7L 5s: Difference between revisions
Wikispaces>keenanpepper **Imported revision 228067634 - Original comment: ** |
Wikispaces>guest **Imported revision 249050661 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : 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> | : The original revision id was <tt>249050661</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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The meantone chromatic scale is [[Rothenberg propriety|proper]]. | 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 || | 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> | <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.<br /> | <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.<br /> | ||
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<tr> | <tr> | ||
<th colspan="5">Generator<br /> | <th colspan="5">Generator<br /> | ||
</th> | |||
<th><br /> | |||
</th> | </th> | ||
<th>in cents<br /> | <th>in cents<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">514.286<br /> | <td style="text-align: center;">514.286<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">17\40<br /> | <td style="text-align: center;">17\40<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">510.000<br /> | <td style="text-align: center;">510.000<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">509.091<br /> | <td style="text-align: center;">509.091<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">25\59<br /> | <td style="text-align: center;">25\59<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">508.475<br /> | <td style="text-align: center;">508.475<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">507.692<br /> | <td style="text-align: center;">507.692<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">30\71<br /> | <td style="text-align: center;">30\71<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">507.042<br /> | <td style="text-align: center;">507.042<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">506.667<br /> | <td style="text-align: center;">506.667<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">27\64<br /> | <td style="text-align: center;">27\64<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">506.250<br /> | <td style="text-align: center;">506.250<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">506.263<br /> | <td style="text-align: center;">506.263<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">29\69<br /> | <td style="text-align: center;">29\69<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">504.348<br /> | <td style="text-align: center;">504.348<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">504.000<br /> | <td style="text-align: center;">504.000<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <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> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">34\81<br /> | <td style="text-align: center;">34\81<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">503.704<br /> | <td style="text-align: center;">503.704<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">503.226<br /> | <td style="text-align: center;">503.226<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">Optimal rank range (L/s=3/2)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">31\74<br /> | <td style="text-align: center;">31\74<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">502.703<br /> | <td style="text-align: center;">502.703<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">502.326<br /> | <td style="text-align: center;">502.326<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">23\55<br /> | <td style="text-align: center;">23\55<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">501.818<br /> | <td style="text-align: center;">501.818<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">500.000<br /> | <td style="text-align: center;">500.000<br /> | ||