Mina: Difference between revisions

Revision as of 13:17, 9 June 2017

IMPORTED REVISION FROM WIKISPACES

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This revision was by author hearneg and made on 2017-06-09 13:17:38 UTC.

The original revision id was 614476031.

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Original Wikitext content:

The //mina// is a unit of interval size which has been proposed by [[George Secor]] and [[Dave Keenan]], and which is defined as 1/2460 of an [[octave]], the step size of [[2460edo]]. 2460 is divisible by both 12 and 41, two important systems, and it's been suggested that degrees and minutes can be used to express values in it, so that for instance 3/2, which is 1439 minas, could be denoted by 23°59', meaning very slightly flat of the 24\41 [[41edo]] fifths. This works out since 41 * 60 = 2460; an octave is therefore expressed as if it were an angle of 41 degrees.

Below the intervals of the [[27-limit]] [[tonality diamond]] are tabulated, with the sizes listed in both [[cent]]s and minas, and expressed as degrees and minutes (rounded to the nearest minute). The value in minas, rounded to the nearest integer, can be found by applying the [[23-limit]] [[patent val]] <2460 3899 5712 6906 8510 9103 10055 10450 11128| for 2460edo; this will not work for [[1200edo]] and cents.
||~ interval
ratio ||~ size
in cent ||~ size
in mina ||~ size as degrees
and minutes ||
|| 1 || 0.000 || 0.000 || 0° ||
|| 28/27 || 62.961 || 129.070 || 2°9' ||
|| 27/26 || 65.337 || 133.942 || 2°14' ||
|| 26/25 || 67.900 || 139.195 || 2°19' ||
|| 25/24 || 70.672 || 144.878 || 2°25' ||
|| 24/23 || 73.681 || 151.045 || 2°31' ||
|| 23/22 || 76.956 || 157.761 || 2°38' ||
|| 22/21 || 80.537 || 165.101 || 2°45' ||
|| 21/20 || 84.467 || 173.158 || 2°53' ||
|| 20/19 || 88.801 || 182.041 || 3°2' ||
|| 19/18 || 93.603 || 191.886 || 3°12' ||
|| 18/17 || 98.955 || 202.857 || 3°23' ||
|| 17/16 || 104.955 || 215.159 || 3°35' ||
|| 16/15 || 111.731 || 229.049 || 3°49' ||
|| 15/14 || 119.443 || 244.858 || 4°5' ||
|| 14/13 || 128.298 || 263.011 || 4°23' ||
|| 27/25 || 133.238 || 273.137 || 4°33' ||
|| 13/12 || 138.573 || 284.074 || 4°44' ||
|| 25/23 || 144.353 || 295.924 || 4°56' ||
|| 12/11 || 150.637 || 308.806 || 5°9' ||
|| 23/21 || 157.493 || 322.862 || 5°23' ||
|| 11/10 || 165.004 || 338.259 || 5°38' ||
|| 21/19 || 173.268 || 355.199 || 5°55' ||
|| 10/9 || 182.404 || 373.928 || 6°14' ||
|| 19/17 || 192.558 || 394.743 || 6°35' ||
|| 28/25 || 196.198 || 402.207 || 6°42' ||
|| 9/8 || 203.910 || 418.016 || 6°58' ||
|| 26/23 || 212.253 || 435.119 || 7°15' ||
|| 17/15 || 216.687 || 444.208 || 7°24' ||
|| 25/22 || 221.309 || 453.684 || 7°34' ||
|| 8/7 || 231.174 || 473.907 || 7°54' ||
|| 23/20 || 241.961 || 496.019 || 8°16' ||
|| 15/13 || 247.741 || 507.869 || 8°28' ||
|| 22/19 || 253.805 || 520.300 || 8°40' ||
|| 7/6 || 266.871 || 547.085 || 9°7' ||
|| 27/23 || 277.591 || 569.061 || 9°29' ||
|| 20/17 || 281.358 || 576.785 || 9°37' ||
|| 13/11 || 289.210 || 592.880 || 9°53' ||
|| 32/27 || 294.135 || 602.977 || 10°3' ||
|| 19/16 || 297.513 || 609.902 || 10°10' ||
|| 25/21 || 301.847 || 618.785 || 10°19' ||
|| 6/5 || 315.641 || 647.065 || 10°47' ||
|| 23/19 || 330.761 || 678.061 || 11°18' ||
|| 17/14 || 336.130 || 689.065 || 11°29' ||
|| 28/23 || 340.552 || 698.131 || 11°38' ||
|| 11/9 || 347.408 || 712.186 || 11°52' ||
|| 27/22 || 354.547 || 726.821 || 12°7' ||
|| 16/13 || 359.472 || 736.918 || 12°17' ||
|| 21/17 || 365.825 || 749.942 || 12°30' ||
|| 26/21 || 369.747 || 757.981 || 12°38' ||
|| 5/4 || 386.314 || 791.943 || 13°12' ||
|| 34/27 || 399.090 || 818.135 || 13°38' ||
|| 24/19 || 404.442 || 829.106 || 13°49' ||
|| 19/15 || 409.244 || 838.951 || 13°59' ||
|| 14/11 || 417.508 || 855.891 || 14°15' ||
|| 23/18 || 424.364 || 869.947 || 14°30' ||
|| 32/25 || 427.373 || 876.114 || 14°36' ||
|| 9/7 || 435.084 || 891.922 || 14°52' ||
|| 22/17 || 446.363 || 915.043 || 15°15' ||
|| 13/10 || 454.214 || 931.139 || 15°31' ||
|| 30/23 || 459.994 || 942.988 || 15°43' ||
|| 17/13 || 464.428 || 952.077 || 15°52' ||
|| 21/16 || 470.781 || 965.101 || 16°5' ||
|| 25/19 || 475.114 || 973.985 || 16°14' ||
|| 4/3 || 498.045 || 1020.992 || 17°1' ||
|| 27/20 || 519.551 || 1065.080 || 17°45' ||
|| 23/17 || 523.319 || 1072.804 || 17°53' ||
|| 19/14 || 528.687 || 1083.809 || 18°4' ||
|| 34/25 || 532.328 || 1091.272 || 18°11' ||
|| 15/11 || 536.951 || 1100.749 || 18°21' ||
|| 26/19 || 543.015 || 1113.180 || 18°33' ||
|| 11/8 || 551.318 || 1130.202 || 18°50' ||
|| 18/13 || 563.382 || 1154.934 || 19°15' ||
|| 25/18 || 568.717 || 1165.871 || 19°26' ||
|| 32/23 || 571.726 || 1172.038 || 19°32' ||
|| 7/5 || 582.512 || 1194.150 || 19°54' ||
|| 38/27 || 591.648 || 1212.878 || 20°13' ||
|| 24/17 || 597.000 || 1223.849 ||   ||
|| 17/12 || 603.000 || 1236.151 ||   ||
|| 27/19 || 608.352 || 1247.122 ||   ||
|| 10/7 || 617.488 || 1265.850 ||   ||
|| 23/16 || 628.274 || 1287.962 ||   ||
|| 36/25 || 631.283 || 1294.129 ||   ||
|| 13/9 || 636.618 || 1305.066 ||   ||
|| 16/11 || 648.682 || 1329.798 ||   ||
|| 19/13 || 656.985 || 1346.820 ||   ||
|| 22/15 || 663.049 || 1359.251 ||   ||
|| 25/17 || 667.672 || 1368.728 ||   ||
|| 28/19 || 671.313 || 1376.191 ||   ||
|| 34/23 || 676.681 || 1387.196 ||   ||
|| 40/27 || 680.449 || 1394.920 ||   ||
|| 3/2 || 701.955 || 1439.008 ||   ||
|| 38/25 || 724.886 || 1486.015 ||   ||
|| 32/21 || 729.219 || 1494.899 ||   ||
|| 26/17 || 735.572 || 1507.923 ||   ||
|| 23/15 || 740.006 || 1517.012 ||   ||
|| 20/13 || 745.786 || 1528.861 ||   ||
|| 17/11 || 753.637 || 1544.957 ||   ||
|| 14/9 || 764.916 || 1568.078 ||   ||
|| 25/16 || 772.627 || 1583.886 ||   ||
|| 36/23 || 775.636 || 1590.053 ||   ||
|| 11/7 || 782.492 || 1604.109 ||   ||
|| 30/19 || 790.756 || 1621.049 ||   ||
|| 19/12 || 795.558 || 1630.894 ||   ||
|| 27/17 || 800.910 || 1641.865 ||   ||
|| 8/5 || 813.686 || 1668.057 ||   ||
|| 21/13 || 830.253 || 1702.019 ||   ||
|| 34/21 || 834.175 || 1710.058 ||   ||
|| 13/8 || 840.528 || 1723.082 ||   ||
|| 44/27 || 845.453 || 1733.179 ||   ||
|| 18/11 || 852.592 || 1747.814 ||   ||
|| 23/14 || 859.448 || 1761.869 ||   ||
|| 28/17 || 863.870 || 1770.935 ||   ||
|| 38/23 || 869.239 || 1781.939 ||   ||
|| 5/3 || 884.359 || 1812.935 ||   ||
|| 42/25 || 898.153 || 1841.215 ||   ||
|| 32/19 || 902.487 || 1850.098 ||   ||
|| 27/16 || 905.865 || 1857.023 ||   ||
|| 22/13 || 910.790 || 1867.120 ||   ||
|| 17/10 || 918.642 || 1883.215 ||   ||
|| 46/27 || 922.409 || 1890.939 ||   ||
|| 12/7 || 933.129 || 1912.915 ||   ||
|| 19/11 || 946.195 || 1939.700 ||   ||
|| 26/15 || 952.259 || 1952.131 ||   ||
|| 40/23 || 958.039 || 1963.981 ||   ||
|| 7/4 || 968.826 || 1986.093 ||   ||
|| 44/25 || 978.691 || 2006.316 ||   ||
|| 30/17 || 983.313 || 2015.792 ||   ||
|| 23/13 || 987.747 || 2024.881 ||   ||
|| 16/9 || 996.090 || 2041.984 ||   ||
|| 25/14 || 1003.802 || 2057.793 ||   ||
|| 34/19 || 1007.442 || 2065.257 ||   ||
|| 9/5 || 1017.596 || 2086.072 ||   ||
|| 38/21 || 1026.732 || 2104.801 ||   ||
|| 20/11 || 1034.996 || 2121.741 ||   ||
|| 42/23 || 1042.507 || 2137.138 ||   ||
|| 11/6 || 1049.363 || 2151.194 ||   ||
|| 46/25 || 1055.647 || 2164.076 ||   ||
|| 24/13 || 1061.427 || 2175.926 ||   ||
|| 50/27 || 1066.762 || 2186.863 ||   ||
|| 13/7 || 1071.702 || 2196.989 ||   ||
|| 28/15 || 1080.557 || 2215.142 ||   ||
|| 15/8 || 1088.269 || 2230.951 ||   ||
|| 32/17 || 1095.045 || 2244.841 ||   ||
|| 17/9 || 1101.045 || 2257.143 ||   ||
|| 36/19 || 1106.397 || 2268.114 ||   ||
|| 19/10 || 1111.199 || 2277.959 ||   ||
|| 40/21 || 1115.533 || 2286.842 ||   ||
|| 21/11 || 1119.463 || 2294.899 ||   ||
|| 44/23 || 1123.044 || 2302.239 ||   ||
|| 23/12 || 1126.319 || 2308.955 ||   ||
|| 48/25 || 1129.328 || 2315.122 ||   ||
|| 25/13 || 1132.100 || 2320.805 ||   ||
|| 52/27 || 1134.663 || 2326.058 ||   ||
|| 27/14 || 1137.039 || 2330.930 ||   ||
|| 2 || 1200.000 || 2460.000 ||   ||

Original HTML content:

<html><head><title>mina</title></head><body>The <em>mina</em> is a unit of interval size which has been proposed by <a class="wiki_link" href="/George%20Secor">George Secor</a> and <a class="wiki_link" href="/Dave%20Keenan">Dave Keenan</a>, and which is defined as 1/2460 of an <a class="wiki_link" href="/octave">octave</a>, the step size of <a class="wiki_link" href="/2460edo">2460edo</a>. 2460 is divisible by both 12 and 41, two important systems, and it's been suggested that degrees and minutes can be used to express values in it, so that for instance 3/2, which is 1439 minas, could be denoted by 23°59', meaning very slightly flat of the 24\41 <a class="wiki_link" href="/41edo">41edo</a> fifths. This works out since 41 * 60 = 2460; an octave is therefore expressed as if it were an angle of 41 degrees.<br />
<br />
Below the intervals of the <a class="wiki_link" href="/27-limit">27-limit</a> <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a> are tabulated, with the sizes listed in both <a class="wiki_link" href="/cent">cent</a>s and minas, and expressed as degrees and minutes (rounded to the nearest minute). The value in minas, rounded to the nearest integer, can be found by applying the <a class="wiki_link" href="/23-limit">23-limit</a> <a class="wiki_link" href="/patent%20val">patent val</a> &lt;2460 3899 5712 6906 8510 9103 10055 10450 11128| for 2460edo; this will not work for <a class="wiki_link" href="/1200edo">1200edo</a> and cents.<br />


<table class="wiki_table">
    <tr>
        <th>interval<br />
ratio<br />
</th>
        <th>size<br />
in cent<br />
</th>
        <th>size<br />
in mina<br />
</th>
        <th>size as degrees<br />
and minutes<br />
</th>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>0.000<br />
</td>
        <td>0.000<br />
</td>
        <td>0°<br />
</td>
    </tr>
    <tr>
        <td>28/27<br />
</td>
        <td>62.961<br />
</td>
        <td>129.070<br />
</td>
        <td>2°9'<br />
</td>
    </tr>
    <tr>
        <td>27/26<br />
</td>
        <td>65.337<br />
</td>
        <td>133.942<br />
</td>
        <td>2°14'<br />
</td>
    </tr>
    <tr>
        <td>26/25<br />
</td>
        <td>67.900<br />
</td>
        <td>139.195<br />
</td>
        <td>2°19'<br />
</td>
    </tr>
    <tr>
        <td>25/24<br />
</td>
        <td>70.672<br />
</td>
        <td>144.878<br />
</td>
        <td>2°25'<br />
</td>
    </tr>
    <tr>
        <td>24/23<br />
</td>
        <td>73.681<br />
</td>
        <td>151.045<br />
</td>
        <td>2°31'<br />
</td>
    </tr>
    <tr>
        <td>23/22<br />
</td>
        <td>76.956<br />
</td>
        <td>157.761<br />
</td>
        <td>2°38'<br />
</td>
    </tr>
    <tr>
        <td>22/21<br />
</td>
        <td>80.537<br />
</td>
        <td>165.101<br />
</td>
        <td>2°45'<br />
</td>
    </tr>
    <tr>
        <td>21/20<br />
</td>
        <td>84.467<br />
</td>
        <td>173.158<br />
</td>
        <td>2°53'<br />
</td>
    </tr>
    <tr>
        <td>20/19<br />
</td>
        <td>88.801<br />
</td>
        <td>182.041<br />
</td>
        <td>3°2'<br />
</td>
    </tr>
    <tr>
        <td>19/18<br />
</td>
        <td>93.603<br />
</td>
        <td>191.886<br />
</td>
        <td>3°12'<br />
</td>
    </tr>
    <tr>
        <td>18/17<br />
</td>
        <td>98.955<br />
</td>
        <td>202.857<br />
</td>
        <td>3°23'<br />
</td>
    </tr>
    <tr>
        <td>17/16<br />
</td>
        <td>104.955<br />
</td>
        <td>215.159<br />
</td>
        <td>3°35'<br />
</td>
    </tr>
    <tr>
        <td>16/15<br />
</td>
        <td>111.731<br />
</td>
        <td>229.049<br />
</td>
        <td>3°49'<br />
</td>
    </tr>
    <tr>
        <td>15/14<br />
</td>
        <td>119.443<br />
</td>
        <td>244.858<br />
</td>
        <td>4°5'<br />
</td>
    </tr>
    <tr>
        <td>14/13<br />
</td>
        <td>128.298<br />
</td>
        <td>263.011<br />
</td>
        <td>4°23'<br />
</td>
    </tr>
    <tr>
        <td>27/25<br />
</td>
        <td>133.238<br />
</td>
        <td>273.137<br />
</td>
        <td>4°33'<br />
</td>
    </tr>
    <tr>
        <td>13/12<br />
</td>
        <td>138.573<br />
</td>
        <td>284.074<br />
</td>
        <td>4°44'<br />
</td>
    </tr>
    <tr>
        <td>25/23<br />
</td>
        <td>144.353<br />
</td>
        <td>295.924<br />
</td>
        <td>4°56'<br />
</td>
    </tr>
    <tr>
        <td>12/11<br />
</td>
        <td>150.637<br />
</td>
        <td>308.806<br />
</td>
        <td>5°9'<br />
</td>
    </tr>
    <tr>
        <td>23/21<br />
</td>
        <td>157.493<br />
</td>
        <td>322.862<br />
</td>
        <td>5°23'<br />
</td>
    </tr>
    <tr>
        <td>11/10<br />
</td>
        <td>165.004<br />
</td>
        <td>338.259<br />
</td>
        <td>5°38'<br />
</td>
    </tr>
    <tr>
        <td>21/19<br />
</td>
        <td>173.268<br />
</td>
        <td>355.199<br />
</td>
        <td>5°55'<br />
</td>
    </tr>
    <tr>
        <td>10/9<br />
</td>
        <td>182.404<br />
</td>
        <td>373.928<br />
</td>
        <td>6°14'<br />
</td>
    </tr>
    <tr>
        <td>19/17<br />
</td>
        <td>192.558<br />
</td>
        <td>394.743<br />
</td>
        <td>6°35'<br />
</td>
    </tr>
    <tr>
        <td>28/25<br />
</td>
        <td>196.198<br />
</td>
        <td>402.207<br />
</td>
        <td>6°42'<br />
</td>
    </tr>
    <tr>
        <td>9/8<br />
</td>
        <td>203.910<br />
</td>
        <td>418.016<br />
</td>
        <td>6°58'<br />
</td>
    </tr>
    <tr>
        <td>26/23<br />
</td>
        <td>212.253<br />
</td>
        <td>435.119<br />
</td>
        <td>7°15'<br />
</td>
    </tr>
    <tr>
        <td>17/15<br />
</td>
        <td>216.687<br />
</td>
        <td>444.208<br />
</td>
        <td>7°24'<br />
</td>
    </tr>
    <tr>
        <td>25/22<br />
</td>
        <td>221.309<br />
</td>
        <td>453.684<br />
</td>
        <td>7°34'<br />
</td>
    </tr>
    <tr>
        <td>8/7<br />
</td>
        <td>231.174<br />
</td>
        <td>473.907<br />
</td>
        <td>7°54'<br />
</td>
    </tr>
    <tr>
        <td>23/20<br />
</td>
        <td>241.961<br />
</td>
        <td>496.019<br />
</td>
        <td>8°16'<br />
</td>
    </tr>
    <tr>
        <td>15/13<br />
</td>
        <td>247.741<br />
</td>
        <td>507.869<br />
</td>
        <td>8°28'<br />
</td>
    </tr>
    <tr>
        <td>22/19<br />
</td>
        <td>253.805<br />
</td>
        <td>520.300<br />
</td>
        <td>8°40'<br />
</td>
    </tr>
    <tr>
        <td>7/6<br />
</td>
        <td>266.871<br />
</td>
        <td>547.085<br />
</td>
        <td>9°7'<br />
</td>
    </tr>
    <tr>
        <td>27/23<br />
</td>
        <td>277.591<br />
</td>
        <td>569.061<br />
</td>
        <td>9°29'<br />
</td>
    </tr>
    <tr>
        <td>20/17<br />
</td>
        <td>281.358<br />
</td>
        <td>576.785<br />
</td>
        <td>9°37'<br />
</td>
    </tr>
    <tr>
        <td>13/11<br />
</td>
        <td>289.210<br />
</td>
        <td>592.880<br />
</td>
        <td>9°53'<br />
</td>
    </tr>
    <tr>
        <td>32/27<br />
</td>
        <td>294.135<br />
</td>
        <td>602.977<br />
</td>
        <td>10°3'<br />
</td>
    </tr>
    <tr>
        <td>19/16<br />
</td>
        <td>297.513<br />
</td>
        <td>609.902<br />
</td>
        <td>10°10'<br />
</td>
    </tr>
    <tr>
        <td>25/21<br />
</td>
        <td>301.847<br />
</td>
        <td>618.785<br />
</td>
        <td>10°19'<br />
</td>
    </tr>
    <tr>
        <td>6/5<br />
</td>
        <td>315.641<br />
</td>
        <td>647.065<br />
</td>
        <td>10°47'<br />
</td>
    </tr>
    <tr>
        <td>23/19<br />
</td>
        <td>330.761<br />
</td>
        <td>678.061<br />
</td>
        <td>11°18'<br />
</td>
    </tr>
    <tr>
        <td>17/14<br />
</td>
        <td>336.130<br />
</td>
        <td>689.065<br />
</td>
        <td>11°29'<br />
</td>
    </tr>
    <tr>
        <td>28/23<br />
</td>
        <td>340.552<br />
</td>
        <td>698.131<br />
</td>
        <td>11°38'<br />
</td>
    </tr>
    <tr>
        <td>11/9<br />
</td>
        <td>347.408<br />
</td>
        <td>712.186<br />
</td>
        <td>11°52'<br />
</td>
    </tr>
    <tr>
        <td>27/22<br />
</td>
        <td>354.547<br />
</td>
        <td>726.821<br />
</td>
        <td>12°7'<br />
</td>
    </tr>
    <tr>
        <td>16/13<br />
</td>
        <td>359.472<br />
</td>
        <td>736.918<br />
</td>
        <td>12°17'<br />
</td>
    </tr>
    <tr>
        <td>21/17<br />
</td>
        <td>365.825<br />
</td>
        <td>749.942<br />
</td>
        <td>12°30'<br />
</td>
    </tr>
    <tr>
        <td>26/21<br />
</td>
        <td>369.747<br />
</td>
        <td>757.981<br />
</td>
        <td>12°38'<br />
</td>
    </tr>
    <tr>
        <td>5/4<br />
</td>
        <td>386.314<br />
</td>
        <td>791.943<br />
</td>
        <td>13°12'<br />
</td>
    </tr>
    <tr>
        <td>34/27<br />
</td>
        <td>399.090<br />
</td>
        <td>818.135<br />
</td>
        <td>13°38'<br />
</td>
    </tr>
    <tr>
        <td>24/19<br />
</td>
        <td>404.442<br />
</td>
        <td>829.106<br />
</td>
        <td>13°49'<br />
</td>
    </tr>
    <tr>
        <td>19/15<br />
</td>
        <td>409.244<br />
</td>
        <td>838.951<br />
</td>
        <td>13°59'<br />
</td>
    </tr>
    <tr>
        <td>14/11<br />
</td>
        <td>417.508<br />
</td>
        <td>855.891<br />
</td>
        <td>14°15'<br />
</td>
    </tr>
    <tr>
        <td>23/18<br />
</td>
        <td>424.364<br />
</td>
        <td>869.947<br />
</td>
        <td>14°30'<br />
</td>
    </tr>
    <tr>
        <td>32/25<br />
</td>
        <td>427.373<br />
</td>
        <td>876.114<br />
</td>
        <td>14°36'<br />
</td>
    </tr>
    <tr>
        <td>9/7<br />
</td>
        <td>435.084<br />
</td>
        <td>891.922<br />
</td>
        <td>14°52'<br />
</td>
    </tr>
    <tr>
        <td>22/17<br />
</td>
        <td>446.363<br />
</td>
        <td>915.043<br />
</td>
        <td>15°15'<br />
</td>
    </tr>
    <tr>
        <td>13/10<br />
</td>
        <td>454.214<br />
</td>
        <td>931.139<br />
</td>
        <td>15°31'<br />
</td>
    </tr>
    <tr>
        <td>30/23<br />
</td>
        <td>459.994<br />
</td>
        <td>942.988<br />
</td>
        <td>15°43'<br />
</td>
    </tr>
    <tr>
        <td>17/13<br />
</td>
        <td>464.428<br />
</td>
        <td>952.077<br />
</td>
        <td>15°52'<br />
</td>
    </tr>
    <tr>
        <td>21/16<br />
</td>
        <td>470.781<br />
</td>
        <td>965.101<br />
</td>
        <td>16°5'<br />
</td>
    </tr>
    <tr>
        <td>25/19<br />
</td>
        <td>475.114<br />
</td>
        <td>973.985<br />
</td>
        <td>16°14'<br />
</td>
    </tr>
    <tr>
        <td>4/3<br />
</td>
        <td>498.045<br />
</td>
        <td>1020.992<br />
</td>
        <td>17°1'<br />
</td>
    </tr>
    <tr>
        <td>27/20<br />
</td>
        <td>519.551<br />
</td>
        <td>1065.080<br />
</td>
        <td>17°45'<br />
</td>
    </tr>
    <tr>
        <td>23/17<br />
</td>
        <td>523.319<br />
</td>
        <td>1072.804<br />
</td>
        <td>17°53'<br />
</td>
    </tr>
    <tr>
        <td>19/14<br />
</td>
        <td>528.687<br />
</td>
        <td>1083.809<br />
</td>
        <td>18°4'<br />
</td>
    </tr>
    <tr>
        <td>34/25<br />
</td>
        <td>532.328<br />
</td>
        <td>1091.272<br />
</td>
        <td>18°11'<br />
</td>
    </tr>
    <tr>
        <td>15/11<br />
</td>
        <td>536.951<br />
</td>
        <td>1100.749<br />
</td>
        <td>18°21'<br />
</td>
    </tr>
    <tr>
        <td>26/19<br />
</td>
        <td>543.015<br />
</td>
        <td>1113.180<br />
</td>
        <td>18°33'<br />
</td>
    </tr>
    <tr>
        <td>11/8<br />
</td>
        <td>551.318<br />
</td>
        <td>1130.202<br />
</td>
        <td>18°50'<br />
</td>
    </tr>
    <tr>
        <td>18/13<br />
</td>
        <td>563.382<br />
</td>
        <td>1154.934<br />
</td>
        <td>19°15'<br />
</td>
    </tr>
    <tr>
        <td>25/18<br />
</td>
        <td>568.717<br />
</td>
        <td>1165.871<br />
</td>
        <td>19°26'<br />
</td>
    </tr>
    <tr>
        <td>32/23<br />
</td>
        <td>571.726<br />
</td>
        <td>1172.038<br />
</td>
        <td>19°32'<br />
</td>
    </tr>
    <tr>
        <td>7/5<br />
</td>
        <td>582.512<br />
</td>
        <td>1194.150<br />
</td>
        <td>19°54'<br />
</td>
    </tr>
    <tr>
        <td>38/27<br />
</td>
        <td>591.648<br />
</td>
        <td>1212.878<br />
</td>
        <td>20°13'<br />
</td>
    </tr>
    <tr>
        <td>24/17<br />
</td>
        <td>597.000<br />
</td>
        <td>1223.849<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>17/12<br />
</td>
        <td>603.000<br />
</td>
        <td>1236.151<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>27/19<br />
</td>
        <td>608.352<br />
</td>
        <td>1247.122<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>10/7<br />
</td>
        <td>617.488<br />
</td>
        <td>1265.850<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>23/16<br />
</td>
        <td>628.274<br />
</td>
        <td>1287.962<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>36/25<br />
</td>
        <td>631.283<br />
</td>
        <td>1294.129<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>13/9<br />
</td>
        <td>636.618<br />
</td>
        <td>1305.066<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>16/11<br />
</td>
        <td>648.682<br />
</td>
        <td>1329.798<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>19/13<br />
</td>
        <td>656.985<br />
</td>
        <td>1346.820<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>22/15<br />
</td>
        <td>663.049<br />
</td>
        <td>1359.251<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>25/17<br />
</td>
        <td>667.672<br />
</td>
        <td>1368.728<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>28/19<br />
</td>
        <td>671.313<br />
</td>
        <td>1376.191<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>34/23<br />
</td>
        <td>676.681<br />
</td>
        <td>1387.196<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>40/27<br />
</td>
        <td>680.449<br />
</td>
        <td>1394.920<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3/2<br />
</td>
        <td>701.955<br />
</td>
        <td>1439.008<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>38/25<br />
</td>
        <td>724.886<br />
</td>
        <td>1486.015<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>32/21<br />
</td>
        <td>729.219<br />
</td>
        <td>1494.899<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>26/17<br />
</td>
        <td>735.572<br />
</td>
        <td>1507.923<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>23/15<br />
</td>
        <td>740.006<br />
</td>
        <td>1517.012<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>20/13<br />
</td>
        <td>745.786<br />
</td>
        <td>1528.861<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>17/11<br />
</td>
        <td>753.637<br />
</td>
        <td>1544.957<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>14/9<br />
</td>
        <td>764.916<br />
</td>
        <td>1568.078<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>25/16<br />
</td>
        <td>772.627<br />
</td>
        <td>1583.886<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>36/23<br />
</td>
        <td>775.636<br />
</td>
        <td>1590.053<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>11/7<br />
</td>
        <td>782.492<br />
</td>
        <td>1604.109<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>30/19<br />
</td>
        <td>790.756<br />
</td>
        <td>1621.049<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>19/12<br />
</td>
        <td>795.558<br />
</td>
        <td>1630.894<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>27/17<br />
</td>
        <td>800.910<br />
</td>
        <td>1641.865<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>8/5<br />
</td>
        <td>813.686<br />
</td>
        <td>1668.057<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>21/13<br />
</td>
        <td>830.253<br />
</td>
        <td>1702.019<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>34/21<br />
</td>
        <td>834.175<br />
</td>
        <td>1710.058<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>13/8<br />
</td>
        <td>840.528<br />
</td>
        <td>1723.082<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>44/27<br />
</td>
        <td>845.453<br />
</td>
        <td>1733.179<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>18/11<br />
</td>
        <td>852.592<br />
</td>
        <td>1747.814<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>23/14<br />
</td>
        <td>859.448<br />
</td>
        <td>1761.869<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>28/17<br />
</td>
        <td>863.870<br />
</td>
        <td>1770.935<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>38/23<br />
</td>
        <td>869.239<br />
</td>
        <td>1781.939<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5/3<br />
</td>
        <td>884.359<br />
</td>
        <td>1812.935<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>42/25<br />
</td>
        <td>898.153<br />
</td>
        <td>1841.215<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>32/19<br />
</td>
        <td>902.487<br />
</td>
        <td>1850.098<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>27/16<br />
</td>
        <td>905.865<br />
</td>
        <td>1857.023<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>22/13<br />
</td>
        <td>910.790<br />
</td>
        <td>1867.120<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>17/10<br />
</td>
        <td>918.642<br />
</td>
        <td>1883.215<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>46/27<br />
</td>
        <td>922.409<br />
</td>
        <td>1890.939<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>12/7<br />
</td>
        <td>933.129<br />
</td>
        <td>1912.915<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>19/11<br />
</td>
        <td>946.195<br />
</td>
        <td>1939.700<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>26/15<br />
</td>
        <td>952.259<br />
</td>
        <td>1952.131<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>40/23<br />
</td>
        <td>958.039<br />
</td>
        <td>1963.981<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>7/4<br />
</td>
        <td>968.826<br />
</td>
        <td>1986.093<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>44/25<br />
</td>
        <td>978.691<br />
</td>
        <td>2006.316<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>30/17<br />
</td>
        <td>983.313<br />
</td>
        <td>2015.792<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>23/13<br />
</td>
        <td>987.747<br />
</td>
        <td>2024.881<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>16/9<br />
</td>
        <td>996.090<br />
</td>
        <td>2041.984<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>25/14<br />
</td>
        <td>1003.802<br />
</td>
        <td>2057.793<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>34/19<br />
</td>
        <td>1007.442<br />
</td>
        <td>2065.257<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>9/5<br />
</td>
        <td>1017.596<br />
</td>
        <td>2086.072<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>38/21<br />
</td>
        <td>1026.732<br />
</td>
        <td>2104.801<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>20/11<br />
</td>
        <td>1034.996<br />
</td>
        <td>2121.741<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>42/23<br />
</td>
        <td>1042.507<br />
</td>
        <td>2137.138<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>11/6<br />
</td>
        <td>1049.363<br />
</td>
        <td>2151.194<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>46/25<br />
</td>
        <td>1055.647<br />
</td>
        <td>2164.076<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>24/13<br />
</td>
        <td>1061.427<br />
</td>
        <td>2175.926<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>50/27<br />
</td>
        <td>1066.762<br />
</td>
        <td>2186.863<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>13/7<br />
</td>
        <td>1071.702<br />
</td>
        <td>2196.989<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>28/15<br />
</td>
        <td>1080.557<br />
</td>
        <td>2215.142<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>15/8<br />
</td>
        <td>1088.269<br />
</td>
        <td>2230.951<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>32/17<br />
</td>
        <td>1095.045<br />
</td>
        <td>2244.841<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>17/9<br />
</td>
        <td>1101.045<br />
</td>
        <td>2257.143<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>36/19<br />
</td>
        <td>1106.397<br />
</td>
        <td>2268.114<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>19/10<br />
</td>
        <td>1111.199<br />
</td>
        <td>2277.959<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>40/21<br />
</td>
        <td>1115.533<br />
</td>
        <td>2286.842<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>21/11<br />
</td>
        <td>1119.463<br />
</td>
        <td>2294.899<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>44/23<br />
</td>
        <td>1123.044<br />
</td>
        <td>2302.239<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>23/12<br />
</td>
        <td>1126.319<br />
</td>
        <td>2308.955<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>48/25<br />
</td>
        <td>1129.328<br />
</td>
        <td>2315.122<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>25/13<br />
</td>
        <td>1132.100<br />
</td>
        <td>2320.805<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>52/27<br />
</td>
        <td>1134.663<br />
</td>
        <td>2326.058<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>27/14<br />
</td>
        <td>1137.039<br />
</td>
        <td>2330.930<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>1200.000<br />
</td>
        <td>2460.000<br />
</td>
        <td><br />
</td>
    </tr>
</table>

</body></html>

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