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>2015-05~~-23 15~~:24:59 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-05 13:01:28 UTC</tt>.

: The original revision id was <tt>~~551971800~~</tt>.

: The original revision id was <tt>565337619</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 near 3/28edo (L near 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 (133.333 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 ||= ||= ||

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

|| || || || || 1/13 || 92.308 ||= ||= ||

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

|| || || || || 2/23 || 104.~~347826~~ ||= ||= ||

|| || || || || 2/23 || 104.348 ||= ||= ||

|| || || || || || 1200/(8+pi)) || || ||

|| || || || || || 1200/(8+pi) || || ||

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

|| || || 1/11 || || || 109.091 ||= Miracle generators from here... ||= L/s = 3 ||

|| || || || || || 1200/(8+e) || || ||

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

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

|| || || || || || 1200/(9+phi) || || ||

|| || || || || 3/31 || 116.~~129032~~ ||= ||= ||

|| || || || 2/21 || || 114.286 ||= ||= ||

|| || || || || 3/31 || 116.129 ||= ||= ||

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

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

generators larger than this are proper ||

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

|| || || || || || 1200/(8+sqrt(3)) || || ||

|| || || || 3/29 || || 124.~~137931~~ ||= ||= ||

|| || || || || 4/39 || 123.077 ||= ||= ||

|| || || || 3/29 || || 124.138 ||= ||= ||

|| || || || || || 1200/(8+phi) || || ||

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

|| || || 2/19 || || || 126.~~315789~~ ||= ...to here ||= ||

|| || || || || || 1200/(8+pih) || || ||

|| || || || || 5/47 || 127.~~659574~~ ||= ||= ||

|| || || 2/19 || || || 126.316 ||= ...to here ||= ||

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

|| || || || || 5/47 || 127.66 ||= ||= ||

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

|| || || || 3/28 || || 128.571 ||= ||= ||

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

|| || || || || 4/37 || 129.73 ||= ||= ||

|| 1/9 || || || || || 133.333 ||= ||= ||</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 near 3/28edo (L near 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 (133.333 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>1/13

</td>

<td>92 ~~4/13~~

<td>92.308

</td>

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<td>2/23

</td>

<td>104.~~347826~~

<td>104.348

</td>

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<td>

</td>

<td>1200/(8+pi))

<td>1200/(8+pi)

</td>

<td>

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<td>

</td>

<td>109 ~~1/11~~

<td>109.091

</td>

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

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</td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>1200/(9+phi)

</td>

<td>

</td>

<td>

</td>

</tr>

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<td>

</td>

<td>114 ~~2/7~~

<td>114.286

</td>

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<td>3/31

</td>

<td>116.~~129032~~

<td>116.129

</td>

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

generators larger than this are proper

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>1200/(8+sqrt(3))

</td>

<td>

</td>

<td>

</td>

</tr>

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<td>4/39

</td>

<td>123 ~~1/13~~

<td>123.077

</td>

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<td>

</td>

<td>124.~~137931~~

<td>124.138

</td>

</td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>1200/(8+phi)

</td>

<td>

</td>

<td>

</td>

</tr>

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</td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>1200/(8+pih)

</td>

<td>

</td>

<td>

</td>

</tr>

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<td>

</td>

<td>126.~~315789~~

<td>126.316

</td>

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

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<td>5/47

</td>

<td>127.~~659574~~

<td>127.66

</td>

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<td>

</td>

<td>128 ~~4/7~~

<td>128.571

</td>

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<td>4/37

</td>

<td>129 ~~27/37~~

<td>129.73

</td>

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<td>

</td>

<td>133 ~~1/3~~

<td>133.333

</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 15:24:59 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-05 13:01:28 UTC</tt>.<br>
-: The original revision id was <tt>551971800</tt>.<br>
+: The original revision id was <tt>565337619</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 near 3/28edo (L near 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 (133.333 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 ||=   ||=   ||
-||   ||   ||   ||   || 1/13 || 92 4/13 ||=   ||=   ||
+||   ||   ||   ||   || 1/13 || 92.308 ||=   ||=   ||
 ||   ||   ||   || 1/12 ||   || 100 ||=   ||= L/s = 4 ||
-||   ||   ||   ||   || 2/23 || 104.347826 ||=   ||=   ||
+||   ||   ||   ||   || 2/23 || 104.348 ||=   ||=   ||
-||   ||   ||   ||   ||   || 1200/(8+pi)) ||   ||   ||
+||   ||   ||   ||   ||   || 1200/(8+pi) ||   ||   ||
-||   ||   || 1/11 ||   ||   || 109 1/11 ||= Miracle generators from here... ||= L/s = 3 ||
+||   ||   || 1/11 ||   ||   || 109.091 ||= Miracle generators from here... ||= L/s = 3 ||
 ||   ||   ||   ||   ||   || 1200/(8+e) ||   ||   ||
 ||   ||   ||   ||   || 3/32 || 112.5 ||=   ||=   ||
-||   ||   ||   || 2/21 ||   || 114 2/7 ||=   ||=   ||
+||   ||   ||   ||   ||   || 1200/(9+phi) ||   ||   ||
-||   ||   ||   ||   || 3/31 || 116.129032 ||=   ||=   ||
+||   ||   ||   || 2/21 ||   || 114.286 ||=   ||=   ||
+||   ||   ||   ||   || 3/31 || 116.129 ||=   ||=   ||
 ||   || 1/10 ||   ||   ||   || 120 ||= ...to here;
 Negri generators from here... ||= Boundary of propriety:
 generators larger than this are proper ||
-||   ||   ||   ||   || 4/39 || 123 1/13 ||=   ||=   ||
+||   ||   ||   ||   ||   || 1200/(8+&lt;span style="line-height: 1.5;"&gt;sqrt(3))&lt;/span&gt; ||   ||   ||
-||   ||   ||   || 3/29 ||   || 124.137931 ||=   ||=   ||
+||   ||   ||   ||   || 4/39 || 123.077 ||=   ||=   ||
+||   ||   ||   || 3/29 ||   || 124.138 ||=   ||=   ||
+||   ||   ||   ||   ||   || 1200/(8+phi) ||   ||   ||
 ||   ||   ||   ||   || 5/48 || 125 ||=   ||=   ||
-||   ||   || 2/19 ||   ||   || 126.315789 ||= ...to here ||=   ||
+||   ||   ||   ||   ||   || 1200/(8+pih) ||   ||   ||
-||   ||   ||   ||   || 5/47 || 127.659574 ||=   ||=   ||
+||   ||   || 2/19 ||   ||   || 126.316 ||= ...to here ||=   ||
-||   ||   ||   || 3/28 ||   || 128 4/7 ||=   ||=   ||
+||   ||   ||   ||   || 5/47 || 127.66 ||=   ||=   ||
-||   ||   ||   ||   || 4/37 || 129 27/37 ||=   ||=   ||
+||   ||   ||   || 3/28 ||   || 128.571 ||=   ||=   ||
-|| 1/9 ||   ||   ||   ||   || 133 1/3 ||=   ||=   ||</pre></div>
+||   ||   ||   ||   || 4/37 || 129.73 ||=   ||=   ||
+|| 1/9 ||   ||   ||   ||   || 133.333 ||=   ||=   ||</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 near 3/28edo (L near 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 (133.333 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 62: / Line 66: @@
          &lt;td&gt;1/13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;92 4/13&lt;br /&gt;
+         &lt;td&gt;92.308&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 98: / Line 102: @@
          &lt;td&gt;2/23&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;104.347826&lt;br /&gt;
+         &lt;td&gt;104.348&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 116: / Line 120: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1200/(8+pi))&lt;br /&gt;
+         &lt;td&gt;1200/(8+pi)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 134: / Line 138: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;109 1/11&lt;br /&gt;
+         &lt;td&gt;109.091&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Miracle generators from here...&lt;br /&gt;
@@ Line 175: / Line 179: @@
 &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;1200/(9+phi)&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;/tr&gt;
@@ Line 188: / Line 210: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;114 2/7&lt;br /&gt;
+         &lt;td&gt;114.286&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 206: / Line 228: @@
          &lt;td&gt;3/31&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;116.129032&lt;br /&gt;
+         &lt;td&gt;116.129&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 231: / Line 253: @@
          &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;
+    &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;1200/(8+&lt;span style="line-height: 1.5;"&gt;sqrt(3))&lt;/span&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;/tr&gt;
@@ Line 244: / Line 284: @@
          &lt;td&gt;4/39&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;123 1/13&lt;br /&gt;
+         &lt;td&gt;123.077&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 262: / Line 302: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;124.137931&lt;br /&gt;
+         &lt;td&gt;124.138&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;
+&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;1200/(8+phi)&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;/tr&gt;
@@ Line 285: / Line 343: @@
 &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;1200/(8+pih)&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;/tr&gt;
@@ Line 298: / Line 374: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;126.315789&lt;br /&gt;
+         &lt;td&gt;126.316&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;...to here&lt;br /&gt;
@@ Line 316: / Line 392: @@
          &lt;td&gt;5/47&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;127.659574&lt;br /&gt;
+         &lt;td&gt;127.66&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 334: / Line 410: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;128 4/7&lt;br /&gt;
+         &lt;td&gt;128.571&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 352: / Line 428: @@
          &lt;td&gt;4/37&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;129 27/37&lt;br /&gt;
+         &lt;td&gt;129.73&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 370: / Line 446: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;133 1/3&lt;br /&gt;
+         &lt;td&gt;133.333&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;