7L 5s: Difference between revisions

Revision as of 12:49, 15 October 2012

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author genewardsmith and made on 2012-10-15 12:49:16 UTC.

The original revision id was 373189022.

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 ||=   ||
||   ||   ||   ||   ||   || 20/47 || 510.638 ||   ||
||=   ||=   ||=   ||=   ||= 17\40 ||   ||= 510.000 ||=   ||
||   ||   ||   ||   ||   || 31/73 || 509.589 ||   ||
||=   ||=   ||=   ||= 14\33 ||=   ||   ||= 509.091 ||=   ||
||   ||   ||   ||   ||   || 39/92 || 508.696 ||   ||
||=   ||=   ||=   ||=   ||= 25\59 ||   ||= 508.475 ||=   ||
||   ||   ||   ||   ||   || 36/85 || 508.235 ||   ||
||=   ||=   ||= 11\26 ||=   ||=   ||   ||= 507.692 ||=   ||
||   ||   ||   ||   ||   || 41/97 || 507.216 ||   ||
||=   ||=   ||=   ||=   ||= 30\71 ||   ||= 507.042 ||=  Flattone ||
||   ||   ||   ||   ||   || 49/116 || 506.897 ||   ||
||=   ||=   ||=   ||= 19\45 ||=   ||   ||= 506.667 ||=  Flattone ||
||   ||   ||   ||   ||   || 46/109 || 506.422 ||   ||
||=   ||=   ||=   ||=   ||= 27\64 ||   ||= 506.250 ||=  Flattone ||
||   ||   ||   ||   ||   || 35/83 || 506.024 ||   ||
||=   ||= 8\19 ||=   ||=   ||=   ||   ||= 505.263 ||= Boundary of propriety: generators
smaller than this are proper ||
||   ||   ||   ||   ||   || 37/88 || 504.545 ||= LucyTuning ||
||=   ||=   ||=   ||=   ||= 29\69 ||   ||= 504.348 ||=   ||
||   ||   ||   ||   ||   || 50/119 || 504.202 ||   ||
||=   ||=   ||=   ||= 21\50 ||=   ||   ||= 504.000 ||=   ||
||   ||   ||   ||   ||   || 55\131 || 503.817 ||= Golden meantone ||
||=   ||=   ||=   ||=   ||= 34\81 ||   ||= 503.704 ||= Optimal meantone is around here ||
||   ||   ||   ||   ||   || 47/112 || 503.571 ||   ||
||=   ||=   ||= 13\31 ||=   ||=   ||   ||= 503.226 ||= Optimal rank range (L/s=3/2) ||
||   ||   ||   ||   ||   || 44/105 || 502.857 ||   ||
||=   ||=   ||=   ||=   ||= 31\74 ||   ||= 502.703 ||=   ||
||   ||   ||   ||   ||   || 49/117 || 502.564 ||   ||
||=   ||=   ||=   ||= 18\43 ||=   ||   ||= 502.326 ||=   ||
||   ||   ||   ||   ||   || 41/98 || 502.041 ||   ||
||=   ||=   ||=   ||=   ||= 23\55 ||   ||= 501.818 ||=   ||
||   ||   ||   ||   ||   || 28/67 || 501.493 ||   ||
||= 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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>20/47<br />
</td>
        <td>510.638<br />
</td>
        <td><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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>31/73<br />
</td>
        <td>509.589<br />
</td>
        <td><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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>39/92<br />
</td>
        <td>508.696<br />
</td>
        <td><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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>36/85<br />
</td>
        <td>508.235<br />
</td>
        <td><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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>41/97<br />
</td>
        <td>507.216<br />
</td>
        <td><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;">Flattone<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>49/116<br />
</td>
        <td>506.897<br />
</td>
        <td><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;">Flattone<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>46/109<br />
</td>
        <td>506.422<br />
</td>
        <td><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;">Flattone<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>35/83<br />
</td>
        <td>506.024<br />
</td>
        <td><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;">505.263<br />
</td>
        <td style="text-align: center;">Boundary of propriety: generators<br />
smaller than this are proper<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>37/88<br />
</td>
        <td>504.545<br />
</td>
        <td style="text-align: center;">LucyTuning<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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>50/119<br />
</td>
        <td>504.202<br />
</td>
        <td><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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>47/112<br />
</td>
        <td>503.571<br />
</td>
        <td><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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>44/105<br />
</td>
        <td>502.857<br />
</td>
        <td><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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>49/117<br />
</td>
        <td>502.564<br />
</td>
        <td><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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>41/98<br />
</td>
        <td>502.041<br />
</td>
        <td><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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>28/67<br />
</td>
        <td>501.493<br />
</td>
        <td><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:guest|guest]] and made on <tt>2012-04-25 13:40:07 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-10-15 12:49:16 UTC</tt>.<br>
-: The original revision id was <tt>325148388</tt>.<br>
+: The original revision id was <tt>373189022</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 20: / Line 20: @@
 ||=   ||=   ||= 11\26 ||=   ||=   ||   ||= 507.692 ||=   ||
 ||   ||   ||   ||   ||   || 41/97 || 507.216 ||   ||
-||=   ||=   ||=   ||=   ||= 30\71 ||   ||= 507.042 ||=   ||
+||=   ||=   ||=   ||=   ||= 30\71 ||   ||= 507.042 ||=  Flattone ||
 ||   ||   ||   ||   ||   || 49/116 || 506.897 ||   ||
-||=   ||=   ||=   ||= 19\45 ||=   ||   ||= 506.667 ||=   ||
+||=   ||=   ||=   ||= 19\45 ||=   ||   ||= 506.667 ||=  Flattone ||
 ||   ||   ||   ||   ||   || 46/109 || 506.422 ||   ||
-||=   ||=   ||=   ||=   ||= 27\64 ||   ||= 506.250 ||=   ||
+||=   ||=   ||=   ||=   ||= 27\64 ||   ||= 506.250 ||=  Flattone ||
 ||   ||   ||   ||   ||   || 35/83 || 506.024 ||   ||
 ||=   ||= 8\19 ||=   ||=   ||=   ||   ||= 505.263 ||= Boundary of propriety: generators
@@ Line 256: / Line 256: @@
          &lt;td style="text-align: center;"&gt;507.042&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Flattone&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 292: / Line 292: @@
          &lt;td style="text-align: center;"&gt;506.667&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Flattone&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 328: / Line 328: @@
          &lt;td style="text-align: center;"&gt;506.250&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Flattone&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

7L 5s: Difference between revisions

Revision as of 12:49, 15 October 2012

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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