7L 5s
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author keenanpepper and made on 2011-05-12 21:21:42 UTC.
- The original revision id was 228067080.
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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 ||~ scale in steps of an [[edo]] ||~ Comments || ||= 3\7 ||= ||= ||= ||= ||= 514.286 ||= 1 1 1 1 1 1 1 ||= || ||= ||= ||= ||= ||= 17\40 ||= 510.000 ||= 6 6 5 6 6 6 5 ||= || ||= ||= ||= ||= 14\33 ||= ||= 509.091 ||= 5 5 4 5 5 5 4 ||= || ||= ||= ||= ||= ||= 25\59 ||= 508.475 ||= 9 9 7 9 9 9 7 ||= || ||= ||= ||= 11\26 ||= ||= ||= 507.692 ||= 4 4 3 4 4 4 3 ||= || ||= ||= ||= ||= ||= 30\71 ||= 507.042 ||= 11 11 8 11 11 11 8 ||= || ||= ||= ||= ||= 19\45 ||= ||= 506.667 ||= 7 7 5 7 7 7 5 ||= || ||= ||= ||= ||= ||= 27\64 ||= 506.250 ||= 10 10 7 10 10 10 7 ||= || ||= ||= 8\19 ||= ||= ||= ||= 506.263 ||= 3 3 2 3 3 3 2 ||= Boundary of propriety: generators smaller than this are proper || ||= ||= ||= ||= ||= 29\69 ||= 504.348 ||= 11 11 7 11 11 11 7 ||= || ||= ||= ||= ||= 21\50 ||= ||= 504.000 ||= 8 8 5 8 8 8 5 ||= || ||= ||= ||= ||= ||= 34\81 ||= 503.704 ||= 13 13 8 13 13 13 8 ||= Optimal meantone is around here || ||= ||= ||= 13\31 ||= ||= ||= 503.226 ||= 5 5 3 5 5 5 3 ||= || ||= ||= ||= ||= ||= 31\74 ||= 502.703 ||= 12 12 7 12 12 12 7 ||= || ||= ||= ||= ||= 18\43 ||= ||= 502.326 ||= 7 7 4 7 7 7 4 ||= || ||= ||= ||= ||= ||= 23\55 ||= 501.818 ||= 9 9 5 9 9 9 5 ||= || ||= 5\12 ||= ||= ||= ||= ||= 500.000 ||= 2 2 1 2 2 2 1 ||= ||
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>in cents<br />
</th>
<th>scale in steps of an <a class="wiki_link" href="/edo">edo</a><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 style="text-align: center;">514.286<br />
</td>
<td style="text-align: center;">1 1 1 1 1 1 1<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 style="text-align: center;">510.000<br />
</td>
<td style="text-align: center;">6 6 5 6 6 6 5<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 style="text-align: center;">509.091<br />
</td>
<td style="text-align: center;">5 5 4 5 5 5 4<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 style="text-align: center;">508.475<br />
</td>
<td style="text-align: center;">9 9 7 9 9 9 7<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 style="text-align: center;">507.692<br />
</td>
<td style="text-align: center;">4 4 3 4 4 4 3<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 style="text-align: center;">507.042<br />
</td>
<td style="text-align: center;">11 11 8 11 11 11 8<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 style="text-align: center;">506.667<br />
</td>
<td style="text-align: center;">7 7 5 7 7 7 5<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 style="text-align: center;">506.250<br />
</td>
<td style="text-align: center;">10 10 7 10 10 10 7<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 style="text-align: center;">506.263<br />
</td>
<td style="text-align: center;">3 3 2 3 3 3 2<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 style="text-align: center;">504.348<br />
</td>
<td style="text-align: center;">11 11 7 11 11 11 7<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 style="text-align: center;">504.000<br />
</td>
<td style="text-align: center;">8 8 5 8 8 8 5<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;">34\81<br />
</td>
<td style="text-align: center;">503.704<br />
</td>
<td style="text-align: center;">13 13 8 13 13 13 8<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 style="text-align: center;">503.226<br />
</td>
<td style="text-align: center;">5 5 3 5 5 5 3<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;">31\74<br />
</td>
<td style="text-align: center;">502.703<br />
</td>
<td style="text-align: center;">12 12 7 12 12 12 7<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 style="text-align: center;">502.326<br />
</td>
<td style="text-align: center;">7 7 4 7 7 7 4<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 style="text-align: center;">501.818<br />
</td>
<td style="text-align: center;">9 9 5 9 9 9 5<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 style="text-align: center;">500.000<br />
</td>
<td style="text-align: center;">2 2 1 2 2 2 1<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
</table>
</body></html>