2L 10s: Difference between revisions

Revision as of 15:10, 10 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 2015-11-10 15:10:50 UTC.

The original revision id was 565944071.

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, being two periods of L s s s s s, is always proper. Its generator is 1/12edo (100 cents) or smaller and it appears as the chromatic scale of Injera and Shrutar temperaments, among others. Injera is the harmonic entropy minimum for this pattern, generating 5/4 by moving up four generators from the root.
|| 0/2 ||   ||   ||   ||   ||   || 0 ||
||   ||   ||   ||   || 1/20 ||   || 60 ||
||   ||   ||   || 1/18 ||   ||   || 66.667 ||
||   ||   ||   ||   || 2/34 ||   || 70.588 ||
||   ||   ||   ||   ||   ||   || 600/(5+pi) ||
||   ||   || 1/16 ||   ||   ||   || 75 ||
||   ||   ||   ||   ||   ||   || 600/(5+e) ||
||   ||   ||   ||   || 3/46 ||   || 78.261 ||
||   ||   ||   ||   ||   ||   || 600/(6+phi) ||
||   ||   ||   || 2/30 ||   ||   || 80 ||
||   ||   ||   ||   || 3/44 ||   || 81.818 ||
||   || 1/14 ||   ||   ||   ||   || 85.714 ||
||   ||   ||   ||   || 4/54 ||   || 88.889 ||
||   ||   ||   ||   ||   ||   || 600/(5+sqrt(3)) ||
||   ||   ||   || 3/40 ||   ||   || 90 ||
||   ||   ||   ||   ||   ||   || 600/(5+phi) ||
||   ||   ||   ||   || 5/66 ||   || 90.909 ||
||   ||   ||   ||   ||   ||   || 600/(5+pi/2) ||
||   ||   ||   ||   ||   || 7/92 || 91.304 ||
||   ||   || 2/26 ||   ||   ||   || 92.308 ||
||   ||   ||   ||   || 5/64 ||   || 93.75 ||
||   ||   ||   || 3/38 ||   ||   || 94.737 ||
||   ||   ||   ||   || 4/50 ||   || 96 ||
|| 1/12 ||   ||   ||   ||   ||   || 100 ||

Original HTML content:

<html><head><title>2L 10s</title></head><body>This MOS, being two periods of L s s s s s, is always proper. Its generator is 1/12edo (100 cents) or smaller and it appears as the chromatic scale of Injera and Shrutar temperaments, among others. Injera is the harmonic entropy minimum for this pattern, generating 5/4 by moving up four generators from the root.<br />


<table class="wiki_table">
    <tr>
        <td>0/2<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>0<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1/20<br />
</td>
        <td><br />
</td>
        <td>60<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1/18<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>66.667<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2/34<br />
</td>
        <td><br />
</td>
        <td>70.588<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>600/(5+pi)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>1/16<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>75<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>600/(5+e)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3/46<br />
</td>
        <td><br />
</td>
        <td>78.261<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>600/(6+phi)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2/30<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>80<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3/44<br />
</td>
        <td><br />
</td>
        <td>81.818<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>1/14<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>85.714<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4/54<br />
</td>
        <td><br />
</td>
        <td>88.889<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>600/(5+sqrt(3))<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3/40<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>90<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>600/(5+phi)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5/66<br />
</td>
        <td><br />
</td>
        <td>90.909<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>600/(5+pi/2)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7/92<br />
</td>
        <td>91.304<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>2/26<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>92.308<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5/64<br />
</td>
        <td><br />
</td>
        <td>93.75<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3/38<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>94.737<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4/50<br />
</td>
        <td><br />
</td>
        <td>96<br />
</td>
    </tr>
    <tr>
        <td>1/12<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>100<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 17:14:15 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-10 15:10:50 UTC</tt>.<br>
-: The original revision id was <tt>551976632</tt>.<br>
+: The original revision id was <tt>565944071</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">This MOS, being two periods of L s s s s s, is always proper. Its generator is 1/12edo (100 cents) or smaller and it appears as the chromatic scale of Injera and Shrutar temperaments, among others. Injera is the harmonic entropy minimum for this pattern, generating 5/4 by moving up four generators from the root.
-|| 0/2 ||   ||   ||   ||   || 0 ||
+|| 0/2 ||   ||   ||   ||   ||   || 0 ||
-||   ||   ||   ||   || 1/20 || 60 ||
+||   ||   ||   ||   || 1/20 ||   || 60 ||
-||   ||   ||   || 1/18 ||   || 66 2/3 ||
+||   ||   ||   || 1/18 ||   ||   || 66.667 ||
-||   ||   ||   ||   || 2/34 || 70.58823 ||
+||   ||   ||   ||   || 2/34 ||   || 70.588 ||
-||   ||   ||   ||   ||   || 600/(5+pi) ||
+||   ||   ||   ||   ||   ||   || 600/(5+pi) ||
-||   ||   || 1/16 ||   ||   || 75 ||
+||   ||   || 1/16 ||   ||   ||   || 75 ||
-||   ||   ||   ||   ||   || 600/(5+e) ||
+||   ||   ||   ||   ||   ||   || 600/(5+e) ||
-||   ||   ||   ||   || 3/46 || 78.26087 ||
+||   ||   ||   ||   || 3/46 ||   || 78.261 ||
-||   ||   ||   || 2/30 ||   || 80 ||
+||   ||   ||   ||   ||   ||   || 600/(6+phi) ||
-||   ||   ||   ||   || 3/44 || 81 9/11 ||
+||   ||   ||   || 2/30 ||   ||   || 80 ||
-||   || 1/14 ||   ||   ||   || 85 5/7 ||
+||   ||   ||   ||   || 3/44 ||   || 81.818 ||
-||   ||   ||   ||   || 4/54 || 88 8/9 ||
+||   || 1/14 ||   ||   ||   ||   || 85.714 ||
-||   ||   ||   || 3/40 ||   || 90 ||
+||   ||   ||   ||   || 4/54 ||   || 88.889 ||
-||   ||   ||   ||   || 5/66 || 90 10/11 ||
+||   ||   ||   ||   ||   ||   || 600/(5+sqrt(3)) ||
-||   ||   || 2/26 ||   ||   || 92 4/13 ||
+||   ||   ||   || 3/40 ||   ||   || 90 ||
-||   ||   ||   ||   || 5/64 || 93.75 ||
+||   ||   ||   ||   ||   ||   || 600/(5+phi) ||
-||   ||   ||   || 3/38 ||   || 94.736842 ||
+||   ||   ||   ||   || 5/66 ||   || 90.909 ||
-||   ||   ||   ||   || 4/50 || 96 ||
+||   ||   ||   ||   ||   ||   || 600/(5+pi/2) ||
-|| 1/12 ||   ||   ||   ||   || 100 ||</pre></div>
+||   ||   ||   ||   ||   || 7/92 || 91.304 ||
+||   ||   || 2/26 ||   ||   ||   || 92.308 ||
+||   ||   ||   ||   || 5/64 ||   || 93.75 ||
+||   ||   ||   || 3/38 ||   ||   || 94.737 ||
+||   ||   ||   ||   || 4/50 ||   || 96 ||
+|| 1/12 ||   ||   ||   ||   ||   || 100 ||</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;2L 10s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS, being two periods of L s s s s s, is always proper. Its generator is 1/12edo (100 cents) or smaller and it appears as the chromatic scale of Injera and Shrutar temperaments, among others. Injera is the harmonic entropy minimum for this pattern, generating 5/4 by moving up four generators from the root.&lt;br /&gt;
@@ Line 33: / Line 38: @@
      &lt;tr&gt;
          &lt;td&gt;0/2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 55: / Line 62: @@
 &lt;/td&gt;
          &lt;td&gt;1/20&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;60&lt;br /&gt;
@@ Line 70: / Line 79: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;66 2/3&lt;br /&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;66.667&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 84: / Line 95: @@
          &lt;td&gt;2/34&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;70.58823&lt;br /&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;70.588&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;
@@ Line 107: / Line 122: @@
 &lt;/td&gt;
          &lt;td&gt;1/16&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 116: / Line 133: @@
      &lt;/tr&gt;
      &lt;tr&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
@@ Line 140: / Line 159: @@
          &lt;td&gt;3/46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;78.26087&lt;br /&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;78.261&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;600/(6+phi)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 151: / Line 188: @@
 &lt;/td&gt;
          &lt;td&gt;2/30&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 168: / Line 207: @@
          &lt;td&gt;3/44&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;81 9/11&lt;br /&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;81.818&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 182: / Line 223: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;85 5/7&lt;br /&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;85.714&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 196: / Line 239: @@
          &lt;td&gt;4/54&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;88 8/9&lt;br /&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;88.889&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;600/(5+sqrt(3))&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 207: / Line 268: @@
 &lt;/td&gt;
          &lt;td&gt;3/40&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;90&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;600/(5+phi)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 224: / Line 303: @@
          &lt;td&gt;5/66&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;90 10/11&lt;br /&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;90.909&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;600/(5+pi/2)&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7/92&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;91.304&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 238: / Line 351: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;92 4/13&lt;br /&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;92.308&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 251: / Line 366: @@
 &lt;/td&gt;
          &lt;td&gt;5/64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;93.75&lt;br /&gt;
@@ Line 266: / Line 383: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;94.736842&lt;br /&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;94.737&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 279: / Line 398: @@
 &lt;/td&gt;
          &lt;td&gt;4/50&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;96&lt;br /&gt;
@@ Line 285: / Line 406: @@
      &lt;tr&gt;
          &lt;td&gt;1/12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;

2L 10s: Difference between revisions

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