3L 2s: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-11-~~25 20~~:35:14 UTC</tt>.

: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-11-28 19:05:21 UTC</tt>.

: The original revision id was <tt>~~279101494~~</tt>.

: The original revision id was <tt>279903100</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

<h4>Original Wikitext content:</h4>

<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">The only notable low-harmonic-entropy scale for this [[MOSScales|MOS]] pattern is [[Sensipent family|sensi]], in which two generators make a 5/3. The harmonic entropy of sensi[5] is still fairly high relative to other pentatonic scales, such as meantone. It's also improper.

||||||||||||||~ Generator ||~ Cents ||~ Comments ||

||||||||||||||~ Generator ||~ Cents ||~ s ||~ L-s ||~ Comments ||

|| 1\3 || || || || || || || 400 ||= ||

|| 1\3 || || || || || || || 400 || 0 || 400 ||= ||

|| || || 4\11 || || || || || 436.36 ||= ||

|| || || 4\11 || || || || || 436.36 || 109.09 || 218.18 ||= ||

|| || || || 7\19 || || || || 442.11 ||= Sensi is around here ||

|| || || || 7\19 || || || || 442.11 || 126.32 || 189.47 ||= Sensi is around here ||

|| || 3\8 || || || || || || 450 ||= Boundary of propriety (larger

|| || 3\8 || || || || || || 450 || 150 || 150 ||= Boundary of propriety (larger

generators than this are proper) ||

|| || || || 8\21 || || || || 457.14 ||= ||

|| || || || 8\21 || || || || 457.14 || || ||= ||

|| || || || || || 21\55 || || 458.18 ||= ||

|| || || || || || 21\55 || || 458.18 || || ||= ||

|| || || || || || || || 1200/(1+phi) ||= Golden father ||

|| || || || || || || || 1200/(1+phi) || 175.08 || 108.20 ||= Golden father ||

|| || || || || 13\34 || || || 458.82 ||= ||

|| || || || || 13\34 || || || 458.82 || || ||= ||

|| || || 5\13 || || || || || 461.54 ||= Optimum rank range (L/s=3/2) father ||

|| || || 5\13 || || || || || 461.54 || 184.62 || 92.31 ||= Optimum rank range (L/s=3/2) father ||

|| || || || 7\18 || || || || 466.67 ||= ||

|| || || || 7\18 || || || || 466.67 || 200 || 66.67 ||= ||

|| || || || || 9\23 || || || 469.57 ||= ||

|| || || || || 9\23 || || || 469.57 || 208.70 || 52.17 ||= ||

|| || || || || || 11\28 || || 471.43 ||= ||

|| || || || || || 11\28 || || 471.43 || 214.29 || 42.86 ||= ||

|| || || || || || || 13\33 || 472.73 ||= Slendro-like scales in this region ||

|| || || || || || || 13\33 || 472.73 || || ||= Slendro-like scales in this region ||

|| 2\5 || || || || || || || 480 ||= ||</pre></div>

|| 2\5 || || || || || || || 480 || 240 || 0 ||= ||</pre></div>

<h4>Original HTML content:</h4>

<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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>3L 2s</title></head><body>The only notable low-harmonic-entropy scale for this <a class="wiki_link" href="/MOSScales">MOS</a> pattern is <a class="wiki_link" href="/Sensipent%20family">sensi</a>, in which two generators make a 5/3. The harmonic entropy of sensi[5] is still fairly high relative to other pentatonic scales, such as meantone. It's also improper.

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</th>

<th>Cents

</th>

<th>s

</th>

<th>L-s

</th>

<th>Comments

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</td>

<td>

</td>

<td>400

</td>

<td>0

</td>

<td>400

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</td>

<td>436.36

</td>

<td>109.09

</td>

<td>218.18

</td>

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</td>

<td>442.11

</td>

<td>126.32

</td>

<td>189.47

</td>

<td style="text-align: center;">Sensi is around here

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</td>

<td>450

</td>

<td>150

</td>

<td>150

</td>

<td style="text-align: center;">Boundary of propriety (larger

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</td>

<td>457.14

</td>

<td>

</td>

<td>

</td>

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</td>

<td>458.18

</td>

<td>

</td>

<td>

</td>

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</td>

<td>1200/(1+phi)

</td>

<td>175.08

</td>

<td>108.20

</td>

<td style="text-align: center;">Golden father

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</td>

<td>458.82

</td>

<td>

</td>

<td>

</td>

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</td>

<td>461.54

</td>

<td>184.62

</td>

<td>92.31

</td>

<td style="text-align: center;">Optimum rank range (L/s=3/2) father

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</td>

<td>466.67

</td>

<td>200

</td>

<td>66.67

</td>

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</td>

<td>469.57

</td>

<td>208.70

</td>

<td>52.17

</td>

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</td>

<td>471.43

</td>

<td>214.29

</td>

<td>42.86

</td>

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</td>

<td>472.73

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">Slendro-like scales in this region

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</td>

<td>480

</td>

<td>240

</td>

<td>0

</td>

@@ 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:keenanpepper|keenanpepper]] and made on <tt>2011-11-25 20:35:14 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-11-28 19:05:21 UTC</tt>.<br>
-: The original revision id was <tt>279101494</tt>.<br>
+: The original revision id was <tt>279903100</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>
 <h4>Original Wikitext content:</h4>
 <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">The only notable low-harmonic-entropy scale for this [[MOSScales|MOS]] pattern is [[Sensipent family|sensi]], in which two generators make a 5/3. The harmonic entropy of sensi[5] is still fairly high relative to other pentatonic scales, such as meantone. It's also improper.
-||||||||||||||~ Generator ||~ Cents ||~ Comments ||
+||||||||||||||~ Generator ||~ Cents ||~ s ||~ L-s ||~ Comments ||
-|| 1\3 ||   ||   ||   ||   ||   ||   || 400 ||=   ||
+|| 1\3 ||   ||   ||   ||   ||   ||   || 400 || 0 || 400 ||=   ||
-||   ||   || 4\11 ||   ||   ||   ||   || 436.36 ||=   ||
+||   ||   || 4\11 ||   ||   ||   ||   || 436.36 || 109.09 || 218.18 ||=   ||
-||   ||   ||   || 7\19 ||   ||   ||   || 442.11 ||= Sensi is around here ||
+||   ||   ||   || 7\19 ||   ||   ||   || 442.11 || 126.32 || 189.47 ||= Sensi is around here ||
-||   || 3\8 ||   ||   ||   ||   ||   || 450 ||= Boundary of propriety (larger
+||   || 3\8 ||   ||   ||   ||   ||   || 450 || 150 || 150 ||= Boundary of propriety (larger
 generators than this are proper) ||
-||   ||   ||   || 8\21 ||   ||   ||   || 457.14 ||=   ||
+||   ||   ||   || 8\21 ||   ||   ||   || 457.14 ||   ||   ||=   ||
-||   ||   ||   ||   ||   || 21\55 ||   || 458.18 ||=   ||
+||   ||   ||   ||   ||   || 21\55 ||   || 458.18 ||   ||   ||=   ||
-||   ||   ||   ||   ||   ||   ||   || 1200/(1+phi) ||= Golden father ||
+||   ||   ||   ||   ||   ||   ||   || 1200/(1+phi) || 175.08 || 108.20 ||= Golden father ||
-||   ||   ||   ||   || 13\34 ||   ||   || 458.82 ||=   ||
+||   ||   ||   ||   || 13\34 ||   ||   || 458.82 ||   ||   ||=   ||
-||   ||   || 5\13 ||   ||   ||   ||   || 461.54 ||= Optimum rank range (L/s=3/2) father ||
+||   ||   || 5\13 ||   ||   ||   ||   || 461.54 || 184.62 || 92.31 ||= Optimum rank range (L/s=3/2) father ||
-||   ||   ||   || 7\18 ||   ||   ||   || 466.67 ||=   ||
+||   ||   ||   || 7\18 ||   ||   ||   || 466.67 || 200 || 66.67 ||=   ||
-||   ||   ||   ||   || 9\23 ||   ||   || 469.57 ||=   ||
+||   ||   ||   ||   || 9\23 ||   ||   || 469.57 || 208.70 || 52.17 ||=   ||
-||   ||   ||   ||   ||   || 11\28 ||   || 471.43 ||=   ||
+||   ||   ||   ||   ||   || 11\28 ||   || 471.43 || 214.29 || 42.86 ||=   ||
-||   ||   ||   ||   ||   ||   || 13\33 || 472.73 ||= Slendro-like scales in this region ||
+||   ||   ||   ||   ||   ||   || 13\33 || 472.73 ||   ||   ||= Slendro-like scales in this region ||
-|| 2\5 ||   ||   ||   ||   ||   ||   || 480 ||=   ||</pre></div>
+|| 2\5 ||   ||   ||   ||   ||   ||   || 480 || 240 || 0 ||=   ||</pre></div>
 <h4>Original HTML content:</h4>
 <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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;3L 2s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The only notable low-harmonic-entropy scale for this &lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt; pattern is &lt;a class="wiki_link" href="/Sensipent%20family"&gt;sensi&lt;/a&gt;, in which two generators make a 5/3. The harmonic entropy of sensi[5] is still fairly high relative to other pentatonic scales, such as meantone. It's also improper.&lt;br /&gt;
@@ Line 32: / Line 32: @@
 &lt;/th&gt;
          &lt;th&gt;Cents&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;s&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;L-s&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;Comments&lt;br /&gt;
@@ Line 50: / Line 54: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;400&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;400&lt;br /&gt;
@@ Line 72: / Line 80: @@
 &lt;/td&gt;
          &lt;td&gt;436.36&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;109.09&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;218.18&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 92: / Line 104: @@
 &lt;/td&gt;
          &lt;td&gt;442.11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;126.32&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;189.47&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Sensi is around here&lt;br /&gt;
@@ Line 112: / Line 128: @@
 &lt;/td&gt;
          &lt;td&gt;450&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;150&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;150&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Boundary of propriety (larger&lt;br /&gt;
@@ Line 133: / Line 153: @@
 &lt;/td&gt;
          &lt;td&gt;457.14&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 style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 153: / Line 177: @@
 &lt;/td&gt;
          &lt;td&gt;458.18&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 style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 173: / Line 201: @@
 &lt;/td&gt;
          &lt;td&gt;1200/(1+phi)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;175.08&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;108.20&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Golden father&lt;br /&gt;
@@ Line 193: / Line 225: @@
 &lt;/td&gt;
          &lt;td&gt;458.82&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 style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 213: / Line 249: @@
 &lt;/td&gt;
          &lt;td&gt;461.54&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;184.62&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;92.31&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Optimum rank range (L/s=3/2) father&lt;br /&gt;
@@ Line 233: / Line 273: @@
 &lt;/td&gt;
          &lt;td&gt;466.67&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;200&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;66.67&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 253: / Line 297: @@
 &lt;/td&gt;
          &lt;td&gt;469.57&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;208.70&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;52.17&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 273: / Line 321: @@
 &lt;/td&gt;
          &lt;td&gt;471.43&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;214.29&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;42.86&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 293: / Line 345: @@
 &lt;/td&gt;
          &lt;td&gt;472.73&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 style="text-align: center;"&gt;Slendro-like scales in this region&lt;br /&gt;
@@ Line 313: / Line 369: @@
 &lt;/td&gt;
          &lt;td&gt;480&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;240&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;