1L 12s: Difference between revisions

Revision as of 15:11, 11 November 2015

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author JosephRuhf and made on 2015-11-11 15:11:03 UTC.

The original revision id was 566086773.

The revision comment was:

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

Original Wikitext content:

This MOS, the Happy tridecatonic scale, has its first harmonic entropy minimum at 1/14edo-3/40edo, where 3:2 is +8 generators (Octacot). However, the absolute harmonic entropy minimum is Nautilus (3:2=-6 generators), and that is not complete until 14 tones.
||   ||   || Cents ||
|| 0/1 ||   || 0 ||
|| 1/17 ||   || 70.588 ||
||   || 4/67 || 71.641 ||
||   || 3/50 || 72 ||
||   || 2/33 || 72.727 ||
||   || 3/49 || 73.469 ||
||   || 4/65 || 73.846 ||
||   || 5/81 || 74.074 ||
|| 1/16 ||   || 75 ||
||   || 3/47 || 76.596 ||
||   || 2/31 || 77.419 ||
||   || 3/46 || 78.261 ||
||   || 4/61 || 78.6885 ||
||   || 5/76 || 78.947 ||
||   || 6/91 || 79.121 ||
||   ||   || 1200/(12+pi) ||
|| 1/15 ||   || 80 ||
||   ||   || 1200/(12+e) ||
||   || 3/44 || 81.818 ||
||   ||   || 1200/(13+phi) ||
||   || 2/29 || 82.759 ||
||   || 3/43 || 83.721 ||
||   || 4/57 || 84.2105 ||
|| 1/14 ||   || 85.714 ||
||   || 4/55 || 86.364 ||
||   ||   || 1200/(12+sqrt(3)) ||
||   || 3/41 || 87.805 ||
||   ||   || 1200/(12+phi) ||
||   || 5/68 || 88.235 ||
||   ||   || 1200/(12+pi/2) ||
|| 2/27 ||   || 88.889 ||
||   || 5/67 || 89.552 ||
|| 3/40 ||   || 90 ||
|| 4/53 ||   || 90.556 ||
|| 1/13 ||   || 92.308 ||

Original HTML content:

<html><head><title>1L 12s</title></head><body>This MOS, the Happy tridecatonic scale, has its first harmonic entropy minimum at 1/14edo-3/40edo, where 3:2 is +8 generators (Octacot). However, the absolute harmonic entropy minimum is Nautilus (3:2=-6 generators), and that is not complete until 14 tones.<br />


<table class="wiki_table">
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>Cents<br />
</td>
    </tr>
    <tr>
        <td>0/1<br />
</td>
        <td><br />
</td>
        <td>0<br />
</td>
    </tr>
    <tr>
        <td>1/17<br />
</td>
        <td><br />
</td>
        <td>70.588<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>4/67<br />
</td>
        <td>71.641<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>3/50<br />
</td>
        <td>72<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>2/33<br />
</td>
        <td>72.727<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>3/49<br />
</td>
        <td>73.469<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>4/65<br />
</td>
        <td>73.846<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>5/81<br />
</td>
        <td>74.074<br />
</td>
    </tr>
    <tr>
        <td>1/16<br />
</td>
        <td><br />
</td>
        <td>75<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>3/47<br />
</td>
        <td>76.596<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>2/31<br />
</td>
        <td>77.419<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>3/46<br />
</td>
        <td>78.261<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>4/61<br />
</td>
        <td>78.6885<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>5/76<br />
</td>
        <td>78.947<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>6/91<br />
</td>
        <td>79.121<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>1200/(12+pi)<br />
</td>
    </tr>
    <tr>
        <td>1/15<br />
</td>
        <td><br />
</td>
        <td>80<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>1200/(12+e)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>3/44<br />
</td>
        <td>81.818<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>1200/(13+phi)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>2/29<br />
</td>
        <td>82.759<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>3/43<br />
</td>
        <td>83.721<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>4/57<br />
</td>
        <td>84.2105<br />
</td>
    </tr>
    <tr>
        <td>1/14<br />
</td>
        <td><br />
</td>
        <td>85.714<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>4/55<br />
</td>
        <td>86.364<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>1200/(12+sqrt(3))<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>3/41<br />
</td>
        <td>87.805<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>1200/(12+phi)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>5/68<br />
</td>
        <td>88.235<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>1200/(12+pi/2)<br />
</td>
    </tr>
    <tr>
        <td>2/27<br />
</td>
        <td><br />
</td>
        <td>88.889<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>5/67<br />
</td>
        <td>89.552<br />
</td>
    </tr>
    <tr>
        <td>3/40<br />
</td>
        <td><br />
</td>
        <td>90<br />
</td>
    </tr>
    <tr>
        <td>4/53<br />
</td>
        <td><br />
</td>
        <td>90.556<br />
</td>
    </tr>
    <tr>
        <td>1/13<br />
</td>
        <td><br />
</td>
        <td>92.308<br />
</td>
    </tr>
</table>

</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-23 17:52:48 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-11 15:11:03 UTC</tt>.<br>
-: The original revision id was <tt>551978114</tt>.<br>
+: The original revision id was <tt>566086773</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>
@@ Line 9: / Line 9: @@
 ||   ||   || Cents ||
 || 0/1 ||   || 0 ||
-|| 1/17 ||   || 70 10/17 ||
+|| 1/17 ||   || 70.588 ||
-||   || 4/67 || 71 43/67 ||
+||   || 4/67 || 71.641 ||
 ||   || 3/50 || 72 ||
-||   || 2/33 || 72 8/11 ||
+||   || 2/33 || 72.727 ||
-||   || 3/49 || 73 23/49 ||
+||   || 3/49 || 73.469 ||
-||   || 4/65 || 73 11/13 ||
+||   || 4/65 || 73.846 ||
-||   || 5/81 || 74 2/27 ||
+||   || 5/81 || 74.074 ||
-||   ||   || 1200/(13+pi) ||
 || 1/16 ||   || 75 ||
-||   ||   || 1200/(13+e) ||
+||   || 3/47 || 76.596 ||
-||   || 3/47 || 76 28/47 ||
+||   || 2/31 || 77.419 ||
-||   || 2/31 || 77 13/31 ||
+||   || 3/46 || 78.261 ||
-||   || 3/46 || 78 6/23 ||
+||   || 4/61 || 78.6885 ||
-||   || 4/61 || 78 42/61 ||
+||   || 5/76 || 78.947 ||
-||   || 5/76 || 78 18/19 ||
+||   || 6/91 || 79.121 ||
-||   || 6/91 || 79 11/91 ||
+||   ||   || 1200/(12+pi) ||
 || 1/15 ||   || 80 ||
-||   || 3/44 || 81 9/11 ||
+||   ||   || 1200/(12+e) ||
-||   || 2/29 || 82 22/29 ||
+||   || 3/44 || 81.818 ||
-||   || 3/43 || 83 31/43 ||
+||   ||   || 1200/(13+phi) ||
-||   || 4/57 || 84 4/19 ||
+||   || 2/29 || 82.759 ||
-|| 1/14 ||   || 85 5/7 ||
+||   || 3/43 || 83.721 ||
-||   || 4/55 || 86 4/11 ||
+||   || 4/57 || 84.2105 ||
-||   || 3/41 || 87 33/41 ||
+|| 1/14 ||   || 85.714 ||
-|| 2/27 ||   || 88 8/9 ||
+||   || 4/55 || 86.364 ||
-||   || 5/67 || 89 37/67 ||
+||   ||   || 1200/(12+sqrt(3)) ||
+||   || 3/41 || 87.805 ||
+||   ||   || 1200/(12+phi) ||
+||   || 5/68 || 88.235 ||
+||   ||   || 1200/(12+pi/2) ||
+|| 2/27 ||   || 88.889 ||
+||   || 5/67 || 89.552 ||
 || 3/40 ||   || 90 ||
-|| 4/53 ||   || 90 30/53 ||
+|| 4/53 ||   || 90.556 ||
-|| 1/13 ||   || 92 4/13 ||</pre></div>
+|| 1/13 ||   || 92.308 ||</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;1L 12s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS, the Happy tridecatonic scale, has its first harmonic entropy minimum at 1/14edo-3/40edo, where 3:2 is +8 generators (Octacot). However, the absolute harmonic entropy minimum is Nautilus (3:2=-6 generators), and that is not complete until 14 tones.&lt;br /&gt;
@@ Line 64: / Line 69: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;70 10/17&lt;br /&gt;
+         &lt;td&gt;70.588&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 72: / Line 77: @@
          &lt;td&gt;4/67&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;71 43/67&lt;br /&gt;
+         &lt;td&gt;71.641&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 88: / Line 93: @@
          &lt;td&gt;2/33&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;72 8/11&lt;br /&gt;
+         &lt;td&gt;72.727&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 96: / Line 101: @@
          &lt;td&gt;3/49&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;73 23/49&lt;br /&gt;
+         &lt;td&gt;73.469&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 104: / Line 109: @@
          &lt;td&gt;4/65&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;73 11/13&lt;br /&gt;
+         &lt;td&gt;73.846&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 112: / Line 117: @@
          &lt;td&gt;5/81&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;74 2/27&lt;br /&gt;
+         &lt;td&gt;74.074&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;1/16&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1200/(13+pi)&lt;br /&gt;
+         &lt;td&gt;75&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1/16&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;3/47&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;75&lt;br /&gt;
+         &lt;td&gt;76.596&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 134: / Line 139: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;2/31&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1200/(13+e)&lt;br /&gt;
+         &lt;td&gt;77.419&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 142: / Line 147: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;3/47&lt;br /&gt;
+         &lt;td&gt;3/46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;76 28/47&lt;br /&gt;
+         &lt;td&gt;78.261&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 150: / Line 155: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2/31&lt;br /&gt;
+         &lt;td&gt;4/61&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;77 13/31&lt;br /&gt;
+         &lt;td&gt;78.6885&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 158: / Line 163: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;3/46&lt;br /&gt;
+         &lt;td&gt;5/76&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;78 6/23&lt;br /&gt;
+         &lt;td&gt;78.947&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 166: / Line 171: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;4/61&lt;br /&gt;
+         &lt;td&gt;6/91&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;78 42/61&lt;br /&gt;
+         &lt;td&gt;79.121&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 174: / Line 179: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;5/76&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;78 18/19&lt;br /&gt;
+         &lt;td&gt;1200/(12+pi)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
+        &lt;td&gt;1/15&lt;br /&gt;
+&lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;6/91&lt;br /&gt;
+         &lt;td&gt;80&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;79 11/91&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1/15&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;80&lt;br /&gt;
+         &lt;td&gt;1200/(12+e)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 200: / Line 205: @@
          &lt;td&gt;3/44&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;81 9/11&lt;br /&gt;
+         &lt;td&gt;81.818&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1200/(13+phi)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 208: / Line 221: @@
          &lt;td&gt;2/29&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;82 22/29&lt;br /&gt;
+         &lt;td&gt;82.759&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 216: / Line 229: @@
          &lt;td&gt;3/43&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;83 31/43&lt;br /&gt;
+         &lt;td&gt;83.721&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 224: / Line 237: @@
          &lt;td&gt;4/57&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;84 4/19&lt;br /&gt;
+         &lt;td&gt;84.2105&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 232: / Line 245: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;85 5/7&lt;br /&gt;
+         &lt;td&gt;85.714&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 240: / Line 253: @@
          &lt;td&gt;4/55&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;86 4/11&lt;br /&gt;
+         &lt;td&gt;86.364&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1200/(12+sqrt(3))&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 248: / Line 269: @@
          &lt;td&gt;3/41&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;87 33/41&lt;br /&gt;
+         &lt;td&gt;87.805&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1200/(12+phi)&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5/68&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;88.235&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1200/(12+pi/2)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 256: / Line 301: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;88 8/9&lt;br /&gt;
+         &lt;td&gt;88.889&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 264: / Line 309: @@
          &lt;td&gt;5/67&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;89 37/67&lt;br /&gt;
+         &lt;td&gt;89.552&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 280: / Line 325: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;90 30/53&lt;br /&gt;
+         &lt;td&gt;90.556&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 288: / Line 333: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;92 4/13&lt;br /&gt;
+         &lt;td&gt;92.308&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

1L 12s: Difference between revisions

Revision as of 15:11, 11 November 2015

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