1L 8s: 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>2012-11-25 20:46:26 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-11-25 21:15:48 UTC</tt>.

: The original revision id was <tt>~~385887062~~</tt>.

: The original revision id was <tt>385895740</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 MOS, with a generator of up to 1/9edo (133 1/3 cents), represents temperaments like Miracle (2<L<3 s=1) and Negri (3<L<4 s=2). Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval ~~of at least~~ 3/28edo (L~~<=~~ 4 s=3).

<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 MOS, with a generator of up to 1/9edo (133 1/3 cents), represents temperaments like Miracle (2<L<3 s=1) and Negri (3<L<4 s=2). Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval near 3/28edo (L near 4 s=3).

|| 0/1 || || || || || 0 ||= ||

|| 0/1 || || || || || 0 ||= ||= ||

|| || || || || 1/13 || 92 4/13 ||= ||

|| || || || || 1/13 || 92 4/13 ||= ||= ||

|| || || || 1/12 || || 100 ||= L/s=4:

|| || || || 1/12 || || 100 ||= ||= L/s=4:

generators smaller than this are "impractical" ||

|| || || || || 2/23 || 104.347826 ||= ||

|| || || || || 2/23 || 104.347826 ||= ||= ||

|| || || 1/11 || || || 109 1/11 ||= L/s=3:

|| || || 1/11 || || || 109 1/11 ||= Miracle generators from here... ||= L/s=3:

generators smaller than this may be considered "impractical" ||

|| || || || || 3/32 || 112.5 ||= ||

|| || || || || 3/32 || 112.5 ||= ||= ||

|| || || || 2/21 || || 114 2/7 ||= ||

|| || || || 2/21 || || 114 2/7 ||= ||= ||

|| || || || || 3/31 || 116.129032 ||= ||

|| || || || || 3/31 || 116.129032 ||= ||= ||

|| || 1/10 || || || || 120 ||= ||

|| || 1/10 || || || || 120 ||= ...to here;

|| || || || || 4/39 || 123 1/13 ||= ||

Negri generators from here... ||= Boundary of propriety:

|| || || || 3/29 || || 124.137931 ||= ||

generators larger than this are proper ||

|| || || || || 5/48 || 125 ||= ||

|| || || || || 4/39 || 123 1/13 ||= ||= ||

|| || || 2/19 || || || 126.315789 ||= ||

|| || || || 3/29 || || 124.137931 ||= ||= ||

|| || || || || 5/47 || 127.659574 ||= ||

|| || || || || 5/48 || 125 ||= ||= ||

|| || || || 3/28 || || 128 4/7 ||= ||

|| || || 2/19 || || || 126.315789 ||= ...to here ||= ||

|| || || || || 4/37 || 129 27/37 ||= ||

|| || || || || 5/47 || 127.659574 ||= ||= ||

|| 1/9 || || || || || 133 1/3 ||= ||</pre></div>

|| || || || 3/28 || || 128 4/7 ||= ||= ||

|| || || || || 4/37 || 129 27/37 ||= ||= ||

|| 1/9 || || || || || 133 1/3 ||= ||= ||</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>1L 8s</title></head><body>This MOS, with a generator of up to 1/9edo (133 1/3 cents), represents temperaments like Miracle (2&lt;L&lt;3 s=1) and Negri (3&lt;L&lt;4 s=2). Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval ~~of at least~~ 3/28edo (L~~&lt;=~~ 4 s=3).

<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>1L 8s</title></head><body>This MOS, with a generator of up to 1/9edo (133 1/3 cents), represents temperaments like Miracle (2&lt;L&lt;3 s=1) and Negri (3&lt;L&lt;4 s=2). Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval near 3/28edo (L near 4 s=3).

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</td>

<td>0

</td>

</td>

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</td>

<td>92 4/13

</td>

</td>

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</td>

<td>100

</td>

</td>

<td style="text-align: center;">L/s=4:

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</td>

<td>104.347826

</td>

</td>

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</td>

<td>109 1/11

</td>

<td style="text-align: center;">Miracle generators from here...

</td>

<td style="text-align: center;">L/s=3:

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</td>

<td>112.5

</td>

</td>

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</td>

<td>114 2/7

</td>

</td>

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</td>

<td>116.129032

</td>

</td>

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<td>120

</td>

<td style="text-align: center;">...to here;

Negri generators from here...

</td>

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

generators larger than this are proper

</td>

</tr>

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</td>

<td>123 1/13

</td>

</td>

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</td>

<td>124.137931

</td>

</td>

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</td>

<td>125

</td>

</td>

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</td>

<td>126.315789

</td>

<td style="text-align: center;">...to here

</td>

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</td>

<td>127.659574

</td>

</td>

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</td>

<td>128 4/7

</td>

</td>

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</td>

<td>129 27/37

</td>

</td>

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</td>

<td>133 1/3

</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>2012-11-25 20:46:26 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-11-25 21:15:48 UTC</tt>.<br>
-: The original revision id was <tt>385887062</tt>.<br>
+: The original revision id was <tt>385895740</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 MOS, with a generator of up to 1/9edo (133 1/3 cents), represents temperaments like Miracle (2&lt;L&lt;3 s=1) and Negri (3&lt;L&lt;4 s=2). Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval of at least 3/28edo (L&lt;= 4 s=3).
+<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 MOS, with a generator of up to 1/9edo (133 1/3 cents), represents temperaments like Miracle (2&lt;L&lt;3 s=1) and Negri (3&lt;L&lt;4 s=2). Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval near 3/28edo (L near 4 s=3).
-|| 0/1 ||   ||   ||   ||   || 0 ||=   ||
+|| 0/1 ||   ||   ||   ||   || 0 ||=   ||=   ||
-||   ||   ||   ||   || 1/13 || 92 4/13 ||=   ||
+||   ||   ||   ||   || 1/13 || 92 4/13 ||=   ||=   ||
-||   ||   ||   || 1/12 ||   || 100 ||= L/s=4:
+||   ||   ||   || 1/12 ||   || 100 ||=   ||= L/s=4:
 generators smaller than this are "impractical" ||
-||   ||   ||   ||   || 2/23 || 104.347826 ||=   ||
+||   ||   ||   ||   || 2/23 || 104.347826 ||=   ||=   ||
-||   ||   || 1/11 ||   ||   || 109 1/11 ||= L/s=3:
+||   ||   || 1/11 ||   ||   || 109 1/11 ||= Miracle generators from here... ||= L/s=3:
 generators smaller than this may be considered "impractical" ||
-||   ||   ||   ||   || 3/32 || 112.5 ||=   ||
+||   ||   ||   ||   || 3/32 || 112.5 ||=   ||=   ||
-||   ||   ||   || 2/21 ||   || 114 2/7 ||=   ||
+||   ||   ||   || 2/21 ||   || 114 2/7 ||=   ||=   ||
-||   ||   ||   ||   || 3/31 || 116.129032 ||=   ||
+||   ||   ||   ||   || 3/31 || 116.129032 ||=   ||=   ||
-||   || 1/10 ||   ||   ||   || 120 ||=   ||
+||   || 1/10 ||   ||   ||   || 120 ||= ...to here;
-||   ||   ||   ||   || 4/39 || 123 1/13 ||=   ||
+Negri generators from here... ||= Boundary of propriety:
-||   ||   ||   || 3/29 ||   || 124.137931 ||=   ||
+generators larger than this are proper ||
-||   ||   ||   ||   || 5/48 || 125 ||=   ||
+||   ||   ||   ||   || 4/39 || 123 1/13 ||=   ||=   ||
-||   ||   || 2/19 ||   ||   || 126.315789 ||=   ||
+||   ||   ||   || 3/29 ||   || 124.137931 ||=   ||=   ||
-||   ||   ||   ||   || 5/47 || 127.659574 ||=   ||
+||   ||   ||   ||   || 5/48 || 125 ||=   ||=   ||
-||   ||   ||   || 3/28 ||   || 128 4/7 ||=   ||
+||   ||   || 2/19 ||   ||   || 126.315789 ||= ...to here ||=   ||
-||   ||   ||   ||   || 4/37 || 129 27/37 ||=   ||
+||   ||   ||   ||   || 5/47 || 127.659574 ||=   ||=   ||
-|| 1/9 ||   ||   ||   ||   || 133 1/3 ||=   ||</pre></div>
+||   ||   ||   || 3/28 ||   || 128 4/7 ||=   ||=   ||
+||   ||   ||   ||   || 4/37 || 129 27/37 ||=   ||=   ||
+|| 1/9 ||   ||   ||   ||   || 133 1/3 ||=   ||=   ||</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;1L 8s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS, with a generator of up to 1/9edo (133 1/3 cents), represents temperaments like Miracle (2&amp;lt;L&amp;lt;3 s=1) and Negri (3&amp;lt;L&amp;lt;4 s=2). Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval of at least 3/28edo (L&amp;lt;= 4 s=3).&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;1L 8s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS, with a generator of up to 1/9edo (133 1/3 cents), represents temperaments like Miracle (2&amp;lt;L&amp;lt;3 s=1) and Negri (3&amp;lt;L&amp;lt;4 s=2). Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval near 3/28edo (L near 4 s=3).&lt;br /&gt;
@@ Line 43: / Line 45: @@
 &lt;/td&gt;
          &lt;td&gt;0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 59: / Line 63: @@
 &lt;/td&gt;
          &lt;td&gt;92 4/13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 75: / Line 81: @@
 &lt;/td&gt;
          &lt;td&gt;100&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;L/s=4:&lt;br /&gt;
@@ Line 92: / Line 100: @@
 &lt;/td&gt;
          &lt;td&gt;104.347826&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 108: / Line 118: @@
 &lt;/td&gt;
          &lt;td&gt;109 1/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Miracle generators from here...&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;L/s=3:&lt;br /&gt;
@@ Line 125: / Line 137: @@
 &lt;/td&gt;
          &lt;td&gt;112.5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 141: / Line 155: @@
 &lt;/td&gt;
          &lt;td&gt;114 2/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 157: / Line 173: @@
 &lt;/td&gt;
          &lt;td&gt;116.129032&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 174: / Line 192: @@
          &lt;td&gt;120&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;...to here;&lt;br /&gt;
+Negri generators from here...&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Boundary of propriety:&lt;br /&gt;
+generators larger than this are proper&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 189: / Line 211: @@
 &lt;/td&gt;
          &lt;td&gt;123 1/13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 205: / Line 229: @@
 &lt;/td&gt;
          &lt;td&gt;124.137931&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 221: / Line 247: @@
 &lt;/td&gt;
          &lt;td&gt;125&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 237: / Line 265: @@
 &lt;/td&gt;
          &lt;td&gt;126.315789&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;...to here&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 253: / Line 283: @@
 &lt;/td&gt;
          &lt;td&gt;127.659574&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 269: / Line 301: @@
 &lt;/td&gt;
          &lt;td&gt;128 4/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 285: / Line 319: @@
 &lt;/td&gt;
          &lt;td&gt;129 27/37&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 301: / Line 337: @@
 &lt;/td&gt;
          &lt;td&gt;133 1/3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;