3L 3s: Difference between revisions

Revision as of 21:07, 25 November 2011

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author keenanpepper and made on 2011-11-25 21:07:11 UTC.

The original revision id was 279104918.

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Original Wikitext content:

Associated with the [[augmented family]], which comprises the only significant minimum of harmonic entropy for these scales.
||||||||||~ Generator ||~ Cents ||~ Comments ||
|| 0\3 ||   ||   ||   ||   || 0 ||=   ||
||   ||   ||   || 1\15 ||   || 80 ||=   ||
||   ||   ||   ||   || 2\27 || 88.88 ||= Optimal augmented is around here ||
||   ||   || 1\12 ||   ||   || 100 ||=   ||
||   || 1\9 ||   ||   ||   || 133.33 ||= Boundary of propriety for near-MOS
Optimum rank range (L/s=2/1) for MOS ||
||   ||   ||   || 3\24 ||   || 150 ||=   ||
||   ||   ||   ||   ||   || 400/(1+phi) ||= Golden triforce ||
||   ||   ||   ||   || 5\39 || 153.85 ||=   ||
||   ||   || 2\15 ||   ||   || 160 ||=   ||
|| 1\6 ||   ||   ||   ||   || 200 ||=   ||
The true MOS is LsLsLs but interesting near-MOSs include LLsLss and LLssLs. The MOS is always proper but the other forms are only proper if the generator is larger than 1\9 of an octave (so not augmented).

Out of all **[[Rothenberg propriety|proper]]** six-note MOS scales, this augmented scale probably has the lowest harmonic entropy.

Original HTML content:

<html><head><title>3L 3s</title></head><body>Associated with the <a class="wiki_link" href="/augmented%20family">augmented family</a>, which comprises the only significant minimum of harmonic entropy for these scales.<br />


<table class="wiki_table">
    <tr>
        <th colspan="5">Generator<br />
</th>
        <th>Cents<br />
</th>
        <th>Comments<br />
</th>
    </tr>
    <tr>
        <td>0\3<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>1\15<br />
</td>
        <td><br />
</td>
        <td>80<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2\27<br />
</td>
        <td>88.88<br />
</td>
        <td style="text-align: center;">Optimal augmented is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>1\12<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>100<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>1\9<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>133.33<br />
</td>
        <td style="text-align: center;">Boundary of propriety for near-MOS<br />
Optimum rank range (L/s=2/1) for MOS<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3\24<br />
</td>
        <td><br />
</td>
        <td>150<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>400/(1+phi)<br />
</td>
        <td style="text-align: center;">Golden triforce<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\39<br />
</td>
        <td>153.85<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>2\15<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>160<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>1\6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>200<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

The true MOS is LsLsLs but interesting near-MOSs include LLsLss and LLssLs. The MOS is always proper but the other forms are only proper if the generator is larger than 1\9 of an octave (so not augmented).<br />
<br />
Out of all <strong><a class="wiki_link" href="/Rothenberg%20propriety">proper</a></strong> six-note MOS scales, this augmented scale probably has the lowest harmonic entropy.</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:guest|guest]] and made on <tt>2011-08-29 04:08:34 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-11-25 21:07:11 UTC</tt>.<br>
-: The original revision id was <tt>249048971</tt>.<br>
+: The original revision id was <tt>279104918</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 15: / Line 15: @@
 Optimum rank range (L/s=2/1) for MOS ||
 ||   ||   ||   || 3\24 ||   || 150 ||=   ||
-||   ||   ||   ||   || 5\39 || 153.85 ||= Golden triforce ||
+||   ||   ||   ||   ||   || 400/(1+phi) ||= Golden triforce ||
+||   ||   ||   ||   || 5\39 || 153.85 ||=   ||
 ||   ||   || 2\15 ||   ||   || 160 ||=   ||
 || 1\6 ||   ||   ||   ||   || 200 ||=   ||
@@ Line 129: / Line 130: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;400/(1+phi)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Golden triforce&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 144: / Line 161: @@
          &lt;td&gt;153.85&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Golden triforce&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

3L 3s: Difference between revisions

Revision as of 21:07, 25 November 2011

IMPORTED REVISION FROM WIKISPACES

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