4L 5s: Difference between revisions
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Wikispaces>JosephRuhf **Imported revision 540651568 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 551972212 - 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:JosephRuhf|JosephRuhf]] and made on <tt>2015- | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-23 15:34:15 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>551972212</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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|| || || || 7\30 || ||= 2 5 2 5 2 5 2 5 2 || 280.000 ||= || | || || || || 7\30 || ||= 2 5 2 5 2 5 2 5 2 || 280.000 ||= || | ||
|| || || || || 11\47 ||= 3 8 3 8 3 8 3 8 3 || 280.851 || || | || || || || || 11\47 ||= 3 8 3 8 3 8 3 8 3 || 280.851 || || | ||
|| || || || || ||= 1 | || || || || || ||= 1 e 1 e 1 e 1 e 1 || 281.100 ||= <span style="display: block; text-align: center;">L/s = e</span> || | ||
|| || || 4\17 || || ||= 1 3 1 3 1 3 1 3 1 || 282.353 ||= L/s = 3 || | || || || 4\17 || || ||= 1 3 1 3 1 3 1 3 1 || 282.353 ||= L/s = 3 || | ||
|| || || || || ||= 1 | || || || || || ||= 1 pi 1 pi 1 pi 1 pi 1 || 282.922 ||= <span style="display: block; text-align: center;">L/s = pi</span> || | ||
|| || || || || 9\38 ||= 2 7 2 <span style="font-size: 12.8000001907349px; line-height: 1.5;">7 </span><span style="font-size: 13px; line-height: 1.5;">2 7 2 7 2 </span> || 284.2105 || || | || || || || || 9\38 ||= 2 7 2 <span style="font-size: 12.8000001907349px; line-height: 1.5;">7 </span><span style="font-size: 13px; line-height: 1.5;">2 7 2 7 2 </span> || 284.2105 || || | ||
|| || || || 5\21 || ||= 1 4 1 4 1 4 1 4 1 || 285.714 ||= L/s = 4 || | || || || || 5\21 || ||= 1 4 1 4 1 4 1 4 1 || 285.714 ||= L/s = 4 || | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1 | <td style="text-align: center;">1 e 1 e 1 e 1 e 1<br /> | ||
</td> | </td> | ||
<td> | <td>281.100<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><span style="display: block; text-align: center;">L/s = | <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = e</span><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 311: | Line 311: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1 | <td style="text-align: center;">1 pi 1 pi 1 pi 1 pi 1<br /> | ||
</td> | </td> | ||
<td>282. | <td>282.922<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><span style="display: block; text-align: center;">L/s = | <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = pi</span><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Revision as of 15:34, 23 May 2015
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 2015-05-23 15:34:15 UTC.
- The original revision id was 551972212.
- 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:
4L 5s refers to the structure of [[MOSScales|MOS Scales]] whose generator falls between 2\9 (two degrees of [[9edo]] = approx. 266.667¢) and 1\4 (one degree of [[4edo]] = 300¢). In the case of 9edo, L and s are the same size; in the case of 4edo, s is so small it disappears. The spectrum, then, goes something like: ||||||||||~ Generator ||~ Scale ||~ Generator in cents ||~ Comments || || 2\9 || || || || ||= 1 1 1 1 1 1 1 1 1 || 266.667 ||= || || || || || || 9\40 ||= 4 5 4 5 4 5 4 5 4 || 270 || || || || || || 7\31 || ||= 3 4 3 4 3 4 3 4 3 || 270.968 ||= || || || || || || 12\53 ||= 5 7 5 7 5 7 5 7 5 || 271.698 ||= Orwell is around here || || || || 5\22 || || ||= 2 3 2 3 2 3 2 3 2 || 272.727 ||= Optimum rank range (L/s=3/2) orwell || || || || || || 13\57 ||= 5 8 5 8 5 8 5 8 5 || 273.684 ||= Golden orwell (bad tuning) || || || || || 8\35 || ||= 3 5 3 5 3 5 3 5 3 || 274.286 ||= || || || || || || 11\48 ||= 4 7 4 7 4 7 4 7 4 || 275 || || || || 3\13 || || || ||= 1 2 1 2 1 2 1 2 1 || 276.923 ||= Boundary of propriety: generators smaller than this are proper || || || || || || 10\43 ||= 3 7 3 7 3 7 3 7 3 || 279.07 || || || || || || 7\30 || ||= 2 5 2 5 2 5 2 5 2 || 280.000 ||= || || || || || || 11\47 ||= 3 8 3 8 3 8 3 8 3 || 280.851 || || || || || || || ||= 1 e 1 e 1 e 1 e 1 || 281.100 ||= <span style="display: block; text-align: center;">L/s = e</span> || || || || 4\17 || || ||= 1 3 1 3 1 3 1 3 1 || 282.353 ||= L/s = 3 || || || || || || ||= 1 pi 1 pi 1 pi 1 pi 1 || 282.922 ||= <span style="display: block; text-align: center;">L/s = pi</span> || || || || || || 9\38 ||= 2 7 2 <span style="font-size: 12.8000001907349px; line-height: 1.5;">7 </span><span style="font-size: 13px; line-height: 1.5;">2 7 2 7 2 </span> || 284.2105 || || || || || || 5\21 || ||= 1 4 1 4 1 4 1 4 1 || 285.714 ||= L/s = 4 || || || || || || 6\25 ||= 1 5 1 5 1 5 1 5 1 || 288 || || || 1\4 || || || || ||= 0 1 0 1 0 1 0 1 0 || 300.000 ||= || Note that between 7\31 and 5\22, g approximates frequency ratio 7:6, 2g approximates 11:8, and 3g approximates 8:5. This defines the range of Orwell Temperament, which is the only notable harmonic entropy minimum with this MOS pattern. 4L 5s scales outside of that range are not suitable for Orwell.
Original HTML content:
<html><head><title>4L 5s</title></head><body>4L 5s refers to the structure of <a class="wiki_link" href="/MOSScales">MOS Scales</a> whose generator falls between 2\9 (two degrees of <a class="wiki_link" href="/9edo">9edo</a> = approx. 266.667¢) and 1\4 (one degree of <a class="wiki_link" href="/4edo">4edo</a> = 300¢). In the case of 9edo, L and s are the same size; in the case of 4edo, s is so small it disappears. The spectrum, then, goes something like:<br />
<br />
<table class="wiki_table">
<tr>
<th colspan="5">Generator<br />
</th>
<th>Scale<br />
</th>
<th>Generator in cents<br />
</th>
<th>Comments<br />
</th>
</tr>
<tr>
<td>2\9<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">1 1 1 1 1 1 1 1 1<br />
</td>
<td>266.667<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>9\40<br />
</td>
<td style="text-align: center;">4 5 4 5 4 5 4 5 4<br />
</td>
<td>270<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>7\31<br />
</td>
<td><br />
</td>
<td style="text-align: center;">3 4 3 4 3 4 3 4 3<br />
</td>
<td>270.968<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>12\53<br />
</td>
<td style="text-align: center;">5 7 5 7 5 7 5 7 5<br />
</td>
<td>271.698<br />
</td>
<td style="text-align: center;">Orwell is around here<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>5\22<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">2 3 2 3 2 3 2 3 2<br />
</td>
<td>272.727<br />
</td>
<td style="text-align: center;">Optimum rank range (L/s=3/2) orwell<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>13\57<br />
</td>
<td style="text-align: center;">5 8 5 8 5 8 5 8 5<br />
</td>
<td>273.684<br />
</td>
<td style="text-align: center;">Golden orwell (bad tuning)<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>8\35<br />
</td>
<td><br />
</td>
<td style="text-align: center;">3 5 3 5 3 5 3 5 3<br />
</td>
<td>274.286<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>11\48<br />
</td>
<td style="text-align: center;">4 7 4 7 4 7 4 7 4<br />
</td>
<td>275<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>3\13<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">1 2 1 2 1 2 1 2 1<br />
</td>
<td>276.923<br />
</td>
<td style="text-align: center;">Boundary of propriety:<br />
generators smaller than this are proper<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>10\43<br />
</td>
<td style="text-align: center;">3 7 3 7 3 7 3 7 3<br />
</td>
<td>279.07<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>7\30<br />
</td>
<td><br />
</td>
<td style="text-align: center;">2 5 2 5 2 5 2 5 2<br />
</td>
<td>280.000<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>11\47<br />
</td>
<td style="text-align: center;">3 8 3 8 3 8 3 8 3<br />
</td>
<td>280.851<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">1 e 1 e 1 e 1 e 1<br />
</td>
<td>281.100<br />
</td>
<td style="text-align: center;"><span style="display: block; text-align: center;">L/s = e</span><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>4\17<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">1 3 1 3 1 3 1 3 1<br />
</td>
<td>282.353<br />
</td>
<td style="text-align: center;">L/s = 3<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">1 pi 1 pi 1 pi 1 pi 1<br />
</td>
<td>282.922<br />
</td>
<td style="text-align: center;"><span style="display: block; text-align: center;">L/s = pi</span><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>9\38<br />
</td>
<td style="text-align: center;">2 7 2 <span style="font-size: 12.8000001907349px; line-height: 1.5;">7 </span><span style="font-size: 13px; line-height: 1.5;">2 7 2 7 2 </span><br />
</td>
<td>284.2105<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>5\21<br />
</td>
<td><br />
</td>
<td style="text-align: center;">1 4 1 4 1 4 1 4 1<br />
</td>
<td>285.714<br />
</td>
<td style="text-align: center;">L/s = 4<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>6\25<br />
</td>
<td style="text-align: center;">1 5 1 5 1 5 1 5 1<br />
</td>
<td>288<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>1\4<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">0 1 0 1 0 1 0 1 0<br />
</td>
<td>300.000<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
</table>
<br />
Note that between 7\31 and 5\22, g approximates frequency ratio 7:6, 2g approximates 11:8, and 3g approximates 8:5. This defines the range of Orwell Temperament, which is the only notable harmonic entropy minimum with this MOS pattern. 4L 5s scales outside of that range are not suitable for Orwell.</body></html>