4L 4s: Difference between revisions

Revision as of 11:10, 5 November 2015

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This revision was by author JosephRuhf and made on 2015-11-05 11:10:13 UTC.

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The minimum harmonic entropy scale with this [[MOSScales|MOS]] pattern is [[Jubilismic clan|diminished]][8], basically the familiar [[Octatonic scale|octatonic scale]] of 12edo.

There are 4 different near-MOSes such that multiples of the period are the only generic intervals with more than two specific representatives: LLsLsLss, LLsLssLs, LLssLLss, LLssLsLs. However, none are strictly proper in 12edo. (They are only proper if the generator is larger than 100 cents, which unfortunately is the wrong direction for good diminished tunings.)
||||||||||~ Generator ||~ Cents ||~ Comments ||
|| 0\4 ||   ||   ||   ||   || 0 ||=   ||
||   ||   ||   ||   || 1\24 || 50 ||   ||
||   ||   ||   || 1\20 ||   || 60 ||= L/s = 4 ||
||   ||   ||   ||   ||   || 300/(1+pi) ||   ||
||   ||   || 1\16 ||   ||   || 75 ||= L/s = 3 ||
||   ||   ||   ||   ||   || 300/(1+e) ||   ||
||   ||   ||   ||   || 3\44 || 81.82 ||   ||
||   ||   ||   || 2\28 ||   || 85.71 ||   ||
||   || 1\12 ||   ||   ||   || 100 ||= Diminished is around here
Optimum rank range (L/s=2/1) for MOS ||
||   ||   ||   ||   ||   || 300/(1+sqrt(3)) ||   ||
||   ||   ||   || 3\32 ||   || 112.5 ||=   ||
||   ||   ||   ||   || 5\52 || 115.38 ||= Golden diminished ||
||   ||   ||   ||   ||   || 300/(1+pi/2) ||   ||
||   ||   || 2\20 ||   ||   || 120 ||=   ||
|| 1\8 ||   ||   ||   ||   || 150 ||=   ||

Original HTML content:

<html><head><title>4L 4s</title></head><body>The minimum harmonic entropy scale with this <a class="wiki_link" href="/MOSScales">MOS</a> pattern is <a class="wiki_link" href="/Jubilismic%20clan">diminished</a>[8], basically the familiar <a class="wiki_link" href="/Octatonic%20scale">octatonic scale</a> of 12edo.<br />
<br />
There are 4 different near-MOSes such that multiples of the period are the only generic intervals with more than two specific representatives: LLsLsLss, LLsLssLs, LLssLLss, LLssLsLs. However, none are strictly proper in 12edo. (They are only proper if the generator is larger than 100 cents, which unfortunately is the wrong direction for good diminished tunings.)<br />


<table class="wiki_table">
    <tr>
        <th colspan="5">Generator<br />
</th>
        <th>Cents<br />
</th>
        <th>Comments<br />
</th>
    </tr>
    <tr>
        <td>0\4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>0<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1\24<br />
</td>
        <td>50<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1\20<br />
</td>
        <td><br />
</td>
        <td>60<br />
</td>
        <td style="text-align: center;">L/s = 4<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>300/(1+pi)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>1\16<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>75<br />
</td>
        <td style="text-align: center;">L/s = 3<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>300/(1+e)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3\44<br />
</td>
        <td>81.82<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2\28<br />
</td>
        <td><br />
</td>
        <td>85.71<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>1\12<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>100<br />
</td>
        <td style="text-align: center;">Diminished is around here<br />
Optimum rank range (L/s=2/1) for MOS<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>300/(1+sqrt(3))<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3\32<br />
</td>
        <td><br />
</td>
        <td>112.5<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\52<br />
</td>
        <td>115.38<br />
</td>
        <td style="text-align: center;">Golden diminished<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>300/(1+pi/2)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>2\20<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>120<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>1\8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>150<br />
</td>
        <td style="text-align: center;"><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 14:53:15 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-05 11:10:13 UTC</tt>.<br>
-: The original revision id was <tt>551970338</tt>.<br>
+: The original revision id was <tt>565317985</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 16: / Line 16: @@
 ||   ||   || 1\16 ||   ||   || 75 ||= L/s = 3 ||
 ||   ||   ||   ||   ||   || 300/(1+e) ||   ||
+||   ||   ||   ||   || 3\44 || 81.82 ||   ||
+||   ||   ||   || 2\28 ||   || 85.71 ||   ||
 ||   || 1\12 ||   ||   ||   || 100 ||= Diminished is around here
 Optimum rank range (L/s=2/1) for MOS ||
+||   ||   ||   ||   ||   || 300/(1+sqrt(3)) ||   ||
 ||   ||   ||   || 3\32 ||   || 112.5 ||=   ||
 ||   ||   ||   ||   || 5\52 || 115.38 ||= Golden diminished ||
+||   ||   ||   ||   ||   || 300/(1+pi/2) ||   ||
 ||   ||   || 2\20 ||   ||   || 120 ||=   ||
 || 1\8 ||   ||   ||   ||   || 150 ||=   ||</pre></div>
@@ Line 129: / Line 133: @@
 &lt;/td&gt;
          &lt;td&gt;300/(1+e)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&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;3\44&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;81.82&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&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;2\28&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;85.71&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 148: / Line 184: @@
          &lt;td style="text-align: center;"&gt;Diminished is around here&lt;br /&gt;
 Optimum rank range (L/s=2/1) for MOS&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;300/(1+sqrt(3))&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 180: / Line 232: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Golden diminished&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;300/(1+pi/2)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

4L 4s: Difference between revisions

Revision as of 11:10, 5 November 2015

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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