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:keenanpepper|keenanpepper]] and made on <tt>2012-10-15 15:46:51 UTC</tt>.

: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-10-15 15:52:45 UTC</tt>.

: The original revision id was <tt>~~373262730~~</tt>.

: The original revision id was <tt>373264978</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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The meantone chromatic scale is [[Rothenberg propriety|proper]].

||||||||||~~~ Generator~~ ||~ ||~ in cents ||~ Comments ||

||||||||||||~ Generator ||~ in cents ||~ Comments ||

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

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

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

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

||= ||= ||= ||= ||= 17\40 ||= ||= 510.000 ||= ||

||= ||= ||= ||= ||= 17\40 ||= ||< 510.000 ||= ||

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

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

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

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

||= ||= ||= ||= ||= ||= 39\92 ||= 508.696 ||= ||

||= ||= ||= ||= ||= ||= 39\92 ||< 508.696 ||= ||

||= ||= ||= ||= ||= 25\59 ||= ||= 508.475 ||= ||

||= ||= ||= ||= ||= 25\59 ||= ||< 508.475 ||= ||

||= ||= ||= ||= ||= ||= 36\85 ||= 508.235 ||= ||

||= ||= ||= ||= ||= ||= 36\85 ||< 508.235 ||= ||

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

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

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

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

||= ||= ||= ||= ||= 30\71 ||= ||= 507.042 ||= Flattone ||

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

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

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

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

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

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

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

||= ||= ||= ||= ||= 27\64 ||= ||= 506.250 ||= Flattone ||

||= ||= ||= ||= ||= 27\64 ||= ||< 506.250 ||= Flattone ||

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

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

||= ||= 8\19 ||= ||= ||= ||= ||= 505.263 ||= Boundary of propriety: generators

||= ||= 8\19 ||= ||= ||= ||= ||< 505.263 ||= Boundary of propriety: generators

smaller than this are proper.

Meanenneadecal ||

||= ||= ||= ||= ||= ||= 37\88 ||= 504.545 ||= LucyTuning ||

||= ||= ||= ||= ||= ||= 37\88 ||< 504.545 ||= LucyTuning ||

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

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

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

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

||= ||= ||= ||= 21\50 ||= ||= ||= 504.000 ||= Meantone/Meanpop ||

||= ||= ||= ||= 21\50 ||= ||= ||< 504.000 ||= Meantone/Meanpop ||

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

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

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

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

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

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

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

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

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

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

||= ||= ||= ||= ||= 31\74 ||= ||= 502.703 ||= Meantone/Huygens ||

||= ||= ||= ||= ||= 31\74 ||= ||< 502.703 ||= Meantone/Huygens ||

||= ||= ||= ||= ||= ||= 49\117 ||= 502.564 ||= ||

||= ||= ||= ||= ||= ||= 49\117 ||< 502.564 ||= ||

||= ||= ||= ||= 18\43 ||= ||= ||= 502.326 ||= Meantone/Meridetone ||

||= ||= ||= ||= 18\43 ||= ||= ||< 502.326 ||= Meantone/Meridetone ||

||= ||= ||= ||= ||= ||= 41\98 ||= 502.041 ||= ||

||= ||= ||= ||= ||= ||= 41\98 ||< 502.041 ||= ||

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

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

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

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

||= 5\12 ||= ||= ||= ||= ||= ||= 500.000 ||= ||</pre></div>

||= 5\12 ||= ||= ||= ||= ||= ||< 500.000 ||= ||</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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<tr>

<th colspan="5">Generator~~ ~~

<th colspan="6">Generator

~~</th>~~

~~<th>~~

</th>

<th>in cents

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</td>

<td style="text-align: ~~center~~;">514.286

<td style="text-align: left;">514.286

</td>

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<td style="text-align: center;">20\47

</td>

<td style="text-align: ~~center~~;">510.638

<td style="text-align: left;">510.638

</td>

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</td>

<td style="text-align: ~~center~~;">510.000

<td style="text-align: left;">510.000

</td>

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<td style="text-align: center;">31\73

</td>

<td style="text-align: ~~center~~;">509.589

<td style="text-align: left;">509.589

</td>

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</td>

<td style="text-align: ~~center~~;">509.091

<td style="text-align: left;">509.091

</td>

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<td style="text-align: center;">39\92

</td>

<td style="text-align: ~~center~~;">508.696

<td style="text-align: left;">508.696

</td>

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</td>

<td style="text-align: ~~center~~;">508.475

<td style="text-align: left;">508.475

</td>

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<td style="text-align: center;">36\85

</td>

<td style="text-align: ~~center~~;">508.235

<td style="text-align: left;">508.235

</td>

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</td>

<td style="text-align: ~~center~~;">507.692

<td style="text-align: left;">507.692

</td>

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

</td>

<td style="text-align: ~~center~~;">507.216

<td style="text-align: left;">507.216

</td>

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</td>

<td style="text-align: ~~center~~;">507.042

<td style="text-align: left;">507.042

</td>

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

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<td style="text-align: center;">49\116

</td>

<td style="text-align: ~~center~~;">506.897

<td style="text-align: left;">506.897

</td>

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

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</td>

<td style="text-align: ~~center~~;">506.667

<td style="text-align: left;">506.667

</td>

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

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<td style="text-align: center;">46\109

</td>

<td style="text-align: ~~center~~;">506.422

<td style="text-align: left;">506.422

</td>

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

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</td>

<td style="text-align: ~~center~~;">506.250

<td style="text-align: left;">506.250

</td>

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

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<td style="text-align: center;">35\83

</td>

<td style="text-align: ~~center~~;">506.024

<td style="text-align: left;">506.024

</td>

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</td>

<td style="text-align: ~~center~~;">505.263

<td style="text-align: left;">505.263

</td>

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

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

</td>

<td style="text-align: ~~center~~;">504.545

<td style="text-align: left;">504.545

</td>

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

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</td>

<td style="text-align: ~~center~~;">504.348

<td style="text-align: left;">504.348

</td>

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<td style="text-align: center;">50\119

</td>

<td style="text-align: ~~center~~;">504.202

<td style="text-align: left;">504.202

</td>

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</td>

<td style="text-align: ~~center~~;">504.000

<td style="text-align: left;">504.000

</td>

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

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<td style="text-align: center;">55\131

</td>

<td style="text-align: ~~center~~;">503.817

<td style="text-align: left;">503.817

</td>

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

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</td>

<td style="text-align: ~~center~~;">503.704

<td style="text-align: left;">503.704

</td>

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

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<td style="text-align: center;">47\112

</td>

<td style="text-align: ~~center~~;">503.571

<td style="text-align: left;">503.571

</td>

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

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</td>

<td style="text-align: ~~center~~;">503.226

<td style="text-align: left;">503.226

</td>

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

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<td style="text-align: center;">44\105

</td>

<td style="text-align: ~~center~~;">502.857

<td style="text-align: left;">502.857

</td>

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

Line 545:

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</td>

<td style="text-align: ~~center~~;">502.703

<td style="text-align: left;">502.703

</td>

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

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<td style="text-align: center;">49\117

</td>

<td style="text-align: ~~center~~;">502.564

<td style="text-align: left;">502.564

</td>

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</td>

<td style="text-align: ~~center~~;">502.326

<td style="text-align: left;">502.326

</td>

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

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<td style="text-align: center;">41\98

</td>

<td style="text-align: ~~center~~;">502.041

<td style="text-align: left;">502.041

</td>

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</td>

<td style="text-align: ~~center~~;">501.818

<td style="text-align: left;">501.818

</td>

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<td style="text-align: center;">28\67

</td>

<td style="text-align: ~~center~~;">501.493

<td style="text-align: left;">501.493

</td>

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</td>

<td style="text-align: ~~center~~;">500.000

<td style="text-align: left;">500.000

</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>2012-10-15 15:46:51 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-10-15 15:52:45 UTC</tt>.<br>
-: The original revision id was <tt>373262730</tt>.<br>
+: The original revision id was <tt>373264978</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 9: / Line 9: @@
 The meantone chromatic scale is [[Rothenberg propriety|proper]].
-||||||||||~ Generator ||~   ||~ in cents ||~ Comments ||
+||||||||||||~ Generator ||~ in cents ||~ Comments ||
-||= 3\7 ||=   ||=   ||=   ||=   ||=   ||= 514.286 ||=   ||
+||= 3\7 ||=   ||=   ||=   ||=   ||=   ||&lt; 514.286 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= 20\47 ||= 510.638 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 20\47 ||&lt; 510.638 ||=   ||
-||=   ||=   ||=   ||=   ||= 17\40 ||=   ||= 510.000 ||=   ||
+||=   ||=   ||=   ||=   ||= 17\40 ||=   ||&lt; 510.000 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= 31\73 ||= 509.589 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 31\73 ||&lt; 509.589 ||=   ||
-||=   ||=   ||=   ||= 14\33 ||=   ||=   ||= 509.091 ||=   ||
+||=   ||=   ||=   ||= 14\33 ||=   ||=   ||&lt; 509.091 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= 39\92 ||= 508.696 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 39\92 ||&lt; 508.696 ||=   ||
-||=   ||=   ||=   ||=   ||= 25\59 ||=   ||= 508.475 ||=   ||
+||=   ||=   ||=   ||=   ||= 25\59 ||=   ||&lt; 508.475 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= 36\85 ||= 508.235 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 36\85 ||&lt; 508.235 ||=   ||
-||=   ||=   ||= 11\26 ||=   ||=   ||=   ||= 507.692 ||=   ||
+||=   ||=   ||= 11\26 ||=   ||=   ||=   ||&lt; 507.692 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= 41\97 ||= 507.216 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 41\97 ||&lt; 507.216 ||=   ||
-||=   ||=   ||=   ||=   ||= 30\71 ||=   ||= 507.042 ||= Flattone ||
+||=   ||=   ||=   ||=   ||= 30\71 ||=   ||&lt; 507.042 ||= Flattone ||
-||=   ||=   ||=   ||=   ||=   ||= 49\116 ||= 506.897 ||= Flattone ||
+||=   ||=   ||=   ||=   ||=   ||= 49\116 ||&lt; 506.897 ||= Flattone ||
-||=   ||=   ||=   ||= 19\45 ||=   ||=   ||= 506.667 ||= Flattone ||
+||=   ||=   ||=   ||= 19\45 ||=   ||=   ||&lt; 506.667 ||= Flattone ||
-||=   ||=   ||=   ||=   ||=   ||= 46\109 ||= 506.422 ||= Flattone ||
+||=   ||=   ||=   ||=   ||=   ||= 46\109 ||&lt; 506.422 ||= Flattone ||
-||=   ||=   ||=   ||=   ||= 27\64 ||=   ||= 506.250 ||= Flattone ||
+||=   ||=   ||=   ||=   ||= 27\64 ||=   ||&lt; 506.250 ||= Flattone ||
-||=   ||=   ||=   ||=   ||=   ||= 35\83 ||= 506.024 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 35\83 ||&lt; 506.024 ||=   ||
-||=   ||= 8\19 ||=   ||=   ||=   ||=   ||= 505.263 ||= Boundary of propriety: generators
+||=   ||= 8\19 ||=   ||=   ||=   ||=   ||&lt; 505.263 ||= Boundary of propriety: generators
 smaller than this are proper.
 Meanenneadecal ||
-||=   ||=   ||=   ||=   ||=   ||= 37\88 ||= 504.545 ||= LucyTuning ||
+||=   ||=   ||=   ||=   ||=   ||= 37\88 ||&lt; 504.545 ||= LucyTuning ||
-||=   ||=   ||=   ||=   ||= 29\69 ||=   ||= 504.348 ||=   ||
+||=   ||=   ||=   ||=   ||= 29\69 ||=   ||&lt; 504.348 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= 50\119 ||= 504.202 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 50\119 ||&lt; 504.202 ||=   ||
-||=   ||=   ||=   ||= 21\50 ||=   ||=   ||= 504.000 ||= Meantone/Meanpop ||
+||=   ||=   ||=   ||= 21\50 ||=   ||=   ||&lt; 504.000 ||= Meantone/Meanpop ||
-||=   ||=   ||=   ||=   ||=   ||= 55\131 ||= 503.817 ||= Golden meantone ||
+||=   ||=   ||=   ||=   ||=   ||= 55\131 ||&lt; 503.817 ||= Golden meantone ||
-||=   ||=   ||=   ||=   ||= 34\81 ||=   ||= 503.704 ||= Optimal meantone is around here ||
+||=   ||=   ||=   ||=   ||= 34\81 ||=   ||&lt; 503.704 ||= Optimal meantone is around here ||
-||=   ||=   ||=   ||=   ||=   ||= 47\112 ||= 503.571 ||= Meantone/Meanpop ||
+||=   ||=   ||=   ||=   ||=   ||= 47\112 ||&lt; 503.571 ||= Meantone/Meanpop ||
-||=   ||=   ||= 13\31 ||=   ||=   ||=   ||= 503.226 ||= Optimal rank range (L/s=3/2) ||
+||=   ||=   ||= 13\31 ||=   ||=   ||=   ||&lt; 503.226 ||= Optimal rank range (L/s=3/2) ||
-||=   ||=   ||=   ||=   ||=   ||= 44\105 ||= 502.857 ||= Meantone/Huygens ||
+||=   ||=   ||=   ||=   ||=   ||= 44\105 ||&lt; 502.857 ||= Meantone/Huygens ||
-||=   ||=   ||=   ||=   ||= 31\74 ||=   ||= 502.703 ||= Meantone/Huygens ||
+||=   ||=   ||=   ||=   ||= 31\74 ||=   ||&lt; 502.703 ||= Meantone/Huygens ||
-||=   ||=   ||=   ||=   ||=   ||= 49\117 ||= 502.564 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 49\117 ||&lt; 502.564 ||=   ||
-||=   ||=   ||=   ||= 18\43 ||=   ||=   ||= 502.326 ||= Meantone/Meridetone ||
+||=   ||=   ||=   ||= 18\43 ||=   ||=   ||&lt; 502.326 ||= Meantone/Meridetone ||
-||=   ||=   ||=   ||=   ||=   ||= 41\98 ||= 502.041 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 41\98 ||&lt; 502.041 ||=   ||
-||=   ||=   ||=   ||=   ||= 23\55 ||=   ||= 501.818 ||=   ||
+||=   ||=   ||=   ||=   ||= 23\55 ||=   ||&lt; 501.818 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= 28\67 ||= 501.493 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 28\67 ||&lt; 501.493 ||=   ||
-||= 5\12 ||=   ||=   ||=   ||=   ||=   ||= 500.000 ||=   ||</pre></div>
+||= 5\12 ||=   ||=   ||=   ||=   ||=   ||&lt; 500.000 ||=   ||</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 53: / Line 53: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;th colspan="5"&gt;Generator&lt;br /&gt;
+         &lt;th colspan="6"&gt;Generator&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;in cents&lt;br /&gt;
@@ Line 75: / Line 73: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;514.286&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;514.286&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 93: / Line 91: @@
          &lt;td style="text-align: center;"&gt;20\47&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;510.638&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;510.638&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 111: / Line 109: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;510.000&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;510.000&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 129: / Line 127: @@
          &lt;td style="text-align: center;"&gt;31\73&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;509.589&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;509.589&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 147: / Line 145: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;509.091&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;509.091&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 165: / Line 163: @@
          &lt;td style="text-align: center;"&gt;39\92&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;508.696&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;508.696&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 183: / Line 181: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;508.475&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;508.475&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 201: / Line 199: @@
          &lt;td style="text-align: center;"&gt;36\85&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;508.235&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;508.235&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 219: / Line 217: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;507.692&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;507.692&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 237: / Line 235: @@
          &lt;td style="text-align: center;"&gt;41\97&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;507.216&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;507.216&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 255: / Line 253: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;507.042&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;507.042&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Flattone&lt;br /&gt;
@@ Line 273: / Line 271: @@
          &lt;td style="text-align: center;"&gt;49\116&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;506.897&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;506.897&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Flattone&lt;br /&gt;
@@ Line 291: / Line 289: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;506.667&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;506.667&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Flattone&lt;br /&gt;
@@ Line 309: / Line 307: @@
          &lt;td style="text-align: center;"&gt;46\109&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;506.422&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;506.422&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Flattone&lt;br /&gt;
@@ Line 327: / Line 325: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;506.250&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;506.250&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Flattone&lt;br /&gt;
@@ Line 345: / Line 343: @@
          &lt;td style="text-align: center;"&gt;35\83&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;506.024&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;506.024&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 363: / Line 361: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;505.263&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;505.263&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Boundary of propriety: generators&lt;br /&gt;
@@ Line 383: / Line 381: @@
          &lt;td style="text-align: center;"&gt;37\88&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;504.545&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;504.545&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;LucyTuning&lt;br /&gt;
@@ Line 401: / Line 399: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;504.348&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;504.348&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 419: / Line 417: @@
          &lt;td style="text-align: center;"&gt;50\119&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;504.202&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;504.202&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 437: / Line 435: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;504.000&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;504.000&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Meantone/Meanpop&lt;br /&gt;
@@ Line 455: / Line 453: @@
          &lt;td style="text-align: center;"&gt;55\131&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;503.817&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;503.817&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Golden meantone&lt;br /&gt;
@@ Line 473: / Line 471: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;503.704&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;503.704&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Optimal meantone is around here&lt;br /&gt;
@@ Line 491: / Line 489: @@
          &lt;td style="text-align: center;"&gt;47\112&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;503.571&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;503.571&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Meantone/Meanpop&lt;br /&gt;
@@ Line 509: / Line 507: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;503.226&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;503.226&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Optimal rank range (L/s=3/2)&lt;br /&gt;
@@ Line 527: / Line 525: @@
          &lt;td style="text-align: center;"&gt;44\105&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;502.857&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;502.857&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Meantone/Huygens&lt;br /&gt;
@@ Line 545: / Line 543: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;502.703&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;502.703&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Meantone/Huygens&lt;br /&gt;
@@ Line 563: / Line 561: @@
          &lt;td style="text-align: center;"&gt;49\117&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;502.564&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;502.564&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 581: / Line 579: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;502.326&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;502.326&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Meantone/Meridetone&lt;br /&gt;
@@ Line 599: / Line 597: @@
          &lt;td style="text-align: center;"&gt;41\98&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;502.041&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;502.041&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 617: / Line 615: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;501.818&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;501.818&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 635: / Line 633: @@
          &lt;td style="text-align: center;"&gt;28\67&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;501.493&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;501.493&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 653: / Line 651: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;500.000&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;500.000&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;