Golden meantone: 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:~~xenwolf~~|~~xenwolf~~]] and made on <tt>~~2014~~-06-~~03 03~~:25:29 UTC</tt>.

: This revision was by author [[User:MartinGough|MartinGough]] and made on <tt>2015-02-22 15:02:18 UTC</tt>.

: The original revision id was <tt>~~512577552~~</tt>.

: The original revision id was <tt>541721110</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.

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==Construction==

~~If you use two neighboring~~ numbers from the Fibonacci ~~series~~ 1 1 2 3 5 ~~8 13 21~~... ~~you get~~ the ~~following approximations~~:

Golden Meantone is approximated with increasing accuracy by the infinite sequence of temperaments indicated in the table below. In any meantone temperament the five intervals in the column headings form part of a Fibonacci sequence (in the sense that each adjacent pair sums to the interval to its immediate right) and in these equal temperaments the sizes of these intervals (expressed in step units) are consecutive numbers from the integer Fibonacci sequence 0, 1, 1, 2, 3, 5... Both the rows and the columns of the table form Fibonacci sequences, and because the five intervals sums to an octave, the octave cardinalities in the first column are formed by summing the five numbers to their right. As the cardinality increases the interval sequence better approximates a geometric progression.

~~1, 1 -~~> [[7edo]]

1, 2 -> [[12edo]]

|| # //Temperament//# || # //chroma//# || #//semitone//# || #//tone//# || #//minor third//# || #//fourth//# ||

2, 3 -> [[19edo]]

|| # [[xenharmonic/7edo|7edo]] || # 0 || #1 || #1 || #2 || #3 ||

3, 5 -> [[31edo]]

|| # [[xenharmonic/12edo|12edo]] || # 1 || #1 || #2 || #3 || #5 ||

5, 8 -> [[50edo]]

|| # [[xenharmonic/19edo|19edo]] || # 1 || #2 || #3 || #5 || #8 ||

8, 13 -> [[81edo]]

|| # [[xenharmonic/31edo|31edo]] || # 2 || #3 || #5 || #8 || #13 ||

13, 21 -> [[~~131edo~~]]

|| # [[xenharmonic/50edo|50edo]] || # 3 || #5 || #8 || #13 || #21 ||

|| # [[xenharmonic/81edo|81edo]] || # 5 || #8 || #13 || #21 || #34 ||

|| # [[xenharmonic/131edo|131edo]] || # 8 || #13 || #21 || #34 || #55 ||

|| # ... || # ... || ... || ... || #... || #... ||

The success of Golden Meantone can be understood in terms of the properties of [[Logarithmic approximants|quadratic approximants]] (q.v.) and the small size of the [[32805_32768|schisma]].

==Evaluation==

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<h2 id="toc0"><a name="x-Construction"></a>Construction</h2>

~~If you use two neighboring~~ numbers from the Fibonacci ~~series~~ 1 1 2 3 5 ~~8 13 21~~... ~~you get~~ the ~~following approximations~~:

Golden Meantone is approximated with increasing accuracy by the infinite sequence of temperaments indicated in the table below. In any meantone temperament the five intervals in the column headings form part of a Fibonacci sequence (in the sense that each adjacent pair sums to the interval to its immediate right) and in these equal temperaments the sizes of these intervals (expressed in step units) are consecutive numbers from the integer Fibonacci sequence 0, 1, 1, 2, 3, 5... Both the rows and the columns of the table form Fibonacci sequences, and because the five intervals sums to an octave, the octave cardinalities in the first column are formed by summing the five numbers to their right. As the cardinality increases the interval sequence better approximates a geometric progression.

~~1, 1 -~~&~~amp~~;gt; <a class="wiki_link" href="/7edo">7edo</a>

1, 2 -&~~amp~~;gt; <a class="wiki_link" href="/12edo">12edo</a>

2, 3 -&~~amp~~;gt; <a class="wiki_link" href="/19edo">19edo</a>

3, 5 -&~~amp~~;gt; <a class="wiki_link" href="/31edo">31edo</a>

5, 8 -&~~amp~~;gt; <a class="wiki_link" href="/50edo">50edo</a>

<tr>

8, 13 -&~~amp~~;gt; <a class="wiki_link" href="/81edo">81edo</a>

<td># Temperament#

13, 21 -&~~amp~~;gt; <a class="wiki_link" href="/131edo">131edo</a>

</td>

<td># chroma#

</td>

<td>#semitone#

</td>

<td>#tone#

</td>

<td>#minor third#

</td>

<td>#fourth#

</td>

</tr>

<tr>

</td>

<td># 0

</td>

<td>#1

</td>

<td>#1

</td>

<td>#2

</td>

<td>#3

</td>

</tr>

<tr>

</td>

<td># 1

</td>

<td>#1

</td>

<td>#2

</td>

<td>#3

</td>

<td>#5

</td>

</tr>

<tr>

</td>

<td># 1

</td>

<td>#2

</td>

<td>#3

</td>

<td>#5

</td>

<td>#8

</td>

</tr>

<tr>

</td>

<td># 2

</td>

<td>#3

</td>

<td>#5

</td>

<td>#8

</td>

<td>#13

</td>

</tr>

<tr>

</td>

<td># 3

</td>

<td>#5

</td>

<td>#8

</td>

<td>#13

</td>

<td>#21

</td>

</tr>

<tr>

</td>

<td># 5

</td>

<td>#8

</td>

<td>#13

</td>

<td>#21

</td>

<td>#34

</td>

</tr>

<tr>

</td>

<td># 8

</td>

<td>#13

</td>

<td>#21

</td>

<td>#34

</td>

<td>#55

</td>

</tr>

<tr>

<td># ...

</td>

<td># ...

</td>

<td>...

</td>

<td>...

</td>

<td>#...

</td>

<td>#...

</td>

</tr>

</table>

The success of Golden Meantone can be understood in terms of the properties of <a class="wiki_link" href="/Logarithmic%20approximants">quadratic approximants</a> (q.v.) and the small size of the <a class="wiki_link" href="/32805_32768">schisma</a>.

<h2 id="toc1"><a name="x-Evaluation"></a>Evaluation</h2>

@@ 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:xenwolf|xenwolf]] and made on <tt>2014-06-03 03:25:29 UTC</tt>.<br>
+: This revision was by author [[User:MartinGough|MartinGough]] and made on <tt>2015-02-22 15:02:18 UTC</tt>.<br>
-: The original revision id was <tt>512577552</tt>.<br>
+: The original revision id was <tt>541721110</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 29: / Line 29: @@
 ==Construction==
-If you use two neighboring numbers from the Fibonacci series 1 1 2 3 5 8 13 21... you get the following approximations:
+Golden Meantone is approximated with increasing accuracy by the infinite sequence of temperaments indicated in the table below. In any meantone temperament the five intervals in the column headings form part of a Fibonacci sequence (in the sense that each adjacent pair sums to the interval to its immediate right) and in these equal temperaments the sizes of these intervals (expressed in step units) are consecutive numbers from the integer Fibonacci sequence 0, 1, 1, 2, 3, 5... Both the rows and the columns of the table form Fibonacci sequences, and because the five intervals sums to an octave, the octave cardinalities in the first column are formed by summing the five numbers to their right. As the cardinality increases the interval sequence better approximates a geometric progression.
-, 1 -&gt; [[7edo]]
-, 2 -&gt; [[12edo]]
+|| &lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;//Temperament//&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt; || &lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;//chroma//&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt; || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;//semitone//&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt; || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;//tone//&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt; || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;//minor third//&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt; || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;//fourth//&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt; ||
-, 3 -&gt; [[19edo]]
+|| &lt;span style="color: #ffffff;"&gt;# [[xenharmonic/7edo|7edo]]&lt;/span&gt; || &lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;0 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;1 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;1 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;2 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;3 ||
-, 5 -&gt; [[31edo]]
+|| &lt;span style="color: #ffffff;"&gt;# [[xenharmonic/12edo|12edo]]&lt;/span&gt; || &lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;1 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;1 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;2 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;3 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;5 ||
-, 8 -&gt; [[50edo]]
+|| &lt;span style="color: #ffffff;"&gt;# [[xenharmonic/19edo|19edo]]&lt;/span&gt; || &lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;1 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;2 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;3 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;5 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;8 ||
-, 13 -&gt; [[81edo]]
+|| &lt;span style="color: #ffffff;"&gt;&lt;span style="color: #000000;"&gt; &lt;/span&gt;&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;[[xenharmonic/31edo|31edo]]&lt;/span&gt; || &lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;2 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;3 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;5 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;8 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;13 ||
-, 21 -&gt; [[131edo]]
+|| &lt;span style="color: #ffffff;"&gt;# [[xenharmonic/50edo|50edo]]&lt;/span&gt; || &lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;3 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;5 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;8 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;13 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;21 ||
+|| &lt;span style="color: #ffffff;"&gt;# [[xenharmonic/81edo|81edo]]&lt;/span&gt; || &lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;5 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;8 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;13 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;21 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;34 ||
+|| &lt;span style="color: #ffffff;"&gt;# [[xenharmonic/131edo|131edo]]&lt;/span&gt; || &lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;8 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;13 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;21 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;34 || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;55 ||
+|| &lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;... || &lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;... || ... || ... || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;... || &lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;... ||
+The success of Golden Meantone can be understood in terms of the properties of [[Logarithmic approximants|quadratic approximants]] (q.v.) and the small size of the [[32805_32768|schisma]].
 ==Evaluation==
@@ Line 76: / Line 81: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Construction"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;Construction&lt;/h2&gt;
-  If you use two neighboring numbers from the Fibonacci series 1 1 2 3 5 8 13 21... you get the following approximations:&lt;br /&gt;
+  Golden Meantone is approximated with increasing accuracy by the infinite sequence of temperaments indicated in the table below. In any meantone temperament the five intervals in the column headings form part of a Fibonacci sequence (in the sense that each adjacent pair sums to the interval to its immediate right) and in these equal temperaments the sizes of these intervals (expressed in step units) are consecutive numbers from the integer Fibonacci sequence 0, 1, 1, 2, 3, 5... Both the rows and the columns of the table form Fibonacci sequences, and because the five intervals sums to an octave, the octave cardinalities in the first column are formed by summing the five numbers to their right. As the cardinality increases the interval sequence better approximates a geometric progression.&lt;br /&gt;
-, 1 -&amp;gt; &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;&lt;br /&gt;
+&lt;br /&gt;
-, 2 -&amp;gt; &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;&lt;br /&gt;
-, 3 -&amp;gt; &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;&lt;br /&gt;
-, 5 -&amp;gt; &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
-, 8 -&amp;gt; &lt;a class="wiki_link" href="/50edo"&gt;50edo&lt;/a&gt;&lt;br /&gt;
+    &lt;tr&gt;
-, 13 -&amp;gt; &lt;a class="wiki_link" href="/81edo"&gt;81edo&lt;/a&gt;&lt;br /&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;&lt;em&gt;Temperament&lt;/em&gt;&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;&lt;br /&gt;
-, 21 -&amp;gt; &lt;a class="wiki_link" href="/131edo"&gt;131edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;&lt;em&gt;chroma&lt;/em&gt;&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;&lt;em&gt;semitone&lt;/em&gt;&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;&lt;em&gt;tone&lt;/em&gt;&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;&lt;em&gt;minor third&lt;/em&gt;&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;&lt;em&gt;fourth&lt;/em&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;# &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/7edo"&gt;7edo&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;3&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;# &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/12edo"&gt;12edo&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;5&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;# &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/19edo"&gt;19edo&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;8&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;&lt;span style="color: #000000;"&gt; &lt;/span&gt;&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/31edo"&gt;31edo&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;13&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;# &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/50edo"&gt;50edo&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;21&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;# &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/81edo"&gt;81edo&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;21&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;34&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;# &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/131edo"&gt;131edo&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;21&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;34&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;55&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;# &lt;/span&gt;...&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;# &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;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;...&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;span style="color: #ffffff;"&gt;#&lt;/span&gt;...&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;br /&gt;
+The success of Golden Meantone can be understood in terms of the properties of &lt;a class="wiki_link" href="/Logarithmic%20approximants"&gt;quadratic approximants&lt;/a&gt; (q.v.) and the small size of the &lt;a class="wiki_link" href="/32805_32768"&gt;schisma&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Evaluation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;Evaluation&lt;/h2&gt;