7L 5s: 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:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-23 17:33:32 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-10 17:50:24 UTC</tt>.

: The original revision id was <tt>~~551977454~~</tt>.

: The original revision id was <tt>565970535</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.

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||= 3\7 ||= ||= ||= ||= ||= ||< 514.286 ||= ||

||= ||= ||= ||= ||= ||= 20\47 ||< 510.638 ||= ||

||= ||= ||= ||= ||= 17\40 ||= ||< 510~~.000~~ ||= ||

||= ||= ||= ||= ||= 17\40 ||= ||< 510 ||= ||

||= ||= ||= ||= ||= ||= 31\73 ||< 509.589 ||= ||

||= ||= ||= ||= 14\33 ||= ||= ||< 509.091 ||= ||

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|| || || || || || || 507.934 || ||

||= ||= ||= 11\26 ||= ||= ||= ||< 507.692 ||= ||

|| || || || || ||= 41\97 || 507.216 ||= ||

|| || || || || ||= 41\97 || 507.216 ||= ||

||= ||= ||= ||= ||= ||= ||< 507.151 ||= Flattone ||

||= ||= ||= ||= ||= 30\71 ||= ||< 507.042 ||= ||

|| || || || || || || 506.9365 || ||

||= ||= ||= ||= ||= ||= 49\116 ||< 506.897 ||= Flattone ||

||= ||= ||= ||= 19\45 ||= ||= ||< 506.667 ||= Flattone ||

||= ||= ||= ||= ||= ||= 46\109 ||< 506.422 ||= Flattone ||

||= ||= ||= ||= ||= 27\64 ||= ||< 506.~~250~~ ||= Flattone ||

||= ||= ||= ||= ||= 27\64 ||= ||< 506.25 ||= Flattone ||

||= ||= ||= ||= ||= ||= 35\83 ||< 506.024 ||= ||

||= ||= 8\19 ||= ||= ||= ||= ||< 505.263 ||= Boundary of propriety: generators smaller than this are proper.

Meanenneadecal ||

||= ||= ||= ||= ||= ||= 37\88 ||< 504.~~545~~ ||= LucyTuning ||

||= ||= ||= ||= ||= ||= 37\88 ||< 504.5455 ||= LucyTuning ||

||= ||= ||= ||= ||= 29\69 ||= ||< 504.348 ||= ||

|| || || || || || || 504.275 || ||

||= ||= ||= ||= ||= ||= 50\119 ||< 504.202 ||= ||

||= ||= ||= ||= 21\50 ||= ||= ||< 504~~.000~~ ||= Meantone/Meanpop ||

||= ||= ||= ||= 21\50 ||= ||= ||< 504 ||= Meantone/Meanpop ||

||= ||= ||= ||= ||= ||= 55\131 ||< 503.817 ||= Golden meantone ||

|| || || || || || || 503.7855 || ||

||= ||= ||= ||= ||= 34\81 ||= ||< 503.704 ||= Optimal meantone is around here ||

||= ||= ||= ||= ||= ||= 47\112 ||< 503.571 ||= Meantone/Meanpop ||

|| || || || || || || 503.5685 || ||

||= ||= ||= 13\31 ||= ||= ||= ||< 503.226 ||= Optimal rank range (L/s=3/2) ||

||= ||= ||= ||= ||= ||= 44\105 ||< 502.857 ||= Meantone/Huygens ||

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||= ||= ||= ||= ||= 23\55 ||= ||< 501.818 ||= ||

||= ||= ||= ||= ||= ||= 28\67 ||< 501.493 ||= ||

||= 5\12 ||= ||= ||= ||= ||= ||< 500~~.000~~ ||= ||</pre></div>

||= 5\12 ||= ||= ||= ||= ||= ||< 500 ||= ||</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>7L 5s</title></head><body>This is the MOS pattern of the <a class="wiki_link" href="/Meantone%20family">meantone</a> chromatic scale, which is the only notable harmonic entropy minimum in this range of possible scales. In meantone, &quot;diatonic&quot; semitones (~16/15), such as appear in the <a class="wiki_link" href="/5L%202s">diatonic scale</a>, for example B-C, are larger than &quot;chromatic&quot; semitones (~25/24), the intervals by which flats and sharps alter pitches.

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</td>

<td style="text-align: left;">510~~.000~~

<td style="text-align: left;">510

</td>

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<td>

</td>

<td style="text-align: center;">41\97

<td style="text-align: center;">41\97

</td>

<td>507.216

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</td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>506.9365

</td>

<td>

</td>

</tr>

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</td>

<td style="text-align: left;">506.~~250~~

<td style="text-align: left;">506.25

</td>

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

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<td style="text-align: center;">37\88

</td>

<td style="text-align: left;">504.~~545~~

<td style="text-align: left;">504.5455

</td>

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

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</td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>504.275

</td>

<td>

</td>

</tr>

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</td>

<td style="text-align: left;">504~~.000~~

<td style="text-align: left;">504

</td>

<td style="text-align: center;">Meantone/Meanpop

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</td>

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

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>503.7855

</td>

<td>

</td>

</tr>

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</td>

<td style="text-align: center;">Meantone/Meanpop

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>503.5685

</td>

<td>

</td>

</tr>

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</td>

<td style="text-align: left;">500~~.000~~

<td style="text-align: left;">500

</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:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-23 17:33:32 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-10 17:50:24 UTC</tt>.<br>
-: The original revision id was <tt>551977454</tt>.<br>
+: The original revision id was <tt>565970535</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 12: / Line 12: @@
 ||= 3\7 ||=   ||=   ||=   ||=   ||=   ||&lt; 514.286 ||=   ||
 ||=   ||=   ||=   ||=   ||=   ||= 20\47 ||&lt; 510.638 ||=   ||
-||=   ||=   ||=   ||=   ||= 17\40 ||=   ||&lt; 510.000 ||=   ||
+||=   ||=   ||=   ||=   ||= 17\40 ||=   ||&lt; 510 ||=   ||
 ||=   ||=   ||=   ||=   ||=   ||= 31\73 ||&lt; 509.589 ||=   ||
 ||=   ||=   ||=   ||= 14\33 ||=   ||=   ||&lt; 509.091 ||=   ||
@@ Line 20: / Line 20: @@
 ||   ||   ||   ||   ||   ||   || 507.934 ||   ||
 ||=   ||=   ||= 11\26 ||=   ||=   ||=   ||&lt; 507.692 ||=   ||
-||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;41\97 &lt;/span&gt; || 507.216 ||=   ||
+||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;41\97&lt;/span&gt; || 507.216 ||=   ||
 ||=   ||=   ||=   ||=   ||=   ||=   ||&lt; 507.151 ||= &lt;span style="display: block; text-align: center;"&gt;Flattone&lt;/span&gt; ||
 ||=   ||=   ||=   ||=   ||= 30\71 ||=   ||&lt; 507.042 ||=   ||
+||   ||   ||   ||   ||   ||   || 506.9365 ||   ||
 ||=   ||=   ||=   ||=   ||=   ||= 49\116 ||&lt; 506.897 ||= Flattone ||
 ||=   ||=   ||=   ||= 19\45 ||=   ||=   ||&lt; 506.667 ||= Flattone ||
 ||=   ||=   ||=   ||=   ||=   ||= 46\109 ||&lt; 506.422 ||= Flattone ||
-||=   ||=   ||=   ||=   ||= 27\64 ||=   ||&lt; 506.250 ||= Flattone ||
+||=   ||=   ||=   ||=   ||= 27\64 ||=   ||&lt; 506.25 ||= Flattone ||
 ||=   ||=   ||=   ||=   ||=   ||= 35\83 ||&lt; 506.024 ||=   ||
 ||=   ||= 8\19 ||=   ||=   ||=   ||=   ||&lt; 505.263 ||= Boundary of propriety: generators smaller than this are proper.
 Meanenneadecal ||
-||=   ||=   ||=   ||=   ||=   ||= 37\88 ||&lt; 504.545 ||= LucyTuning ||
+||=   ||=   ||=   ||=   ||=   ||= 37\88 ||&lt; 504.5455 ||= LucyTuning ||
 ||=   ||=   ||=   ||=   ||= 29\69 ||=   ||&lt; 504.348 ||=   ||
+||   ||   ||   ||   ||   ||   || 504.275 ||   ||
 ||=   ||=   ||=   ||=   ||=   ||= 50\119 ||&lt; 504.202 ||=   ||
-||=   ||=   ||=   ||= 21\50 ||=   ||=   ||&lt; 504.000 ||= Meantone/Meanpop ||
+||=   ||=   ||=   ||= 21\50 ||=   ||=   ||&lt; 504 ||= Meantone/Meanpop ||
 ||=   ||=   ||=   ||=   ||=   ||= 55\131 ||&lt; 503.817 ||= Golden meantone ||
+||   ||   ||   ||   ||   ||   || 503.7855 ||   ||
 ||=   ||=   ||=   ||=   ||= 34\81 ||=   ||&lt; 503.704 ||= Optimal meantone is around here ||
 ||=   ||=   ||=   ||=   ||=   ||= 47\112 ||&lt; 503.571 ||= Meantone/Meanpop ||
+||   ||   ||   ||   ||   ||   || 503.5685 ||   ||
 ||=   ||=   ||= 13\31 ||=   ||=   ||=   ||&lt; 503.226 ||= Optimal rank range (L/s=3/2) ||
 ||=   ||=   ||=   ||=   ||=   ||= 44\105 ||&lt; 502.857 ||= Meantone/Huygens ||
@@ Line 45: / Line 49: @@
 ||=   ||=   ||=   ||=   ||= 23\55 ||=   ||&lt; 501.818 ||=   ||
 ||=   ||=   ||=   ||=   ||=   ||= 28\67 ||&lt; 501.493 ||=   ||
-||= 5\12 ||=   ||=   ||=   ||=   ||=   ||&lt; 500.000 ||=   ||</pre></div>
+||= 5\12 ||=   ||=   ||=   ||=   ||=   ||&lt; 500 ||=   ||</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;7L 5s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This is the MOS pattern of the &lt;a class="wiki_link" href="/Meantone%20family"&gt;meantone&lt;/a&gt; chromatic scale, which is the only notable harmonic entropy minimum in this range of possible scales. In meantone, &amp;quot;diatonic&amp;quot; semitones (~16/15), such as appear in the &lt;a class="wiki_link" href="/5L%202s"&gt;diatonic scale&lt;/a&gt;, for example B-C, are larger than &amp;quot;chromatic&amp;quot; semitones (~25/24), the intervals by which flats and sharps alter pitches.&lt;br /&gt;
@@ Line 110: / Line 114: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;510.000&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;510&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 252: / Line 256: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;41\97 &lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;41\97&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;507.216&lt;br /&gt;
@@ Line 293: / Line 297: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&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;506.9365&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 362: / Line 384: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;506.250&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;506.25&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Flattone&lt;br /&gt;
@@ Line 417: / Line 439: @@
          &lt;td style="text-align: center;"&gt;37\88&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;504.545&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;504.5455&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;LucyTuning&lt;br /&gt;
@@ Line 438: / Line 460: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&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;504.275&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 471: / Line 511: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;504.000&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;504&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Meantone/Meanpop&lt;br /&gt;
@@ Line 492: / Line 532: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Golden meantone&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;503.7855&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 528: / Line 586: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Meantone/Meanpop&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;503.5685&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 687: / Line 763: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;500.000&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;500&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;