3L 3s: Difference between revisions

Revision as of 03:48, 29 August 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 guest and made on 2011-08-29 03:48:44 UTC.

The original revision id was 249047433.

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:

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 ||
||   ||   ||   || 3\24 ||   || 150 ||=   ||
||   ||   ||   ||   || 5\39 || 153.85 ||= Golden triforce ||
||   ||   || 2\15 ||   ||   || 160 ||= Optimum rank range (L/s=3/2) ||
|| 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 />
</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>5\39<br />
</td>
        <td>153.85<br />
</td>
        <td style="text-align: center;">Golden triforce<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;">Optimum rank range (L/s=3/2)<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>2011-08-28 00:30:41 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2011-08-29 03:48:44 UTC</tt>.<br>
-: The original revision id was <tt>248860913</tt>.<br>
+: The original revision id was <tt>249047433</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 8: / Line 8: @@
 <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">Associated with the [[augmented family]], which comprises the only significant minimum of harmonic entropy for these scales.
 ||||||||||~ Generator ||~ Cents ||~ Comments ||
-|| 0\3 ||   ||   ||   ||   || 0 ||   ||
+|| 0\3 ||   ||   ||   ||   || 0 ||=   ||
-||   ||   ||   || 1\15 ||   || 80 ||   ||
+||   ||   ||   || 1\15 ||   || 80 ||=   ||
-||   ||   ||   ||   || 2\27 || 88.88 || Optimal augmented is around here ||
+||   ||   ||   ||   || 2\27 || 88.88 ||= Optimal augmented is around here ||
-||   ||   || 1\12 ||   ||   || 100 ||   ||
+||   ||   || 1\12 ||   ||   || 100 ||=   ||
-||   || 1\9 ||   ||   ||   || 133.33 || Boundary of propriety for near-MOS ||
+||   || 1\9 ||   ||   ||   || 133.33 ||= Boundary of propriety for near-MOS ||
-||   ||   ||   || 3\24 ||   || 150 ||   ||
+||   ||   ||   || 3\24 ||   || 150 ||=   ||
-||   ||   ||   ||   || 5\39 || 153.85 || Golden triforce ||
+||   ||   ||   ||   || 5\39 || 153.85 ||= Golden triforce ||
-||   ||   || 2\15 ||   ||   || 160 ||   ||
+||   ||   || 2\15 ||   ||   || 160 ||= Optimum rank range (L/s=3/2) ||
-|| 1\6 ||   ||   ||   ||   || 200 ||   ||
+|| 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).
@@ Line 46: / Line 46: @@
          &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 62: / Line 62: @@
          &lt;td&gt;80&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 78: / Line 78: @@
          &lt;td&gt;88.88&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Optimal augmented is around here&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Optimal augmented is around here&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 94: / Line 94: @@
          &lt;td&gt;100&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 110: / Line 110: @@
          &lt;td&gt;133.33&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Boundary of propriety for near-MOS&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Boundary of propriety for near-MOS&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 126: / Line 126: @@
          &lt;td&gt;150&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 142: / Line 142: @@
          &lt;td&gt;153.85&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Golden triforce&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Golden triforce&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 158: / Line 158: @@
          &lt;td&gt;160&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Optimum rank range (L/s=3/2)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 174: / Line 174: @@
          &lt;td&gt;200&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&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 03:48, 29 August 2011

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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