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 keenanpepper and made on 2012-10-15 15:46:51 UTC.
- The original revision id was 373262730.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
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 style="text-align: center;"><br />
</td>
<td style="text-align: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">505.263<br />
</td>
<td style="text-align: center;">Boundary of propriety: generators<br />
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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">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: center;">500.000<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
</table>
</body></html>