31edo: 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:<br>

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-~~05 15~~:27:17 UTC</tt>.<br>

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-06 08:16:46 UTC</tt>.<br>

: The original revision id was <tt>~~601450806~~</tt>.<br>

: The original revision id was <tt>601501924</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>

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===9\31 octave - approx. 348.39¢ - Neutral Third or mid 3rd===

A neutral 3rd, about 1¢ away from 11:9 (347.41¢). 9\31 is half a perfect fifth (making it a suitable generator for [[mohajira|mohajira temperament]]), and also thrice a major semitone. It is closer in quality to a minor third than a major third, but indeed, it is distinct. It is 11¢ shy of 16/13 (359.47¢), suggesting a [[13-limit]] interpretation for 31edo. However, its close proximity to 11/9 makes it hard to hear it as 16/13, which in JI has a different quality (and, as a neutral third, is more "major-like" than "minor-like"). Also, its inversion, 22\31 (851.61¢) is wide of the 13th harmonic by about 11¢, while all the lower harmonics are either near-just or narrow. This means the errors can accumulate, for instance, with 13/9 (636.62¢) represented by 17\31 (658.06¢), a good 21.4¢ sharp.

A neutral 3rd, about 1¢ away from 11:9 (347.41¢). 9\31 is half a perfect fifth (making it a suitable generator for [[mohajira|mohajira temperament]]), and also thrice a major semitone. It is closer in quality to a minor third than a major third, but indeed, it is distinct. It is 11¢ shy of 16/13 (359.47¢), suggesting a [[13-limit]] interpretation for 31edo. However, its close proximity to 11/9 makes it hard to hear it as 16/13, which in JI has a different quality (and, as a neutral third, is more "major-like" than "minor-like"). Also, its inversion, 22\31 (851.61¢) is wide of the 13th harmonic by about 11¢, which leaves the 143rd harmonic only about 2¢ wide after cancelling with the narrow 11th harmonic, while all the lower harmonics are either near-just or narrow. This means the errors can accumulate, for instance, with 13/9 (636.62¢) represented by 17\31 (658.06¢), a good 21.4¢ sharp.

====MOS Scales generated by 9\31:====

||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||

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===12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth or down 4th===

Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). It is also quite close to the [[17-limit]] interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-limit consonances. Generates [[semisept]] temperament.

Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). It is also quite close to the [[17-limit]] interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-limit consonances, and the only intervals in the 31edo octave that are not 15-limit consonances. Generates [[semisept]] temperament.

====MOS Scales generated by 12\31:====

||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||

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|| 27-tone || [[2L 25s]] || 3 || || || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 3 || || || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 ||

|| 29-tone || [[2L 27s]] || 2 || || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 2 || || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 ||

===16\31 Large Tritone or dim 5th===

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= =

=Commas=

31 EDO tempers out the following commas. (Note: This assumes the val < ~~[[tel:~~31 49 72 87 107 115~~|31 49 72 87 107 115]]~~ |, comma values rounded to 5 significant digits.)

31 EDO tempers out the following commas. (Note: This assumes the val < 31 49 72 87 107 115/1 |, comma values rounded to 5 significant digits.)

||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||

||= ||< | -25 7 6 > ||> 31.567 ||= [[ampersand|Ampersand's Comma]] ||= ||= ||

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<br />

<h3 id="toc18"><a name="Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third or mid 3rd"></a>9\31 octave - approx. 348.39¢ - Neutral Third or mid 3rd</h3>

A neutral 3rd, about 1¢ away from 11:9 (347.41¢). 9\31 is half a perfect fifth (making it a suitable generator for <a class="wiki_link" href="/mohajira">mohajira temperament</a>), and also thrice a major semitone. It is closer in quality to a minor third than a major third, but indeed, it is distinct. It is 11¢ shy of 16/13 (359.47¢), suggesting a <a class="wiki_link" href="/13-limit">13-limit</a> interpretation for 31edo. However, its close proximity to 11/9 makes it hard to hear it as 16/13, which in JI has a different quality (and, as a neutral third, is more &quot;major-like&quot; than &quot;minor-like&quot;). Also, its inversion, 22\31 (851.61¢) is wide of the 13th harmonic by about 11¢, while all the lower harmonics are either near-just or narrow. This means the errors can accumulate, for instance, with 13/9 (636.62¢) represented by 17\31 (658.06¢), a good 21.4¢ sharp.<br />

A neutral 3rd, about 1¢ away from 11:9 (347.41¢). 9\31 is half a perfect fifth (making it a suitable generator for <a class="wiki_link" href="/mohajira">mohajira temperament</a>), and also thrice a major semitone. It is closer in quality to a minor third than a major third, but indeed, it is distinct. It is 11¢ shy of 16/13 (359.47¢), suggesting a <a class="wiki_link" href="/13-limit">13-limit</a> interpretation for 31edo. However, its close proximity to 11/9 makes it hard to hear it as 16/13, which in JI has a different quality (and, as a neutral third, is more &quot;major-like&quot; than &quot;minor-like&quot;). Also, its inversion, 22\31 (851.61¢) is wide of the 13th harmonic by about 11¢, which leaves the 143rd harmonic only about 2¢ wide after cancelling with the narrow 11th harmonic, while all the lower harmonics are either near-just or narrow. This means the errors can accumulate, for instance, with 13/9 (636.62¢) represented by 17\31 (658.06¢), a good 21.4¢ sharp.<br />

<h4 id="toc19"><a name="Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third or mid 3rd-MOS Scales generated by 9\31:"></a>MOS Scales generated by 9\31:</h4>

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<br />

<h3 id="toc24"><a name="Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth or down 4th"></a>12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth or down 4th</h3>

Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). It is also quite close to the <a class="wiki_link" href="/17-limit">17-limit</a> interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-limit consonances. Generates <a class="wiki_link" href="/semisept">semisept</a> temperament.<br />

Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). It is also quite close to the <a class="wiki_link" href="/17-limit">17-limit</a> interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-limit consonances, and the only intervals in the 31edo octave that are not 15-limit consonances. Generates <a class="wiki_link" href="/semisept">semisept</a> temperament.<br />

<h4 id="toc25"><a name="Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth or down 4th-MOS Scales generated by 12\31:"></a>MOS Scales generated by 12\31:</h4>

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</table>

~~<br />~~

<br />

<h3 id="toc32"><a name="Intervals-Selected just intervals by error-16\31 Large Tritone or dim 5th"></a>16\31 Large Tritone or dim 5th</h3>

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<h1 id="toc34"> </h1>

<h1 id="toc35"><a name="Commas"></a>Commas</h1>

31 EDO tempers out the following commas. (Note: This assumes the val &lt~~; <a class="wiki_link" href="http://tel.wikispaces.com/31%2049%2072%2087%20107%20115"&gt~~;31 49 72 87 107 115~~<~~/~~a>~~ |, comma values rounded to 5 significant digits.)<br />

31 EDO tempers out the following commas. (Note: This assumes the val &lt; 31 49 72 87 107 115/1 |, comma values rounded to 5 significant digits.)<br />

@@ 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>2016-12-05 15:27:17 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-06 08:16:46 UTC</tt>.<br>
-: The original revision id was <tt>601450806</tt>.<br>
+: The original revision id was <tt>601501924</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 139: / Line 139: @@
 ===9\31 octave - approx. 348.39¢ - Neutral Third or mid 3rd===
-A neutral 3rd, about 1¢ away from 11:9 (347.41¢). 9\31 is half a perfect fifth (making it a suitable generator for [[mohajira|mohajira temperament]]), and also thrice a major semitone. It is closer in quality to a minor third than a major third, but indeed, it is distinct. It is 11¢ shy of 16/13 (359.47¢), suggesting a [[13-limit]] interpretation for 31edo. However, its close proximity to 11/9 makes it hard to hear it as 16/13, which in JI has a different quality (and, as a neutral third, is more "major-like" than "minor-like"). Also, its inversion, 22\31 (851.61¢) is wide of the 13th harmonic by about 11¢, while all the lower harmonics are either near-just or narrow. This means the errors can accumulate, for instance, with 13/9 (636.62¢) represented by 17\31 (658.06¢), a good 21.4¢ sharp.
+A neutral 3rd, about 1¢ away from 11:9 (347.41¢). 9\31 is half a perfect fifth (making it a suitable generator for [[mohajira|mohajira temperament]]), and also thrice a major semitone. It is closer in quality to a minor third than a major third, but indeed, it is distinct. It is 11¢ shy of 16/13 (359.47¢), suggesting a [[13-limit]] interpretation for 31edo. However, its close proximity to 11/9 makes it hard to hear it as 16/13, which in JI has a different quality (and, as a neutral third, is more "major-like" than "minor-like"). Also, its inversion, 22\31 (851.61¢) is wide of the 13th harmonic by about 11¢, which leaves the 143rd harmonic only about 2¢ wide after cancelling with the narrow 11th harmonic, while all the lower harmonics are either near-just or narrow. This means the errors can accumulate, for instance, with 13/9 (636.62¢) represented by 17\31 (658.06¢), a good 21.4¢ sharp.
 ====MOS Scales generated by 9\31:====
 ||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
@@ Line 177: / Line 177: @@
 ===12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth or down 4th===
-Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). It is also quite close to the [[17-limit]] interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-limit consonances. Generates [[semisept]] temperament.
+Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). It is also quite close to the [[17-limit]] interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-limit consonances, and the only intervals in the 31edo octave that are not 15-limit consonances. Generates [[semisept]] temperament.
 ====MOS Scales generated by 12\31:====
 ||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
@@ Line 228: / Line 228: @@
 || 27-tone || [[2L 25s]] || 3 ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 3 ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 ||
 || 29-tone || [[2L 27s]] || 2 ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 2 ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 ||
 ===16\31 Large Tritone or dim 5th===
@@ Line 273: / Line 272: @@
 = =
 =Commas=
-EDO tempers out the following commas. (Note: This assumes the val &lt; [[tel:31 49 72 87 107 115|31 49 72 87 107 115]] |, comma values rounded to 5 significant digits.)
+EDO tempers out the following commas. (Note: This assumes the val &lt; 31 49 72 87 107 115/1 |, comma values rounded to 5 significant digits.)
 ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
 ||=   ||&lt; | -25 7 6 &gt; ||&gt; 31.567 ||= [[ampersand|Ampersand's Comma]] ||=   ||=   ||
@@ Line 3,461: / Line 3,460: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:37:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc18"&gt;&lt;a name="Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third or mid 3rd"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:37 --&gt;9\31 octave - approx. 348.39¢ - Neutral Third or mid 3rd&lt;/h3&gt;
-  A neutral 3rd, about 1¢ away from 11:9 (347.41¢). 9\31 is half a perfect fifth (making it a suitable generator for &lt;a class="wiki_link" href="/mohajira"&gt;mohajira temperament&lt;/a&gt;), and also thrice a major semitone. It is closer in quality to a minor third than a major third, but indeed, it is distinct. It is 11¢ shy of 16/13 (359.47¢), suggesting a &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; interpretation for 31edo. However, its close proximity to 11/9 makes it hard to hear it as 16/13, which in JI has a different quality (and, as a neutral third, is more &amp;quot;major-like&amp;quot; than &amp;quot;minor-like&amp;quot;). Also, its inversion, 22\31 (851.61¢) is wide of the 13th harmonic by about 11¢, while all the lower harmonics are either near-just or narrow. This means the errors can accumulate, for instance, with 13/9 (636.62¢) represented by 17\31 (658.06¢), a good 21.4¢ sharp.&lt;br /&gt;
+  A neutral 3rd, about 1¢ away from 11:9 (347.41¢). 9\31 is half a perfect fifth (making it a suitable generator for &lt;a class="wiki_link" href="/mohajira"&gt;mohajira temperament&lt;/a&gt;), and also thrice a major semitone. It is closer in quality to a minor third than a major third, but indeed, it is distinct. It is 11¢ shy of 16/13 (359.47¢), suggesting a &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; interpretation for 31edo. However, its close proximity to 11/9 makes it hard to hear it as 16/13, which in JI has a different quality (and, as a neutral third, is more &amp;quot;major-like&amp;quot; than &amp;quot;minor-like&amp;quot;). Also, its inversion, 22\31 (851.61¢) is wide of the 13th harmonic by about 11¢, which leaves the 143rd harmonic only about 2¢ wide after cancelling with the narrow 11th harmonic, while all the lower harmonics are either near-just or narrow. This means the errors can accumulate, for instance, with 13/9 (636.62¢) represented by 17\31 (658.06¢), a good 21.4¢ sharp.&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:39:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc19"&gt;&lt;a name="Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third or mid 3rd-MOS Scales generated by 9\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:39 --&gt;MOS Scales generated by 9\31:&lt;/h4&gt;
@@ Line 5,122: / Line 5,121: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:49:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc24"&gt;&lt;a name="Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth or down 4th"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:49 --&gt;12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth or down 4th&lt;/h3&gt;
-  Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). It is also quite close to the &lt;a class="wiki_link" href="/17-limit"&gt;17-limit&lt;/a&gt; interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-limit consonances. Generates &lt;a class="wiki_link" href="/semisept"&gt;semisept&lt;/a&gt; temperament.&lt;br /&gt;
+  Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). It is also quite close to the &lt;a class="wiki_link" href="/17-limit"&gt;17-limit&lt;/a&gt; interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-limit consonances, and the only intervals in the 31edo octave that are not 15-limit consonances. Generates &lt;a class="wiki_link" href="/semisept"&gt;semisept&lt;/a&gt; temperament.&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:51:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc25"&gt;&lt;a name="Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth or down 4th-MOS Scales generated by 12\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:51 --&gt;MOS Scales generated by 12\31:&lt;/h4&gt;
@@ Line 7,471: / Line 7,470: @@
 &lt;/table&gt;
-&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:65:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc32"&gt;&lt;a name="Intervals-Selected just intervals by error-16\31 Large Tritone or dim 5th"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:65 --&gt;16\31 Large Tritone or dim 5th&lt;/h3&gt;
@@ Line 7,721: / Line 7,719: @@
 &lt;!-- ws:start:WikiTextHeadingRule:69:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc34"&gt;&lt;!-- ws:end:WikiTextHeadingRule:69 --&gt; &lt;/h1&gt;
   &lt;!-- ws:start:WikiTextHeadingRule:71:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc35"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:71 --&gt;Commas&lt;/h1&gt;
-EDO tempers out the following commas. (Note: This assumes the val &amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/31%2049%2072%2087%20107%20115"&gt;31 49 72 87 107 115&lt;/a&gt; |, comma values rounded to 5 significant digits.)&lt;br /&gt;
+EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 31 49 72 87 107 115/1 |, comma values rounded to 5 significant digits.)&lt;br /&gt;