4L 5s: Difference between revisions

Revision as of 04:01, 28 August 2011

IMPORTED REVISION FROM WIKISPACES

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This revision was by author guest and made on 2011-08-28 04:01:44 UTC.

The original revision id was 248871461.

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 ||=   ||
||   ||   ||   || 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 ||=   ||
||   ||   ||   ||   || 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 ||=   ||
||   || 3\13 ||   ||   ||   || 1 2 1 2 1 2 1 2 1 || 276.923 ||= Boundary of propriety: generators
smaller than this are proper ||
||   ||   ||   || 7\30 ||   || 2 5 2 5 2 5 2 5 2 || 280.000 ||=   ||
||   ||   || 4\17 ||   ||   || 1 3 1 3 1 3 1 3 1 || 282.353 ||=   ||
||   ||   ||   || 5\21 ||   || 1 4 1 4 1 4 1 4 1 || 285.714 ||=   ||
|| 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>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>7\31<br />
</td>
        <td><br />
</td>
        <td>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>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>2 3 2 3 2 3 2 3 2<br />
</td>
        <td>272.727<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>13\57<br />
</td>
        <td>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>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>3\13<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1 2 1 2 1 2 1 2 1<br />
</td>
        <td>276.923<br />
</td>
        <td style="text-align: center;">Boundary of propriety: generators<br />
smaller than this are proper<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7\30<br />
</td>
        <td><br />
</td>
        <td>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>4\17<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1 3 1 3 1 3 1 3 1<br />
</td>
        <td>282.353<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\21<br />
</td>
        <td><br />
</td>
        <td>1 4 1 4 1 4 1 4 1<br />
</td>
        <td>285.714<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>1\4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>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>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-05-11 13:29:44 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2011-08-28 04:01:44 UTC</tt>.<br>
-: The original revision id was <tt>227574018</tt>.<br>
+: The original revision id was <tt>248871461</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>
@@ Line 13: / Line 13: @@
 ||   ||   ||   ||   || 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 ||=   ||
+||   ||   ||   ||   || 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 ||=   ||
 ||   || 3\13 ||   ||   ||   || 1 2 1 2 1 2 1 2 1 || 276.923 ||= Boundary of propriety: generators
@@ Line 21: / Line 22: @@
 || 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 16:11, 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.</pre></div>
+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.</pre></div>
 <h4>Original HTML content:</h4>
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;4L 5s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;4L 5s refers to the structure of &lt;a class="wiki_link" href="/MOSScales"&gt;MOS Scales&lt;/a&gt; whose generator falls between 2\9 (two degrees of &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt; = approx. 266.667¢) and 1\4 (one degree of &lt;a class="wiki_link" href="/4edo"&gt;4edo&lt;/a&gt; = 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:&lt;br /&gt;
@@ Line 108: / Line 109: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13\57&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5 8 5 8 5 8 5 8 5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;273.684&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Golden orwell (bad tuning)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 222: / Line 241: @@
 &lt;br /&gt;
-Note that between 7\31 and 5\22, g approximates frequency ratio 7:6, 2g approximates 16:11, 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.&lt;/body&gt;&lt;/html&gt;</pre></div>
+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.&lt;/body&gt;&lt;/html&gt;</pre></div>

4L 5s: Difference between revisions

Revision as of 04:01, 28 August 2011

IMPORTED REVISION FROM WIKISPACES

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