |
| <td style="text-align: center;">929.032<br />
| |
| </td>
| |
| <td style="text-align: center;">193.549<br />
| |
| </td>
| |
| <td style="text-align: center;">658.065<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5\13<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">2 1 2</span><br />
| |
| </td>
| |
| <td style="text-align: center;">461.538<br />
| |
| </td>
| |
| <td style="text-align: center;">923.077<br />
| |
| </td>
| |
| <td style="text-align: center;">184.615<br />
| |
| </td>
| |
| <td style="text-align: center;">646.154<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="background-color: #ffffff;">√3 1 √3</span><br />
| |
| </td>
| |
| <td style="text-align: center;">459.417<br />
| |
| </td>
| |
| <td style="text-align: center;">918.8345<br />
| |
| </td>
| |
| <td style="text-align: center;">178.252<br />
| |
| </td>
| |
| <td style="text-align: center;">637.669<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>13\34<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">5 3 5</span><br />
| |
| </td>
| |
| <td style="text-align: center;">458.824<br />
| |
| </td>
| |
| <td style="text-align: center;">917.647<br />
| |
| </td>
| |
| <td style="text-align: center;">176.471<br />
| |
| </td>
| |
| <td style="text-align: center;">635.294<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>34\89<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">13 8 13</span><br />
| |
| </td>
| |
| <td style="text-align: center;">458.427<br />
| |
| </td>
| |
| <td style="text-align: center;">916.854<br />
| |
| </td>
| |
| <td style="text-align: center;">175.281<br />
| |
| </td>
| |
| <td style="text-align: center;">633.708<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>89\233<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">34 21 34</span><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="line-height: 15.6000003814697px;">458.369</span><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">916.738</span><br />
| |
| </td>
| |
| <td style="text-align: center;">175.107<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="line-height: 15.6000003814697px;">633.473</span><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>233\610<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">89 55 89</span><br />
| |
| </td>
| |
| <td style="text-align: center;">458.361<br />
| |
| </td>
| |
| <td style="text-align: center;">916.721<br />
| |
| </td>
| |
| <td style="text-align: center;">175.082<br />
| |
| </td>
| |
| <td style="text-align: center;">633.443<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">Golden father</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>144\377<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">55 34 55</span><br />
| |
| </td>
| |
| <td style="text-align: center;">458.355<br />
| |
| </td>
| |
| <td style="text-align: center;">916.711<br />
| |
| </td>
| |
| <td style="text-align: center;">175.066<br />
| |
| </td>
| |
| <td style="text-align: center;">633.422<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>55\144<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">21 13 21</span><br />
| |
| </td>
| |
| <td style="text-align: center;">458.333<br />
| |
| </td>
| |
| <td style="text-align: center;">916.666<br />
| |
| </td>
| |
| <td style="text-align: center;">175<br />
| |
| </td>
| |
| <td style="text-align: center;">633.333<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>21\55<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">8 5 8</span><br />
| |
| </td>
| |
| <td style="text-align: center;">458.182<br />
| |
| </td>
| |
| <td style="text-align: center;">916.364<br />
| |
| </td>
| |
| <td style="text-align: center;">174.545<br />
| |
| </td>
| |
| <td style="text-align: center;">632.727<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">pi 2 pi</span><br />
| |
| </td>
| |
| <td style="text-align: center;">457.883<br />
| |
| </td>
| |
| <td style="text-align: center;">915.777<br />
| |
| </td>
| |
| <td style="text-align: center;">173.665<br />
| |
| </td>
| |
| <td style="text-align: center;">631.553<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8\21<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">3 2 3</span><br />
| |
| </td>
| |
| <td style="text-align: center;">457.143<br />
| |
| </td>
| |
| <td style="text-align: center;">914.286<br />
| |
| </td>
| |
| <td style="text-align: center;">171.429<br />
| |
| </td>
| |
| <td style="text-align: center;">628.571<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">Optimum rank range (L/s=3/2) father</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11\29<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">4 3 4</span><br />
| |
| </td>
| |
| <td style="text-align: center;">455.172<br />
| |
| </td>
| |
| <td style="text-align: center;">910.345<br />
| |
| </td>
| |
| <td style="text-align: center;">165.517<br />
| |
| </td>
| |
| <td style="text-align: center;">620.690<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14\37<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">5 4 5<br />
| |
| </td>
| |
| <td style="text-align: center;">454.054<br />
| |
| </td>
| |
| <td style="text-align: center;">908.108<br />
| |
| </td>
| |
| <td style="text-align: center;">162.162<br />
| |
| </td>
| |
| <td style="text-align: center;">616.216<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17\45<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">6 5 6<br />
| |
| </td>
| |
| <td style="text-align: center;">453.333<br />
| |
| </td>
| |
| <td style="text-align: center;">906.667<br />
| |
| </td>
| |
| <td style="text-align: center;">160<br />
| |
| </td>
| |
| <td style="text-align: center;">613.333<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20\53<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">7 6 7<br />
| |
| </td>
| |
| <td style="text-align: center;">452.83<br />
| |
| </td>
| |
| <td style="text-align: center;">905.66<br />
| |
| </td>
| |
| <td style="text-align: center;">158.491<br />
| |
| </td>
| |
| <td style="text-align: center;">611.321<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23\61<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">8 7 8<br />
| |
| </td>
| |
| <td style="text-align: center;">452.459<br />
| |
| </td>
| |
| <td style="text-align: center;">904.918<br />
| |
| </td>
| |
| <td style="text-align: center;">157.377<br />
| |
| </td>
| |
| <td style="text-align: center;">609.836<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26\69<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">9 8 9<br />
| |
| </td>
| |
| <td style="text-align: center;">452.174<br />
| |
| </td>
| |
| <td style="text-align: center;">904.348<br />
| |
| </td>
| |
| <td style="text-align: center;">156.522<br />
| |
| </td>
| |
| <td style="text-align: center;">608.696<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>29\77<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">10 9 10<br />
| |
| </td>
| |
| <td style="text-align: center;">451.948<br />
| |
| </td>
| |
| <td style="text-align: center;">903.896<br />
| |
| </td>
| |
| <td style="text-align: center;">155.844<br />
| |
| </td>
| |
| <td style="text-align: center;">607.792<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3\8<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">1 1 1</span><br />
| |
| </td>
| |
| <td style="text-align: center;">450.000<br />
| |
| </td>
| |
| <td style="text-align: center;">900.000<br />
| |
| </td>
| |
| <td style="text-align: center;">150.000<br />
| |
| </td>
| |
| <td style="text-align: center;">600.000<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| The only notable harmonic entropy minimum is Vulture/<a class="wiki_link" href="/Hemifamity%20temperaments">Buzzard</a>, in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes.<br />
| | === Generator chain === |
| <br />
| | {{MOS genchain}} |
| By a weird coincidence, the other generator for this MOS will generate the same pattern within a tritave equivalence. By yet another weird coincidence, this MOS belongs to a temperament which has <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> as its index-2 subtemperament. In addition to being harmonious, this tuning of the MOS gives an L/s ratio between 3/1 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.<br />
| |
| <br />
| |
|
| |
|
| | === Modes === |
| | {{MOS mode degrees}} |
|
| |
|
| <table class="wiki_table">
| | ==== Proposed mode names ==== |
| <tr>
| | The following names have been proposed for the modes of 5L 3s, and are named after cities in the Dreamlands. |
| <th colspan="5">generator<br />
| | {{MOS modes |
| </th>
| | | Mode Names= |
| <th>tetrachord<br />
| | Dylathian $ |
| </th>
| | Ilarnekian $ |
| <th>g in cents<br />
| | Celephaïsian $ |
| </th>
| | Ultharian $ |
| <th>2g<br />
| | Mnarian $ |
| </th>
| | Kadathian $ |
| <th>3g<br />
| | Hlanithian $ |
| </th>
| | Sarnathian $ |
| <th>4g<br />
| | | Collapsed=1 |
| </th>
| | }} |
| <th>Comments<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">2\5<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">1 0 1<br />
| |
| </td>
| |
| <td style="text-align: center;">760.782<br />
| |
| </td>
| |
| <td style="text-align: center;">1521.564<br />
| |
| </td>
| |
| <td style="text-align: center;">380.391<br />
| |
| </td>
| |
| <td style="text-align: center;">1141.173<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">27\68<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">13 1 13<br />
| |
| </td>
| |
| <td style="text-align: center;">755.188<br />
| |
| </td>
| |
| <td style="text-align: center;">1510.376<br />
| |
| </td>
| |
| <td style="text-align: center;">363.609<br />
| |
| </td>
| |
| <td style="text-align: center;">1118.797<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">~6626 515 6626<br />
| |
| </td>
| |
| <td style="text-align: center;">755.132<br />
| |
| </td>
| |
| <td style="text-align: center;">1510.265<br />
| |
| </td>
| |
| <td style="text-align: center;">363.442<br />
| |
| </td>
| |
| <td style="text-align: center;">1118.574<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">2g=12/5 minus quarter comma</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">25\63<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">12 1 12<br />
| |
| </td>
| |
| <td style="text-align: center;">754.744<br />
| |
| </td>
| |
| <td style="text-align: center;">1509.488<br />
| |
| </td>
| |
| <td style="text-align: center;">362.277<br />
| |
| </td>
| |
| <td style="text-align: center;">1117.021<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">23\58<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">11 1 11<br />
| |
| </td>
| |
| <td style="text-align: center;">754.2235<br />
| |
| </td>
| |
| <td style="text-align: center;">1508.447<br />
| |
| </td>
| |
| <td style="text-align: center;">360.716<br />
| |
| </td>
| |
| <td style="text-align: center;">1114.939<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">21\53<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">10 1 10<br />
| |
| </td>
| |
| <td style="text-align: center;">753.605<br />
| |
| </td>
| |
| <td style="text-align: center;">1507.21<br />
| |
| </td>
| |
| <td style="text-align: center;">358.859<br />
| |
| </td>
| |
| <td style="text-align: center;">1112.464<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">19\48<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">9 1 9<br />
| |
| </td>
| |
| <td style="text-align: center;">752.857<br />
| |
| </td>
| |
| <td style="text-align: center;">1505.714<br />
| |
| </td>
| |
| <td style="text-align: center;">356.617<br />
| |
| </td>
| |
| <td style="text-align: center;">1109.474<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">17\43<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">8 1 8<br />
| |
| </td>
| |
| <td style="text-align: center;">751.936<br />
| |
| </td>
| |
| <td style="text-align: center;">1503.871<br />
| |
| </td>
| |
| <td style="text-align: center;">353.852<br />
| |
| </td>
| |
| <td style="text-align: center;">1105.788<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">15\38<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">7 1 7<br />
| |
| </td>
| |
| <td style="text-align: center;">750.771<br />
| |
| </td>
| |
| <td style="text-align: center;">1501.543<br />
| |
| </td>
| |
| <td style="text-align: center;">350.36<br />
| |
| </td>
| |
| <td style="text-align: center;">1101.132<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">28/71<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">13 2 13<br />
| |
| </td>
| |
| <td style="text-align: center;">750.067<br />
| |
| </td>
| |
| <td style="text-align: center;">1500.1335<br />
| |
| </td>
| |
| <td style="text-align: center;">348.245<br />
| |
| </td>
| |
| <td style="text-align: center;">1098.312<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">41\104<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">19 3 19<br />
| |
| </td>
| |
| <td style="text-align: center;">749.809<br />
| |
| </td>
| |
| <td style="text-align: center;">1466.618<br />
| |
| </td>
| |
| <td style="text-align: center;">347.4725<br />
| |
| </td>
| |
| <td style="text-align: center;">1097.282<br />
| |
| </td>
| |
| <td style="text-align: center;">3g=11/3 near here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">13\33<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">6 1 6<br />
| |
| </td>
| |
| <td style="text-align: center;">749.255<br />
| |
| </td>
| |
| <td style="text-align: center;">1498.51<br />
| |
| </td>
| |
| <td style="text-align: center;">345.81<br />
| |
| </td>
| |
| <td style="text-align: center;">1095.065<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">24\61<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">11 2 11<br />
| |
| </td>
| |
| <td style="text-align: center;">748.31<br />
| |
| </td>
| |
| <td style="text-align: center;">1496.62<br />
| |
| </td>
| |
| <td style="text-align: center;">342.976<br />
| |
| </td>
| |
| <td style="text-align: center;">1091.286<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">35\89<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">16 3 16<br />
| |
| </td>
| |
| <td style="text-align: center;">747.96<br />
| |
| </td>
| |
| <td style="text-align: center;">1495.92<br />
| |
| </td>
| |
| <td style="text-align: center;">341.924<br />
| |
| </td>
| |
| <td style="text-align: center;">1089.884<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">46\117<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">21 4 21<br />
| |
| </td>
| |
| <td style="text-align: center;">747.777<br />
| |
| </td>
| |
| <td style="text-align: center;">1495.554<br />
| |
| </td>
| |
| <td style="text-align: center;">341.377<br />
| |
| </td>
| |
| <td style="text-align: center;">1089.154<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">57\145<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">26 5 26<br />
| |
| </td>
| |
| <td style="text-align: center;">747.665<br />
| |
| </td>
| |
| <td style="text-align: center;">1495.33<br />
| |
| </td>
| |
| <td style="text-align: center;">341.04<br />
| |
| </td>
| |
| <td style="text-align: center;">1088.705<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">5+<span style="background-color: #ffffff;">√29 2 5+√29</span><br />
| |
| </td>
| |
| <td style="text-align: center;">747.648<br />
| |
| </td>
| |
| <td style="text-align: center;">1495.297<br />
| |
| </td>
| |
| <td style="text-align: center;">340.99<br />
| |
| </td>
| |
| <td style="text-align: center;">1088.638<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">68\173<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">31 6 31<br />
| |
| </td>
| |
| <td style="text-align: center;">747.589<br />
| |
| </td>
| |
| <td style="text-align: center;">1495.178<br />
| |
| </td>
| |
| <td style="text-align: center;">340.813<br />
| |
| </td>
| |
| <td style="text-align: center;">1088.402<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">147\374<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">67 13 67<br />
| |
| </td>
| |
| <td style="text-align: center;">747.56<br />
| |
| </td>
| |
| <td style="text-align: center;">1495.12<br />
| |
| </td>
| |
| <td style="text-align: center;">340.725<br />
| |
| </td>
| |
| <td style="text-align: center;">1088.285<br />
| |
| </td>
| |
| <td style="text-align: center;">4g=45/8 near here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">79\201<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">36 7 36<br />
| |
| </td>
| |
| <td style="text-align: center;">747.535<br />
| |
| </td>
| |
| <td style="text-align: center;">1495.069<br />
| |
| </td>
| |
| <td style="text-align: center;">340.649<br />
| |
| </td>
| |
| <td style="text-align: center;">1088.183<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">11\28<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">5 1 5<br />
| |
| </td>
| |
| <td style="text-align: center;">747.197<br />
| |
| </td>
| |
| <td style="text-align: center;">1494.393<br />
| |
| </td>
| |
| <td style="text-align: center;">339.635<br />
| |
| </td>
| |
| <td style="text-align: center;">1086.831<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">20\51<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">9 2 9<br />
| |
| </td>
| |
| <td style="text-align: center;">745.865<br />
| |
| </td>
| |
| <td style="text-align: center;">1491.729<br />
| |
| </td>
| |
| <td style="text-align: center;">335.639<br />
| |
| </td>
| |
| <td style="text-align: center;">1081.50<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">29\74<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">13 3 13<br />
| |
| </td>
| |
| <td style="text-align: center;">745.361<br />
| |
| </td>
| |
| <td style="text-align: center;">1490.721<br />
| |
| </td>
| |
| <td style="text-align: center;">334.127<br />
| |
| </td>
| |
| <td style="text-align: center;">1079.488<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">38/97<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">17 4 17<br />
| |
| </td>
| |
| <td style="text-align: center;">745.096<br />
| |
| </td>
| |
| <td style="text-align: center;">1490.192<br />
| |
| </td>
| |
| <td style="text-align: center;">333.332<br />
| |
| </td>
| |
| <td style="text-align: center;">1078.428<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">2+<span style="background-color: #ffffff;">√5 1 </span>2+<span style="background-color: #ffffff;">√5</span><br />
| |
| </td>
| |
| <td style="text-align: center;">754.051<br />
| |
| </td>
| |
| <td style="text-align: center;">1490.101<br />
| |
| </td>
| |
| <td style="text-align: center;">333.197<br />
| |
| </td>
| |
| <td style="text-align: center;">1078.247<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">47\120<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">21 5 21<br />
| |
| </td>
| |
| <td style="text-align: center;">744.932<br />
| |
| </td>
| |
| <td style="text-align: center;">1489.865<br />
| |
| </td>
| |
| <td style="text-align: center;">332.842<br />
| |
| </td>
| |
| <td style="text-align: center;">1077.7745<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">9\23<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">4 1 4<br />
| |
| </td>
| |
| <td style="text-align: center;">744.243<br />
| |
| </td>
| |
| <td style="text-align: center;">1488.487<br />
| |
| </td>
| |
| <td style="text-align: center;">330.775<br />
| |
| </td>
| |
| <td style="text-align: center;">1075.018<br />
| |
| </td>
| |
| <td style="text-align: center;">L/s = 4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">43\110<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">19 5 19<br />
| |
| </td>
| |
| <td style="text-align: center;">743.4915<br />
| |
| </td>
| |
| <td style="text-align: center;">1486.983<br />
| |
| </td>
| |
| <td style="text-align: center;">328.5195<br />
| |
| </td>
| |
| <td style="text-align: center;">1072.011<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">77\197<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">34 9 34<br />
| |
| </td>
| |
| <td style="text-align: center;">743.404<br />
| |
| </td>
| |
| <td style="text-align: center;">1486.807<br />
| |
| </td>
| |
| <td style="text-align: center;">328.256<br />
| |
| </td>
| |
| <td style="text-align: center;">1071.66<br />
| |
| </td>
| |
| <td style="text-align: center;">4g=39/7 near here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">34\87<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">15 4 15<br />
| |
| </td>
| |
| <td style="text-align: center;">743.293<br />
| |
| </td>
| |
| <td style="text-align: center;">1486.586<br />
| |
| </td>
| |
| <td style="text-align: center;">327.923<br />
| |
| </td>
| |
| <td style="text-align: center;">1071.216<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">25\64<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">11 3 11<br />
| |
| </td>
| |
| <td style="text-align: center;">742.951<br />
| |
| </td>
| |
| <td style="text-align: center;">1485.902<br />
| |
| </td>
| |
| <td style="text-align: center;">326.899<br />
| |
| </td>
| |
| <td style="text-align: center;">1069.85<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">16\41<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">7 2 7<br />
| |
| </td>
| |
| <td style="text-align: center;">742.226<br />
| |
| </td>
| |
| <td style="text-align: center;">1484.453<br />
| |
| </td>
| |
| <td style="text-align: center;">324.724<br />
| |
| </td>
| |
| <td style="text-align: center;">1066.95<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">23\59<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">10 3 10<br />
| |
| </td>
| |
| <td style="text-align: center;">741.44<br />
| |
| </td>
| |
| <td style="text-align: center;">1482.88<br />
| |
| </td>
| |
| <td style="text-align: center;">322.365<br />
| |
| </td>
| |
| <td style="text-align: center;">1063.805<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">3+<span style="background-color: #ffffff;">√13 2 3+√13</span><br />
| |
| </td>
| |
| <td style="text-align: center;">741.289<br />
| |
| </td>
| |
| <td style="text-align: center;">1482.577<br />
| |
| </td>
| |
| <td style="text-align: center;">321.911<br />
| |
| </td>
| |
| <td style="text-align: center;">1063.20<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">30\77<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">13 4 13<br />
| |
| </td>
| |
| <td style="text-align: center;">741.021<br />
| |
| </td>
| |
| <td style="text-align: center;">1482.043<br />
| |
| </td>
| |
| <td style="text-align: center;">321.109<br />
| |
| </td>
| |
| <td style="text-align: center;">1062.131<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">pi 1 pi<br />
| |
| </td>
| |
| <td style="text-align: center;">740.449<br />
| |
| </td>
| |
| <td style="text-align: center;">1480.898<br />
| |
| </td>
| |
| <td style="text-align: center;">319.392<br />
| |
| </td>
| |
| <td style="text-align: center;">1056.841<br />
| |
| </td>
| |
| <td style="text-align: center;">L/s = pi<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">7\18<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">3 1 3<br />
| |
| </td>
| |
| <td style="text-align: center;">739.649<br />
| |
| </td>
| |
| <td style="text-align: center;">1479.298<br />
| |
| </td>
| |
| <td style="text-align: center;">316.992<br />
| |
| </td>
| |
| <td style="text-align: center;">1056.642<br />
| |
| </td>
| |
| <td style="text-align: center;">L/s = 3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">89\229<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">38 13 38<br />
| |
| </td>
| |
| <td style="text-align: center;">739.188<br />
| |
| </td>
| |
| <td style="text-align: center;">1478.376<br />
| |
| </td>
| |
| <td style="text-align: center;">315.608<br />
| |
| </td>
| |
| <td style="text-align: center;">1054.796<br />
| |
| </td>
| |
| <td style="text-align: center;">3g=18/5 near here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">82\211<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">35 12 35<br />
| |
| </td>
| |
| <td style="text-align: center;">739.148<br />
| |
| </td>
| |
| <td style="text-align: center;">1478.297<br />
| |
| </td>
| |
| <td style="text-align: center;">315.49<br />
| |
| </td>
| |
| <td style="text-align: center;">1054.639<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">75\193<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">32 11 32<br />
| |
| </td>
| |
| <td style="text-align: center;">739.102<br />
| |
| </td>
| |
| <td style="text-align: center;">1478.203<br />
| |
| </td>
| |
| <td style="text-align: center;">315.35<br />
| |
| </td>
| |
| <td style="text-align: center;">1054.452<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">68\175<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">29 10 29<br />
| |
| </td>
| |
| <td style="text-align: center;">739.045<br />
| |
| </td>
| |
| <td style="text-align: center;">1478.091<br />
| |
| </td>
| |
| <td style="text-align: center;">315.181<br />
| |
| </td>
| |
| <td style="text-align: center;">1054.227<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">61/157<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">26 9 26<br />
| |
| </td>
| |
| <td style="text-align: center;">738.976<br />
| |
| </td>
| |
| <td style="text-align: center;">1477.952<br />
| |
| </td>
| |
| <td style="text-align: center;">314.973<br />
| |
| </td>
| |
| <td style="text-align: center;">1053.949<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">54\139<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">23 8 23<br />
| |
| </td>
| |
| <td style="text-align: center;">738.889<br />
| |
| </td>
| |
| <td style="text-align: center;">1477.778<br />
| |
| </td>
| |
| <td style="text-align: center;">314.712<br />
| |
| </td>
| |
| <td style="text-align: center;">1053.601<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">47\121<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">20 7 20<br />
| |
| </td>
| |
| <td style="text-align: center;">738.776<br />
| |
| </td>
| |
| <td style="text-align: center;">1477.552<br />
| |
| </td>
| |
| <td style="text-align: center;">314.373<br />
| |
| </td>
| |
| <td style="text-align: center;">1053.149<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">40\103<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">17 6 17<br />
| |
| </td>
| |
| <td style="text-align: center;">738.623<br />
| |
| </td>
| |
| <td style="text-align: center;">1477.247<br />
| |
| </td>
| |
| <td style="text-align: center;">313.915<br />
| |
| </td>
| |
| <td style="text-align: center;">1052.538<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">33\85<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">14 5 14<br />
| |
| </td>
| |
| <td style="text-align: center;">738.406<br />
| |
| </td>
| |
| <td style="text-align: center;">1476.812<br />
| |
| </td>
| |
| <td style="text-align: center;">313.263<br />
| |
| </td>
| |
| <td style="text-align: center;">1051.669<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">26\67<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">11 4 11<br />
| |
| </td>
| |
| <td style="text-align: center;">738.072<br />
| |
| </td>
| |
| <td style="text-align: center;">1476.144<br />
| |
| </td>
| |
| <td style="text-align: center;">312.261<br />
| |
| </td>
| |
| <td style="text-align: center;">1050.333<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">e 1 e<br />
| |
| </td>
| |
| <td style="text-align: center;">737.855<br />
| |
| </td>
| |
| <td style="text-align: center;">1478.71<br />
| |
| </td>
| |
| <td style="text-align: center;">311.61<br />
| |
| </td>
| |
| <td style="text-align: center;">1049.465<br />
| |
| </td>
| |
| <td style="text-align: center;">L/s = e<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">19\49<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">8 3 8<br />
| |
| </td>
| |
| <td style="text-align: center;">737.493<br />
| |
| </td>
| |
| <td style="text-align: center;">1474.986<br />
| |
| </td>
| |
| <td style="text-align: center;">310.523<br />
| |
| </td>
| |
| <td style="text-align: center;">1048.016<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">164\423<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">69 26 69<br />
| |
| </td>
| |
| <td style="text-align: center;">737.401<br />
| |
| </td>
| |
| <td style="text-align: center;">1474.802<br />
| |
| </td>
| |
| <td style="text-align: center;">310.248<br />
| |
| </td>
| |
| <td style="text-align: center;">1047.649<br />
| |
| </td>
| |
| <td style="text-align: center;">3g=18/5 minus quarter comma near here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">145\374<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">61 23 61<br />
| |
| </td>
| |
| <td style="text-align: center;">737.389<br />
| |
| </td>
| |
| <td style="text-align: center;">1474.778<br />
| |
| </td>
| |
| <td style="text-align: center;">310.212<br />
| |
| </td>
| |
| <td style="text-align: center;">1047.601<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">126\325<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">53 20 53<br />
| |
| </td>
| |
| <td style="text-align: center;">737.373<br />
| |
| </td>
| |
| <td style="text-align: center;">1474.747<br />
| |
| </td>
| |
| <td style="text-align: center;">310.165<br />
| |
| </td>
| |
| <td style="text-align: center;">1047.538<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">107\276<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">45 17 45<br />
| |
| </td>
| |
| <td style="text-align: center;">737.352<br />
| |
| </td>
| |
| <td style="text-align: center;">1474.704<br />
| |
| </td>
| |
| <td style="text-align: center;">310.101<br />
| |
| </td>
| |
| <td style="text-align: center;">1047.453<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">88\227<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">37 14 37<br />
| |
| </td>
| |
| <td style="text-align: center;">737.322<br />
| |
| </td>
| |
| <td style="text-align: center;">1474.644<br />
| |
| </td>
| |
| <td style="text-align: center;">310.01<br />
| |
| </td>
| |
| <td style="text-align: center;">1047.332<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">69\178<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">29 11 29<br />
| |
| </td>
| |
| <td style="text-align: center;">737.275<br />
| |
| </td>
| |
| <td style="text-align: center;">1474.549<br />
| |
| </td>
| |
| <td style="text-align: center;">309.869<br />
| |
| </td>
| |
| <td style="text-align: center;">1047.144<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">50\129<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">21 8 21<br />
| |
| </td>
| |
| <td style="text-align: center;">737.192<br />
| |
| </td>
| |
| <td style="text-align: center;">1474.384<br />
| |
| </td>
| |
| <td style="text-align: center;">309.621<br />
| |
| </td>
| |
| <td style="text-align: center;">1046.812<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">131\338<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">55 21 55<br />
| |
| </td>
| |
| <td style="text-align: center;">737.148<br />
| |
| </td>
| |
| <td style="text-align: center;">1474.296<br />
| |
| </td>
| |
| <td style="text-align: center;">309.49<br />
| |
| </td>
| |
| <td style="text-align: center;">1046.638<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">212\547<br />
| |
| </td>
| |
| <td style="text-align: center;">89 34 89<br />
| |
| </td>
| |
| <td style="text-align: center;">737.138<br />
| |
| </td>
| |
| <td style="text-align: center;">1474.276<br />
| |
| </td>
| |
| <td style="text-align: center;">309.459<br />
| |
| </td>
| |
| <td style="text-align: center;">1046.597<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">81\209<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">34 13 34<br />
| |
| </td>
| |
| <td style="text-align: center;">737.121<br />
| |
| </td>
| |
| <td style="text-align: center;">1474.243<br />
| |
| </td>
| |
| <td style="text-align: center;">309.409<br />
| |
| </td>
| |
| <td style="text-align: center;">1046.53<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">31\80<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">13 5 13<br />
| |
| </td>
| |
| <td style="text-align: center;">737.008<br />
| |
| </td>
| |
| <td style="text-align: center;">1474.015<br />
| |
| </td>
| |
| <td style="text-align: center;">309.068<br />
| |
| </td>
| |
| <td style="text-align: center;">1046.075<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">12\31<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">5 2 5<br />
| |
| </td>
| |
| <td style="text-align: center;">736.241<br />
| |
| </td>
| |
| <td style="text-align: center;">1472.481<br />
| |
| </td>
| |
| <td style="text-align: center;">306.767<br />
| |
| </td>
| |
| <td style="text-align: center;">1043.007<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="background-color: #ffffff;">1+√2 1 1+√2</span><br />
| |
| </td>
| |
| <td style="text-align: center;">735.542<br />
| |
| </td>
| |
| <td style="text-align: center;">1471.084<br />
| |
| </td>
| |
| <td style="text-align: center;">304.6715<br />
| |
| </td>
| |
| <td style="text-align: center;">1040.214<br />
| |
| </td>
| |
| <td style="text-align: center;">Silver false father<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">17\44<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">7 3 7<br />
| |
| </td>
| |
| <td style="text-align: center;">734.846<br />
| |
| </td>
| |
| <td style="text-align: center;">1469.693<br />
| |
| </td>
| |
| <td style="text-align: center;">302.584<br />
| |
| </td>
| |
| <td style="text-align: center;">1037.41<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">22\57<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">9 4 9<br />
| |
| </td>
| |
| <td style="text-align: center;">734.088<br />
| |
| </td>
| |
| <td style="text-align: center;">1468.176<br />
| |
| </td>
| |
| <td style="text-align: center;">300.309<br />
| |
| </td>
| |
| <td style="text-align: center;">1034.397<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">27\70<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">11 5 11<br />
| |
| </td>
| |
| <td style="text-align: center;">733.611<br />
| |
| </td>
| |
| <td style="text-align: center;">1467.222<br />
| |
| </td>
| |
| <td style="text-align: center;">298.879<br />
| |
| </td>
| |
| <td style="text-align: center;">1032.49<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">59\153<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">24 11 24<br />
| |
| </td>
| |
| <td style="text-align: center;">733.434<br />
| |
| </td>
| |
| <td style="text-align: center;">1466.867<br />
| |
| </td>
| |
| <td style="text-align: center;">298.346<br />
| |
| </td>
| |
| <td style="text-align: center;">1031.779<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">32\83<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">13 6 13<br />
| |
| </td>
| |
| <td style="text-align: center;">733.284<br />
| |
| </td>
| |
| <td style="text-align: center;">1466.568<br />
| |
| </td>
| |
| <td style="text-align: center;">297.897<br />
| |
| </td>
| |
| <td style="text-align: center;">1031.181<br />
| |
| </td>
| |
| <td style="text-align: center;">2g=7/3 near here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">5\13<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">2 1 2<br />
| |
| </td>
| |
| <td style="text-align: center;">731.521<br />
| |
| </td>
| |
| <td style="text-align: center;">1463.042<br />
| |
| </td>
| |
| <td style="text-align: center;">292.609<br />
| |
| </td>
| |
| <td style="text-align: center;">1024.13<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">53\138<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">21 11 21<br />
| |
| </td>
| |
| <td style="text-align: center;">730.461<br />
| |
| </td>
| |
| <td style="text-align: center;">1460.922<br />
| |
| </td>
| |
| <td style="text-align: center;">289.428<br />
| |
| </td>
| |
| <td style="text-align: center;">1018.889<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">101\263<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">40 21 40<br />
| |
| </td>
| |
| <td style="text-align: center;">730.409<br />
| |
| </td>
| |
| <td style="text-align: center;">1460.817<br />
| |
| </td>
| |
| <td style="text-align: center;">289.271<br />
| |
| </td>
| |
| <td style="text-align: center;">1019.679<br />
| |
| </td>
| |
| <td style="text-align: center;">3g=39/11 near here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">48\125<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">19 10 19<br />
| |
| </td>
| |
| <td style="text-align: center;">730.35<br />
| |
| </td>
| |
| <td style="text-align: center;">1460.701<br />
| |
| </td>
| |
| <td style="text-align: center;">289.097<br />
| |
| </td>
| |
| <td style="text-align: center;">1019.448<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">43\112<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">17 9 17<br />
| |
| </td>
| |
| <td style="text-align: center;">730.215<br />
| |
| </td>
| |
| <td style="text-align: center;">1460.43<br />
| |
| </td>
| |
| <td style="text-align: center;">288.69<br />
| |
| </td>
| |
| <td style="text-align: center;">1018.905<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">38\99<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">15 8 15<br />
| |
| </td>
| |
| <td style="text-align: center;">730.043<br />
| |
| </td>
| |
| <td style="text-align: center;">1460.087<br />
| |
| </td>
| |
| <td style="text-align: center;">288.175<br />
| |
| </td>
| |
| <td style="text-align: center;">1018.218<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">71\185<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">28 15 28<br />
| |
| </td>
| |
| <td style="text-align: center;">729.9395<br />
| |
| </td>
| |
| <td style="text-align: center;">1459.879<br />
| |
| </td>
| |
| <td style="text-align: center;">287.8635<br />
| |
| </td>
| |
| <td style="text-align: center;">1017.803<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">104\271<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">41 22 41<br />
| |
| </td>
| |
| <td style="text-align: center;">729.902<br />
| |
| </td>
| |
| <td style="text-align: center;">1459.803<br />
| |
| </td>
| |
| <td style="text-align: center;">287.75<br />
| |
| </td>
| |
| <td style="text-align: center;">1017.651<br />
| |
| </td>
| |
| <td style="text-align: center;">4g=27/5 near here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">33\86<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">13 7 13<br />
| |
| </td>
| |
| <td style="text-align: center;">729.82<br />
| |
| </td>
| |
| <td style="text-align: center;">1459.64<br />
| |
| </td>
| |
| <td style="text-align: center;">287.505<br />
| |
| </td>
| |
| <td style="text-align: center;">1017.325<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">28\73<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">11 6 11<br />
| |
| </td>
| |
| <td style="text-align: center;">729.547<br />
| |
| </td>
| |
| <td style="text-align: center;">1459.034<br />
| |
| </td>
| |
| <td style="text-align: center;">286.596<br />
| |
| </td>
| |
| <td style="text-align: center;">1016.113<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">23\60<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">9 5 9<br />
| |
| </td>
| |
| <td style="text-align: center;">729.083<br />
| |
| </td>
| |
| <td style="text-align: center;">1458.1655<br />
| |
| </td>
| |
| <td style="text-align: center;">285.293<br />
| |
| </td>
| |
| <td style="text-align: center;">1014.376<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">41\107<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">16 9 16<br />
| |
| </td>
| |
| <td style="text-align: center;">728.7865<br />
| |
| </td>
| |
| <td style="text-align: center;">1457.573<br />
| |
| </td>
| |
| <td style="text-align: center;">284.4045<br />
| |
| </td>
| |
| <td style="text-align: center;">1013.191<br />
| |
| </td>
| |
| <td style="text-align: center;">3g=99/28 near here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">59\154<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">23 13 23<br />
| |
| </td>
| |
| <td style="text-align: center;">728.671<br />
| |
| </td>
| |
| <td style="text-align: center;">1457.342<br />
| |
| </td>
| |
| <td style="text-align: center;">284.058<br />
| |
| </td>
| |
| <td style="text-align: center;">1012.729<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">77\201<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">30 17 30<br />
| |
| </td>
| |
| <td style="text-align: center;">728.61<br />
| |
| </td>
| |
| <td style="text-align: center;">1457.219<br />
| |
| </td>
| |
| <td style="text-align: center;">283.874<br />
| |
| </td>
| |
| <td style="text-align: center;">1012.483<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">95\248<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">37 21 37<br />
| |
| </td>
| |
| <td style="text-align: center;">728.5715<br />
| |
| </td>
| |
| <td style="text-align: center;">1457.143<br />
| |
| </td>
| |
| <td style="text-align: center;">283.7595<br />
| |
| </td>
| |
| <td style="text-align: center;">1012.331<br />
| |
| </td>
| |
| <td style="text-align: center;">Golden BP is index-2 near here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">18\47<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">7 4 7<br />
| |
| </td>
| |
| <td style="text-align: center;">728.408<br />
| |
| </td>
| |
| <td style="text-align: center;">1456.817<br />
| |
| </td>
| |
| <td style="text-align: center;">283.27<br />
| |
| </td>
| |
| <td style="text-align: center;">1011.678<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="background-color: #ffffff;">√3 1 √3</span><br />
| |
| </td>
| |
| <td style="text-align: center;">728.159<br />
| |
| </td>
| |
| <td style="text-align: center;">1456.318<br />
| |
| </td>
| |
| <td style="text-align: center;">282.522<br />
| |
| </td>
| |
| <td style="text-align: center;">1010.6815<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">49\128<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">19 11 19<br />
| |
| </td>
| |
| <td style="text-align: center;">728.092<br />
| |
| </td>
| |
| <td style="text-align: center;">1456.184<br />
| |
| </td>
| |
| <td style="text-align: center;">282.321<br />
| |
| </td>
| |
| <td style="text-align: center;">1010.413<br />
| |
| </td>
| |
| <td style="text-align: center;">4g=27/5 minus third comma near here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">31\81<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">12 7 12<br />
| |
| </td>
| |
| <td style="text-align: center;">727.909<br />
| |
| </td>
| |
| <td style="text-align: center;">1455.817<br />
| |
| </td>
| |
| <td style="text-align: center;">281.771<br />
| |
| </td>
| |
| <td style="text-align: center;">1009.68<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">13\34<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">5 3 5<br />
| |
| </td>
| |
| <td style="text-align: center;">727.218<br />
| |
| </td>
| |
| <td style="text-align: center;">1454.436<br />
| |
| </td>
| |
| <td style="text-align: center;">279.699<br />
| |
| </td>
| |
| <td style="text-align: center;">1006.917<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">34\89<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">13 8 13<br />
| |
| </td>
| |
| <td style="text-align: center;">726.59<br />
| |
| </td>
| |
| <td style="text-align: center;">1453.179<br />
| |
| </td>
| |
| <td style="text-align: center;">277.814<br />
| |
| </td>
| |
| <td style="text-align: center;">1004.403<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">89\233<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">34 21 34<br />
| |
| </td>
| |
| <td style="text-align: center;">726.498<br />
| |
| </td>
| |
| <td style="text-align: center;">1452.996<br />
| |
| </td>
| |
| <td style="text-align: center;">277.538<br />
| |
| </td>
| |
| <td style="text-align: center;">1004.036<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">233\610<br />
| |
| </td>
| |
| <td style="text-align: center;">89 55 89<br />
| |
| </td>
| |
| <td style="text-align: center;">726.4845<br />
| |
| </td>
| |
| <td style="text-align: center;">1452.969<br />
| |
| </td>
| |
| <td style="text-align: center;">277.4985<br />
| |
| </td>
| |
| <td style="text-align: center;">1003.983<br />
| |
| </td>
| |
| <td style="text-align: center;">Golden false father<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">144\377<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">55 34 55<br />
| |
| </td>
| |
| <td style="text-align: center;">726.476<br />
| |
| </td>
| |
| <td style="text-align: center;">1452.952<br />
| |
| </td>
| |
| <td style="text-align: center;">277.473<br />
| |
| </td>
| |
| <td style="text-align: center;">1003.95<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">55\144<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">21 13 21<br />
| |
| </td>
| |
| <td style="text-align: center;">726.441<br />
| |
| </td>
| |
| <td style="text-align: center;">1452.882<br />
| |
| </td>
| |
| <td style="text-align: center;">277.368<br />
| |
| </td>
| |
| <td style="text-align: center;">1003.809<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">21\55<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">8 5 8<br />
| |
| </td>
| |
| <td style="text-align: center;">726.201<br />
| |
| </td>
| |
| <td style="text-align: center;">1452.402<br />
| |
| </td>
| |
| <td style="text-align: center;">276.468<br />
| |
| </td>
| |
| <td style="text-align: center;">1002.849<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">pi 2 pi<br />
| |
| </td>
| |
| <td style="text-align: center;">725.736<br />
| |
| </td>
| |
| <td style="text-align: center;">1451.472<br />
| |
| </td>
| |
| <td style="text-align: center;">275.252<br />
| |
| </td>
| |
| <td style="text-align: center;">1000.988<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">8\21<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">3 2 3<br />
| |
| </td>
| |
| <td style="text-align: center;">724.554<br />
| |
| </td>
| |
| <td style="text-align: center;">1449.109<br />
| |
| </td>
| |
| <td style="text-align: center;">271.708<br />
| |
| </td>
| |
| <td style="text-align: center;">996.226<br />
| |
| </td>
| |
| <td style="text-align: center;">Optimum rank range (L/s=3/2) false father<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">~543 361 543<br />
| |
| </td>
| |
| <td style="text-align: center;">724.511<br />
| |
| </td>
| |
| <td style="text-align: center;">1449.022<br />
| |
| </td>
| |
| <td style="text-align: center;">271.579<br />
| |
| </td>
| |
| <td style="text-align: center;">996.09<br />
| |
| </td>
| |
| <td style="text-align: center;">4g=16/3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">27\71<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">10 7 10<br />
| |
| </td>
| |
| <td style="text-align: center;">723.279<br />
| |
| </td>
| |
| <td style="text-align: center;">1446.557<br />
| |
| </td>
| |
| <td style="text-align: center;">267.881<br />
| |
| </td>
| |
| <td style="text-align: center;">991.16<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">46\121<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">17 12 17<br />
| |
| </td>
| |
| <td style="text-align: center;">723.057<br />
| |
| </td>
| |
| <td style="text-align: center;">1446.115<br />
| |
| </td>
| |
| <td style="text-align: center;">267.217<br />
| |
| </td>
| |
| <td style="text-align: center;">990.274<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">65\171<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">24 17 24<br />
| |
| </td>
| |
| <td style="text-align: center;">722.965<br />
| |
| </td>
| |
| <td style="text-align: center;">1445.931<br />
| |
| </td>
| |
| <td style="text-align: center;">266.941<br />
| |
| </td>
| |
| <td style="text-align: center;">989.907<br />
| |
| </td>
| |
| <td style="text-align: center;">3g=7/2 near here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">19\50<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">7 5 7<br />
| |
| </td>
| |
| <td style="text-align: center;">722.743<br />
| |
| </td>
| |
| <td style="text-align: center;">1445.486<br />
| |
| </td>
| |
| <td style="text-align: center;">266.274<br />
| |
| </td>
| |
| <td style="text-align: center;">989.017<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">11\29<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">4 3 4<br />
| |
| </td>
| |
| <td style="text-align: center;">721.431<br />
| |
| </td>
| |
| <td style="text-align: center;">1442.862<br />
| |
| </td>
| |
| <td style="text-align: center;">262.338<br />
| |
| </td>
| |
| <td style="text-align: center;">983.77<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">25\66<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">9 7 9<br />
| |
| </td>
| |
| <td style="text-align: center;">720.4375<br />
| |
| </td>
| |
| <td style="text-align: center;">1440.875<br />
| |
| </td>
| |
| <td style="text-align: center;">259.3575<br />
| |
| </td>
| |
| <td style="text-align: center;">979.795<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">64\169<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">23 18 23<br />
| |
| </td>
| |
| <td style="text-align: center;">720.267<br />
| |
| </td>
| |
| <td style="text-align: center;">1440.534<br />
| |
| </td>
| |
| <td style="text-align: center;">258.848<br />
| |
| </td>
| |
| <td style="text-align: center;">979.113<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">167\441<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">60 47 60<br />
| |
| </td>
| |
| <td style="text-align: center;">720.2415<br />
| |
| </td>
| |
| <td style="text-align: center;">1440.483<br />
| |
| </td>
| |
| <td style="text-align: center;">258.7965<br />
| |
| </td>
| |
| <td style="text-align: center;">979.001<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">437\1154<br />
| |
| </td>
| |
| <td style="text-align: center;">157 123 157<br />
| |
| </td>
| |
| <td style="text-align: center;">720.238<br />
| |
| </td>
| |
| <td style="text-align: center;">1440.475<br />
| |
| </td>
| |
| <td style="text-align: center;">258.758<br />
| |
| </td>
| |
| <td style="text-align: center;">978.996<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">270\713<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">97 76 97<br />
| |
| </td>
| |
| <td style="text-align: center;">720.235<br />
| |
| </td>
| |
| <td style="text-align: center;">1440.471<br />
| |
| </td>
| |
| <td style="text-align: center;">258.751<br />
| |
| </td>
| |
| <td style="text-align: center;">978.987<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">103\272<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">37 29 37<br />
| |
| </td>
| |
| <td style="text-align: center;">720.226<br />
| |
| </td>
| |
| <td style="text-align: center;">1440.451<br />
| |
| </td>
| |
| <td style="text-align: center;">258.722<br />
| |
| </td>
| |
| <td style="text-align: center;">978.947<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">39\103<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">14 11 14<br />
| |
| </td>
| |
| <td style="text-align: center;">720.158<br />
| |
| </td>
| |
| <td style="text-align: center;">1440.315<br />
| |
| </td>
| |
| <td style="text-align: center;">258.518<br />
| |
| </td>
| |
| <td style="text-align: center;">978.676<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">14\37<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">5 4 5<br />
| |
| </td>
| |
| <td style="text-align: center;">719.659<br />
| |
| </td>
| |
| <td style="text-align: center;">1439.317<br />
| |
| </td>
| |
| <td style="text-align: center;">257.021<br />
| |
| </td>
| |
| <td style="text-align: center;">976.679<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">31\82<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">11 9 11<br />
| |
| </td>
| |
| <td style="text-align: center;">719.032<br />
| |
| </td>
| |
| <td style="text-align: center;">1438.064<br />
| |
| </td>
| |
| <td style="text-align: center;">255.14<br />
| |
| </td>
| |
| <td style="text-align: center;">974.172<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">79\209<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">28 23 28<br />
| |
| </td>
| |
| <td style="text-align: center;">718.921<br />
| |
| </td>
| |
| <td style="text-align: center;">1437.842<br />
| |
| </td>
| |
| <td style="text-align: center;">254.807<br />
| |
| </td>
| |
| <td style="text-align: center;">973.728<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">206\545<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">73 60 73<br />
| |
| </td>
| |
| <td style="text-align: center;">718.904<br />
| |
| </td>
| |
| <td style="text-align: center;">1437.808<br />
| |
| </td>
| |
| <td style="text-align: center;">254.757<br />
| |
| </td>
| |
| <td style="text-align: center;">973.661<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">539\1426<br />
| |
| </td>
| |
| <td style="text-align: center;">191 117 191<br />
| |
| </td>
| |
| <td style="text-align: center;">718.902<br />
| |
| </td>
| |
| <td style="text-align: center;">1437.803<br />
| |
| </td>
| |
| <td style="text-align: center;">254.75<br />
| |
| </td>
| |
| <td style="text-align: center;">973.652<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">333\881<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">118 97 118<br />
| |
| </td>
| |
| <td style="text-align: center;">718.90<br />
| |
| </td>
| |
| <td style="text-align: center;">1437.80<br />
| |
| </td>
| |
| <td style="text-align: center;">254.745<br />
| |
| </td>
| |
| <td style="text-align: center;">973.6455<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">127\336<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">45 37 45<br />
| |
| </td>
| |
| <td style="text-align: center;">718.893<br />
| |
| </td>
| |
| <td style="text-align: center;">1437.787<br />
| |
| </td>
| |
| <td style="text-align: center;">254.726<br />
| |
| </td>
| |
| <td style="text-align: center;">973.619<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">48\127<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">17 14 17<br />
| |
| </td>
| |
| <td style="text-align: center;">718.849<br />
| |
| </td>
| |
| <td style="text-align: center;">1437.698<br />
| |
| </td>
| |
| <td style="text-align: center;">254.592<br />
| |
| </td>
| |
| <td style="text-align: center;">973.441<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">17\45<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">6 5 6<br />
| |
| </td>
| |
| <td style="text-align: center;">718.516<br />
| |
| </td>
| |
| <td style="text-align: center;">1437.032<br />
| |
| </td>
| |
| <td style="text-align: center;">253.549<br />
| |
| </td>
| |
| <td style="text-align: center;">972.11<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">20\53<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">7 6 7<br />
| |
| </td>
| |
| <td style="text-align: center;">717.719<br />
| |
| </td>
| |
| <td style="text-align: center;">1435.438<br />
| |
| </td>
| |
| <td style="text-align: center;">251.202<br />
| |
| </td>
| |
| <td style="text-align: center;">968.9205<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">~401 344 401<br />
| |
| </td>
| |
| <td style="text-align: center;">717.695<br />
| |
| </td>
| |
| <td style="text-align: center;">1435.3905<br />
| |
| </td>
| |
| <td style="text-align: center;">251.131<br />
| |
| </td>
| |
| <td style="text-align: center;">968.826<br />
| |
| </td>
| |
| <td style="text-align: center;">4g=21/4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">23\61<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">8 7 8<br />
| |
| </td>
| |
| <td style="text-align: center;">717.131<br />
| |
| </td>
| |
| <td style="text-align: center;">1434.261<br />
| |
| </td>
| |
| <td style="text-align: center;">249.437<br />
| |
| </td>
| |
| <td style="text-align: center;">966.567<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">~6682 5875 6682<br />
| |
| </td>
| |
| <td style="text-align: center;">716.9925<br />
| |
| </td>
| |
| <td style="text-align: center;">1433.985<br />
| |
| </td>
| |
| <td style="text-align: center;">249.0225<br />
| |
| </td>
| |
| <td style="text-align: center;">966.015<br />
| |
| </td>
| |
| <td style="text-align: center;">6g=12<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">26\69<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">9 8 9<br />
| |
| </td>
| |
| <td style="text-align: center;">716.679<br />
| |
| </td>
| |
| <td style="text-align: center;">1433.357<br />
| |
| </td>
| |
| <td style="text-align: center;">248.081<br />
| |
| </td>
| |
| <td style="text-align: center;">964.76<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">29\77<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">10 9 10<br />
| |
| </td>
| |
| <td style="text-align: center;">716.321<br />
| |
| </td>
| |
| <td style="text-align: center;">1432.641<br />
| |
| </td>
| |
| <td style="text-align: center;">247.007<br />
| |
| </td>
| |
| <td style="text-align: center;">963.328<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">32\85<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">11 10 11<br />
| |
| </td>
| |
| <td style="text-align: center;">716.03<br />
| |
| </td>
| |
| <td style="text-align: center;">1432.06<br />
| |
| </td>
| |
| <td style="text-align: center;">246.135<br />
| |
| </td>
| |
| <td style="text-align: center;">962.1655<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">35\93<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">12 11 12<br />
| |
| </td>
| |
| <td style="text-align: center;">715.7895<br />
| |
| </td>
| |
| <td style="text-align: center;">1431.759<br />
| |
| </td>
| |
| <td style="text-align: center;">245.4135<br />
| |
| </td>
| |
| <td style="text-align: center;">961.203<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">38/101<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">13 12 13<br />
| |
| </td>
| |
| <td style="text-align: center;">715.587<br />
| |
| </td>
| |
| <td style="text-align: center;">1431.174<br />
| |
| </td>
| |
| <td style="text-align: center;">244.806<br />
| |
| </td>
| |
| <td style="text-align: center;">960.393<br />
| |
| </td>
| |
| <td style="text-align: center;">2g=16\7 near here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">3\8<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">1 1 1<br />
| |
| </td>
| |
| <td style="text-align: center;">713.233<br />
| |
| </td>
| |
| <td style="text-align: center;">1426.466<br />
| |
| </td>
| |
| <td style="text-align: center;">237.744<br />
| |
| </td>
| |
| <td style="text-align: center;">950.9775<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| .</body></html></pre></div> | | == Tunings== |
| | === Simple tunings === |
| | The simplest tuning for 5L 3s correspond to 13edo, 18edo, and 21edo, with step ratios 2:1, 3:1, and 3:2, respectively. |
| | |
| | {{MOS tunings|JI Ratios=Int Limit: 30; Prime Limit: 19; Tenney Height: 7.7}} |
| | |
| | === Hypohard tunings === |
| | [[Hypohard]] oneirotonic tunings have step ratios between 2:1 and 3:1 and can be considered "meantone oneirotonic", sharing the following features with [[meantone]] diatonic tunings: |
| | * The large step is a "meantone", around the range of [[10/9]] to [[9/8]]. |
| | * The major 2-mosstep is a [[meantone]]- to [[flattone]]-sized major third, thus is a stand-in for the classical diatonic major third. |
| | |
| | With step ratios between 5:2 and 2:1, the minor 2-mosstep is close to [[7/6]]. |
| | |
| | EDOs that are in the hypohard range include [[13edo]], [[18edo]], and [[31edo]], and are associated with [[5L 3s/Temperaments#A-Team|A-Team]] temperament. |
| | * 13edo has characteristically small 1-mossteps of about 185{{c}}. It is uniformly compressed 12edo, so it has distorted versions of non-diatonic 12edo scales. It essentially has the best [[11/8]] out of all hypohard tunings. |
| | * 18edo can be used for a large step ratio of 3, (thus 18edo oneirotonic is distorted 17edo diatonic, or for its nearly pure 9/8 and 7/6. It also makes rising fifths (733.3{{c}}, a perfect 5-mosstep) and falling fifths (666.7{{c}}, a major 4-mosstep) almost equally off from a just perfect fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry. |
| | * 31edo can be used to make the major 2-mosstep a near-just 5/4. |
| | * [[44edo]] (generator {{nowrap|17\44 {{=}} 463.64{{c}}}}), [[57edo]] (generator {{nowrap|22\57 {{=}} 463.16{{c}}}}), and [[70edo]] (generator 27\70 {{=}} 462.857{{c}}}}) offer a compromise between 31edo's major third and 13edo's 11/8 and 13/8. In particular, 70edo has an essentially pure 13/8. |
| | |
| | {{MOS tunings|Step Ratios=Hypohard|JI Ratios=Subgroup: 2.5.9.21; Int Limit:40; Complements Only: 1|Tolerance=15}} |
| | |
| | === Hyposoft tunings === |
| | [[Hyposoft]] oneirotonic tunings have step ratios between 3:2 and 2:1, which remains relatively unexplored. In these tunings, |
| | * The large step of oneirotonic tends to be intermediate in size between [[10/9]] and [[11/10]]; the small step size is a semitone close to [[17/16]], about 92{{c}} to 114{{c}}. |
| | * The major 2-mosstep (made of two large steps) in these tunings tends to be more of a neutral third, ranging from 6\21 (342{{c}}) to 4\13 (369{{c}}). |
| | |
| | * [[21edo]]'s P1-L1ms-L2ms-L4ms approximates 9:10:11:13 better than the corresponding 13edo chord does. 21edo will serve those who like the combination of neogothic minor thirds (285.71{{c}}) and Baroque diatonic semitones (114.29{{c}}, close to quarter-comma meantone's 117.11{{c}}). |
| | * [[34edo]]'s 9:10:11:13 is even better. |
| | |
| | This set of JI identifications is associated with [[5L 3s/Temperaments#Petrtri|petrtri]] temperament. (P1-M1ms-P3ms could be said to approximate 5:11:13 in all soft-of-basic tunings, which is what "basic" [[petrtri]] temperament is.) |
| | |
| | {{MOS tunings |
| | | Step Ratios = Hyposoft |
| | | JI Ratios = |
| | 1/1; |
| | 16/15; |
| | 10/9; 11/10; |
| | 13/11; 20/17; |
| | 11/9; |
| | 5/4; |
| | 13/10; |
| | 18/13; 32/23; |
| | 13/9; 23/16; |
| | 20/13; |
| | 8/5; |
| | 18/11; |
| | 22/13; 17/10; |
| | 9/5; |
| | 15/8; |
| | 2/1 |
| | }} |
| | |
| | === Parasoft and ultrasoft tunings === |
| | The range of oneirotonic tunings of step ratio between 6:5 and 3:2 is closely related to [[porcupine]] temperament; these tunings equate three oneirotonic large steps to a diatonic perfect fourth, i.e. they equate the oneirotonic large step to a [[porcupine]] generator. The chord 10:11:13 is very well approximated in 29edo. |
| | |
| | {{MOS tunings |
| | | Step Ratios = 6/5; 3/2; 4/3 |
| | | JI Ratios = |
| | 1/1; |
| | 14/13; |
| | 11/10; |
| | 9/8; |
| | 15/13; |
| | 13/11; |
| | 14/11; |
| | 13/10; |
| | 4/3; |
| | 15/11; |
| | 7/5; |
| | 10/7; |
| | 22/15; |
| | 3/2; |
| | 20/13; |
| | 11/7; |
| | 22/13; |
| | 26/15; |
| | 16/9; |
| | 20/11; |
| | 13/7; |
| | 2/1 |
| | }} |
| | |
| | === Parahard tunings === |
| | 23edo oneiro combines the sound of neogothic tunings like [[46edo]] and the sounds of "superpyth" and "semaphore" scales. This is because 23edo oneirotonic has a large step of 208.7¢, same as [[46edo]]'s neogothic major second, and is both a warped [[22edo]] [[superpyth]] [[diatonic]] and a warped [[24edo]] [[semaphore]] [[semiquartal]] (and both nearby scales are [[superhard]] MOSes). |
| | |
| | {{MOS tunings |
| | | JI Ratios = |
| | 1/1; |
| | 21/17; |
| | 17/16; |
| | 14/11; |
| | 6/5; |
| | 21/16; |
| | 21/17; |
| | 34/21; |
| | 32/21; |
| | 5/3; |
| | 11/7; |
| | 32/17; |
| | 34/21; |
| | 2/1 |
| | | Step Ratios = 4/1 |
| | }} |
| | |
| | === Ultrahard tunings === |
| | {{Main|5L 3s/Temperaments#Buzzard}} |
| | |
| | [[Buzzard]] is a rank-2 temperament in the [[Step ratio|pseudocollapsed]] range. It represents the only [[harmonic entropy]] minimum of the oneirotonic spectrum. |
| | |
| | In the broad sense, Buzzard can be viewed as any tuning that divides the 3rd harmonic into 4 equal parts. [[23edo]], [[28edo]] and [[33edo]] can nominally be viewed as supporting it, but are still very flat and in an ambiguous zone between 18edo and true Buzzard in terms of harmonies. [[38edo]] & [[43edo]] are good compromises between melodic utility and harmonic accuracy, as the small step is still large enough to be obvious to the untrained ear, but [[48edo]] is where it really comes into its own in terms of harmonies, providing not only an excellent [[3/2]], but also [[7/4]] and [[The_Archipelago|archipelago]] harmonies, as by dividing the 5th in 4 it obviously also divides it in two as well. |
| | |
| | Beyond that, it's a question of which intervals you want to favor. [[53edo]] has an essentially perfect [[3/2]], [[58edo]] gives the lowest overall error for the Barbados triads 10:13:15 and 26:30:39, while [[63edo]] does the same for the basic 4:6:7 triad. You could in theory go up to [[83edo]] if you want to favor the [[7/4]] above everything else, but beyond that, general accuracy drops off rapidly and you might as well be playing equal pentatonic. |
| | |
| | {{MOS tunings |
| | | JI Ratios = |
| | 1/1; |
| | 8/7; |
| | 13/10; |
| | 21/16; |
| | 3/2; |
| | 12/7, 22/13; |
| | 26/15; |
| | 49/25, 160/81; |
| | 2/1 |
| | | Step Ratios = 7/1; 10/1; 12/1 |
| | | Tolerance = 30 |
| | }} |
| | |
| | == Approaches == |
| | * [[5L 3s/Temperaments]] |
| | |
| | == Samples == |
| | [[File:The Angels' Library edo.mp3]] [[:File:The Angels' Library edo.mp3|The Angels' Library]] by [[Inthar]] in the Sarnathian (23233233) mode of 21edo oneirotonic ([[:File:The Angels' Library Score.pdf|score]]) |
| | |
| | [[File:13edo Prelude in J Oneirominor.mp3]] |
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| | [[WT13C]] [[:File:13edo Prelude in J Oneirominor.mp3|Prelude II (J Oneirominor)]] ([[:File:13edo Prelude in J Oneirominor Score.pdf|score]]) – Simple two-part Baroque piece. It stays in oneirotonic even though it modulates to other keys a little. |
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| | [[File:13edo_1MC.mp3]] |
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| | (13edo, first 30 seconds is in J Celephaïsian) |
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| | [[File:A Moment of Respite.mp3]] |
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| | (13edo, L Ilarnekian) |
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| | [[File:Lunar Approach.mp3]] |
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| | (by [[Igliashon Jones]], 13edo, J Celephaïsian) |
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| | === 13edo Oneirotonic Modal Studies === |
| | * [[File:Inthar-13edo Oneirotonic Studies 1 Dylathian.mp3]]: Tonal Study in Dylathian |
| | * [[File:Inthar-13edo Oneirotonic Studies 2 Ultharian.mp3]]: Tonal Study in Ultharian |
| | * [[File:Inthar-13edo Oneirotonic Studies 3 Hlanithian.mp3]]: Tonal Study in Hlanithian |
| | * [[File:Inthar-13edo Oneirotonic Studies 4 Illarnekian.mp3]]: Tonal Study in Ilarnekian |
| | * [[File:Inthar-13edo Oneirotonic Studies 5 Mnarian.mp3]]: Tonal Study in Mnarian |
| | * [[File:Inthar-13edo Oneirotonic Studies 6 Sarnathian.mp3]]: Tonal Study in Sarnathian |
| | * [[File:Inthar-13edo Oneirotonic Studies 7 Celephaisian.mp3]]: Tonal Study in Celephaïsian |
| | * [[File:Inthar-13edo Oneirotonic Studies 8 Kadathian.mp3]]: Tonal Study in Kadathian |
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| | == Scale tree == |
| | {{MOS tuning spectrum |
| | | 13/8 = Golden oneirotonic (458.3592{{c}}) |
| | | 13/5 = Golden A-Team (465.0841{{c}}) |
| | }} |
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| | [[Category:Oneirotonic| ]] <!-- sort order in category: this page shows above A --> |
| | [[Category:Pages with internal sound examples]] |