2L 4s: Difference between revisions

Revision as of 00:27, 28 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 2011-08-28 00:27:38 UTC.

The original revision id was 248860749.

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:

The only scale with this [[MOSScales|MOS]] pattern that's a really significant minimum of harmonic entropy is [[Diaschismic family|srutal/pajara]], in which the period plus the generator is 3/2. Other scales include shrutar, in which the generator is **half** of that (about a quartertone), so 3/2 is a period plus two generators; and [[Porcupine family#Hedgehog|hedgehog]], in which two generators make a 6/5, and 4/3 would be three generators (except that it doesn't appear in this MOS).

In addition to the true MOS with pattern LssLss, all these scales also come in a near-MOS version, LsLsss, in which the period is the only generic interval that has more than two specific representatives.

Srutal/pajara probably has the lowest harmonic entropy of all 6-note MOS scales. The near-MOS version has even lower harmonic entropy.
||||||||||||||||||||||~ Generator ||~ Cents ||~ Comments ||
|| 0\2 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 0 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   || 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 ||   ||
||   ||   ||   || 1\12 ||   ||   ||   ||   ||   ||   ||   || 100 ||   ||
||   ||   ||   ||   || 2\22 ||   ||   ||   ||   ||   ||   || 109.09 || Srutal/Pajara is around here ||
||   ||   || 1\10 ||   ||   ||   ||   ||   ||   ||   ||   || 120 ||   ||
||   || 1\8 ||   ||   ||   ||   ||   ||   ||   ||   ||   || 150 ||= Boundary of propriety (generators
larger than this are proper) ||
||   ||   ||   || 3\22 ||   ||   ||   ||   ||   ||   ||   || 163.64 || Hedgehog and echidna are both around here ||
||   ||   ||   ||   ||   || 8\58 ||   ||   ||   ||   ||   || 165.52 ||   ||
||   ||   ||   ||   ||   ||   || 13\94 ||   ||   ||   ||   || 165.96 || Golden hedgehog/echidna ||
||   ||   ||   ||   || 5\36 ||   ||   ||   ||   ||   ||   || 166.67 ||   ||
||   ||   || 2\14 ||   ||   ||   ||   ||   ||   ||   ||   || 171.43 ||   ||
|| 1\6 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 200 ||   ||

Original HTML content:

<html><head><title>2L 4s</title></head><body>The only scale with this <a class="wiki_link" href="/MOSScales">MOS</a> pattern that's a really significant minimum of harmonic entropy is <a class="wiki_link" href="/Diaschismic%20family">srutal/pajara</a>, in which the period plus the generator is 3/2. Other scales include shrutar, in which the generator is <strong>half</strong> of that (about a quartertone), so 3/2 is a period plus two generators; and <a class="wiki_link" href="/Porcupine%20family#Hedgehog">hedgehog</a>, in which two generators make a 6/5, and 4/3 would be three generators (except that it doesn't appear in this MOS).<br />
<br />
In addition to the true MOS with pattern LssLss, all these scales also come in a near-MOS version, LsLsss, in which the period is the only generic interval that has more than two specific representatives.<br />
<br />
Srutal/pajara probably has the lowest harmonic entropy of all 6-note MOS scales. The near-MOS version has even lower harmonic entropy.<br />


<table class="wiki_table">
    <tr>
        <th colspan="11">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><br />
</td>
        <td>0<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>1\24<br />
</td>
        <td><br />
</td>
        <td>50<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><br />
</td>
        <td>2\46<br />
</td>
        <td>52.17<br />
</td>
        <td>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><br />
</td>
        <td>1\22<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>54.55<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>1\20<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>60<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>1\18<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>66.67<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <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>Srutal/Pajara is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <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;">Boundary of propriety (generators<br />
larger than this are proper)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3\22<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>163.64<br />
</td>
        <td>Hedgehog and echidna are both around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>8\58<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>165.52<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\94<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>165.96<br />
</td>
        <td>Golden hedgehog/echidna<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\36<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>166.67<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>2\14<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>171.43<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1\6<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><br />
</td>
        <td>200<br />
</td>
        <td><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:clumma|clumma]] and made on <tt>2011-08-19 23:37:27 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2011-08-28 00:27:38 UTC</tt>.<br>
-: The original revision id was <tt>247113653</tt>.<br>
+: The original revision id was <tt>248860749</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 25: / Line 25: @@
 ||   || 1\8 ||   ||   ||   ||   ||   ||   ||   ||   ||   || 150 ||= Boundary of propriety (generators
 larger than this are proper) ||
-||   ||   ||   || 3\22 ||   ||   ||   ||   ||   ||   ||   || 163.64 || Hedgehog is around here ||
+||   ||   ||   || 3\22 ||   ||   ||   ||   ||   ||   ||   || 163.64 || Hedgehog and echidna are both around here ||
+||   ||   ||   ||   ||   || 8\58 ||   ||   ||   ||   ||   || 165.52 ||   ||
+||   ||   ||   ||   ||   ||   || 13\94 ||   ||   ||   ||   || 165.96 || Golden hedgehog/echidna ||
+||   ||   ||   ||   || 5\36 ||   ||   ||   ||   ||   ||   || 166.67 ||   ||
 ||   ||   || 2\14 ||   ||   ||   ||   ||   ||   ||   ||   || 171.43 ||   ||
 || 1\6 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 200 ||   ||</pre></div>
@@ Line 407: / Line 410: @@
          &lt;td&gt;163.64&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Hedgehog is around here&lt;br /&gt;
+         &lt;td&gt;Hedgehog and echidna are both 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;8\58&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;165.52&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13\94&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;165.96&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Golden hedgehog/echidna&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;5\36&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;166.67&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

2L 4s: Difference between revisions

Revision as of 00:27, 28 August 2011

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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