7L 5s
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author JosephRuhf and made on 2014-11-29 09:34:40 UTC.
- The original revision id was 533089140.
- The revision comment was:
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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="6">Generator<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 style="text-align: center;"><br />
</td>
<td style="text-align: left;">514.286<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;"><br />
</td>
<td style="text-align: center;">20\47<br />
</td>
<td style="text-align: left;">510.638<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;"><br />
</td>
<td style="text-align: left;">510.000<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;"><br />
</td>
<td style="text-align: center;">31\73<br />
</td>
<td style="text-align: left;">509.589<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;"><br />
</td>
<td style="text-align: left;">509.091<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;"><br />
</td>
<td style="text-align: center;">39\92<br />
</td>
<td style="text-align: left;">508.696<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;"><br />
</td>
<td style="text-align: left;">508.475<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;"><br />
</td>
<td style="text-align: center;">36\85<br />
</td>
<td style="text-align: left;">508.235<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;"><br />
</td>
<td style="text-align: left;">507.692<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;"><br />
</td>
<td style="text-align: center;">41\97<br />
</td>
<td style="text-align: left;">507.216<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;"><br />
</td>
<td style="text-align: left;">507.042<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;"><br />
</td>
<td style="text-align: center;">49\116<br />
</td>
<td style="text-align: left;">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 style="text-align: center;"><br />
</td>
<td style="text-align: left;">506.667<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;"><br />
</td>
<td style="text-align: center;">46\109<br />
</td>
<td style="text-align: left;">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 style="text-align: center;"><br />
</td>
<td style="text-align: left;">506.250<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;"><br />
</td>
<td style="text-align: center;">35\83<br />
</td>
<td style="text-align: left;">506.024<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;"><br />
</td>
<td style="text-align: left;">505.263<br />
</td>
<td style="text-align: center;">Boundary of propriety: generators smaller than this are proper.<br />
Meanenneadecal<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;"><br />
</td>
<td style="text-align: center;">37\88<br />
</td>
<td style="text-align: left;">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 style="text-align: center;"><br />
</td>
<td style="text-align: left;">504.348<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;"><br />
</td>
<td style="text-align: center;">50\119<br />
</td>
<td style="text-align: left;">504.202<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;"><br />
</td>
<td style="text-align: left;">504.000<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;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">55\131<br />
</td>
<td style="text-align: left;">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 style="text-align: center;"><br />
</td>
<td style="text-align: left;">503.704<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;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">47\112<br />
</td>
<td style="text-align: left;">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 style="text-align: center;"><br />
</td>
<td style="text-align: left;">503.226<br />
</td>
<td style="text-align: center;">Optimal rank range (L/s=3/2)<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;"><br />
</td>
<td style="text-align: center;">44\105<br />
</td>
<td style="text-align: left;">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 style="text-align: center;"><br />
</td>
<td style="text-align: left;">502.703<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;"><br />
</td>
<td style="text-align: center;">49\117<br />
</td>
<td style="text-align: left;">502.564<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;"><br />
</td>
<td style="text-align: left;">502.326<br />
</td>
<td style="text-align: center;">Meantone/Meridetone<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;"><br />
</td>
<td style="text-align: center;">41\98<br />
</td>
<td style="text-align: left;">502.041<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;"><br />
</td>
<td style="text-align: left;">501.818<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;"><br />
</td>
<td style="text-align: center;">28\67<br />
</td>
<td style="text-align: left;">501.493<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;"><br />
</td>
<td style="text-align: left;">500.000<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
</table>
</body></html>