7L 5s: Difference between revisions

Revision as of 04:29, 29 August 2011

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author guest and made on 2011-08-29 04:29:49 UTC.

The original revision id was 249050661.

The revision comment was:

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

Original Wikitext content:

This is the MOS pattern of the [[Meantone family|meantone]] chromatic scale, which is the only notable harmonic entropy minimum in this range of possible scales. In meantone, "diatonic" semitones (~16/15), such as appear in the [[5L 2s|diatonic scale]], for example B-C, are larger than "chromatic" semitones (~25/24), the intervals by which flats and sharps alter pitches.

The meantone chromatic scale is [[Rothenberg propriety|proper]].
||||||||||~ Generator ||~   ||~ in cents ||~ Comments ||
||= 3\7 ||=   ||=   ||=   ||=   ||   ||= 514.286 ||=   ||
||=   ||=   ||=   ||=   ||= 17\40 ||   ||= 510.000 ||=   ||
||=   ||=   ||=   ||= 14\33 ||=   ||   ||= 509.091 ||=   ||
||=   ||=   ||=   ||=   ||= 25\59 ||   ||= 508.475 ||=   ||
||=   ||=   ||= 11\26 ||=   ||=   ||   ||= 507.692 ||=   ||
||=   ||=   ||=   ||=   ||= 30\71 ||   ||= 507.042 ||=   ||
||=   ||=   ||=   ||= 19\45 ||=   ||   ||= 506.667 ||=   ||
||=   ||=   ||=   ||=   ||= 27\64 ||   ||= 506.250 ||=   ||
||=   ||= 8\19 ||=   ||=   ||=   ||   ||= 506.263 ||= Boundary of propriety: generators
smaller than this are proper ||
||=   ||=   ||=   ||=   ||= 29\69 ||   ||= 504.348 ||=   ||
||=   ||=   ||=   ||= 21\50 ||=   ||   ||= 504.000 ||=   ||
||   ||   ||   ||   ||   || 55\131 || 503.817 ||= Golden meantone ||
||=   ||=   ||=   ||=   ||= 34\81 ||   ||= 503.704 ||= Optimal meantone is around here ||
||=   ||=   ||= 13\31 ||=   ||=   ||   ||= 503.226 ||= Optimal rank range (L/s=3/2) ||
||=   ||=   ||=   ||=   ||= 31\74 ||   ||= 502.703 ||=   ||
||=   ||=   ||=   ||= 18\43 ||=   ||   ||= 502.326 ||=   ||
||=   ||=   ||=   ||=   ||= 23\55 ||   ||= 501.818 ||=   ||
||= 5\12 ||=   ||=   ||=   ||=   ||   ||= 500.000 ||=   ||

Original HTML content:

<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.<br />
<br />
The meantone chromatic scale is <a class="wiki_link" href="/Rothenberg%20propriety">proper</a>.<br />


<table class="wiki_table">
    <tr>
        <th colspan="5">Generator<br />
</th>
        <th><br />
</th>
        <th>in cents<br />
</th>
        <th>Comments<br />
</th>
    </tr>
    <tr>
        <td style="text-align: center;">3\7<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">514.286<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">17\40<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">510.000<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">14\33<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">509.091<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">25\59<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">508.475<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">11\26<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">507.692<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">30\71<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">507.042<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">19\45<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">506.667<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">27\64<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">506.250<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">8\19<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">506.263<br />
</td>
        <td style="text-align: center;">Boundary of propriety: generators<br />
smaller than this are proper<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">29\69<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">504.348<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">21\50<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">504.000<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>55\131<br />
</td>
        <td>503.817<br />
</td>
        <td style="text-align: center;">Golden meantone<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">34\81<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">503.704<br />
</td>
        <td style="text-align: center;">Optimal meantone is around here<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">13\31<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">503.226<br />
</td>
        <td style="text-align: center;">Optimal rank range (L/s=3/2)<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">31\74<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">502.703<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">18\43<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">502.326<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">23\55<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">501.818<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">5\12<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">500.000<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

</body></html>

@@ 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 21:24:11 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2011-08-29 04:29:49 UTC</tt>.<br>
-: The original revision id was <tt>228067634</tt>.<br>
+: The original revision id was <tt>249050661</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 ||=   ||=   ||=   ||=   ||   ||= 514.286 ||=   ||
-||=   ||=   ||=   ||=   ||= 17\40 ||= 510.000 ||=   ||
+||=   ||=   ||=   ||=   ||= 17\40 ||   ||= 510.000 ||=   ||
-||=   ||=   ||=   ||= 14\33 ||=   ||= 509.091 ||=   ||
+||=   ||=   ||=   ||= 14\33 ||=   ||   ||= 509.091 ||=   ||
-||=   ||=   ||=   ||=   ||= 25\59 ||= 508.475 ||=   ||
+||=   ||=   ||=   ||=   ||= 25\59 ||   ||= 508.475 ||=   ||
-||=   ||=   ||= 11\26 ||=   ||=   ||= 507.692 ||=   ||
+||=   ||=   ||= 11\26 ||=   ||=   ||   ||= 507.692 ||=   ||
-||=   ||=   ||=   ||=   ||= 30\71 ||= 507.042 ||=   ||
+||=   ||=   ||=   ||=   ||= 30\71 ||   ||= 507.042 ||=   ||
-||=   ||=   ||=   ||= 19\45 ||=   ||= 506.667 ||=   ||
+||=   ||=   ||=   ||= 19\45 ||=   ||   ||= 506.667 ||=   ||
-||=   ||=   ||=   ||=   ||= 27\64 ||= 506.250 ||=   ||
+||=   ||=   ||=   ||=   ||= 27\64 ||   ||= 506.250 ||=   ||
-||=   ||= 8\19 ||=   ||=   ||=   ||= 506.263 ||= Boundary of propriety: generators
+||=   ||= 8\19 ||=   ||=   ||=   ||   ||= 506.263 ||= Boundary of propriety: generators
 smaller than this are proper ||
-||=   ||=   ||=   ||=   ||= 29\69 ||= 504.348 ||=   ||
+||=   ||=   ||=   ||=   ||= 29\69 ||   ||= 504.348 ||=   ||
-||=   ||=   ||=   ||= 21\50 ||=   ||= 504.000 ||=   ||
+||=   ||=   ||=   ||= 21\50 ||=   ||   ||= 504.000 ||=   ||
-||=   ||=   ||=   ||=   ||= 34\81 ||= 503.704 ||= Optimal meantone is around here ||
+||   ||   ||   ||   ||   || 55\131 || 503.817 ||= Golden meantone ||
-||=   ||=   ||= 13\31 ||=   ||=   ||= 503.226 ||=   ||
+||=   ||=   ||=   ||=   ||= 34\81 ||   ||= 503.704 ||= Optimal meantone is around here ||
-||=   ||=   ||=   ||=   ||= 31\74 ||= 502.703 ||=   ||
+||=   ||=   ||= 13\31 ||=   ||=   ||   ||= 503.226 ||= Optimal rank range (L/s=3/2) ||
-||=   ||=   ||=   ||= 18\43 ||=   ||= 502.326 ||=   ||
+||=   ||=   ||=   ||=   ||= 31\74 ||   ||= 502.703 ||=   ||
-||=   ||=   ||=   ||=   ||= 23\55 ||= 501.818 ||=   ||
+||=   ||=   ||=   ||= 18\43 ||=   ||   ||= 502.326 ||=   ||
-||= 5\12 ||=   ||=   ||=   ||=   ||= 500.000 ||=   ||</pre></div>
+||=   ||=   ||=   ||=   ||= 23\55 ||   ||= 501.818 ||=   ||
+||= 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 37: / Line 38: @@
      &lt;tr&gt;
          &lt;th colspan="5"&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 53: / Line 56: @@
 &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;514.286&lt;br /&gt;
@@ Line 69: / Line 74: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;17\40&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;510.000&lt;br /&gt;
@@ Line 85: / Line 92: @@
 &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;509.091&lt;br /&gt;
@@ Line 101: / Line 110: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;25\59&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;508.475&lt;br /&gt;
@@ Line 117: / Line 128: @@
 &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;507.692&lt;br /&gt;
@@ Line 133: / Line 146: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;30\71&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;507.042&lt;br /&gt;
@@ Line 149: / Line 164: @@
 &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;506.667&lt;br /&gt;
@@ Line 165: / Line 182: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;27\64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;506.250&lt;br /&gt;
@@ Line 181: / Line 200: @@
 &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;506.263&lt;br /&gt;
@@ Line 198: / Line 219: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;29\69&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;504.348&lt;br /&gt;
@@ Line 214: / Line 237: @@
 &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;504.000&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;55\131&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;503.817&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Golden meantone&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 230: / Line 273: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;34\81&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;503.704&lt;br /&gt;
@@ Line 246: / Line 291: @@
 &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;503.226&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Optimal rank range (L/s=3/2)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 262: / Line 309: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;31\74&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;502.703&lt;br /&gt;
@@ Line 278: / Line 327: @@
 &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;502.326&lt;br /&gt;
@@ Line 294: / Line 345: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;23\55&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;501.818&lt;br /&gt;
@@ Line 310: / Line 363: @@
 &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;

7L 5s: Difference between revisions

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