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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | 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. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-14 20:55:08 UTC</tt>.<br>
| |
| : The original revision id was <tt>236712956</tt>.<br>
| |
| : The revision comment was: <tt></tt><br>
| |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| |
| <h4>Original Wikitext content:</h4>
| |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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]].
| |
|
| |
|
| Below the intervals of the [[27-limit]] [[tonality diamond]] are tabulated, with the sizes listed in both [[cent]]s and minas. 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.
| | Other popular systems that can be represented exactly in whole numbers of minas include [[10edo]] and [[15edo]]. Moreover a cent is exactly 2.05 minas, and a ''[[mem]]'', 1\205 octaves, is exactly 12 minas. |
| ||~ interval
| |
| ratio ||~ size
| |
| in cent ||~ size
| |
| in mina
| |
| ||
| |
| || 1 || 0.000 || 0.000 ||
| |
| || 28/27 || 62.961 || 129.070 ||
| |
| || 27/26 || 65.337 || 133.942 ||
| |
| || 26/25 || 67.900 || 139.195 ||
| |
| || 25/24 || 70.672 || 144.878 ||
| |
| || 24/23 || 73.681 || 151.045 ||
| |
| || 23/22 || 76.956 || 157.761 ||
| |
| || 22/21 || 80.537 || 165.101 ||
| |
| || 21/20 || 84.467 || 173.158 ||
| |
| || 20/19 || 88.801 || 182.041 ||
| |
| || 19/18 || 93.603 || 191.886 ||
| |
| || 18/17 || 98.955 || 202.857 ||
| |
| || 17/16 || 104.955 || 215.159 ||
| |
| || 16/15 || 111.731 || 229.049 ||
| |
| || 15/14 || 119.443 || 244.858 ||
| |
| || 14/13 || 128.298 || 263.011 ||
| |
| || 27/25 || 133.238 || 273.137 ||
| |
| || 13/12 || 138.573 || 284.074 ||
| |
| || 25/23 || 144.353 || 295.924 ||
| |
| || 12/11 || 150.637 || 308.806 ||
| |
| || 23/21 || 157.493 || 322.862 ||
| |
| || 11/10 || 165.004 || 338.259 ||
| |
| || 21/19 || 173.268 || 355.199 ||
| |
| || 10/9 || 182.404 || 373.928 ||
| |
| || 19/17 || 192.558 || 394.743 ||
| |
| || 28/25 || 196.198 || 402.207 ||
| |
| || 9/8 || 203.910 || 418.016 ||
| |
| || 26/23 || 212.253 || 435.119 ||
| |
| || 17/15 || 216.687 || 444.208 ||
| |
| || 25/22 || 221.309 || 453.684 ||
| |
| || 8/7 || 231.174 || 473.907 ||
| |
| || 23/20 || 241.961 || 496.019 ||
| |
| || 15/13 || 247.741 || 507.869 ||
| |
| || 22/19 || 253.805 || 520.300 ||
| |
| || 7/6 || 266.871 || 547.085 ||
| |
| || 27/23 || 277.591 || 569.061 ||
| |
| || 20/17 || 281.358 || 576.785 ||
| |
| || 13/11 || 289.210 || 592.880 ||
| |
| || 32/27 || 294.135 || 602.977 ||
| |
| || 19/16 || 297.513 || 609.902 ||
| |
| || 25/21 || 301.847 || 618.785 ||
| |
| || 6/5 || 315.641 || 647.065 ||
| |
| || 23/19 || 330.761 || 678.061 ||
| |
| || 17/14 || 336.130 || 689.065 ||
| |
| || 28/23 || 340.552 || 698.131 ||
| |
| || 11/9 || 347.408 || 712.186 ||
| |
| || 27/22 || 354.547 || 726.821 ||
| |
| || 16/13 || 359.472 || 736.918 ||
| |
| || 21/17 || 365.825 || 749.942 ||
| |
| || 26/21 || 369.747 || 757.981 ||
| |
| || 5/4 || 386.314 || 791.943 ||
| |
| || 34/27 || 399.090 || 818.135 ||
| |
| || 24/19 || 404.442 || 829.106 ||
| |
| || 19/15 || 409.244 || 838.951 ||
| |
| || 14/11 || 417.508 || 855.891 ||
| |
| || 23/18 || 424.364 || 869.947 ||
| |
| || 32/25 || 427.373 || 876.114 ||
| |
| || 9/7 || 435.084 || 891.922 ||
| |
| || 22/17 || 446.363 || 915.043 ||
| |
| || 13/10 || 454.214 || 931.139 ||
| |
| || 30/23 || 459.994 || 942.988 ||
| |
| || 17/13 || 464.428 || 952.077 ||
| |
| || 21/16 || 470.781 || 965.101 ||
| |
| || 25/19 || 475.114 || 973.985 ||
| |
| || 4/3 || 498.045 || 1020.992 ||
| |
| || 27/20 || 519.551 || 1065.080 ||
| |
| || 23/17 || 523.319 || 1072.804 ||
| |
| || 19/14 || 528.687 || 1083.809 ||
| |
| || 34/25 || 532.328 || 1091.272 ||
| |
| || 15/11 || 536.951 || 1100.749 ||
| |
| || 26/19 || 543.015 || 1113.180 ||
| |
| || 11/8 || 551.318 || 1130.202 ||
| |
| || 18/13 || 563.382 || 1154.934 ||
| |
| || 25/18 || 568.717 || 1165.871 ||
| |
| || 32/23 || 571.726 || 1172.038 ||
| |
| || 7/5 || 582.512 || 1194.150 ||
| |
| || 38/27 || 591.648 || 1212.878 ||
| |
| || 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 ||
| |
| </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>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>. <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. 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 />
| |
|
| |
|
| | The following table lists some intervals which may be represented exactly in minas and in degrees and minutes, with the sizes listed in both [[cent]]s and minas and expressed as degrees and minutes. |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>interval <br />
| | ! Interval |
| ratio<br />
| | ! Size in<br />cents |
| </th>
| | ! Size in<br />minas |
| <th>size<br />
| | ! Size as degrees<br />and minutes |
| in cent<br /> | | |- |
| </th>
| | | 1\2460 |
| <th>size<br />
| | | 0.488 |
| in mina<br />
| | | 1 |
| </th>
| | | 1' |
| </tr>
| | |- |
| <tr>
| | | 1\205 |
| <td>1<br />
| | | 5.835 |
| </td>
| | | 12 |
| <td>0.000<br />
| | | 12' |
| </td>
| | |- |
| <td>0.000<br />
| | | 1\41 |
| </td>
| | | 29.268 |
| </tr>
| | | 60 |
| <tr>
| | | 1° |
| <td>28/27<br />
| | |- |
| </td>
| | | 1\15 |
| <td>62.961<br />
| | | 80 |
| </td>
| | | 164 |
| <td>129.070<br />
| | | 2°44' |
| </td>
| | |- |
| </tr>
| | | 1\12 |
| <tr>
| | | 100 |
| <td>27/26<br />
| | | 205 |
| </td>
| | | 3°25' |
| <td>65.337<br />
| | |- |
| </td>
| | | 1\10 |
| <td>133.942<br />
| | | 120 |
| </td>
| | | 246 |
| </tr>
| | | 4°6' |
| <tr>
| | |- |
| <td>26/25<br />
| | | 1\6 |
| </td>
| | | 200 |
| <td>67.900<br />
| | | 410 |
| </td>
| | | 6°50' |
| <td>139.195<br />
| | |- |
| </td>
| | | 1\5 |
| </tr>
| | | 240 |
| <tr>
| | | 492 |
| <td>25/24<br />
| | | 8°12' |
| </td>
| | |- |
| <td>70.672<br />
| | | 1\4 |
| </td>
| | | 300 |
| <td>144.878<br />
| | | 615 |
| </td>
| | | 10°15' |
| </tr>
| | |- |
| <tr>
| | | 1\3 |
| <td>24/23<br />
| | | 400 |
| </td>
| | | 820 |
| <td>73.681<br />
| | | 13°40' |
| </td>
| | |- |
| <td>151.045<br />
| | | 2\5 |
| </td>
| | | 480 |
| </tr>
| | | 984 |
| <tr>
| | | 16°24' |
| <td>23/22<br />
| | |- |
| </td>
| | | 5\12 |
| <td>76.956<br />
| | | 500 |
| </td>
| | | 1025 |
| <td>157.761<br />
| | | 17°5' |
| </td>
| | |- |
| </tr>
| | | 1\2 |
| <tr>
| | | 600 |
| <td>22/21<br />
| | | 1230 |
| </td>
| | | 20°30' |
| <td>80.537<br />
| | |- |
| </td>
| | | 7\12 |
| <td>165.101<br />
| | | 700 |
| </td>
| | | 1435 |
| </tr>
| | | 23°55' |
| <tr>
| | |- |
| <td>21/20<br />
| | | 3\5 |
| </td>
| | | 720 |
| <td>84.467<br />
| | | 1476 |
| </td>
| | | 24°36' |
| <td>173.158<br />
| | |- |
| </td>
| | | 2\3 |
| </tr>
| | | 800 |
| <tr>
| | | 1640 |
| <td>20/19<br />
| | | 27°20' |
| </td>
| | |- |
| <td>88.801<br />
| | | 3\4 |
| </td>
| | | 900 |
| <td>182.041<br />
| | | 1845 |
| </td>
| | | 30°45' |
| </tr>
| | |- |
| <tr>
| | | 4\5 |
| <td>19/18<br />
| | | 960 |
| </td>
| | | 1960 |
| <td>93.603<br />
| | | 32°48' |
| </td>
| | |- |
| <td>191.886<br />
| | | 5\6 |
| </td>
| | | 1000 |
| </tr>
| | | 2050 |
| <tr>
| | | 34°10 |
| <td>18/17<br />
| | |- |
| </td>
| | | 11\12 |
| <td>98.955<br />
| | | 1100 |
| </td>
| | | 2255 |
| <td>202.857<br />
| | | 37°35 |
| </td>
| | |- |
| </tr>
| | | 2/1 |
| <tr>
| | | 1200 |
| <td>17/16<br />
| | | 2460 |
| </td>
| | | 41° |
| <td>104.955<br />
| | |} |
| </td>
| |
| <td>215.159<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/15<br />
| |
| </td>
| |
| <td>111.731<br />
| |
| </td>
| |
| <td>229.049<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/14<br />
| |
| </td>
| |
| <td>119.443<br />
| |
| </td>
| |
| <td>244.858<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/13<br />
| |
| </td>
| |
| <td>128.298<br />
| |
| </td>
| |
| <td>263.011<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27/25<br />
| |
| </td>
| |
| <td>133.238<br />
| |
| </td>
| |
| <td>273.137<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/12<br />
| |
| </td>
| |
| <td>138.573<br />
| |
| </td>
| |
| <td>284.074<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25/23<br />
| |
| </td>
| |
| <td>144.353<br />
| |
| </td>
| |
| <td>295.924<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12/11<br />
| |
| </td>
| |
| <td>150.637<br />
| |
| </td>
| |
| <td>308.806<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23/21<br />
| |
| </td>
| |
| <td>157.493<br />
| |
| </td>
| |
| <td>322.862<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/10<br />
| |
| </td>
| |
| <td>165.004<br />
| |
| </td>
| |
| <td>338.259<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21/19<br />
| |
| </td>
| |
| <td>173.268<br />
| |
| </td>
| |
| <td>355.199<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10/9<br />
| |
| </td>
| |
| <td>182.404<br />
| |
| </td>
| |
| <td>373.928<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19/17<br />
| |
| </td>
| |
| <td>192.558<br />
| |
| </td>
| |
| <td>394.743<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>28/25<br />
| |
| </td>
| |
| <td>196.198<br />
| |
| </td>
| |
| <td>402.207<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9/8<br />
| |
| </td>
| |
| <td>203.910<br />
| |
| </td>
| |
| <td>418.016<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26/23<br />
| |
| </td>
| |
| <td>212.253<br />
| |
| </td>
| |
| <td>435.119<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17/15<br />
| |
| </td>
| |
| <td>216.687<br />
| |
| </td>
| |
| <td>444.208<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25/22<br />
| |
| </td>
| |
| <td>221.309<br />
| |
| </td>
| |
| <td>453.684<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8/7<br />
| |
| </td>
| |
| <td>231.174<br />
| |
| </td>
| |
| <td>473.907<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23/20<br />
| |
| </td>
| |
| <td>241.961<br />
| |
| </td>
| |
| <td>496.019<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/13<br />
| |
| </td>
| |
| <td>247.741<br />
| |
| </td>
| |
| <td>507.869<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22/19<br />
| |
| </td>
| |
| <td>253.805<br />
| |
| </td>
| |
| <td>520.300<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/6<br />
| |
| </td>
| |
| <td>266.871<br />
| |
| </td>
| |
| <td>547.085<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27/23<br />
| |
| </td>
| |
| <td>277.591<br />
| |
| </td>
| |
| <td>569.061<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20/17<br />
| |
| </td>
| |
| <td>281.358<br />
| |
| </td>
| |
| <td>576.785<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/11<br />
| |
| </td>
| |
| <td>289.210<br />
| |
| </td>
| |
| <td>592.880<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32/27<br />
| |
| </td>
| |
| <td>294.135<br />
| |
| </td>
| |
| <td>602.977<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19/16<br />
| |
| </td>
| |
| <td>297.513<br />
| |
| </td>
| |
| <td>609.902<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25/21<br />
| |
| </td>
| |
| <td>301.847<br />
| |
| </td>
| |
| <td>618.785<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6/5<br />
| |
| </td>
| |
| <td>315.641<br />
| |
| </td>
| |
| <td>647.065<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23/19<br />
| |
| </td>
| |
| <td>330.761<br />
| |
| </td>
| |
| <td>678.061<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17/14<br />
| |
| </td>
| |
| <td>336.130<br />
| |
| </td>
| |
| <td>689.065<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>28/23<br />
| |
| </td>
| |
| <td>340.552<br />
| |
| </td>
| |
| <td>698.131<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/9<br />
| |
| </td>
| |
| <td>347.408<br />
| |
| </td>
| |
| <td>712.186<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27/22<br />
| |
| </td>
| |
| <td>354.547<br />
| |
| </td>
| |
| <td>726.821<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/13<br />
| |
| </td>
| |
| <td>359.472<br />
| |
| </td>
| |
| <td>736.918<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21/17<br />
| |
| </td>
| |
| <td>365.825<br />
| |
| </td>
| |
| <td>749.942<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26/21<br />
| |
| </td>
| |
| <td>369.747<br />
| |
| </td>
| |
| <td>757.981<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5/4<br />
| |
| </td>
| |
| <td>386.314<br />
| |
| </td>
| |
| <td>791.943<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34/27<br />
| |
| </td>
| |
| <td>399.090<br />
| |
| </td>
| |
| <td>818.135<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>24/19<br />
| |
| </td>
| |
| <td>404.442<br />
| |
| </td>
| |
| <td>829.106<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19/15<br />
| |
| </td>
| |
| <td>409.244<br />
| |
| </td>
| |
| <td>838.951<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/11<br />
| |
| </td>
| |
| <td>417.508<br />
| |
| </td>
| |
| <td>855.891<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23/18<br />
| |
| </td>
| |
| <td>424.364<br />
| |
| </td>
| |
| <td>869.947<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32/25<br />
| |
| </td>
| |
| <td>427.373<br />
| |
| </td>
| |
| <td>876.114<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9/7<br />
| |
| </td>
| |
| <td>435.084<br />
| |
| </td>
| |
| <td>891.922<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22/17<br />
| |
| </td>
| |
| <td>446.363<br />
| |
| </td>
| |
| <td>915.043<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/10<br />
| |
| </td>
| |
| <td>454.214<br />
| |
| </td>
| |
| <td>931.139<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>30/23<br />
| |
| </td>
| |
| <td>459.994<br />
| |
| </td>
| |
| <td>942.988<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17/13<br />
| |
| </td>
| |
| <td>464.428<br />
| |
| </td>
| |
| <td>952.077<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21/16<br />
| |
| </td>
| |
| <td>470.781<br />
| |
| </td>
| |
| <td>965.101<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25/19<br />
| |
| </td>
| |
| <td>475.114<br />
| |
| </td>
| |
| <td>973.985<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4/3<br />
| |
| </td>
| |
| <td>498.045<br />
| |
| </td>
| |
| <td>1020.992<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27/20<br />
| |
| </td>
| |
| <td>519.551<br />
| |
| </td>
| |
| <td>1065.080<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23/17<br />
| |
| </td>
| |
| <td>523.319<br />
| |
| </td>
| |
| <td>1072.804<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19/14<br />
| |
| </td>
| |
| <td>528.687<br />
| |
| </td>
| |
| <td>1083.809<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34/25<br />
| |
| </td>
| |
| <td>532.328<br />
| |
| </td>
| |
| <td>1091.272<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/11<br />
| |
| </td>
| |
| <td>536.951<br />
| |
| </td>
| |
| <td>1100.749<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26/19<br />
| |
| </td>
| |
| <td>543.015<br />
| |
| </td>
| |
| <td>1113.180<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/8<br />
| |
| </td>
| |
| <td>551.318<br />
| |
| </td>
| |
| <td>1130.202<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18/13<br />
| |
| </td>
| |
| <td>563.382<br />
| |
| </td>
| |
| <td>1154.934<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25/18<br />
| |
| </td>
| |
| <td>568.717<br />
| |
| </td>
| |
| <td>1165.871<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32/23<br />
| |
| </td>
| |
| <td>571.726<br />
| |
| </td>
| |
| <td>1172.038<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/5<br />
| |
| </td>
| |
| <td>582.512<br />
| |
| </td>
| |
| <td>1194.150<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>38/27<br />
| |
| </td>
| |
| <td>591.648<br />
| |
| </td>
| |
| <td>1212.878<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>24/17<br />
| |
| </td>
| |
| <td>597.000<br />
| |
| </td>
| |
| <td>1223.849<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17/12<br />
| |
| </td>
| |
| <td>603.000<br />
| |
| </td>
| |
| <td>1236.151<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27/19<br />
| |
| </td>
| |
| <td>608.352<br />
| |
| </td>
| |
| <td>1247.122<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10/7<br />
| |
| </td>
| |
| <td>617.488<br />
| |
| </td>
| |
| <td>1265.850<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23/16<br />
| |
| </td>
| |
| <td>628.274<br />
| |
| </td>
| |
| <td>1287.962<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>36/25<br />
| |
| </td>
| |
| <td>631.283<br />
| |
| </td>
| |
| <td>1294.129<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/9<br />
| |
| </td>
| |
| <td>636.618<br />
| |
| </td>
| |
| <td>1305.066<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/11<br />
| |
| </td>
| |
| <td>648.682<br />
| |
| </td>
| |
| <td>1329.798<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19/13<br />
| |
| </td>
| |
| <td>656.985<br />
| |
| </td>
| |
| <td>1346.820<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22/15<br />
| |
| </td>
| |
| <td>663.049<br />
| |
| </td>
| |
| <td>1359.251<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25/17<br />
| |
| </td>
| |
| <td>667.672<br />
| |
| </td>
| |
| <td>1368.728<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>28/19<br />
| |
| </td>
| |
| <td>671.313<br />
| |
| </td>
| |
| <td>1376.191<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34/23<br />
| |
| </td>
| |
| <td>676.681<br />
| |
| </td>
| |
| <td>1387.196<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>40/27<br />
| |
| </td>
| |
| <td>680.449<br />
| |
| </td>
| |
| <td>1394.920<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3/2<br />
| |
| </td>
| |
| <td>701.955<br />
| |
| </td>
| |
| <td>1439.008<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>38/25<br />
| |
| </td>
| |
| <td>724.886<br />
| |
| </td>
| |
| <td>1486.015<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32/21<br />
| |
| </td>
| |
| <td>729.219<br />
| |
| </td>
| |
| <td>1494.899<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26/17<br />
| |
| </td>
| |
| <td>735.572<br />
| |
| </td>
| |
| <td>1507.923<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23/15<br />
| |
| </td>
| |
| <td>740.006<br />
| |
| </td>
| |
| <td>1517.012<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20/13<br />
| |
| </td>
| |
| <td>745.786<br />
| |
| </td>
| |
| <td>1528.861<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17/11<br />
| |
| </td>
| |
| <td>753.637<br />
| |
| </td>
| |
| <td>1544.957<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/9<br />
| |
| </td>
| |
| <td>764.916<br />
| |
| </td>
| |
| <td>1568.078<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25/16<br />
| |
| </td>
| |
| <td>772.627<br />
| |
| </td>
| |
| <td>1583.886<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>36/23<br />
| |
| </td>
| |
| <td>775.636<br />
| |
| </td>
| |
| <td>1590.053<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/7<br />
| |
| </td>
| |
| <td>782.492<br />
| |
| </td>
| |
| <td>1604.109<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>30/19<br />
| |
| </td>
| |
| <td>790.756<br />
| |
| </td>
| |
| <td>1621.049<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19/12<br />
| |
| </td>
| |
| <td>795.558<br />
| |
| </td>
| |
| <td>1630.894<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27/17<br />
| |
| </td>
| |
| <td>800.910<br />
| |
| </td>
| |
| <td>1641.865<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8/5<br />
| |
| </td>
| |
| <td>813.686<br />
| |
| </td>
| |
| <td>1668.057<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21/13<br />
| |
| </td>
| |
| <td>830.253<br />
| |
| </td>
| |
| <td>1702.019<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34/21<br />
| |
| </td>
| |
| <td>834.175<br />
| |
| </td>
| |
| <td>1710.058<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/8<br />
| |
| </td>
| |
| <td>840.528<br />
| |
| </td>
| |
| <td>1723.082<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>44/27<br />
| |
| </td>
| |
| <td>845.453<br />
| |
| </td>
| |
| <td>1733.179<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18/11<br />
| |
| </td>
| |
| <td>852.592<br />
| |
| </td>
| |
| <td>1747.814<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23/14<br />
| |
| </td>
| |
| <td>859.448<br />
| |
| </td>
| |
| <td>1761.869<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>28/17<br />
| |
| </td>
| |
| <td>863.870<br />
| |
| </td>
| |
| <td>1770.935<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>38/23<br />
| |
| </td>
| |
| <td>869.239<br />
| |
| </td>
| |
| <td>1781.939<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5/3<br />
| |
| </td>
| |
| <td>884.359<br />
| |
| </td>
| |
| <td>1812.935<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>42/25<br />
| |
| </td>
| |
| <td>898.153<br />
| |
| </td>
| |
| <td>1841.215<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32/19<br />
| |
| </td>
| |
| <td>902.487<br />
| |
| </td>
| |
| <td>1850.098<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27/16<br />
| |
| </td>
| |
| <td>905.865<br />
| |
| </td>
| |
| <td>1857.023<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22/13<br />
| |
| </td>
| |
| <td>910.790<br />
| |
| </td>
| |
| <td>1867.120<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17/10<br />
| |
| </td>
| |
| <td>918.642<br />
| |
| </td>
| |
| <td>1883.215<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>46/27<br />
| |
| </td>
| |
| <td>922.409<br />
| |
| </td>
| |
| <td>1890.939<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12/7<br />
| |
| </td>
| |
| <td>933.129<br />
| |
| </td>
| |
| <td>1912.915<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19/11<br />
| |
| </td>
| |
| <td>946.195<br />
| |
| </td>
| |
| <td>1939.700<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26/15<br />
| |
| </td>
| |
| <td>952.259<br />
| |
| </td>
| |
| <td>1952.131<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>40/23<br />
| |
| </td>
| |
| <td>958.039<br />
| |
| </td>
| |
| <td>1963.981<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/4<br />
| |
| </td>
| |
| <td>968.826<br />
| |
| </td>
| |
| <td>1986.093<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>44/25<br />
| |
| </td>
| |
| <td>978.691<br />
| |
| </td>
| |
| <td>2006.316<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>30/17<br />
| |
| </td>
| |
| <td>983.313<br />
| |
| </td>
| |
| <td>2015.792<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23/13<br />
| |
| </td>
| |
| <td>987.747<br />
| |
| </td>
| |
| <td>2024.881<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/9<br />
| |
| </td>
| |
| <td>996.090<br />
| |
| </td>
| |
| <td>2041.984<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25/14<br />
| |
| </td>
| |
| <td>1003.802<br />
| |
| </td>
| |
| <td>2057.793<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34/19<br />
| |
| </td>
| |
| <td>1007.442<br />
| |
| </td>
| |
| <td>2065.257<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9/5<br />
| |
| </td>
| |
| <td>1017.596<br />
| |
| </td>
| |
| <td>2086.072<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>38/21<br />
| |
| </td>
| |
| <td>1026.732<br />
| |
| </td>
| |
| <td>2104.801<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20/11<br />
| |
| </td>
| |
| <td>1034.996<br />
| |
| </td>
| |
| <td>2121.741<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>42/23<br />
| |
| </td>
| |
| <td>1042.507<br />
| |
| </td>
| |
| <td>2137.138<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/6<br />
| |
| </td>
| |
| <td>1049.363<br />
| |
| </td>
| |
| <td>2151.194<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>46/25<br />
| |
| </td>
| |
| <td>1055.647<br />
| |
| </td>
| |
| <td>2164.076<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>24/13<br />
| |
| </td>
| |
| <td>1061.427<br />
| |
| </td>
| |
| <td>2175.926<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>50/27<br />
| |
| </td>
| |
| <td>1066.762<br />
| |
| </td>
| |
| <td>2186.863<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/7<br />
| |
| </td>
| |
| <td>1071.702<br />
| |
| </td>
| |
| <td>2196.989<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>28/15<br />
| |
| </td>
| |
| <td>1080.557<br />
| |
| </td>
| |
| <td>2215.142<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/8<br />
| |
| </td>
| |
| <td>1088.269<br />
| |
| </td>
| |
| <td>2230.951<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32/17<br />
| |
| </td>
| |
| <td>1095.045<br />
| |
| </td>
| |
| <td>2244.841<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17/9<br />
| |
| </td>
| |
| <td>1101.045<br />
| |
| </td>
| |
| <td>2257.143<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>36/19<br />
| |
| </td>
| |
| <td>1106.397<br />
| |
| </td>
| |
| <td>2268.114<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19/10<br />
| |
| </td>
| |
| <td>1111.199<br />
| |
| </td>
| |
| <td>2277.959<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>40/21<br />
| |
| </td>
| |
| <td>1115.533<br />
| |
| </td>
| |
| <td>2286.842<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21/11<br />
| |
| </td>
| |
| <td>1119.463<br />
| |
| </td>
| |
| <td>2294.899<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>44/23<br />
| |
| </td>
| |
| <td>1123.044<br />
| |
| </td>
| |
| <td>2302.239<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23/12<br />
| |
| </td>
| |
| <td>1126.319<br />
| |
| </td>
| |
| <td>2308.955<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>48/25<br />
| |
| </td>
| |
| <td>1129.328<br />
| |
| </td>
| |
| <td>2315.122<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25/13<br />
| |
| </td>
| |
| <td>1132.100<br />
| |
| </td>
| |
| <td>2320.805<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>52/27<br />
| |
| </td>
| |
| <td>1134.663<br />
| |
| </td>
| |
| <td>2326.058<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27/14<br />
| |
| </td>
| |
| <td>1137.039<br />
| |
| </td>
| |
| <td>2330.930<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2<br />
| |
| </td>
| |
| <td>1200.000<br />
| |
| </td>
| |
| <td>2460.000<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div>
| | Another notable feature of the mina is the accuracy and breadth of its approximations to just intervals. Accordingly it is hardly necessary to express intervals in non-integer values of mina, something that arguably cannot be said of cents. [[2460edo]] is uniquely [[consistent]] through to the [[27-odd-limit|27-limit]], which is not very remarkable in itself ([[388edo]] is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-limit intervals. It is also a [[the Riemann zeta function and tuning#Zeta EDO lists|zeta peak edo]] and has a lower 19-limit [[Tenney–Euclidean temperament measures#TE simple badness|relative error]] than any edo until [[3395edo|3395]], and a lower [[23-limit]] relative error than any until [[8269edo|8269]]. Also it has a lower 23-limit [[Tenney–Euclidean metrics#Logflat TE badness|TE logflat badness]] than any smaller edo and less than any until [[16808edo|16808]]. |
| | |
| | Below the intervals of the [[27-odd-limit|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]] {{val| 2460 3899 5712 6906 8510 9103 10055 10450 11128 }} for 2460edo; this will not work for [[1200edo]] and cents. |
| | |
| | {| class="wikitable" |
| | |- |
| | ! interval<br />ratio |
| | ! size<br />in cent |
| | ! size<br />in mina |
| | ! size as degrees<br />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 |
| | | 20°24' |
| | |- |
| | | 17/12 |
| | | 603.000 |
| | | 1236.151 |
| | | 20°36' |
| | |- |
| | | 27/19 |
| | | 608.352 |
| | | 1247.122 |
| | | 20°47' |
| | |- |
| | | 10/7 |
| | | 617.488 |
| | | 1265.850 |
| | | 21°6' |
| | |- |
| | | 23/16 |
| | | 628.274 |
| | | 1287.962 |
| | | 21°28' |
| | |- |
| | | 36/25 |
| | | 631.283 |
| | | 1294.129 |
| | | 21°34' |
| | |- |
| | | 13/9 |
| | | 636.618 |
| | | 1305.066 |
| | | 21°45' |
| | |- |
| | | 16/11 |
| | | 648.682 |
| | | 1329.798 |
| | | 22°10' |
| | |- |
| | | 19/13 |
| | | 656.985 |
| | | 1346.820 |
| | | 22°27' |
| | |- |
| | | 22/15 |
| | | 663.049 |
| | | 1359.251 |
| | | 22°39' |
| | |- |
| | | 25/17 |
| | | 667.672 |
| | | 1368.728 |
| | | 22°49' |
| | |- |
| | | 28/19 |
| | | 671.313 |
| | | 1376.191 |
| | | 22°56' |
| | |- |
| | | 34/23 |
| | | 676.681 |
| | | 1387.196 |
| | | 23°7' |
| | |- |
| | | 40/27 |
| | | 680.449 |
| | | 1394.920 |
| | | 23°15' |
| | |- |
| | | 3/2 |
| | | 701.955 |
| | | 1439.008 |
| | | 23°59' |
| | |- |
| | | 38/25 |
| | | 724.886 |
| | | 1486.015 |
| | | 24°46' |
| | |- |
| | | 32/21 |
| | | 729.219 |
| | | 1494.899 |
| | | 24°55' |
| | |- |
| | | 26/17 |
| | | 735.572 |
| | | 1507.923 |
| | | 25°8' |
| | |- |
| | | 23/15 |
| | | 740.006 |
| | | 1517.012 |
| | | 25°17' |
| | |- |
| | | 20/13 |
| | | 745.786 |
| | | 1528.861 |
| | | 25°29' |
| | |- |
| | | 17/11 |
| | | 753.637 |
| | | 1544.957 |
| | | 25°45' |
| | |- |
| | | 14/9 |
| | | 764.916 |
| | | 1568.078 |
| | | 26°8' |
| | |- |
| | | 25/16 |
| | | 772.627 |
| | | 1583.886 |
| | | 26°24' |
| | |- |
| | | 36/23 |
| | | 775.636 |
| | | 1590.053 |
| | | 26°30' |
| | |- |
| | | 11/7 |
| | | 782.492 |
| | | 1604.109 |
| | | 26°44' |
| | |- |
| | | 30/19 |
| | | 790.756 |
| | | 1621.049 |
| | | 27°1' |
| | |- |
| | | 19/12 |
| | | 795.558 |
| | | 1630.894 |
| | | 27°11' |
| | |- |
| | | 27/17 |
| | | 800.910 |
| | | 1641.865 |
| | | 27°22' |
| | |- |
| | | 8/5 |
| | | 813.686 |
| | | 1668.057 |
| | | 27°48' |
| | |- |
| | | 21/13 |
| | | 830.253 |
| | | 1702.019 |
| | | 28°22' |
| | |- |
| | | 34/21 |
| | | 834.175 |
| | | 1710.058 |
| | | 28°30' |
| | |- |
| | | 13/8 |
| | | 840.528 |
| | | 1723.082 |
| | | 28°43' |
| | |- |
| | | 44/27 |
| | | 845.453 |
| | | 1733.179 |
| | | 28°53' |
| | |- |
| | | 18/11 |
| | | 852.592 |
| | | 1747.814 |
| | | 29°8' |
| | |- |
| | | 23/14 |
| | | 859.448 |
| | | 1761.869 |
| | | 29°22' |
| | |- |
| | | 28/17 |
| | | 863.870 |
| | | 1770.935 |
| | | 29°31' |
| | |- |
| | | 38/23 |
| | | 869.239 |
| | | 1781.939 |
| | | 29°42' |
| | |- |
| | | 5/3 |
| | | 884.359 |
| | | 1812.935 |
| | | 30°13' |
| | |- |
| | | 42/25 |
| | | 898.153 |
| | | 1841.215 |
| | | 30°41' |
| | |- |
| | | 32/19 |
| | | 902.487 |
| | | 1850.098 |
| | | 30°50' |
| | |- |
| | | 27/16 |
| | | 905.865 |
| | | 1857.023 |
| | | 30°57' |
| | |- |
| | | 22/13 |
| | | 910.790 |
| | | 1867.120 |
| | | 31°7' |
| | |- |
| | | 17/10 |
| | | 918.642 |
| | | 1883.215 |
| | | 31°23' |
| | |- |
| | | 46/27 |
| | | 922.409 |
| | | 1890.939 |
| | | 31°31' |
| | |- |
| | | 12/7 |
| | | 933.129 |
| | | 1912.915 |
| | | 31°53' |
| | |- |
| | | 19/11 |
| | | 946.195 |
| | | 1939.700 |
| | | 32°20' |
| | |- |
| | | 26/15 |
| | | 952.259 |
| | | 1952.131 |
| | | 32°32' |
| | |- |
| | | 40/23 |
| | | 958.039 |
| | | 1963.981 |
| | | 32°44' |
| | |- |
| | | 7/4 |
| | | 968.826 |
| | | 1986.093 |
| | | 33°6' |
| | |- |
| | | 44/25 |
| | | 978.691 |
| | | 2006.316 |
| | | 33°26' |
| | |- |
| | | 30/17 |
| | | 983.313 |
| | | 2015.792 |
| | | 33°36' |
| | |- |
| | | 23/13 |
| | | 987.747 |
| | | 2024.881 |
| | | 33°45' |
| | |- |
| | | 16/9 |
| | | 996.090 |
| | | 2041.984 |
| | | 34°2' |
| | |- |
| | | 25/14 |
| | | 1003.802 |
| | | 2057.793 |
| | | 34°18' |
| | |- |
| | | 34/19 |
| | | 1007.442 |
| | | 2065.257 |
| | | 34°25' |
| | |- |
| | | 9/5 |
| | | 1017.596 |
| | | 2086.072 |
| | | 34°46' |
| | |- |
| | | 38/21 |
| | | 1026.732 |
| | | 2104.801 |
| | | 35°4' |
| | |- |
| | | 20/11 |
| | | 1034.996 |
| | | 2121.741 |
| | | 35°22' |
| | |- |
| | | 42/23 |
| | | 1042.507 |
| | | 2137.138 |
| | | 35°37' |
| | |- |
| | | 11/6 |
| | | 1049.363 |
| | | 2151.194 |
| | | 35°51' |
| | |- |
| | | 46/25 |
| | | 1055.647 |
| | | 2164.076 |
| | | 36°4' |
| | |- |
| | | 24/13 |
| | | 1061.427 |
| | | 2175.926 |
| | | 36°16' |
| | |- |
| | | 50/27 |
| | | 1066.762 |
| | | 2186.863 |
| | | 36°27' |
| | |- |
| | | 13/7 |
| | | 1071.702 |
| | | 2196.989 |
| | | 36°37' |
| | |- |
| | | 28/15 |
| | | 1080.557 |
| | | 2215.142 |
| | | 36°55' |
| | |- |
| | | 15/8 |
| | | 1088.269 |
| | | 2230.951 |
| | | 37°11' |
| | |- |
| | | 32/17 |
| | | 1095.045 |
| | | 2244.841 |
| | | 37°23' |
| | |- |
| | | 17/9 |
| | | 1101.045 |
| | | 2257.143 |
| | | 37°37' |
| | |- |
| | | 36/19 |
| | | 1106.397 |
| | | 2268.114 |
| | | 37°48' |
| | |- |
| | | 19/10 |
| | | 1111.199 |
| | | 2277.959 |
| | | 37°58' |
| | |- |
| | | 40/21 |
| | | 1115.533 |
| | | 2286.842 |
| | | 38°7' |
| | |- |
| | | 21/11 |
| | | 1119.463 |
| | | 2294.899 |
| | | 38°15' |
| | |- |
| | | 44/23 |
| | | 1123.044 |
| | | 2302.239 |
| | | 38°22' |
| | |- |
| | | 23/12 |
| | | 1126.319 |
| | | 2308.955 |
| | | 38°29' |
| | |- |
| | | 48/25 |
| | | 1129.328 |
| | | 2315.122 |
| | | 38°35' |
| | |- |
| | | 25/13 |
| | | 1132.100 |
| | | 2320.805 |
| | | 38°41' |
| | |- |
| | | 52/27 |
| | | 1134.663 |
| | | 2326.058 |
| | | 38°46' |
| | |- |
| | | 27/14 |
| | | 1137.039 |
| | | 2330.930 |
| | | 38°51' |
| | |- |
| | | 2 |
| | | 1200.000 |
| | | 2460.000 |
| | | 41° |
| | |} |
| | |
| | == External links == |
| | * [http://tonalsoft.com/enc/m/mina.aspx mina] on [[Tonalsoft Encyclopedia]] |
| | |
| | [[Category:Mina| ]] <!-- main article --> |
| | [[Category:2460edo]] |
| | [[Category:Interval size measures]] |