2L 6s: Difference between revisions

Revision as of 16:29, 4 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 2015-11-04 16:29:21 UTC.

The original revision id was 565216195.

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:

Two notable harmonic entropy minima for this [[MOSScales|MOS]] pattern are [[Diaschismic family|srutal/pajara]] and shrutar. They are both improper. As for proper scales, I can't think of any.

In addition to the true MOS form, LsssLsss, these scales also have an interesting near-MOS form, LssLssss, in which the period is the only generic interval represented by more than two specific intervals.
||||||||||||||||||||~ Generator ||~ Cents ||~ Comments ||
|| 0\2 ||   ||   ||   ||   ||   ||   ||   ||   ||   || 0 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   || 1\26 || 46.15 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   || 1\24 ||   || 50 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   || 2\46 || 52.17 ||= Shrutar is around here ||
||   ||   ||   ||   ||   ||   ||   || 1\22 ||   ||   || 54.55 ||=   ||
||   ||   ||   ||   ||   ||   || 1\20 ||   ||   ||   || 60 ||=   ||
||   ||   ||   ||   ||   || 1\18 ||   ||   ||   ||   || 66.67 ||=   ||
||   ||   ||   ||   || 1\16 ||   ||   ||   ||   ||   || 75 ||=   ||
||   ||   ||   || 1\14 ||   ||   ||   ||   ||   ||   || 85.71 ||= L/s = 4 ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 600/(3+pi) ||= <span style="display: block; text-align: center;">L/s = pi</span> ||
||   ||   || 1\12 ||   ||   ||   ||   ||   ||   ||   || 100 ||= L/s = 3 ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 600/(3+e) ||= <span style="display: block; text-align: center;">L/s = e</span> ||
||   ||   ||   ||   || 3\34 ||   ||   ||   ||   ||   || 105.88 ||= Srutal/Pajara is around here ||
||   ||   ||   ||   ||   ||   || 8\90 ||   ||   ||   || 106.67 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   || 21\236 ||   || 106.78 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   || 34\382 || 106.81 ||   ||
||   ||   ||   ||   ||   ||   ||   || 13\146 ||   ||   || 106.85 ||   ||
||   ||   ||   ||   ||   || 5\56 ||   ||   ||   ||   || 107.14 ||   ||
||   ||   ||   || 2\22 ||   ||   ||   ||   ||   ||   || 109.09 ||=   ||
||   || 1\10 ||   ||   ||   ||   ||   ||   ||   ||   || 120 ||= Boundary of propriety
(generators larger than this are proper) ||
||   ||   ||   || 3\28 ||   ||   ||   ||   ||   ||   || 128.57 ||= Supersharp ||
||   ||   ||   ||   ||   || 8\74 ||   ||   ||   ||   || 129.73 ||= Supersharp ||
||   ||   ||   ||   ||   ||   ||   || 21\194 ||   ||   || 129.9 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   || 55\508 || 129.92 ||= Unnamed golden temperament ||
||   ||   ||   ||   ||   ||   ||   ||   || 34\314 ||   || 129.94 ||   ||
||   ||   ||   ||   ||   ||   || 13\120 ||   ||   ||   || 130 ||=   ||
||   ||   ||   ||   || 5\46 ||   ||   ||   ||   ||   || 130.43 ||= Twothirdtonic ||
||   ||   || 2\18 ||   ||   ||   ||   ||   ||   ||   || 133.33 ||= Optimum rank range (L/s=3/2) ||
|| 1\8 ||   ||   ||   ||   ||   ||   ||   ||   ||   || 150 ||=   ||

Original HTML content:

<html><head><title>2L 6s</title></head><body>Two notable harmonic entropy minima for this <a class="wiki_link" href="/MOSScales">MOS</a> pattern are <a class="wiki_link" href="/Diaschismic%20family">srutal/pajara</a> and shrutar. They are both improper. As for proper scales, I can't think of any.<br />
<br />
In addition to the true MOS form, LsssLsss, these scales also have an interesting near-MOS form, LssLssss, in which the period is the only generic interval represented by more than two specific intervals.<br />


<table class="wiki_table">
    <tr>
        <th colspan="10">Generator<br />
</th>
        <th>Cents<br />
</th>
        <th>Comments<br />
</th>
    </tr>
    <tr>
        <td>0\2<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1\26<br />
</td>
        <td>46.15<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1\24<br />
</td>
        <td><br />
</td>
        <td>50<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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2\46<br />
</td>
        <td>52.17<br />
</td>
        <td style="text-align: center;">Shrutar is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1\22<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>54.55<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><br />
</td>
        <td>1\20<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>60<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>1\18<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>66.67<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\16<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>75<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1\14<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>85.71<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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>600/(3+pi)<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = pi</span><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>1\12<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>100<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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>600/(3+e)<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = e</span><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3\34<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>105.88<br />
</td>
        <td style="text-align: center;">Srutal/Pajara is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>8\90<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>106.67<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>21\236<br />
</td>
        <td><br />
</td>
        <td>106.78<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>34\382<br />
</td>
        <td>106.81<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>13\146<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>106.85<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\56<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>107.14<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2\22<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>109.09<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>1\10<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>120<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>3\28<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>128.57<br />
</td>
        <td style="text-align: center;">Supersharp<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>8\74<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>129.73<br />
</td>
        <td style="text-align: center;">Supersharp<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>21\194<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>129.9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>55\508<br />
</td>
        <td>129.92<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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>34\314<br />
</td>
        <td><br />
</td>
        <td>129.94<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>13\120<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>130<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\46<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>130.43<br />
</td>
        <td style="text-align: center;">Twothirdtonic<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>2\18<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>133.33<br />
</td>
        <td style="text-align: center;">Optimum rank range (L/s=3/2)<br />
</td>
    </tr>
    <tr>
        <td>1\8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><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 14:49:03 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-04 16:29:21 UTC</tt>.<br>
-: The original revision id was <tt>551970188</tt>.<br>
+: The original revision id was <tt>565216195</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 23: / Line 23: @@
 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 600/(3+e) ||= &lt;span style="display: block; text-align: center;"&gt;L/s = e&lt;/span&gt; ||
 ||   ||   ||   ||   || 3\34 ||   ||   ||   ||   ||   || 105.88 ||= Srutal/Pajara is around here ||
+||   ||   ||   ||   ||   ||   || 8\90 ||   ||   ||   || 106.67 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   || 21\236 ||   || 106.78 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   || 34\382 || 106.81 ||   ||
+||   ||   ||   ||   ||   ||   ||   || 13\146 ||   ||   || 106.85 ||   ||
+||   ||   ||   ||   ||   || 5\56 ||   ||   ||   ||   || 107.14 ||   ||
 ||   ||   ||   || 2\22 ||   ||   ||   ||   ||   ||   || 109.09 ||=   ||
 ||   || 1\10 ||   ||   ||   ||   ||   ||   ||   ||   || 120 ||= Boundary of propriety
@@ Line 386: / Line 391: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Srutal/Pajara is around here&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;8\90&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;106.67&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;
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+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

2L 6s: Difference between revisions

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