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>2011-05-12 21:21:42 UTC</tt>.

: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-05-12 21:24:11 UTC</tt>.

: The original revision id was <tt>~~228067080~~</tt>.

: The original revision id was <tt>228067634</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 ~~||~ scale in steps of an [[edo]]~~ ||~ Comments ||

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

||= 3\7 ||= ||= ||= ||= ||= 514.286 ~~||= 1 1 1 1 1 1 1~~ ||= ||

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

||= ||= ||= ||= ||= 17\40 ||= 510.000 ~~||= 6 6 5 6 6 6 5~~ ||= ||

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

||= ||= ||= ||= 14\33 ||= ||= 509.091 ~~||= 5 5 4 5 5 5 4~~ ||= ||

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

||= ||= ||= ||= ||= 25\59 ||= 508.475 ~~||= 9 9 7 9 9 9 7~~ ||= ||

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

||= ||= ||= 11\26 ||= ||= ||= 507.692 ~~||= 4 4 3 4 4 4 3~~ ||= ||

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

||= ||= ||= ||= ||= 30\71 ||= 507.042 ~~||= 11 11 8 11 11 11 8~~ ||= ||

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

||= ||= ||= ||= 19\45 ||= ||= 506.667 ~~||= 7 7 5 7 7 7 5~~ ||= ||

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

||= ||= ||= ||= ||= 27\64 ||= 506.250 ~~||= 10 10 7 10 10 10 7~~ ||= ||

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

||= ||= 8\19 ||= ||= ||= ||= 506.263 ~~||= 3 3 2 3 3 3 2~~ ||= Boundary of propriety: generators

||= ||= 8\19 ||= ||= ||= ||= 506.263 ||= Boundary of propriety: generators

smaller than this are proper ||

||= ||= ||= ||= ||= 29\69 ||= 504.348 ~~||= 11 11 7 11 11 11 7~~ ||= ||

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

||= ||= ||= ||= 21\50 ||= ||= 504.000 ~~||= 8 8 5 8 8 8 5~~ ||= ||

||= ||= ||= ||= 21\50 ||= ||= 504.000 ||= ||

||= ||= ||= ||= ||= 34\81 ||= 503.704 ~~||= 13 13 8 13 13 13 8~~ ||= Optimal meantone is around here ||

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

||= ||= ||= 13\31 ||= ||= ||= 503.226 ~~||= 5 5 3 5 5 5 3~~ ||= ||

||= ||= ||= 13\31 ||= ||= ||= 503.226 ||= ||

||= ||= ||= ||= ||= 31\74 ||= 502.703 ~~||= 12 12 7 12 12 12 7~~ ||= ||

||= ||= ||= ||= ||= 31\74 ||= 502.703 ||= ||

||= ||= ||= ||= 18\43 ||= ||= 502.326 ~~||= 7 7 4 7 7 7 4~~ ||= ||

||= ||= ||= ||= 18\43 ||= ||= 502.326 ||= ||

||= ||= ||= ||= ||= 23\55 ||= 501.818 ~~||= 9 9 5 9 9 9 5~~ ||= ||

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

||= 5\12 ||= ||= ||= ||= ||= 500.000 ~~||= 2 2 1 2 2 2 1~~ ||= ||</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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</th>

<th>in cents

~~</th>~~

~~<th>scale in steps of an <a class="wiki_link" href="/edo">edo</a> ~~

</th>

<th>Comments

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</td>

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

~~</td>~~

~~<td style="text-align: center;">1 1 1 1 1 1 1 ~~

</td>

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</td>

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

~~</td>~~

~~<td style="text-align: center;">6 6 5 6 6 6 5 ~~

</td>

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</td>

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

~~</td>~~

~~<td style="text-align: center;">5 5 4 5 5 5 4 ~~

</td>

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</td>

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

~~</td>~~

~~<td style="text-align: center;">9 9 7 9 9 9 7 ~~

</td>

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</td>

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

~~</td>~~

~~<td style="text-align: center;">4 4 3 4 4 4 3 ~~

</td>

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</td>

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

~~</td>~~

~~<td style="text-align: center;">11 11 8 11 11 11 8 ~~

</td>

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</td>

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

~~</td>~~

~~<td style="text-align: center;">7 7 5 7 7 7 5 ~~

</td>

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</td>

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

~~</td>~~

~~<td style="text-align: center;">10 10 7 10 10 10 7 ~~

</td>

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</td>

<td style="text-align: center;">506.263

~~</td>~~

~~<td style="text-align: center;">3 3 2 3 3 3 2 ~~

</td>

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

Line 220:

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</td>

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

~~</td>~~

~~<td style="text-align: center;">11 11 7 11 11 11 7 ~~

</td>

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</td>

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

~~</td>~~

~~<td style="text-align: center;">8 8 5 8 8 8 5 ~~

</td>

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</td>

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

~~</td>~~

~~<td style="text-align: center;">13 13 8 13 13 13 8 ~~

</td>

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

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</td>

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

~~</td>~~

~~<td style="text-align: center;">5 5 3 5 5 5 3 ~~

</td>

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</td>

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

~~</td>~~

~~<td style="text-align: center;">12 12 7 12 12 12 7 ~~

</td>

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</td>

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

~~</td>~~

~~<td style="text-align: center;">7 7 4 7 7 7 4 ~~

</td>

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</td>

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

~~</td>~~

~~<td style="text-align: center;">9 9 5 9 9 9 5 ~~

</td>

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</td>

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

~~</td>~~

~~<td style="text-align: center;">2 2 1 2 2 2 1 ~~

</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>2011-05-12 21:21:42 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-05-12 21:24:11 UTC</tt>.<br>
-: The original revision id was <tt>228067080</tt>.<br>
+: The original revision id was <tt>228067634</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 ||~ scale in steps of an [[edo]] ||~ Comments ||
+||||||||||~ Generator ||~ in cents ||~ Comments ||
-||= 3\7 ||=   ||=   ||=   ||=   ||= 514.286 ||= 1 1 1 1 1 1 1 ||=   ||
+||= 3\7 ||=   ||=   ||=   ||=   ||= 514.286 ||=   ||
-||=   ||=   ||=   ||=   ||= 17\40 ||= 510.000 ||= 6 6 5 6 6 6 5 ||=   ||
+||=   ||=   ||=   ||=   ||= 17\40 ||= 510.000 ||=   ||
-||=   ||=   ||=   ||= 14\33 ||=   ||= 509.091 ||= 5 5 4 5 5 5 4 ||=   ||
+||=   ||=   ||=   ||= 14\33 ||=   ||= 509.091 ||=   ||
-||=   ||=   ||=   ||=   ||= 25\59 ||= 508.475 ||= 9 9 7 9 9 9 7 ||=   ||
+||=   ||=   ||=   ||=   ||= 25\59 ||= 508.475 ||=   ||
-||=   ||=   ||= 11\26 ||=   ||=   ||= 507.692 ||= 4 4 3 4 4 4 3 ||=   ||
+||=   ||=   ||= 11\26 ||=   ||=   ||= 507.692 ||=   ||
-||=   ||=   ||=   ||=   ||= 30\71 ||= 507.042 ||= 11 11 8 11 11 11 8 ||=   ||
+||=   ||=   ||=   ||=   ||= 30\71 ||= 507.042 ||=   ||
-||=   ||=   ||=   ||= 19\45 ||=   ||= 506.667 ||= 7 7 5 7 7 7 5 ||=   ||
+||=   ||=   ||=   ||= 19\45 ||=   ||= 506.667 ||=   ||
-||=   ||=   ||=   ||=   ||= 27\64 ||= 506.250 ||= 10 10 7 10 10 10 7 ||=   ||
+||=   ||=   ||=   ||=   ||= 27\64 ||= 506.250 ||=   ||
-||=   ||= 8\19 ||=   ||=   ||=   ||= 506.263 ||= 3 3 2 3 3 3 2 ||= Boundary of propriety: generators
+||=   ||= 8\19 ||=   ||=   ||=   ||= 506.263 ||= Boundary of propriety: generators
 smaller than this are proper ||
-||=   ||=   ||=   ||=   ||= 29\69 ||= 504.348 ||= 11 11 7 11 11 11 7 ||=   ||
+||=   ||=   ||=   ||=   ||= 29\69 ||= 504.348 ||=   ||
-||=   ||=   ||=   ||= 21\50 ||=   ||= 504.000 ||= 8 8 5 8 8 8 5 ||=   ||
+||=   ||=   ||=   ||= 21\50 ||=   ||= 504.000 ||=   ||
-||=   ||=   ||=   ||=   ||= 34\81 ||= 503.704 ||= 13 13 8 13 13 13 8 ||= Optimal meantone is around here ||
+||=   ||=   ||=   ||=   ||= 34\81 ||= 503.704 ||= Optimal meantone is around here ||
-||=   ||=   ||= 13\31 ||=   ||=   ||= 503.226 ||= 5 5 3 5 5 5 3 ||=   ||
+||=   ||=   ||= 13\31 ||=   ||=   ||= 503.226 ||=   ||
-||=   ||=   ||=   ||=   ||= 31\74 ||= 502.703 ||= 12 12 7 12 12 12 7 ||=   ||
+||=   ||=   ||=   ||=   ||= 31\74 ||= 502.703 ||=   ||
-||=   ||=   ||=   ||= 18\43 ||=   ||= 502.326 ||= 7 7 4 7 7 7 4 ||=   ||
+||=   ||=   ||=   ||= 18\43 ||=   ||= 502.326 ||=   ||
-||=   ||=   ||=   ||=   ||= 23\55 ||= 501.818 ||= 9 9 5 9 9 9 5 ||=   ||
+||=   ||=   ||=   ||=   ||= 23\55 ||= 501.818 ||=   ||
-||= 5\12 ||=   ||=   ||=   ||=   ||= 500.000 ||= 2 2 1 2 2 2 1 ||=   ||</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">&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 39: / Line 39: @@
 &lt;/th&gt;
          &lt;th&gt;in cents&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;scale in steps of an &lt;a class="wiki_link" href="/edo"&gt;edo&lt;/a&gt;&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;Comments&lt;br /&gt;
@@ Line 57: / Line 55: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;514.286&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;1 1 1 1 1 1 1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 75: / Line 71: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;510.000&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;6 6 5 6 6 6 5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 93: / Line 87: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;509.091&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;5 5 4 5 5 5 4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 111: / Line 103: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;508.475&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;9 9 7 9 9 9 7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 129: / Line 119: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;507.692&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;4 4 3 4 4 4 3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 147: / Line 135: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;507.042&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;11 11 8 11 11 11 8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 165: / Line 151: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;506.667&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;7 7 5 7 7 7 5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 183: / Line 167: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;506.250&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;10 10 7 10 10 10 7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 201: / Line 183: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;506.263&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;3 3 2 3 3 3 2&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Boundary of propriety: generators&lt;br /&gt;
@@ Line 220: / Line 200: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;504.348&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;11 11 7 11 11 11 7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 238: / Line 216: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;504.000&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;8 8 5 8 8 8 5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 256: / Line 232: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;503.704&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;13 13 8 13 13 13 8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Optimal meantone is around here&lt;br /&gt;
@@ Line 274: / Line 248: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;503.226&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;5 5 3 5 5 5 3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 292: / Line 264: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;502.703&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;12 12 7 12 12 12 7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 310: / Line 280: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;502.326&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;7 7 4 7 7 7 4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 328: / Line 296: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;501.818&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;9 9 5 9 9 9 5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 346: / Line 312: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;500.000&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;2 2 1 2 2 2 1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;