5L 6s: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-~~23 16~~:48:44 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-09 14:05:59 UTC</tt>.

: The original revision id was <tt>~~551975412~~</tt>.

: The original revision id was <tt>565763613</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

<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 pattern, with a generator between 2\11 (218.~~__18__~~ cents) and 1\5 (240), has multiple significant harmonic entropy minima, but they are all improper. The only saving grace for it is that is has harmonic entropy minima where the ratio between the large and small steps is optimal for melody, and that the generator for these scales is less than 6 cents flat of 8/7. The saving grace of the more lopsided scales is that a syntonic fifth is three generators up from the root.

<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 pattern, with a generator between 2\11 (218.182 cents) and 1\5 (240), has multiple significant harmonic entropy minima, but they are all improper. The only saving grace for it is that is has harmonic entropy minima where the ratio between the large and small steps is optimal for melody, and that the generator for these scales is less than 6 cents flat of 8/7. The saving grace of the more lopsided scales is that a syntonic fifth is three generators up from the root.

|| 1\5 || || || || || || || || || 240 ||= ||

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|| || || || || || || || || || 228.944 || ||

|| || || 4\21 || || || || || || || 228.571 ||= ||

|| || || || || 11\58 || || || || || 227.75 || ||

|| || || || || || || || || || 227.75 || ||

|| || || || || 11\58 || || || || || 227.586 || ||

|| || || || || || || 29\153 || || || 227.451 || ||

|| || || || || || || || || 76\401 || 227.431 || ||

|| || || || || || || || 47\248 || || 227.419 || ||

|| || || || || || 18\95 || || || || 227.368 || ||

|| || || || 7\37 || || || || || || 227.027 ||= ||

|| || 3\16 || || || || || || || || 225 ||= Boundary of propriety

(smaller generators are proper) ||

|| || || || || || || || || || 223.692 || ||

|| || || || 8\43 || || || || || || 223.256 ||= ||

|| || || || || || 21\113 || || || || 223.009 || ||

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|| || || || || || || 34\183 || || || 222.951 || ||

|| || || || || 13\70 || || || || || 222.857 || ||

|| || || || || || || || || || 222.6765 || ||

|| || || 5\27 || || || || || || || 222.222 ||= ||

|| || || || 7\38 || || || || || || 221.035 ||= ||

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|| 2\11 || || || || || || || || || 218.182 ||= Machine is around here ||</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"><html><head><title>5L 6s</title></head><body>This pattern, with a generator between 2\11 (218.~~18~~ cents) and 1\5 (240), has multiple significant harmonic entropy minima, but they are all improper. The only saving grace for it is that is has harmonic entropy minima where the ratio between the large and small steps is optimal for melody, and that the generator for these scales is less than 6 cents flat of 8/7. The saving grace of the more lopsided scales is that a syntonic fifth is three generators up from the root.

<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"><html><head><title>5L 6s</title></head><body>This pattern, with a generator between 2\11 (218.182 cents) and 1\5 (240), has multiple significant harmonic entropy minima, but they are all improper. The only saving grace for it is that is has harmonic entropy minima where the ratio between the large and small steps is optimal for melody, and that the generator for these scales is less than 6 cents flat of 8/7. The saving grace of the more lopsided scales is that a syntonic fifth is three generators up from the root.

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</td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>227.75

</td>

<td>

</td>

</tr>

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<td>

</td>

<td>227.75

<td>227.586

</td>

<td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>29\153

</td>

<td>

</td>

<td>

</td>

<td>227.451

</td>

<td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>76\401

</td>

<td>227.431

</td>

<td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

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</td>

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<td>47\248

</td>

<td>

</td>

<td>227.419

</td>

<td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

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</td>

<td>18\95

</td>

<td>

</td>

<td>

</td>

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</td>

<td>227.368

</td>

<td>

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<td style="text-align: center;">Boundary of propriety

(smaller generators are proper)

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

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<td>

</td>

<td>

</td>

<td>223.692

</td>

<td>

</td>

</tr>

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</td>

<td>222.857

</td>

<td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

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<td>

</td>

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</td>

<td>

</td>

<td>222.6765

</td>

<td>

@@ 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>2015-05-23 16:48:44 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-09 14:05:59 UTC</tt>.<br>
-: The original revision id was <tt>551975412</tt>.<br>
+: The original revision id was <tt>565763613</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 pattern, with a generator between 2\11 (218.__18__ cents) and 1\5 (240), has multiple significant harmonic entropy minima, but they are all improper. The only saving grace for it is that is has harmonic entropy minima where the ratio between the large and small steps is optimal for melody, and that the generator for these scales is less than 6 cents flat of 8/7. The saving grace of the more lopsided scales is that a syntonic fifth is three generators up from the root.
+<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 pattern, with a generator between 2\11 (218.182 cents) and 1\5 (240), has multiple significant harmonic entropy minima, but they are all improper. The only saving grace for it is that is has harmonic entropy minima where the ratio between the large and small steps is optimal for melody, and that the generator for these scales is less than 6 cents flat of 8/7. The saving grace of the more lopsided scales is that a syntonic fifth is three generators up from the root.
 || 1\5 ||   ||   ||   ||   ||   ||   ||   ||   || 240 ||=   ||
@@ Line 21: / Line 21: @@
 ||   ||   ||   ||   ||   ||   ||   ||   ||   || 228.944 ||   ||
 ||   ||   || 4\21 ||   ||   ||   ||   ||   ||   || 228.571 ||=   ||
-||   ||   ||   ||   || 11\58 ||   ||   ||   ||   || 227.75 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   || 227.75 ||   ||
+||   ||   ||   ||   || 11\58 ||   ||   ||   ||   || 227.586 ||   ||
+||   ||   ||   ||   ||   ||   || 29\153 ||   ||   || 227.451 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   || 76\401 || 227.431 ||   ||
+||   ||   ||   ||   ||   ||   ||   || 47\248 ||   || 227.419 ||   ||
+||   ||   ||   ||   ||   || 18\95 ||   ||   ||   || 227.368 ||   ||
 ||   ||   ||   || 7\37 ||   ||   ||   ||   ||   || 227.027 ||=   ||
 ||   || 3\16 ||   ||   ||   ||   ||   ||   ||   || 225 ||= Boundary of propriety
 (smaller generators are proper) ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   || 223.692 ||   ||
 ||   ||   ||   || 8\43 ||   ||   ||   ||   ||   || 223.256 ||=   ||
 ||   ||   ||   ||   ||   || 21\113 ||   ||   ||   || 223.009 ||   ||
@@ Line 31: / Line 37: @@
 ||   ||   ||   ||   ||   ||   || 34\183 ||   ||   || 222.951 ||   ||
 ||   ||   ||   ||   || 13\70 ||   ||   ||   ||   || 222.857 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   || 222.6765 ||   ||
 ||   ||   || 5\27 ||   ||   ||   ||   ||   ||   || 222.222 ||=   ||
 ||   ||   ||   || 7\38 ||   ||   ||   ||   ||   || 221.035 ||=   ||
@@ Line 40: / Line 47: @@
 || 2\11 ||   ||   ||   ||   ||   ||   ||   ||   || 218.182 ||= Machine is around here ||</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;5L 6s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This pattern, with a generator between 2\11 (218.&lt;u&gt;18&lt;/u&gt; cents) and 1\5 (240), has multiple significant harmonic entropy minima, but they are all improper. The only saving grace for it is that is has harmonic entropy minima where the ratio between the large and small steps is optimal for melody, and that the generator for these scales is less than 6 cents flat of 8/7. The saving grace of the more lopsided scales is that a syntonic fifth is three generators up from the root.&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;5L 6s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This pattern, with a generator between 2\11 (218.182 cents) and 1\5 (240), has multiple significant harmonic entropy minima, but they are all improper. The only saving grace for it is that is has harmonic entropy minima where the ratio between the large and small steps is optimal for melody, and that the generator for these scales is less than 6 cents flat of 8/7. The saving grace of the more lopsided scales is that a syntonic fifth is three generators up from the root.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 355: / Line 362: @@
 &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;&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;
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+        &lt;td&gt;227.75&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 376: / Line 407: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;227.75&lt;br /&gt;
+         &lt;td&gt;227.586&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;29\153&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;227.451&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&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;&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;76\401&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;227.431&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&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;&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;47\248&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;227.419&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;18\95&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;227.368&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 428: / Line 555: @@
          &lt;td style="text-align: center;"&gt;Boundary of propriety&lt;br /&gt;
 (smaller generators are proper)&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;&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;223.692&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 570: / Line 721: @@
 &lt;/td&gt;
          &lt;td&gt;222.857&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&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;&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;222.6765&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;