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	<id>https://en.xen.wiki/index.php?action=history&amp;feed=atom&amp;title=User%3AHotcrystal0%2F31-tone_commas</id>
	<title>User:Hotcrystal0/31-tone commas - Revision history</title>
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	<updated>2026-06-30T04:51:49Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://en.xen.wiki/index.php?title=User:Hotcrystal0/31-tone_commas&amp;diff=226242&amp;oldid=prev</id>
		<title>Hotcrystal0 at 16:26, 17 March 2026</title>
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		<updated>2026-03-17T16:26:49Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 16:26, 17 March 2026&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;There are three notable 31-tone circular commas involving octave-reduced harmonics.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;There are three notable 31-tone circular commas involving octave-reduced harmonics&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;. These are tempered out in miscellaneous [[31st-octave temperaments]]&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==31-comma==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==31-comma==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Hotcrystal0</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=User:Hotcrystal0/31-tone_commas&amp;diff=226240&amp;oldid=prev</id>
		<title>Hotcrystal0: Created page with &quot;There are three notable 31-tone circular commas involving octave-reduced harmonics.  ==31-comma==  {{Infobox Interval |Monzo = -49 31 |Name = 31-comma |Comma = yes }}  The 31-comma is the amount by which 31 3/2 perfect fifths exceed 18 octaves.  &lt;br /&gt;  &lt;br /&gt;  &lt;br /&gt;  &lt;br /&gt;  &lt;br /&gt;  &lt;br /&gt;  &lt;br /&gt;  &lt;br /&gt;  &lt;br /&gt;  &lt;br /&gt;  ==31-5-comma==  {{Infobox Interval |Monzo = 72 0 -31 |Name = 31-5-comma |Comma = yes }}  The 31-5-comma is the amount by which 31 5/4 classic...&quot;</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=User:Hotcrystal0/31-tone_commas&amp;diff=226240&amp;oldid=prev"/>
		<updated>2026-03-17T16:25:07Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;There are three notable 31-tone circular commas involving octave-reduced harmonics.  ==31-comma==  {{Infobox Interval |Monzo = -49 31 |Name = 31-comma |Comma = yes }}  The 31-comma is the amount by which 31 &lt;a href=&quot;/w/3/2&quot; title=&quot;3/2&quot;&gt;3/2&lt;/a&gt; perfect fifths exceed 18 octaves.  &amp;lt;br /&amp;gt;  &amp;lt;br /&amp;gt;  &amp;lt;br /&amp;gt;  &amp;lt;br /&amp;gt;  &amp;lt;br /&amp;gt;  &amp;lt;br /&amp;gt;  &amp;lt;br /&amp;gt;  &amp;lt;br /&amp;gt;  &amp;lt;br /&amp;gt;  &amp;lt;br /&amp;gt;  ==31-5-comma==  {{Infobox Interval |Monzo = 72 0 -31 |Name = 31-5-comma |Comma = yes }}  The 31-5-comma is the amount by which 31 &lt;a href=&quot;/w/5/4&quot; title=&quot;5/4&quot;&gt;5/4&lt;/a&gt; classic...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;There are three notable 31-tone circular commas involving octave-reduced harmonics.&lt;br /&gt;
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==31-comma==&lt;br /&gt;
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{{Infobox Interval&lt;br /&gt;
|Monzo = -49 31&lt;br /&gt;
|Name = 31-comma&lt;br /&gt;
|Comma = yes&lt;br /&gt;
}}&lt;br /&gt;
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The 31-comma is the amount by which 31 [[3/2]] perfect fifths exceed 18 octaves.&lt;br /&gt;
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==31-5-comma==&lt;br /&gt;
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{{Infobox Interval&lt;br /&gt;
|Monzo = 72 0 -31&lt;br /&gt;
|Name = 31-5-comma&lt;br /&gt;
|Comma = yes&lt;br /&gt;
}}&lt;br /&gt;
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The 31-5-comma is the amount by which 31 [[5/4]] classical major thirds fall short of 10 octaves.&lt;br /&gt;
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==31-7-comma==&lt;br /&gt;
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{{Infobox Interval&lt;br /&gt;
|Monzo = -87 0 0 31&lt;br /&gt;
|Name = 31-7-comma&lt;br /&gt;
|Comma = yes&lt;br /&gt;
}}&lt;br /&gt;
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The 31-7-comma is the amount by which 31 [[7/4]] harmonic sevenths exceed 25 octaves.&lt;/div&gt;</summary>
		<author><name>Hotcrystal0</name></author>
	</entry>
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