5L 7s: Difference between revisions

Line 1:

<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~~:34:55 UTC</tt>.

: This revision was by author [[User:guest|guest]] and made on <tt>2011-08-29 04:36:49 UTC</tt>.

: The original revision id was <tt>~~228069886~~</tt>.

: The original revision id was <tt>249051197</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 Pythagorean/schismatic version is proper, but the superpyth version is improper (it doesn't become proper until you add 5 more notes to form the superpyth "enharmonic" scale, superpyth[17]).

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

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

||= 5\12 ||= ||= ||= ||= ||= 500.000 ||= ||

||= 5\12 ||= ||= ||= ||= || ||= 500.000 ||= ||

||= ||= ||= ||= ||= 22\53 ||= 498.113 ||= Pythagorean/Helmholtz/Garibaldi

||= ||= ||= ||= ||= 22\53 || ||= 498.113 ||= Pythagorean/Helmholtz/Garibaldi

is around here ||

||= ||= ||= ||= 17\41 ||= ||= 497.591 ||= ||

||= ||= ||= ||= 17\41 ||= || ||= 497.591 ||= ||

||= ||= ||= ||= ||= 29\70 ||= 497.143 ||= ||

||= ||= ||= ||= ||= 29\70 || ||= 497.143 ||= ||

||= ||= ||= 12\29 ||= ||= ||= 496.552 ||= ||

||= ||= ||= 12\29 ||= ||= || ||= 496.552 ||= Optimum rank range (L/s=3/2) ||

||= ||= ||= ||= ||= 31\75 ||= 496.000 ||= ||

||= ||= ||= ||= ||= 31\75 || ||= 496.000 ||= ||

||= ||= ||= ||= 19\46 ||= ||= 495.652 ||= ||

|| || || || || || 50\121 || 495.868 ||= Golden leapday (a.k.a. "[[Peppermint-24|Peppermint]]") ||

||= ||= ||= ||= ||= 26\63 ||= 495.238 ||= ||

||= ||= ||= ||= 19\46 ||= || ||= 495.652 ||= ||

||= ||= 7\17 ||= ||= ||= ||= 494.118 ||= Boundary of propriety (generators

||= ||= ||= ||= ||= 26\63 || ||= 495.238 ||= ||

||= ||= 7\17 ||= ||= ||= || ||= 494.118 ||= Boundary of propriety (generators

larger than this are proper) ||

||= ||= ||= ||= ||= 23\56 ||= 492.857 ||= ||

||= ||= ||= ||= ||= 23\56 || ||= 492.857 ||= ||

||= ||= ||= ||= 16\39 ||= ||= 492.308 ||= ||

||= ||= ||= ||= 16\39 ||= || ||= 492.308 ||= ||

||= ||= ||= ||= ||= 25\61 ||= 491.803 ||= ||

||= ||= ||= ||= ||= 25\61 || ||= 491.803 ||= ||

||= ||= ||= 9\22 ||= ||= ||= 490.909 ||= Superpyth is in this region ||

||= ||= ||= 9\22 ||= ||= || ||= 490.909 ||= Superpyth is in this region ||

||= ||= ||= ||= ||= 20\49 ||= 489.796 ||= ||

||= ||= ||= ||= ||= 20\49 || ||= 489.796 ||= ||

||= ||= ||= ||= 11\27 ||= ||= 488.889 ||= ||

||= ||= ||= ||= 11\27 ||= || ||= 488.889 ||= ||

||= ||= ||= ||= ||= 13\32 ||= 487.500 ||= ||

||= ||= ||= ||= ||= 13\32 || ||= 487.500 ||= ||

||= 2\5 ||= ||= ||= ||= ||= 480.000 ||= ||</pre></div>

||= 2\5 ||= ||= ||= ||= || ||= 480.000 ||= ||</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>5L 7s</title></head><body>This is the MOS pattern of the Pythagorean/<a class="wiki_link" href="/Schismatic%20family">schismatic/Helmholtz/Garibaldi</a> chromatic scale, and also the <a class="wiki_link" href="/Archytas%20clan">superpyth</a> chromatic scale. In contrast to the <a class="wiki_link" href="/7L%205s">meantone chromatic scale</a>, in which &quot;diatonic&quot; semitones are larger than &quot;chromatic&quot; semitones, here the reverse is true: diatonic semitones are smaller than chromatic semitones, so the <a class="wiki_link" href="/5L%202s">diatonic scale</a> subset is actually <a class="wiki_link" href="/Rothenberg%20propriety">improper</a>.

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<tr>

<th colspan="5">Generator

<th colspan="6">Generator

</th>

<th>in cents

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</td>

</td>

<td>

</td>

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

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</td>

<td style="text-align: center;">22\53

</td>

<td>

</td>

<td style="text-align: center;">498.113

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</td>

</td>

<td>

</td>

<td style="text-align: center;">497.591

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</td>

<td style="text-align: center;">29\70

</td>

<td>

</td>

<td style="text-align: center;">497.143

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</td>

</td>

<td>

</td>

<td style="text-align: center;">496.552

</td>

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

</td>

</tr>

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</td>

<td style="text-align: center;">31\75

</td>

<td>

</td>

<td style="text-align: center;">496.000

</td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>50\121

</td>

<td>495.868

</td>

<td style="text-align: center;">Golden leapday (a.k.a. &quot;<a class="wiki_link" href="/Peppermint-24">Peppermint</a>&quot;)

</td>

</tr>

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</td>

</td>

<td>

</td>

<td style="text-align: center;">495.652

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</td>

<td style="text-align: center;">26\63

</td>

<td>

</td>

<td style="text-align: center;">495.238

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</td>

</td>

<td>

</td>

<td style="text-align: center;">494.118

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</td>

<td style="text-align: center;">23\56

</td>

<td>

</td>

<td style="text-align: center;">492.857

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</td>

</td>

<td>

</td>

<td style="text-align: center;">492.308

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</td>

<td style="text-align: center;">25\61

</td>

<td>

</td>

<td style="text-align: center;">491.803

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</td>

</td>

<td>

</td>

<td style="text-align: center;">490.909

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</td>

<td style="text-align: center;">20\49

</td>

<td>

</td>

<td style="text-align: center;">489.796

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</td>

</td>

<td>

</td>

<td style="text-align: center;">488.889

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</td>

<td style="text-align: center;">13\32

</td>

<td>

</td>

<td style="text-align: center;">487.500

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</td>

</td>

<td>

</td>

<td style="text-align: center;">480.000

@@ 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 21:34:55 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2011-08-29 04:36:49 UTC</tt>.<br>
-: The original revision id was <tt>228069886</tt>.<br>
+: The original revision id was <tt>249051197</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: @@
 The Pythagorean/schismatic version is proper, but the superpyth version is improper (it doesn't become proper until you add 5 more notes to form the superpyth "enharmonic" scale, superpyth[17]).
-||||||||||~ Generator ||~ in cents ||~ Comments ||
+||||||||||||~ Generator ||~ in cents ||~ Comments ||
-||= 5\12 ||=   ||=   ||=   ||=   ||= 500.000 ||=   ||
+||= 5\12 ||=   ||=   ||=   ||=   ||   ||= 500.000 ||=   ||
-||=   ||=   ||=   ||=   ||= 22\53 ||= 498.113 ||= Pythagorean/Helmholtz/Garibaldi
+||=   ||=   ||=   ||=   ||= 22\53 ||   ||= 498.113 ||= Pythagorean/Helmholtz/Garibaldi
 is around here ||
-||=   ||=   ||=   ||= 17\41 ||=   ||= 497.591 ||=   ||
+||=   ||=   ||=   ||= 17\41 ||=   ||   ||= 497.591 ||=   ||
-||=   ||=   ||=   ||=   ||= 29\70 ||= 497.143 ||=   ||
+||=   ||=   ||=   ||=   ||= 29\70 ||   ||= 497.143 ||=   ||
-||=   ||=   ||= 12\29 ||=   ||=   ||= 496.552 ||=   ||
+||=   ||=   ||= 12\29 ||=   ||=   ||   ||= 496.552 ||= Optimum rank range (L/s=3/2) ||
-||=   ||=   ||=   ||=   ||= 31\75 ||= 496.000 ||=   ||
+||=   ||=   ||=   ||=   ||= 31\75 ||   ||= 496.000 ||=   ||
-||=   ||=   ||=   ||= 19\46 ||=   ||= 495.652 ||=   ||
+||   ||   ||   ||   ||   || 50\121 || 495.868 ||= Golden leapday (a.k.a. "[[Peppermint-24|Peppermint]]") ||
-||=   ||=   ||=   ||=   ||= 26\63 ||= 495.238 ||=   ||
+||=   ||=   ||=   ||= 19\46 ||=   ||   ||= 495.652 ||=   ||
-||=   ||= 7\17 ||=   ||=   ||=   ||= 494.118 ||= Boundary of propriety (generators
+||=   ||=   ||=   ||=   ||= 26\63 ||   ||= 495.238 ||=   ||
+||=   ||= 7\17 ||=   ||=   ||=   ||   ||= 494.118 ||= Boundary of propriety (generators
 larger than this are proper) ||
-||=   ||=   ||=   ||=   ||= 23\56 ||= 492.857 ||=   ||
+||=   ||=   ||=   ||=   ||= 23\56 ||   ||= 492.857 ||=   ||
-||=   ||=   ||=   ||= 16\39 ||=   ||= 492.308 ||=   ||
+||=   ||=   ||=   ||= 16\39 ||=   ||   ||= 492.308 ||=   ||
-||=   ||=   ||=   ||=   ||= 25\61 ||= 491.803 ||=   ||
+||=   ||=   ||=   ||=   ||= 25\61 ||   ||= 491.803 ||=   ||
-||=   ||=   ||= 9\22 ||=   ||=   ||= 490.909 ||= Superpyth is in this region ||
+||=   ||=   ||= 9\22 ||=   ||=   ||   ||= 490.909 ||= Superpyth is in this region ||
-||=   ||=   ||=   ||=   ||= 20\49 ||= 489.796 ||=   ||
+||=   ||=   ||=   ||=   ||= 20\49 ||   ||= 489.796 ||=   ||
-||=   ||=   ||=   ||= 11\27 ||=   ||= 488.889 ||=   ||
+||=   ||=   ||=   ||= 11\27 ||=   ||   ||= 488.889 ||=   ||
-||=   ||=   ||=   ||=   ||= 13\32 ||= 487.500 ||=   ||
+||=   ||=   ||=   ||=   ||= 13\32 ||   ||= 487.500 ||=   ||
-||= 2\5 ||=   ||=   ||=   ||=   ||= 480.000 ||=   ||</pre></div>
+||= 2\5 ||=   ||=   ||=   ||=   ||   ||= 480.000 ||=   ||</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;5L 7s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This is the MOS pattern of the Pythagorean/&lt;a class="wiki_link" href="/Schismatic%20family"&gt;schismatic/Helmholtz/Garibaldi&lt;/a&gt; chromatic scale, and also the &lt;a class="wiki_link" href="/Archytas%20clan"&gt;superpyth&lt;/a&gt; chromatic scale. In contrast to the &lt;a class="wiki_link" href="/7L%205s"&gt;meantone chromatic scale&lt;/a&gt;, in which &amp;quot;diatonic&amp;quot; semitones are larger than &amp;quot;chromatic&amp;quot; semitones, here the reverse is true: diatonic semitones are smaller than chromatic semitones, so the &lt;a class="wiki_link" href="/5L%202s"&gt;diatonic scale&lt;/a&gt; subset is actually &lt;a class="wiki_link" href="/Rothenberg%20propriety"&gt;improper&lt;/a&gt;.&lt;br /&gt;
@@ Line 43: / Line 44: @@
 &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;in cents&lt;br /&gt;
@@ Line 60: / Line 61: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;500.000&lt;br /&gt;
@@ Line 76: / Line 79: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;22\53&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;498.113&lt;br /&gt;
@@ Line 93: / Line 98: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;497.591&lt;br /&gt;
@@ Line 109: / Line 116: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;29\70&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;497.143&lt;br /&gt;
@@ Line 125: / Line 134: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;496.552&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Optimum rank range (L/s=3/2)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 141: / Line 152: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;31\75&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;496.000&lt;br /&gt;
 &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;50\121&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;495.868&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Golden leapday (a.k.a. &amp;quot;&lt;a class="wiki_link" href="/Peppermint-24"&gt;Peppermint&lt;/a&gt;&amp;quot;)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 157: / Line 188: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;495.652&lt;br /&gt;
@@ Line 173: / Line 206: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;26\63&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;495.238&lt;br /&gt;
@@ Line 189: / Line 224: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;494.118&lt;br /&gt;
@@ Line 206: / Line 243: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;23\56&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;492.857&lt;br /&gt;
@@ Line 222: / Line 261: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;492.308&lt;br /&gt;
@@ Line 238: / Line 279: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;25\61&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;491.803&lt;br /&gt;
@@ Line 254: / Line 297: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;490.909&lt;br /&gt;
@@ Line 270: / Line 315: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;20\49&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;489.796&lt;br /&gt;
@@ Line 286: / Line 333: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;488.889&lt;br /&gt;
@@ Line 302: / Line 351: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;13\32&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;487.500&lt;br /&gt;
@@ Line 318: / Line 369: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;480.000&lt;br /&gt;