2L 4s: Difference between revisions

Revision as of 13:12, 24 November 2012

IMPORTED REVISION FROM WIKISPACES

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This revision was by author keenanpepper and made on 2012-11-24 13:12:32 UTC.

The original revision id was 385547336.

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 ||=   ||
||   ||   ||   ||   ||   || 2\26 ||   ||   ||   ||   ||   || 92.31 ||= Injera is around here ||
||   ||   ||   || 1\12 ||   ||   ||   ||   ||   ||   ||   || 100 ||= L/s = 4 ||
||   ||   ||   ||   || 2\22 ||   ||   ||   ||   ||   ||   || 109.09 ||= Srutal/Pajara is around here ||
||   ||   || 1\10 ||   ||   ||   ||   ||   ||   ||   ||   || 120 ||= L/s = 3 ||
||   || 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 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 600/(2+phi) ||= Golden hedgehog/echidna ||
||   ||   ||   ||   ||   ||   || 13\94 ||   ||   ||   ||   || 165.96 ||=   ||
||   ||   ||   ||   || 5\36 ||   ||   ||   ||   ||   ||   || 166.67 ||=   ||
||   ||   || 2\14 ||   ||   ||   ||   ||   ||   ||   ||   || 171.43 ||= Optimum rank range (L/s=3/2) ||
|| 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 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\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><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><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><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><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><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><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;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2\26<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>92.31<br />
</td>
        <td style="text-align: center;">Injera is around here<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 style="text-align: center;">L/s = 4<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 style="text-align: center;">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 style="text-align: center;">L/s = 3<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 style="text-align: center;">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 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><br />
</td>
        <td><br />
</td>
        <td>600/(2+phi)<br />
</td>
        <td style="text-align: center;">Golden hedgehog/echidna<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 style="text-align: center;"><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 style="text-align: center;"><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 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><br />
</td>
        <td><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>

</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>2012-11-19 23:34:38 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-11-24 13:12:32 UTC</tt>.<br>
-: The original revision id was <tt>384235918</tt>.<br>
+: The original revision id was <tt>385547336</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 21: / Line 21: @@
 ||   ||   ||   ||   || 1\14 ||   ||   ||   ||   ||   ||   || 85.71 ||=   ||
 ||   ||   ||   ||   ||   || 2\26 ||   ||   ||   ||   ||   || 92.31 ||= Injera is around here ||
-||   ||   ||   || 1\12 ||   ||   ||   ||   ||   ||   ||   || 100 ||= Boundary of "practicality" ends around here ||
+||   ||   ||   || 1\12 ||   ||   ||   ||   ||   ||   ||   || 100 ||= L/s = 4 ||
 ||   ||   ||   ||   || 2\22 ||   ||   ||   ||   ||   ||   || 109.09 ||= Srutal/Pajara is around here ||
-||   ||   || 1\10 ||   ||   ||   ||   ||   ||   ||   ||   || 120 ||= Boundary of "practicality" begins aaround here ||
+||   ||   || 1\10 ||   ||   ||   ||   ||   ||   ||   ||   || 120 ||= L/s = 3 ||
 ||   || 1\8 ||   ||   ||   ||   ||   ||   ||   ||   ||   || 150 ||= Boundary of propriety (generators
 larger than this are proper) ||
@@ Line 327: / Line 327: @@
          &lt;td&gt;100&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Boundary of &amp;quot;practicality&amp;quot; ends around here&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;L/s = 4&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 383: / Line 383: @@
          &lt;td&gt;120&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Boundary of &amp;quot;practicality&amp;quot; begins aaround here&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;L/s = 3&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

2L 4s: Difference between revisions

Revision as of 13:12, 24 November 2012

IMPORTED REVISION FROM WIKISPACES

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Original HTML content:

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