7L 5s
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2012-10-15 13:01:23 UTC.
- The original revision id was 373193962.
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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 ||= Flattone || ||= ||= ||= ||= 19\45 ||= || ||= 506.667 ||= Flattone || || || || || || || 46/109 || 506.422 ||= Flattone || ||= ||= ||= ||= ||= 27\64 || ||= 506.250 ||= Flattone || || || || || || || 35/83 || 506.024 || || ||= ||= 8\19 ||= ||= ||= || ||= 505.263 ||= Boundary of propriety: generators smaller than this are proper Meanenneadecal || || || || || || || 37/88 || 504.545 ||= LucyTuning || ||= ||= ||= ||= ||= 29\69 || ||= 504.348 ||= || || || || || || || 50/119 || 504.202 || || ||= ||= ||= ||= 21\50 ||= || ||= 504.000 ||= Meantone/Meanpop || || || || || || || 55\131 || 503.817 ||= Golden meantone || ||= ||= ||= ||= ||= 34\81 || ||= 503.704 ||= Optimal meantone is around here || || || || || || || 47/112 || 503.571 ||= Meantone/Meanpop || ||= ||= ||= 13\31 ||= ||= || ||= 503.226 ||= Optimal rank range (L/s=3/2) || || || || || || || 44/105 || 502.857 ||= Meantone/Huygens || ||= ||= ||= ||= ||= 31\74 || ||= 502.703 ||= Meantone/Huygens || || || || || || || 49/117 || 502.564 || || ||= ||= ||= ||= 18\43 ||= || ||= 502.326 ||= Meantone/Meridetone || || || || || || || 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, "diatonic" 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 "chromatic" 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 style="text-align: center;">Flattone<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 style="text-align: center;">Flattone<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 Meanenneadecal<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;">Meantone/Meanpop<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 style="text-align: center;">Meantone/Meanpop<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 style="text-align: center;">Meantone/Huygens<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;">Meantone/Huygens<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;">Meantone/Meridetone<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>