3L 5s: Difference between revisions

Revision as of 20:07, 25 November 2012

IMPORTED REVISION FROM WIKISPACES

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This revision was by author JosephRuhf and made on 2012-11-25 20:07:04 UTC.

The original revision id was 385875704.

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There are two significant harmonic entropy minima with this MOS pattern. [[Sensipent family|Sensi]], in which the generator is 9/7, two of them make 5/3, and seven of them make 6/1, is the proper one. [[Meantone family#Squares|Squares]], in which the generator is also 9/7, but two of them make 18/11 and five of them make 8/3, is improper.
||||||||||||~ Generator ||~ Cents ||~ Comments ||
|| 1\3 ||   ||   ||   ||   ||   || 400 ||=   ||
||   ||   ||   || 6\17 ||   ||   || 423.53 ||= L/s=4:
generators smaller than this are "impractical" ||
||   ||   ||   ||   ||   || 17\48 || 425 ||= Squares is around here ||
||   ||   ||   ||   || 11\31 ||   || 425.81 ||=   ||
||   ||   || 5\14 ||   ||   ||   || 428.57 ||= L/s=3:
generators smaller than this may be considered "impractical" ||
||   || 4\11 ||   ||   ||   ||   || 436.36 ||= Boundary of propriety: 
generators larger than this are proper ||
||   ||   ||   || 11\30 ||   ||   || 440 ||=   ||
||   ||   ||   ||   ||   || 29\79 || 440.51 ||= Unnamed golden temperament ||
||   ||   ||   ||   || 18\49 ||   || 440.82 ||=   ||
||   ||   || 7\19 ||   ||   ||   || 442.11 ||= Optimum rank range (L/s=3/2) sensi ||
||   ||   ||   ||   || 17\46 ||   || 443.48 ||= Sensi is around here ||
||   ||   ||   || 10\27 ||   ||   || 444.44 ||=   ||
|| 3\8 ||   ||   ||   ||   ||   || 450 ||=   ||

Original HTML content:

<html><head><title>3L 5s</title></head><body>There are two significant harmonic entropy minima with this MOS pattern. <a class="wiki_link" href="/Sensipent%20family">Sensi</a>, in which the generator is 9/7, two of them make 5/3, and seven of them make 6/1, is the proper one. <a class="wiki_link" href="/Meantone%20family#Squares">Squares</a>, in which the generator is also 9/7, but two of them make 18/11 and five of them make 8/3, is improper.<br />


<table class="wiki_table">
    <tr>
        <th colspan="6">Generator<br />
</th>
        <th>Cents<br />
</th>
        <th>Comments<br />
</th>
    </tr>
    <tr>
        <td>1\3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>400<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>6\17<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>423.53<br />
</td>
        <td style="text-align: center;">L/s=4:<br />
generators smaller than this are &quot;impractical&quot;<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>17\48<br />
</td>
        <td>425<br />
</td>
        <td style="text-align: center;">Squares is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>11\31<br />
</td>
        <td><br />
</td>
        <td>425.81<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\14<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>428.57<br />
</td>
        <td style="text-align: center;">L/s=3:<br />
generators smaller than this may be considered &quot;impractical&quot;<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>4\11<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>436.36<br />
</td>
        <td style="text-align: center;">Boundary of propriety: <br />
generators larger than this are proper<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>11\30<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>440<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>29\79<br />
</td>
        <td>440.51<br />
</td>
        <td style="text-align: center;">Unnamed golden temperament<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>18\49<br />
</td>
        <td><br />
</td>
        <td>440.82<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>7\19<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>442.11<br />
</td>
        <td style="text-align: center;">Optimum rank range (L/s=3/2) sensi<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>17\46<br />
</td>
        <td><br />
</td>
        <td>443.48<br />
</td>
        <td style="text-align: center;">Sensi is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>10\27<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>444.44<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>3\8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>450<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:guest|guest]] and made on <tt>2011-08-29 04:12:36 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-11-25 20:07:04 UTC</tt>.<br>
-: The original revision id was <tt>249049327</tt>.<br>
+: The original revision id was <tt>385875704</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: @@
 ||||||||||||~ Generator ||~ Cents ||~ Comments ||
 || 1\3 ||   ||   ||   ||   ||   || 400 ||=   ||
-||   ||   ||   || 6\17 ||   ||   || 423.53 ||=   ||
+||   ||   ||   || 6\17 ||   ||   || 423.53 ||= L/s=4:
+generators smaller than this are "impractical" ||
 ||   ||   ||   ||   ||   || 17\48 || 425 ||= Squares is around here ||
 ||   ||   ||   ||   || 11\31 ||   || 425.81 ||=   ||
-||   ||   || 5\14 ||   ||   ||   || 428.57 ||=   ||
+||   ||   || 5\14 ||   ||   ||   || 428.57 ||= L/s=3:
-||   || 4\11 ||   ||   ||   ||   || 436.36 ||= Boundary of propriety: generators
+generators smaller than this may be considered "impractical" ||
-larger than this are proper ||
+||   || 4\11 ||   ||   ||   ||   || 436.36 ||= Boundary of propriety:
+generators larger than this are proper ||
 ||   ||   ||   || 11\30 ||   ||   || 440 ||=   ||
 ||   ||   ||   ||   ||   || 29\79 || 440.51 ||= Unnamed golden temperament ||
@@ Line 68: / Line 70: @@
          &lt;td&gt;423.53&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;L/s=4:&lt;br /&gt;
+generators smaller than this are &amp;quot;impractical&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 122: / Line 125: @@
          &lt;td&gt;428.57&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;L/s=3:&lt;br /&gt;
+generators smaller than this may be considered &amp;quot;impractical&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 140: / Line 144: @@
          &lt;td&gt;436.36&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Boundary of propriety: generators&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Boundary of propriety: &lt;br /&gt;
-larger than this are proper&lt;br /&gt;
+generators larger than this are proper&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

3L 5s: Difference between revisions

Revision as of 20:07, 25 November 2012

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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