2L 19s: Difference between revisions

Revision as of 16:12, 28 October 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 2015-10-28 16:12:32 UTC.

The original revision id was 564250443.

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 where the small steps split 10-9 between the large steps. With a generator no smaller than 10/21edo (571.429 cents), it achieves a harmonic entropy minimum at generator = 7/5 (almost exactly 17/35edo).
|| 1/2 ||   ||   ||   ||   || 600 ||
||   ||   ||   ||   || 14/29 || 579.31 ||
||   ||   ||   || 13/27 ||   || 577.778 ||
||   ||   ||   ||   || 25/52 || 576.923 ||
||   ||   ||   ||   ||   || 576.269 ||
||   ||   || 12/25 ||   ||   || 576 ||
||   ||   ||   ||   ||   || 575.447 ||
||   ||   ||   ||   || 35/73 || 575.3425 ||
||   ||   ||   ||   ||   || 575.2435 ||
||   ||   ||   || 23/48 ||   || 575 ||
||   ||   ||   ||   || 34/71 || 574.648 ||
||   || 11/23 ||   ||   ||   || 573.913 ||
||   ||   ||   ||   || 43/90 || 573.333 ||
||   ||   ||   || 32/67 ||   || 573.134 ||
||   ||   ||   ||   ||   || 573.017 ||
||   ||   ||   ||   || 53/111 || 572.973 ||
||   ||   ||   ||   ||   || 572.902 ||
||   ||   || 21/44 ||   ||   || 572.727 ||
||   ||   ||   ||   || 52/109 || 572.477 ||
||   ||   ||   || 31/65 ||   || 572.308 ||
||   ||   ||   ||   || 41/86 || 572.093 ||
|| 10/21 ||   ||   ||   ||   || 571.429 ||

Original HTML content:

<html><head><title>2L 19s</title></head><body>This is the MOS where the small steps split 10-9 between the large steps. With a generator no smaller than 10/21edo (571.429 cents), it achieves a harmonic entropy minimum at generator = 7/5 (almost exactly 17/35edo).<br />


<table class="wiki_table">
    <tr>
        <td>1/2<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>600<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>14/29<br />
</td>
        <td>579.31<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>13/27<br />
</td>
        <td><br />
</td>
        <td>577.778<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>25/52<br />
</td>
        <td>576.923<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>576.269<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>12/25<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>576<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>575.447<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>35/73<br />
</td>
        <td>575.3425<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>575.2435<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>23/48<br />
</td>
        <td><br />
</td>
        <td>575<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>34/71<br />
</td>
        <td>574.648<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>11/23<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>573.913<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>43/90<br />
</td>
        <td>573.333<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>32/67<br />
</td>
        <td><br />
</td>
        <td>573.134<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>573.017<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>53/111<br />
</td>
        <td>572.973<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>572.902<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>21/44<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>572.727<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>52/109<br />
</td>
        <td>572.477<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>31/65<br />
</td>
        <td><br />
</td>
        <td>572.308<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>41/86<br />
</td>
        <td>572.093<br />
</td>
    </tr>
    <tr>
        <td>10/21<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>571.429<br />
</td>
    </tr>
</table>

</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:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-24 14:12:17 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-10-28 16:12:32 UTC</tt>.<br>
-: The original revision id was <tt>552016088</tt>.<br>
+: The original revision id was <tt>564250443</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>
 <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">This is the MOS where the small steps split 10-9 between the large steps. With a generator no smaller than 10/21edo (571 3/7 cents), it achieves a harmonic entropy minimum at generator = 7/5 (almost exactly 17/35edo).
+<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;white-space: pre-wrap ! important" class="old-revision-html">This is the MOS where the small steps split 10-9 between the large steps. With a generator no smaller than 10/21edo (571.429 cents), it achieves a harmonic entropy minimum at generator = 7/5 (almost exactly 17/35edo).
 || 1/2 ||   ||   ||   ||   || 600 ||
-||   ||   ||   ||   || 14/29 || 579.310345 ||
+||   ||   ||   ||   || 14/29 || 579.31 ||
-||   ||   ||   || 13/27 ||   || 577 7/9 ||
+||   ||   ||   || 13/27 ||   || 577.778 ||
-||   ||   ||   ||   || 25/52 || 576 12/13 ||
+||   ||   ||   ||   || 25/52 || 576.923 ||
-||   ||   ||   ||   ||   || 576.268813 ||
+||   ||   ||   ||   ||   || 576.269 ||
 ||   ||   || 12/25 ||   ||   || 576 ||
-||   ||   ||   ||   ||   || 575.4466295 ||
+||   ||   ||   ||   ||   || 575.447 ||
-||   ||   ||   ||   || 35/73 || 575.342466 ||
+||   ||   ||   ||   || 35/73 || 575.3425 ||
+||   ||   ||   ||   ||   || 575.2435 ||
 ||   ||   ||   || 23/48 ||   || 575 ||
-||   ||   ||   ||   || 34/71 || 574.647887 ||
+||   ||   ||   ||   || 34/71 || 574.648 ||
-||   || 11/23 ||   ||   ||   || 573.9130345 ||
+||   || 11/23 ||   ||   ||   || 573.913 ||
-||   ||   ||   ||   || 43/90 || 573 1/3 ||
+||   ||   ||   ||   || 43/90 || 573.333 ||
-||   ||   ||   || 32/67 ||   || 573.134328 ||
+||   ||   ||   || 32/67 ||   || 573.134 ||
-||   ||   ||   ||   || 53/111 || 572 36/37 ||
+||   ||   ||   ||   ||   || 573.017 ||
-||   ||   || 21/44 ||   ||   || 572 8/11 ||
+||   ||   ||   ||   || 53/111 || 572.973 ||
-||   ||   ||   ||   || 52/109 || 572.477064 ||
+||   ||   ||   ||   ||   || 572.902 ||
-||   ||   ||   || 31/65 ||   || 572 4/13 ||
+||   ||   || 21/44 ||   ||   || 572.727 ||
-||   ||   ||   ||   || 41/86 || 572.093023 ||
+||   ||   ||   ||   || 52/109 || 572.477 ||
-|| 10/21 ||   ||   ||   ||   || 571 3/7 ||</pre></div>
+||   ||   ||   || 31/65 ||   || 572.308 ||
+||   ||   ||   ||   || 41/86 || 572.093 ||
+|| 10/21 ||   ||   ||   ||   || 571.429 ||</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;2L 19s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This is the MOS where the small steps split 10-9 between the large steps. With a generator no smaller than 10/21edo (571 3/7 cents), it achieves a harmonic entropy minimum at generator = 7/5 (almost exactly 17/35edo).&lt;br /&gt;
+<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;2L 19s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This is the MOS where the small steps split 10-9 between the large steps. With a generator no smaller than 10/21edo (571.429 cents), it achieves a harmonic entropy minimum at generator = 7/5 (almost exactly 17/35edo).&lt;br /&gt;
@@ Line 56: / Line 59: @@
          &lt;td&gt;14/29&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;579.310345&lt;br /&gt;
+         &lt;td&gt;579.31&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 70: / Line 73: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;577 7/9&lt;br /&gt;
+         &lt;td&gt;577.778&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 84: / Line 87: @@
          &lt;td&gt;25/52&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;576 12/13&lt;br /&gt;
+         &lt;td&gt;576.923&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 98: / Line 101: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;576.268813&lt;br /&gt;
+         &lt;td&gt;576.269&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 126: / Line 129: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;575.4466295&lt;br /&gt;
+         &lt;td&gt;575.447&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 140: / Line 143: @@
          &lt;td&gt;35/73&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;575.342466&lt;br /&gt;
+         &lt;td&gt;575.3425&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;575.2435&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 168: / Line 185: @@
          &lt;td&gt;34/71&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;574.647887&lt;br /&gt;
+         &lt;td&gt;574.648&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 182: / Line 199: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;573.9130345&lt;br /&gt;
+         &lt;td&gt;573.913&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 196: / Line 213: @@
          &lt;td&gt;43/90&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;573 1/3&lt;br /&gt;
+         &lt;td&gt;573.333&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 210: / Line 227: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;573.134328&lt;br /&gt;
+         &lt;td&gt;573.134&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;573.017&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 224: / Line 255: @@
          &lt;td&gt;53/111&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;572 36/37&lt;br /&gt;
+         &lt;td&gt;572.973&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;572.902&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 238: / Line 283: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;572 8/11&lt;br /&gt;
+         &lt;td&gt;572.727&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 252: / Line 297: @@
          &lt;td&gt;52/109&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;572.477064&lt;br /&gt;
+         &lt;td&gt;572.477&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 266: / Line 311: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;572 4/13&lt;br /&gt;
+         &lt;td&gt;572.308&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 280: / Line 325: @@
          &lt;td&gt;41/86&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;572.093023&lt;br /&gt;
+         &lt;td&gt;572.093&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 294: / Line 339: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;571 3/7&lt;br /&gt;
+         &lt;td&gt;571.429&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

2L 19s: Difference between revisions

Revision as of 16:12, 28 October 2015

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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