7L 5s: Difference between revisions
Wikispaces>genewardsmith **Imported revision 373193962 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 373262730 - 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:keenanpepper|keenanpepper]] and made on <tt>2012-10-15 15:46:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>373262730</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 ||= || | ||
|| || || || || || 20 | ||= ||= ||= ||= ||= ||= 20\47 ||= 510.638 ||= || | ||
||= ||= ||= ||= ||= 17\40 || ||= 510.000 ||= || | ||= ||= ||= ||= ||= 17\40 ||= ||= 510.000 ||= || | ||
|| || || || || || 31 | ||= ||= ||= ||= ||= ||= 31\73 ||= 509.589 ||= || | ||
||= ||= ||= ||= 14\33 ||= || ||= 509.091 ||= || | ||= ||= ||= ||= 14\33 ||= ||= ||= 509.091 ||= || | ||
|| || || || || || 39 | ||= ||= ||= ||= ||= ||= 39\92 ||= 508.696 ||= || | ||
||= ||= ||= ||= ||= 25\59 || ||= 508.475 ||= || | ||= ||= ||= ||= ||= 25\59 ||= ||= 508.475 ||= || | ||
|| || || || || || 36 | ||= ||= ||= ||= ||= ||= 36\85 ||= 508.235 ||= || | ||
||= ||= ||= 11\26 ||= ||= || ||= 507.692 ||= || | ||= ||= ||= 11\26 ||= ||= ||= ||= 507.692 ||= || | ||
|| || || || || || 41 | ||= ||= ||= ||= ||= ||= 41\97 ||= 507.216 ||= || | ||
||= ||= ||= ||= ||= 30\71 || ||= 507.042 ||= | ||= ||= ||= ||= ||= 30\71 ||= ||= 507.042 ||= Flattone || | ||
|| || || || || || 49 | ||= ||= ||= ||= ||= ||= 49\116 ||= 506.897 ||= Flattone || | ||
||= ||= ||= ||= 19\45 ||= || ||= 506.667 ||= | ||= ||= ||= ||= 19\45 ||= ||= ||= 506.667 ||= Flattone || | ||
|| || || || || || 46 | ||= ||= ||= ||= ||= ||= 46\109 ||= 506.422 ||= Flattone || | ||
||= ||= ||= ||= ||= 27\64 || ||= 506.250 ||= | ||= ||= ||= ||= ||= 27\64 ||= ||= 506.250 ||= Flattone || | ||
|| || || || || || 35 | ||= ||= ||= ||= ||= ||= 35\83 ||= 506.024 ||= || | ||
||= ||= 8\19 ||= ||= ||= || ||= 505.263 ||= Boundary of propriety: generators | ||= ||= 8\19 ||= ||= ||= ||= ||= 505.263 ||= Boundary of propriety: generators | ||
smaller than this are proper Meanenneadecal || | smaller than this are proper. | ||
|| || || || || || 37 | Meanenneadecal || | ||
||= ||= ||= ||= ||= 29\69 || ||= 504.348 ||= || | ||= ||= ||= ||= ||= ||= 37\88 ||= 504.545 ||= LucyTuning || | ||
|| || || || || || 50 | ||= ||= ||= ||= ||= 29\69 ||= ||= 504.348 ||= || | ||
||= ||= ||= ||= 21\50 ||= || ||= 504.000 ||= Meantone/Meanpop || | ||= ||= ||= ||= ||= ||= 50\119 ||= 504.202 ||= || | ||
|| || || || || || 55\131 || 503.817 ||= Golden meantone || | ||= ||= ||= ||= 21\50 ||= ||= ||= 504.000 ||= Meantone/Meanpop || | ||
||= ||= ||= ||= ||= 34\81 || ||= 503.704 ||= Optimal meantone is around here || | ||= ||= ||= ||= ||= ||= 55\131 ||= 503.817 ||= Golden meantone || | ||
|| || || || || || 47 | ||= ||= ||= ||= ||= 34\81 ||= ||= 503.704 ||= Optimal meantone is around here || | ||
||= ||= ||= 13\31 ||= ||= || ||= 503.226 ||= Optimal rank range (L/s=3/2) || | ||= ||= ||= ||= ||= ||= 47\112 ||= 503.571 ||= Meantone/Meanpop || | ||
|| || || || || || 44 | ||= ||= ||= 13\31 ||= ||= ||= ||= 503.226 ||= Optimal rank range (L/s=3/2) || | ||
||= ||= ||= ||= ||= 31\74 || ||= 502.703 ||= Meantone/Huygens || | ||= ||= ||= ||= ||= ||= 44\105 ||= 502.857 ||= Meantone/Huygens || | ||
|| || || || || || 49 | ||= ||= ||= ||= ||= 31\74 ||= ||= 502.703 ||= Meantone/Huygens || | ||
||= ||= ||= ||= 18\43 ||= || ||= 502.326 ||= | ||= ||= ||= ||= ||= ||= 49\117 ||= 502.564 ||= || | ||
|| || || || || || 41 | ||= ||= ||= ||= 18\43 ||= ||= ||= 502.326 ||= Meantone/Meridetone || | ||
||= ||= ||= ||= ||= 23\55 || ||= 501.818 ||= || | ||= ||= ||= ||= ||= ||= 41\98 ||= 502.041 ||= || | ||
|| || || || || || 28 | ||= ||= ||= ||= ||= 23\55 ||= ||= 501.818 ||= || | ||
||= 5\12 ||= ||= ||= ||= || ||= 500.000 ||= ||</pre></div> | ||= ||= ||= ||= ||= ||= 28\67 ||= 501.493 ||= || | ||
||= 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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<td style="text-align: center;">514.286<br /> | <td style="text-align: center;">514.286<br /> | ||
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<td>20 | <td style="text-align: center;">20\47<br /> | ||
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<td>510.638<br /> | <td style="text-align: center;">510.638<br /> | ||
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<td style="text-align: center;">17\40<br /> | <td style="text-align: center;">17\40<br /> | ||
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<td style="text-align: center;">510.000<br /> | <td style="text-align: center;">510.000<br /> | ||
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<td>31 | <td style="text-align: center;">31\73<br /> | ||
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<td>509.589<br /> | <td style="text-align: center;">509.589<br /> | ||
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<td style="text-align: center;">509.091<br /> | <td style="text-align: center;">509.091<br /> | ||
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<td>39 | <td style="text-align: center;">39\92<br /> | ||
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<td>508.696<br /> | <td style="text-align: center;">508.696<br /> | ||
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<td style="text-align: center;">25\59<br /> | <td style="text-align: center;">25\59<br /> | ||
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<td style="text-align: center;">508.475<br /> | <td style="text-align: center;">508.475<br /> | ||
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<td>36 | <td style="text-align: center;">36\85<br /> | ||
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<td>508.235<br /> | <td style="text-align: center;">508.235<br /> | ||
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<td style="text-align: center;">507.692<br /> | <td style="text-align: center;">507.692<br /> | ||
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<td>41 | <td style="text-align: center;">41\97<br /> | ||
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<td>507.216<br /> | <td style="text-align: center;">507.216<br /> | ||
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<td style="text-align: center;">30\71<br /> | <td style="text-align: center;">30\71<br /> | ||
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<td style="text-align: center;">507.042<br /> | <td style="text-align: center;">507.042<br /> | ||
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<td>49 | <td style="text-align: center;">49\116<br /> | ||
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<td>506.897<br /> | <td style="text-align: center;">506.897<br /> | ||
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<td style="text-align: center;">Flattone<br /> | <td style="text-align: center;">Flattone<br /> | ||
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<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
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<td style="text-align: center;">506.667<br /> | <td style="text-align: center;">506.667<br /> | ||
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<td>46 | <td style="text-align: center;">46\109<br /> | ||
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<td>506.422<br /> | <td style="text-align: center;">506.422<br /> | ||
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<td style="text-align: center;">Flattone<br /> | <td style="text-align: center;">Flattone<br /> | ||
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<td style="text-align: center;">27\64<br /> | <td style="text-align: center;">27\64<br /> | ||
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<td style="text-align: center;">506.250<br /> | <td style="text-align: center;">506.250<br /> | ||
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<td>35 | <td style="text-align: center;">35\83<br /> | ||
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<td>506.024<br /> | <td style="text-align: center;">506.024<br /> | ||
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<td style="text-align: center;">505.263<br /> | <td style="text-align: center;">505.263<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Boundary of propriety: generators<br /> | <td style="text-align: center;">Boundary of propriety: generators<br /> | ||
smaller than this are proper Meanenneadecal<br /> | smaller than this are proper.<br /> | ||
Meanenneadecal<br /> | |||
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<td>37 | <td style="text-align: center;">37\88<br /> | ||
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<td>504.545<br /> | <td style="text-align: center;">504.545<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">LucyTuning<br /> | <td style="text-align: center;">LucyTuning<br /> | ||
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<td style="text-align: center;">29\69<br /> | <td style="text-align: center;">29\69<br /> | ||
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<td style="text-align: center;">504.348<br /> | <td style="text-align: center;">504.348<br /> | ||
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<td>50 | <td style="text-align: center;">50\119<br /> | ||
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<td>504.202<br /> | <td style="text-align: center;">504.202<br /> | ||
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<td style="text-align: center;">504.000<br /> | <td style="text-align: center;">504.000<br /> | ||
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<td>55\131<br /> | <td style="text-align: center;">55\131<br /> | ||
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<td>503.817<br /> | <td style="text-align: center;">503.817<br /> | ||
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<td style="text-align: center;">Golden meantone<br /> | <td style="text-align: center;">Golden meantone<br /> | ||
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<td style="text-align: center;">34\81<br /> | <td style="text-align: center;">34\81<br /> | ||
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<td style="text-align: center;">503.704<br /> | <td style="text-align: center;">503.704<br /> | ||
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<td>47 | <td style="text-align: center;">47\112<br /> | ||
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<td>503.571<br /> | <td style="text-align: center;">503.571<br /> | ||
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<td style="text-align: center;">Meantone/Meanpop<br /> | <td style="text-align: center;">Meantone/Meanpop<br /> | ||
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<td style="text-align: center;">503.226<br /> | <td style="text-align: center;">503.226<br /> | ||
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<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td>44 | <td style="text-align: center;">44\105<br /> | ||
</td> | </td> | ||
<td>502.857<br /> | <td style="text-align: center;">502.857<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Meantone/Huygens<br /> | <td style="text-align: center;">Meantone/Huygens<br /> | ||
Line 541: | Line 543: | ||
<td style="text-align: center;">31\74<br /> | <td style="text-align: center;">31\74<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">502.703<br /> | <td style="text-align: center;">502.703<br /> | ||
Line 549: | Line 551: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td>49 | <td style="text-align: center;">49\117<br /> | ||
</td> | </td> | ||
<td>502.564<br /> | <td style="text-align: center;">502.564<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 577: | Line 579: | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">502.326<br /> | <td style="text-align: center;">502.326<br /> | ||
Line 585: | Line 587: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td>41 | <td style="text-align: center;">41\98<br /> | ||
</td> | </td> | ||
<td>502.041<br /> | <td style="text-align: center;">502.041<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 613: | Line 615: | ||
<td style="text-align: center;">23\55<br /> | <td style="text-align: center;">23\55<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">501.818<br /> | <td style="text-align: center;">501.818<br /> | ||
Line 621: | Line 623: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td>28 | <td style="text-align: center;">28\67<br /> | ||
</td> | </td> | ||
<td>501.493<br /> | <td style="text-align: center;">501.493<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 649: | Line 651: | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">500.000<br /> | <td style="text-align: center;">500.000<br /> |