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Edo anatomy: Difference between revisions

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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>
| de =
: This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2007-09-17 02:49:55 UTC</tt>.<br>
| en = Edo anatomy
: The original revision id was <tt>8057643</tt>.<br>
| es = Anatomía de un EDO
: The revision comment was: <tt></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>
}}
<h4>Original Wikitext content:</h4>
=Anatomy of an Equal Division per 2/1 (ED2, EDO)=
<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">=Anatomy of an Equal Division (of an Octave)=  


This chart gives a list of fractions between 0 and 1, with numerators between 1 and 31, in order of ascending size, and their corresponding cent values if taken as (logarithmic) fractions of an octave
This chart gives a list of fractions between 0 and 1, with numerators between 1 and 60, in order of descending difference from 1/2, and their corresponding cent values if taken as (logarithmic) fractions of an [[Octave|octave]]


|| fraction || as fraction of octave (1200¢) ||
{| class="wikitable"
|| 0/1 || 0.000 ||
|-
|| 1/31 || 38.710 ||
| | as exponent
|| 1/30 || 40.000 ||
|| 1/29 || 41.379 ||
|| 1/28 || 42.857 ||
|| 1/27 || 44.444 ||
|| 1/25 || 48.000 ||
|| 1/24 || 50.000 ||
|| 1/23 || 52.174 ||
|| 1/22 || 54.545 ||
|| 1/21 || 57.143 ||
|| 1/20 || 60.000 ||
|| 1/19 || 63.158 ||
|| 1/18 || 66.667 ||
|| 1/17 || 70.588 ||
|| 1/16 || 75.000 ||
|| 2/31 || 77.419 ||
|| 1/15 || 80.000 ||
|| 2/29 || 82.759 ||
|| 1/14 || 85.714 ||
|| 2/27 || 88.889 ||
|| 1/13 || 92.308 ||
|| 2/25 || 96.000 ||
|| 1/12 || 100.000 ||
|| 2/23 || 104.348 ||
|| 1/11 || 109.091 ||
|| 2/21 || 114.286 ||
|| 3/31 || 116.129 ||
|| 1/10 || 120.000 ||
|| 3/29 || 124.138 ||
|| 2/19 || 126.316 ||
|| 3/28 || 128.571 ||
|| 1/9 || 133.333 ||
|| 2/17 || 141.176 ||
|| 3/25 || 144.000 ||
|| 1/8 || 150.000 ||
|| 4/31 || 154.839 ||
|| 3/23 || 156.522 ||
|| 2/15 || 160.000 ||
|| 3/22 || 163.636 ||
|| 4/29 || 165.517 ||
|| 1/7 || 171.429 ||
|| 4/27 || 177.778 ||
|| 3/20 || 180.000 ||
|| 2/13 || 184.615 ||
|| 3/19 || 189.474 ||
|| 4/25 || 192.000 ||
|| 5/31 || 193.548 ||
|| 1/6 || 200.000 ||
|| 5/29 || 206.897 ||
|| 4/23 || 208.696 ||
|| 3/17 || 211.765 ||
|| 5/28 || 214.286 ||
|| 2/11 || 218.182 ||
|| 5/27 || 222.222 ||
|| 3/16 || 225.000 ||
|| 4/21 || 228.571 ||
|| 6/31 || 232.258 ||
|| 1/5 || 240.000 ||
|| 6/29 || 248.276 ||
|| 5/24 || 250.000 ||
|| 4/19 || 252.632 ||
|| 3/14 || 257.143 ||
|| 5/23 || 260.870 ||
|| 2/9 || 266.667 ||
|| 7/31 || 270.968 ||
|| 5/22 || 272.727 ||
|| 3/13 || 276.923 ||
|| 7/30 || 280.000 ||
|| 4/17 || 282.353 ||
|| 5/21 || 285.714 ||
|| 6/25 || 288.000 ||
|| 7/29 || 289.655 ||
|| 1/4 || 300.000 ||
|| 8/31 || 309.677 ||
|| 7/27 || 311.111 ||
|| 6/23 || 313.043 ||
|| 5/19 || 315.789 ||
|| 4/15 || 320.000 ||
|| 3/11 || 327.273 ||
|| 8/29 || 331.034 ||
|| 5/18 || 333.333 ||
|| 7/25 || 336.000 ||
|| 2/7 || 342.857 ||
|| 9/31 || 348.387 ||
|| 7/24 || 350.000 ||
|| 5/17 || 352.941 ||
|| 8/27 || 355.556 ||
|| 3/10 || 360.000 ||
|| 7/23 || 365.217 ||
|| 4/13 || 369.231 ||
|| 9/29 || 372.414 ||
|| 5/16 || 375.000 ||
|| 6/19 || 378.947 ||
|| 7/22 || 381.818 ||
|| 8/25 || 384.000 ||
|| 9/28 || 385.714 ||
|| 10/31 || 387.097 ||
|| 1/3 || 400.000 ||
|| 10/29 || 413.793 ||
|| 8/23 || 417.391 ||
|| 7/20 || 420.000 ||
|| 6/17 || 423.529 ||
|| 11/31 || 425.806 ||
|| 5/14 || 428.571 ||
|| 9/25 || 432.000 ||
|| 4/11 || 436.364 ||
|| 11/30 || 440.000 ||
|| 7/19 || 442.105 ||
|| 10/27 || 444.444 ||
|| 3/8 || 450.000 ||
|| 11/29 || 455.172 ||
|| 8/21 || 457.143 ||
|| 5/13 || 461.538 ||
|| 12/31 || 464.516 ||
|| 7/18 || 466.667 ||
|| 9/23 || 469.565 ||
|| 11/28 || 471.429 ||
|| 2/5 || 480.000 ||
|| 11/27 || 488.889 ||
|| 9/22 || 490.909 ||
|| 7/17 || 494.118 ||
|| 12/29 || 496.552 ||
|| 5/12 || 500.000 ||
|| 13/31 || 503.226 ||
|| 8/19 || 505.263 ||
|| 3/7 || 514.286 ||
|| 13/30 || 520.000 ||
|| 10/23 || 521.739 ||
|| 7/16 || 525.000 ||
|| 11/25 || 528.000 ||
|| 4/9 || 533.333 ||
|| 13/29 || 537.931 ||
|| 9/20 || 540.000 ||
|| 14/31 || 541.935 ||
|| 5/11 || 545.455 ||
|| 11/24 || 550.000 ||
|| 6/13 || 553.846 ||
|| 13/28 || 557.143 ||
|| 7/15 || 560.000 ||
|| 8/17 || 564.706 ||
|| 9/19 || 568.421 ||
|| 10/21 || 571.429 ||
|| 11/23 || 573.913 ||
|| 12/25 || 576.000 ||
|| 13/27 || 577.778 ||
|| 14/29 || 579.310 ||
|| 15/31 || 580.645 ||
|| 1/2 || 600.000 ||
|| 16/31 || 619.355 ||
|| 15/29 || 620.690 ||
|| 14/27 || 622.222 ||
|| 13/25 || 624.000 ||
|| 12/23 || 626.087 ||
|| 11/21 || 628.571 ||
|| 10/19 || 631.579 ||
|| 9/17 || 635.294 ||
|| 8/15 || 640.000 ||
|| 15/28 || 642.857 ||
|| 7/13 || 646.154 ||
|| 13/24 || 650.000 ||
|| 6/11 || 654.545 ||
|| 17/31 || 658.065 ||
|| 11/20 || 660.000 ||
|| 16/29 || 662.069 ||
|| 5/9 || 666.667 ||
|| 14/25 || 672.000 ||
|| 9/16 || 675.000 ||
|| 13/23 || 678.261 ||
|| 17/30 || 680.000 ||
|| 4/7 || 685.714 ||
|| 11/19 || 694.737 ||
|| 18/31 || 696.774 ||
|| 7/12 || 700.000 ||
|| 17/29 || 703.448 ||
|| 10/17 || 705.882 ||
|| 13/22 || 709.091 ||
|| 16/27 || 711.111 ||
|| 3/5 || 720.000 ||
|| 17/28 || 728.571 ||
|| 14/23 || 730.435 ||
|| 11/18 || 733.333 ||
|| 19/31 || 735.484 ||
|| 8/13 || 738.462 ||
|| 13/21 || 742.857 ||
|| 18/29 || 744.828 ||
|| 5/8 || 750.000 ||
|| 17/27 || 755.556 ||
|| 12/19 || 757.895 ||
|| 19/30 || 760.000 ||
|| 7/11 || 763.636 ||
|| 16/25 || 768.000 ||
|| 9/14 || 771.429 ||
|| 20/31 || 774.194 ||
|| 11/17 || 776.471 ||
|| 13/20 || 780.000 ||
|| 15/23 || 782.609 ||
|| 19/29 || 786.207 ||
|| 2/3 || 800.000 ||
|| 21/31 || 812.903 ||
|| 19/28 || 814.286 ||
|| 17/25 || 816.000 ||
|| 15/22 || 818.182 ||
|| 13/19 || 821.053 ||
|| 11/16 || 825.000 ||
|| 20/29 || 827.586 ||
|| 9/13 || 830.769 ||
|| 16/23 || 834.783 ||
|| 7/10 || 840.000 ||
|| 19/27 || 844.444 ||
|| 12/17 || 847.059 ||
|| 17/24 || 850.000 ||
|| 22/31 || 851.613 ||
|| 5/7 || 857.143 ||
|| 18/25 || 864.000 ||
|| 13/18 || 866.667 ||
|| 21/29 || 868.966 ||
|| 8/11 || 872.727 ||
|| 11/15 || 880.000 ||
|| 14/19 || 884.211 ||
|| 17/23 || 886.957 ||
|| 20/27 || 888.889 ||
|| 23/31 || 890.323 ||
|| 3/4 || 900.000 ||
|| 22/29 || 910.345 ||
|| 19/25 || 912.000 ||
|| 16/21 || 914.286 ||
|| 13/17 || 917.647 ||
|| 23/30 || 920.000 ||
|| 10/13 || 923.077 ||
|| 17/22 || 927.273 ||
|| 24/31 || 929.032 ||
|| 7/9 || 933.333 ||
|| 18/23 || 939.130 ||
|| 11/14 || 942.857 ||
|| 15/19 || 947.368 ||
|| 19/24 || 950.000 ||
|| 23/29 || 951.724 ||
|| 4/5 || 960.000 ||
|| 25/31 || 967.742 ||
|| 17/21 || 971.429 ||
|| 13/16 || 975.000 ||
|| 22/27 || 977.778 ||
|| 9/11 || 981.818 ||
|| 23/28 || 985.714 ||
|| 14/17 || 988.235 ||
|| 19/23 || 991.304 ||
|| 24/29 || 993.103 ||
|| 5/6 || 1000.000 ||
|| 26/31 || 1006.452 ||
|| 21/25 || 1008.000 ||
|| 16/19 || 1010.526 ||
|| 11/13 || 1015.385 ||
|| 17/20 || 1020.000 ||
|| 23/27 || 1022.222 ||
|| 6/7 || 1028.571 ||
|| 25/29 || 1034.483 ||
|| 19/22 || 1036.364 ||
|| 13/15 || 1040.000 ||
|| 20/23 || 1043.478 ||
|| 27/31 || 1045.161 ||
|| 7/8 || 1050.000 ||
|| 22/25 || 1056.000 ||
|| 15/17 || 1058.824 ||
|| 8/9 || 1066.667 ||
|| 25/28 || 1071.429 ||
|| 17/19 || 1073.684 ||
|| 26/29 || 1075.862 ||
|| 9/10 || 1080.000 ||
|| 28/31 || 1083.871 ||
|| 19/21 || 1085.714 ||
|| 10/11 || 1090.909 ||
|| 21/23 || 1095.652 ||
|| 11/12 || 1100.000 ||
|| 23/25 || 1104.000 ||
|| 12/13 || 1107.692 ||
|| 25/27 || 1111.111 ||
|| 13/14 || 1114.286 ||
|| 27/29 || 1117.241 ||
|| 14/15 || 1120.000 ||
|| 29/31 || 1122.581 ||
|| 15/16 || 1125.000 ||
|| 16/17 || 1129.412 ||
|| 17/18 || 1133.333 ||
|| 18/19 || 1136.842 ||
|| 19/20 || 1140.000 ||
|| 20/21 || 1142.857 ||
|| 21/22 || 1145.455 ||
|| 22/23 || 1147.826 ||
|| 23/24 || 1150.000 ||
|| 24/25 || 1152.000 ||
|| 26/27 || 1155.556 ||
|| 27/28 || 1157.143 ||
|| 28/29 || 1158.621 ||
|| 29/30 || 1160.000 ||
|| 30/31 || 1161.290 ||
|| 1/1 || 1200.000 ||</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;edo anatomy&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Anatomy of an Equal Division (of an Octave)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Anatomy of an Equal Division (of an Octave)&lt;/h1&gt;
&lt;br /&gt;
This chart gives a list of fractions between 0 and 1, with numerators between 1 and 31, in order of ascending size, and their corresponding cent values if taken as (logarithmic) fractions of an octave&lt;br /&gt;
&lt;br /&gt;


<math>2^f</math>
| colspan="2" | in [[cent|cent]]s part of 1200¢
| | as exponent


&lt;table class="wiki_table"&gt;
<math>2^f</math>
    &lt;tr&gt;
|-
        &lt;td&gt;fraction&lt;br /&gt;
| | 0\1
&lt;/td&gt;
| | 0
        &lt;td&gt;as fraction of octave (1200¢)&lt;br /&gt;
| | 1200
&lt;/td&gt;
| | 1\1
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| | 1\32
        &lt;td&gt;0/1&lt;br /&gt;
| | 37.5
&lt;/td&gt;
| | 1162.5
        &lt;td&gt;0.000&lt;br /&gt;
| | 31\32
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 1\31
    &lt;tr&gt;
| | 38.7096
        &lt;td&gt;1/31&lt;br /&gt;
| | 1161.2904
&lt;/td&gt;
| | 30\31
        &lt;td&gt;38.710&lt;br /&gt;
|-
&lt;/td&gt;
| | 2\61
    &lt;/tr&gt;
| | 39.3443
    &lt;tr&gt;
| | 1160.6557
        &lt;td&gt;1/30&lt;br /&gt;
| | 60\61
&lt;/td&gt;
|-
        &lt;td&gt;40.000&lt;br /&gt;
| | 1\30
&lt;/td&gt;
| | 40
    &lt;/tr&gt;
| | 1160
    &lt;tr&gt;
| | 29\30
        &lt;td&gt;1/29&lt;br /&gt;
|-
&lt;/td&gt;
| | 2\59
        &lt;td&gt;41.379&lt;br /&gt;
| | 40.678
&lt;/td&gt;
| | 1159.322
    &lt;/tr&gt;
| | 57\59
    &lt;tr&gt;
|-
        &lt;td&gt;1/28&lt;br /&gt;
| | 1\29
&lt;/td&gt;
| | 41.3793
        &lt;td&gt;42.857&lt;br /&gt;
| | 1158.6207
&lt;/td&gt;
| | 28\29
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| | 2\57
        &lt;td&gt;1/27&lt;br /&gt;
| | 42.1053
&lt;/td&gt;
| | 1157.8947
        &lt;td&gt;44.444&lt;br /&gt;
| | 55\57
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 1\28
    &lt;tr&gt;
| | 42.8571
        &lt;td&gt;1/25&lt;br /&gt;
| | 1157.1429
&lt;/td&gt;
| | 27\28
        &lt;td&gt;48.000&lt;br /&gt;
|-
&lt;/td&gt;
| | 2\55
    &lt;/tr&gt;
| | 43.<u>63</u>
    &lt;tr&gt;
| | 1156.<u>36</u>
        &lt;td&gt;1/24&lt;br /&gt;
| | 53\55
&lt;/td&gt;
|-
        &lt;td&gt;50.000&lt;br /&gt;
| | 1\27
&lt;/td&gt;
| | 44.<u>4</u>
    &lt;/tr&gt;
| | 1155.<u>5</u>
    &lt;tr&gt;
| | 26\27
        &lt;td&gt;1/23&lt;br /&gt;
|-
&lt;/td&gt;
| | 2\53
        &lt;td&gt;52.174&lt;br /&gt;
| | 45.283
&lt;/td&gt;
| | 1054.717
    &lt;/tr&gt;
| | 51\53
    &lt;tr&gt;
|-
        &lt;td&gt;1/22&lt;br /&gt;
| | 1\26
&lt;/td&gt;
| | 46.15385
        &lt;td&gt;54.545&lt;br /&gt;
| | 1153.84615
&lt;/td&gt;
| | 25\26
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| | 2\51
        &lt;td&gt;1/21&lt;br /&gt;
| | 47.0588
&lt;/td&gt;
| | 1152.9412
        &lt;td&gt;57.143&lt;br /&gt;
| | 49\51
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 1\25
    &lt;tr&gt;
| | 48
        &lt;td&gt;1/20&lt;br /&gt;
| | 1152
&lt;/td&gt;
| | 24\25
        &lt;td&gt;60.000&lt;br /&gt;
|-
&lt;/td&gt;
| | 2\49
    &lt;/tr&gt;
| | 48.9796
    &lt;tr&gt;
| | 1151.0204
        &lt;td&gt;1/19&lt;br /&gt;
| | 47\49
&lt;/td&gt;
|-
        &lt;td&gt;63.158&lt;br /&gt;
| | 1\24
&lt;/td&gt;
| | 50
    &lt;/tr&gt;
| | 1150
    &lt;tr&gt;
| | 23\24
        &lt;td&gt;1/18&lt;br /&gt;
|-
&lt;/td&gt;
| | 2\47
        &lt;td&gt;66.667&lt;br /&gt;
| | 51.0638
&lt;/td&gt;
| | 1148.9562
    &lt;/tr&gt;
| | 45\47
    &lt;tr&gt;
|-
        &lt;td&gt;1/17&lt;br /&gt;
| | 1\23
&lt;/td&gt;
| | 52.1739
        &lt;td&gt;70.588&lt;br /&gt;
| | 1047.8261
&lt;/td&gt;
| | 22\23
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| | 2\45
        &lt;td&gt;1/16&lt;br /&gt;
| | 53.<u>3</u>
&lt;/td&gt;
| | 1146.<u>6</u>
        &lt;td&gt;75.000&lt;br /&gt;
| | 43\45
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 1\22
    &lt;tr&gt;
| | 54.<u>54</u>
        &lt;td&gt;2/31&lt;br /&gt;
| | 1145.<u>45</u>
&lt;/td&gt;
| | 21\22
        &lt;td&gt;77.419&lt;br /&gt;
|-
&lt;/td&gt;
| | 2\43
    &lt;/tr&gt;
| | 55.81395
    &lt;tr&gt;
| | 1144.18605
        &lt;td&gt;1/15&lt;br /&gt;
| | 41\43
&lt;/td&gt;
|-
        &lt;td&gt;80.000&lt;br /&gt;
| | 1\21
&lt;/td&gt;
| | 57.1429
    &lt;/tr&gt;
| | 1143.8571
    &lt;tr&gt;
| | 20\21
        &lt;td&gt;2/29&lt;br /&gt;
|-
&lt;/td&gt;
| | 2\41
        &lt;td&gt;82.759&lt;br /&gt;
| | 58.5366
&lt;/td&gt;
| | 1141.4634
    &lt;/tr&gt;
| | 39\41
    &lt;tr&gt;
|-
        &lt;td&gt;1/14&lt;br /&gt;
| | 1\20
&lt;/td&gt;
| | 60
        &lt;td&gt;85.714&lt;br /&gt;
| | 1140
&lt;/td&gt;
| | 19\20
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| | 2\39
        &lt;td&gt;2/27&lt;br /&gt;
| | 61.5385
&lt;/td&gt;
| | 1139.4615
        &lt;td&gt;88.889&lt;br /&gt;
| | 37\39
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 1\19
    &lt;tr&gt;
| | 63.1579
        &lt;td&gt;1/13&lt;br /&gt;
| | 1136.8421
&lt;/td&gt;
| | 18\19
        &lt;td&gt;92.308&lt;br /&gt;
|-
&lt;/td&gt;
| | 2\37
    &lt;/tr&gt;
| | 64.<u>864</u>
    &lt;tr&
| | 1135.<u>135</u>
| | 35\37
|-
| | 1\18
| | 66.<u>6</u>
| | 1133.<u>3</u>
| | 17\18
|-
| | 2\35
| | 68.5714
| | 1131.4286
| | 33\35
|-
| | 1\17
| | 70.5882
| | 1129.4118
| | 16\17
|-
| | 2\33
| | 72.<u>72</u>
| | 1127.<u>27</u>
| | 31\33
|-
| | 1\16
| | 75
| | 1125
| | 15\16
|-
| | 3\47
| | 76.5957
| | 1123.4043
| | 44\47
|-
| | 2\31
| | 77.41935
| | 1122.58065
| | 29\31
|-
| | 3\46
| | 78.2609
| | 1121.7391
| | 43\46
|-
| | 1\15
| | 80
| | 1120
| | 14\15
|-
| | 3\44
| | 81.<u>81</u>
| | 1118.<u>18</u>
| | 41\44
|-
| | 2\29
| | 82.759
| | 1117.241
| | 27\29
|-
| | 3\43
| | 83.7209
| | 1116.2791
| | 40\43
|-
| | 1\14
| | 85.7143
| | 1114.2857
| | 13\14
|-
| | 3\41
| | 87.8049
| | 1112.1951
| | 38\41
|-
| | 2\27
| | 88.<u>8</u>
| | 1111.<u>1</u>
| | 25\27
|-
| | 3\40
| | 90
| | 1110
| | 37\40
|-
| | 1\13
| | 92.3077
| | 1107.6923
| | 12\13
|-
| | 3\38
| | 94.7638
| | 1105.2362
| | 35\38
|-
| | 2\25
| | 96
| | 1104
| | 23\25
|-
| | 3\37
| | 97.<u>297</u>
| | 1102.<u>702</u>
| | 34\37
|-
| | 1\12
| | 100
| | 1100
| | 11\12
|-
| | 3\35
| | 102.8571
| | 1097.1429
| | 32\35
|-
| | 2\23
| | 104.3478
| | 1095.6522
| | 21\23
|-
| | 3\34
| | 105.88235
| | 1094.11765
| | 31\34
|-
| | 1\11
| | 109.<u>09</u>
| | 1090.<u>90</u>
| | 10
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