13/11: 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:~~Andrew_Heathwaite~~|~~Andrew_Heathwaite~~]] and made on <tt>~~2011~~-10-~~01 16~~:08:03 UTC</tt>.

: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-07 22:38:53 UTC</tt>.

: The original revision id was <tt>~~260507250~~</tt>.

: The original revision id was <tt>513213838</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">In [[13-limit]] [[Just Intonation]], 13/11 is the tridecimal minor third (a Neo-Gothic minor third), measuring about 289.2¢. It is the difference between the 11th and 13th harmonics. The 11th harmonic ([[11_8|11/8]], about 551.3¢) and ~~the~~ 13th harmonic ([[13_8|13/8]], about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third. It can even function as such in a 13-limit [[Neo-Gothic]] minor triad of 22:26:33, with a [[3_2|3/2]] perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant [[16_11|16/11]] as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.

<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">**13/11**

|0 0 0 0 -1 1>

289.20972 cents

[[media type="file" key="jid_13_11_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_13_11_pluck_adu_dr220.mp3|sound sample]]

In [[13-limit]] [[Just Intonation]], 13/11 is the tridecimal minor third (or [[Neo-Gothic]] minor third), measuring about 289.2¢. It is the difference between the 11th and 13th harmonics. The (octave-reduced) 11th harmonic ([[11_8|11/8]], about 551.3¢) and 13th harmonic ([[13_8|13/8]], about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third. It can even function as such in a 13-limit Neo-Gothic minor triad of 22:26:33, with a [[3_2|3/2]] perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant [[16_11|16/11]] as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.

13/11 is the classic [[mediant]] between the simpler and more familiar ratios [[6_5|6/5]] and [[7_6|7/6]], as it can be given as (6+7)/(5+6). This puts in between the latter ratios, slightly closer to 7/6. More complex minor thirds can be generated by taking the mediant between 13/11 and 7/6 (which yields (13+7)/(11+6) = [[20_17|20/17]], the septendecimal subminor third, about 281.4¢) and between 13/11 and 6/5 (which yields (13+6)/(11+5) = [[19_16|19/16]], the overtone minor third of [[19-limit]] JI, about 297.5¢). (See the diagram below.)

||~ subminor and minor third ||= **7/6**

||~ subminor and minor third ||= 7/6

**266.9¢** ||= ||= ||= ||= ||= ||= ||= ||= **6/5**

266.9¢ ||= ||= ||= ||= ||= ||= ||= ||= 6/5

**315.6¢** ||

315.6¢ ||

||~ interval in between ||= ||= <= ||= ||= ||= [[36_35|36:35]]

||~ interval in between ||= ||= << ||= ||= ||= [[36_35|36:35]]

48.7¢ ||= ||= ||= => ||= ||

48.7¢ ||= ||= ||= >> || ||

||~ add mediant (13/11) ||= **7/6**

||~ add mediant (13/11) ||= 7/6

**266.9¢** ||= ||= ||= ||= **13/11**

266.9¢ ||= ||= ||= ||= 13/11

**289.2¢** ||= ||= ||= ||= **6/5**

289.2¢ ||= ||= ||= ||= 6/5

**315.6¢** ||

315.6¢ ||

||~ intervals in between ||= ||= <= ||= [[78_77|78:77]]

||~ intervals in between ||= ||= << ||= [[78_77|78:77]]

22.3¢ ||= => ||= ||= <= ||= [[66_65|66:65]]

22.3¢ ||= >> || ||= << ||= [[66_65|66:65]]

26.4¢ ||= => ||= ||

26.4¢ ||= >> || ||

||~ add mediants (20/17 and 19/16) ||= **7/6**

||~ add mediants (20/17 and 19/16) ||= 7/6

**266.9¢** ||= ||= **20/17**

266.9¢ ||= ||= 20/17

**281.4¢** ||= ||= **13/11**

281.4¢ ||= ||= **13/11**

**289.2¢** ||= ||= **19/16**

**289.2¢** ||= ||= 19/16

**297.5¢** ||= ||= **6/5**

297.5¢ ||= ||= 6/5

**315.6¢** ||

315.6¢ ||

||~ intervals in between ||= ||= <= [[120_119|120:119]] =>

||~ intervals in between ||= ||= << [[120_119|120:119]] >>

14.5¢ ||= ||= <= [[221_220|221:220]] =>

14.5¢ ||= ||= << [[221_220|221:220]] >>

7.9¢ ||= ||= <= [[209_208|209:208]] =>

7.9¢ ||= ||= << [[209_208|209:208]] >>

8.3¢ ||= ||= <= [[96_95|96:95]] =>

8.3¢ ||= ||= << [[96_95|96:95]] >>

18.1¢ ||= ||

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[[http://dkeenan.com/Music/NobleMediant.txt|The Noble Mediant]] (earliest description of 13:11 as the "Neo-Gothic" minor third)</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>13_11</title></head><body>In <a class="wiki_link" href="/13-limit">13-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 13/11 is the tridecimal minor third (a Neo-Gothic minor third), measuring about 289.2¢. It is the difference between the 11th and 13th harmonics. The 11th harmonic (<a class="wiki_link" href="/11_8">11/8</a>, about 551.3¢) and ~~the~~ 13th harmonic (<a class="wiki_link" href="/13_8">13/8</a>, about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third. It can even function as such in a 13-limit ~~<a class="wiki_link" href="/Neo-Gothic">~~Neo-Gothic~~</a>~~ minor triad of 22:26:33, with a <a class="wiki_link" href="/3_2">3/2</a> perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant <a class="wiki_link" href="/16_11">16/11</a> as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.

<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>13_11</title></head><body>13/11

|0 0 0 0 -1 1&gt;

289.20972 cents

<embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fjid_13_11_pluck_adu_dr220.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed> <a href="http://xenharmonic.wikispaces.com/file/view/jid_13_11_pluck_adu_dr220.mp3/513213592/jid_13_11_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_13_11_pluck_adu_dr220.mp3/513213592/jid_13_11_pluck_adu_dr220.mp3');">sound sample</a>

In <a class="wiki_link" href="/13-limit">13-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 13/11 is the tridecimal minor third (or <a class="wiki_link" href="/Neo-Gothic">Neo-Gothic</a> minor third), measuring about 289.2¢. It is the difference between the 11th and 13th harmonics. The (octave-reduced) 11th harmonic (<a class="wiki_link" href="/11_8">11/8</a>, about 551.3¢) and 13th harmonic (<a class="wiki_link" href="/13_8">13/8</a>, about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third. It can even function as such in a 13-limit Neo-Gothic minor triad of 22:26:33, with a <a class="wiki_link" href="/3_2">3/2</a> perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant <a class="wiki_link" href="/16_11">16/11</a> as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.

13/11 is the classic <a class="wiki_link" href="/mediant">mediant</a> between the simpler and more familiar ratios <a class="wiki_link" href="/6_5">6/5</a> and <a class="wiki_link" href="/7_6">7/6</a>, as it can be given as (6+7)/(5+6). This puts in between the latter ratios, slightly closer to 7/6. More complex minor thirds can be generated by taking the mediant between 13/11 and 7/6 (which yields (13+7)/(11+6) = <a class="wiki_link" href="/20_17">20/17</a>, the septendecimal subminor third, about 281.4¢) and between 13/11 and 6/5 (which yields (13+6)/(11+5) = <a class="wiki_link" href="/19_16">19/16</a>, the overtone minor third of <a class="wiki_link" href="/19-limit">19-limit</a> JI, about 297.5¢). (See the diagram below.)

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<th>subminor and minor third

</th>

<td style="text-align: center;"~~><strong~~>7/6~~~~

<td style="text-align: center;">7/6

~~~~266.9¢~~~~

266.9¢

</td>

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</td>

<td style="text-align: center;"~~><strong~~>6/5~~~~

<td style="text-align: center;">6/5

~~~~315.6¢~~~~

315.6¢

</td>

</tr>

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</td>

<td style="text-align: center;">&lt;=

<td style="text-align: center;">&lt;&lt;

</td>

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</td>

<td style="text-align: center;">&gt;&gt;

</td>

<td>

</td>

</tr>

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<th>add mediant (13/11)

</th>

<td style="text-align: center;"~~><strong~~>7/6~~~~

<td style="text-align: center;">7/6

~~~~266.9¢~~~~

266.9¢

</td>

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</td>

<td style="text-align: center;"~~><strong~~>13/11~~~~

<td style="text-align: center;">13/11

~~~~289.2¢~~~~

289.2¢

</td>

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</td>

<td style="text-align: center;"~~><strong~~>6/5~~~~

<td style="text-align: center;">6/5

~~~~315.6¢~~~~

315.6¢

</td>

</tr>

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</td>

<td style="text-align: center;">&lt;=

<td style="text-align: center;">&lt;&lt;

</td>

22.3¢

</td>

<td style="text-align: center;">~~<h1 id="toc1"><a name="x&gt; ||"></a><!-- ws:end:WikiTextHeadingRule:2 --&~~gt;&gt;</~~td>~~

<td style="text-align: center;">&gt;&gt;

~~<td></h1~~>

</td>

<td style="text-align: center;">&lt;=

<td>

</td>

<td style="text-align: center;">&lt;&lt;

</td>

26.4¢

</td>

<td style="text-align: center;">&gt;&gt;

</td>

<td>

</td>

</tr>

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<th>add mediants (20/17 and 19/16)

</th>

<td style="text-align: center;"~~><strong~~>7/6~~~~

<td style="text-align: center;">7/6

~~~~266.9¢~~~~

266.9¢

</td>

</td>

<td style="text-align: center;"~~><strong~~>20/17~~~~

<td style="text-align: center;">20/17

~~~~281.4¢~~~~

281.4¢

</td>

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</td>

<td style="text-align: center;"~~><strong~~>19/16~~~~

<td style="text-align: center;">19/16

~~~~297.5¢~~~~

297.5¢

</td>

</td>

<td style="text-align: center;"~~><strong~~>6/5~~~~

<td style="text-align: center;">6/5

~~~~315.6¢~~~~

315.6¢

</td>

</tr>

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</td>

<td style="text-align: center;">&lt;= <a class="wiki_link" href="/120_119">120:119</a> =&gt;

<td style="text-align: center;">&lt;&lt; <a class="wiki_link" href="/120_119">120:119</a> &gt;&gt;

14.5¢

</td>

</td>

<td style="text-align: center;">&lt;= <a class="wiki_link" href="/221_220">221:220</a> =&gt;

<td style="text-align: center;">&lt;&lt; <a class="wiki_link" href="/221_220">221:220</a> &gt;&gt;

7.9¢

</td>

</td>

<td style="text-align: center;">&lt;= <a class="wiki_link" href="/209_208">209:208</a> =&gt;

<td style="text-align: center;">&lt;&lt; <a class="wiki_link" href="/209_208">209:208</a> &gt;&gt;

8.3¢

</td>

</td>

<td style="text-align: center;">&lt;= <a class="wiki_link" href="/96_95">96:95</a> =&gt;

<td style="text-align: center;">&lt;&lt; <a class="wiki_link" href="/96_95">96:95</a> &gt;&gt;

18.1¢

</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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-01 16:08:03 UTC</tt>.<br>
+: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-07 22:38:53 UTC</tt>.<br>
-: The original revision id was <tt>260507250</tt>.<br>
+: The original revision id was <tt>513213838</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">In [[13-limit]] [[Just Intonation]], 13/11 is the tridecimal minor third (a Neo-Gothic minor third), measuring about 289.2¢. It is the difference between the 11th and 13th harmonics. The 11th harmonic ([[11_8|11/8]], about 551.3¢) and the 13th harmonic ([[13_8|13/8]], about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third. It can even function as such in a 13-limit [[Neo-Gothic]] minor triad of 22:26:33, with a [[3_2|3/2]] perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant [[16_11|16/11]] as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.
+<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">**13/11**
+|0 0 0 0 -1 1&gt;
+.20972 cents
+[[media type="file" key="jid_13_11_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_13_11_pluck_adu_dr220.mp3|sound sample]]
+In [[13-limit]] [[Just Intonation]], 13/11 is the tridecimal minor third (or [[Neo-Gothic]] minor third), measuring about 289.2¢. It is the difference between the 11th and 13th harmonics. The (octave-reduced) 11th harmonic ([[11_8|11/8]], about 551.3¢) and 13th harmonic ([[13_8|13/8]], about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third. It can even function as such in a 13-limit Neo-Gothic minor triad of 22:26:33, with a [[3_2|3/2]] perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant [[16_11|16/11]] as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.
 /11 is the classic [[mediant]] between the simpler and more familiar ratios [[6_5|6/5]] and [[7_6|7/6]], as it can be given as (6+7)/(5+6). This puts in between the latter ratios, slightly closer to 7/6. More complex minor thirds can be generated by taking the mediant between 13/11 and 7/6 (which yields (13+7)/(11+6) = [[20_17|20/17]], the septendecimal subminor third, about 281.4¢) and between 13/11 and 6/5 (which yields (13+6)/(11+5) = [[19_16|19/16]], the overtone minor third of [[19-limit]] JI, about 297.5¢). (See the diagram below.)
-||~ subminor and minor third ||= **7/6**
+||~ subminor and minor third ||= 7/6
-**266.9¢** ||=   ||=   ||=   ||=   ||=   ||=   ||=   ||= **6/5**
+.9¢ ||=   ||=   ||=   ||=   ||=   ||=   ||=   ||= 6/5
-**315.6¢** ||
+.6¢ ||
-||~ interval in between ||=   ||= &lt;= ||=   ||=   ||= [[36_35|36:35]]
+||~ interval in between ||=   ||= &lt;&lt; ||=   ||=   ||= [[36_35|36:35]]
-.7¢ ||=   ||=   ||= =&gt; ||=   ||
+.7¢ ||=   ||=   ||= &gt;&gt; ||   ||
-||~ add mediant (13/11) ||= **7/6**
+||~ add mediant (13/11) ||= 7/6
-**266.9¢** ||=   ||=   ||=   ||= **13/11**
+.9¢ ||=   ||=   ||=   ||= 13/11
-**289.2¢** ||=   ||=   ||=   ||= **6/5**
+.2¢ ||=   ||=   ||=   ||= 6/5
-**315.6¢** ||
+.6¢ ||
-||~ intervals in between ||=   ||= &lt;= ||= [[78_77|78:77]]
+||~ intervals in between ||=   ||= &lt;&lt; ||= [[78_77|78:77]]
-.3¢ ||= =&gt; ||=   ||= &lt;= ||= [[66_65|66:65]]
+.3¢ ||= &gt;&gt; ||   ||= &lt;&lt; ||= [[66_65|66:65]]
-.4¢ ||= =&gt; ||=   ||
+.4¢ ||= &gt;&gt; ||   ||
-||~ add mediants (20/17 and 19/16) ||= **7/6**
+||~ add mediants (20/17 and 19/16) ||= 7/6
-**266.9¢** ||=   ||= **20/17**
+.9¢ ||=   ||= 20/17
-**281.4¢** ||=   ||= **13/11**
+.4¢ ||=   ||= **13/11**
-**289.2¢** ||=   ||= **19/16**
+**289.2¢** ||=   ||= 19/16
-**297.5¢** ||=   ||= **6/5**
+.5¢ ||=   ||= 6/5
-**315.6¢** ||
+.6¢ ||
-||~ intervals in between ||=   ||= &lt;= [[120_119|120:119]] =&gt;
+||~ intervals in between ||=   ||= &lt;&lt; [[120_119|120:119]] &gt;&gt;
-.5¢ ||=   ||= &lt;= [[221_220|221:220]] =&gt;
+.5¢ ||=   ||= &lt;&lt; [[221_220|221:220]] &gt;&gt;
-.9¢ ||=   ||= &lt;= [[209_208|209:208]] =&gt;
+.9¢ ||=   ||= &lt;&lt; [[209_208|209:208]] &gt;&gt;
-.3¢ ||=   ||= &lt;= [[96_95|96:95]] =&gt;
+.3¢ ||=   ||= &lt;&lt; [[96_95|96:95]] &gt;&gt;
 .1¢ ||=   ||
@@ Line 41: / Line 46: @@
 [[http://dkeenan.com/Music/NobleMediant.txt|The Noble Mediant]] (earliest description of 13:11 as the "Neo-Gothic" minor third)</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;13_11&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 13/11 is the tridecimal minor third (a Neo-Gothic minor third), measuring about 289.2¢. It is the difference between the 11th and 13th harmonics. The 11th harmonic (&lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt;, about 551.3¢) and the 13th harmonic (&lt;a class="wiki_link" href="/13_8"&gt;13/8&lt;/a&gt;, about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third. It can even function as such in a 13-limit &lt;a class="wiki_link" href="/Neo-Gothic"&gt;Neo-Gothic&lt;/a&gt; minor triad of 22:26:33, with a &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt; perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant &lt;a class="wiki_link" href="/16_11"&gt;16/11&lt;/a&gt; as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.&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;13_11&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;13/11&lt;/strong&gt;&lt;br /&gt;
+|0 0 0 0 -1 1&amp;gt;&lt;br /&gt;
+.20972 cents&lt;br /&gt;
+&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_13_11_pluck_adu_dr220.mp3?h=20&amp;amp;w=240&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;jid_13_11_pluck_adu_dr220.mp3&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;20&amp;quot; width=&amp;quot;240&amp;quot;/&amp;gt; --&gt;&lt;embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fjid_13_11_pluck_adu_dr220.mp3?file_extension=mp3&amp;autostart=false&amp;repeat=false&amp;showdigits=true&amp;showfsbutton=false&amp;width=240&amp;height=20"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt; &lt;a href="http://xenharmonic.wikispaces.com/file/view/jid_13_11_pluck_adu_dr220.mp3/513213592/jid_13_11_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_13_11_pluck_adu_dr220.mp3/513213592/jid_13_11_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;
+&lt;br /&gt;
+In &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 13/11 is the tridecimal minor third (or &lt;a class="wiki_link" href="/Neo-Gothic"&gt;Neo-Gothic&lt;/a&gt; minor third), measuring about 289.2¢. It is the difference between the 11th and 13th harmonics. The (octave-reduced) 11th harmonic (&lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt;, about 551.3¢) and 13th harmonic (&lt;a class="wiki_link" href="/13_8"&gt;13/8&lt;/a&gt;, about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third. It can even function as such in a 13-limit Neo-Gothic minor triad of 22:26:33, with a &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt; perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant &lt;a class="wiki_link" href="/16_11"&gt;16/11&lt;/a&gt; as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.&lt;br /&gt;
 &lt;br /&gt;
 /11 is the classic &lt;a class="wiki_link" href="/mediant"&gt;mediant&lt;/a&gt; between the simpler and more familiar ratios &lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt; and &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;, as it can be given as (6+7)/(5+6). This puts in between the latter ratios, slightly closer to 7/6. More complex minor thirds can be generated by taking the mediant between 13/11 and 7/6 (which yields (13+7)/(11+6) = &lt;a class="wiki_link" href="/20_17"&gt;20/17&lt;/a&gt;, the septendecimal subminor third, about 281.4¢) and between 13/11 and 6/5 (which yields (13+6)/(11+5) = &lt;a class="wiki_link" href="/19_16"&gt;19/16&lt;/a&gt;, the overtone minor third of &lt;a class="wiki_link" href="/19-limit"&gt;19-limit&lt;/a&gt; JI, about 297.5¢). (See the diagram below.)&lt;br /&gt;
@@ Line 51: / Line 61: @@
          &lt;th&gt;subminor and minor third&lt;br /&gt;
 &lt;/th&gt;
-         &lt;td style="text-align: center;"&gt;&lt;strong&gt;7/6&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7/6&lt;br /&gt;
-&lt;strong&gt;266.9¢&lt;/strong&gt;&lt;br /&gt;
+.9¢&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 68: / Line 78: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;strong&gt;6/5&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;6/5&lt;br /&gt;
-&lt;strong&gt;315.6¢&lt;/strong&gt;&lt;br /&gt;
+.6¢&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 77: / Line 87: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&amp;lt;=&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&amp;lt;&amp;lt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 90: / Line 100: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x&amp;gt; ||"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&amp;gt;&lt;/td&gt;
+         &lt;td style="text-align: center;"&gt;&amp;gt;&amp;gt;&lt;br /&gt;
-         &lt;td&gt;&lt;/h1&gt;
+&lt;/td&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 97: / Line 108: @@
          &lt;th&gt;add mediant (13/11)&lt;br /&gt;
 &lt;/th&gt;
-         &lt;td style="text-align: center;"&gt;&lt;strong&gt;7/6&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7/6&lt;br /&gt;
-&lt;strong&gt;266.9¢&lt;/strong&gt;&lt;br /&gt;
+.9¢&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 106: / Line 117: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;strong&gt;13/11&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;13/11&lt;br /&gt;
-&lt;strong&gt;289.2¢&lt;/strong&gt;&lt;br /&gt;
+.2¢&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 115: / Line 126: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;strong&gt;6/5&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;6/5&lt;br /&gt;
-&lt;strong&gt;315.6¢&lt;/strong&gt;&lt;br /&gt;
+.6¢&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 124: / Line 135: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&amp;lt;=&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&amp;lt;&amp;lt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/78_77"&gt;78:77&lt;/a&gt;&lt;br /&gt;
 .3¢&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="x&amp;gt; ||"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&amp;gt;&lt;/td&gt;
+         &lt;td style="text-align: center;"&gt;&amp;gt;&amp;gt;&lt;br /&gt;
-        &lt;td&gt;&lt;/h1&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&amp;lt;=&lt;br /&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td style="text-align: center;"&gt;&amp;lt;&amp;lt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/66_65"&gt;66:65&lt;/a&gt;&lt;br /&gt;
 .4¢&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="x&amp;gt; ||"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&amp;gt;&lt;/td&gt;
+         &lt;td style="text-align: center;"&gt;&amp;gt;&amp;gt;&lt;br /&gt;
-         &lt;td&gt;&lt;/h1&gt;
+&lt;/td&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 144: / Line 157: @@
          &lt;th&gt;add mediants (20/17 and 19/16)&lt;br /&gt;
 &lt;/th&gt;
-         &lt;td style="text-align: center;"&gt;&lt;strong&gt;7/6&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7/6&lt;br /&gt;
-&lt;strong&gt;266.9¢&lt;/strong&gt;&lt;br /&gt;
+.9¢&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;strong&gt;20/17&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;20/17&lt;br /&gt;
-&lt;strong&gt;281.4¢&lt;/strong&gt;&lt;br /&gt;
+.4¢&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 159: / Line 172: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;strong&gt;19/16&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;19/16&lt;br /&gt;
-&lt;strong&gt;297.5¢&lt;/strong&gt;&lt;br /&gt;
+.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;strong&gt;6/5&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;6/5&lt;br /&gt;
-&lt;strong&gt;315.6¢&lt;/strong&gt;&lt;br /&gt;
+.6¢&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 173: / Line 186: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&amp;lt;= &lt;a class="wiki_link" href="/120_119"&gt;120:119&lt;/a&gt; =&amp;gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&amp;lt;&amp;lt; &lt;a class="wiki_link" href="/120_119"&gt;120:119&lt;/a&gt; &amp;gt;&amp;gt;&lt;br /&gt;
 .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;&amp;lt;= &lt;a class="wiki_link" href="/221_220"&gt;221:220&lt;/a&gt; =&amp;gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&amp;lt;&amp;lt; &lt;a class="wiki_link" href="/221_220"&gt;221:220&lt;/a&gt; &amp;gt;&amp;gt;&lt;br /&gt;
 .9¢&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;&amp;lt;= &lt;a class="wiki_link" href="/209_208"&gt;209:208&lt;/a&gt; =&amp;gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&amp;lt;&amp;lt; &lt;a class="wiki_link" href="/209_208"&gt;209:208&lt;/a&gt; &amp;gt;&amp;gt;&lt;br /&gt;
 .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;&amp;lt;= &lt;a class="wiki_link" href="/96_95"&gt;96:95&lt;/a&gt; =&amp;gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&amp;lt;&amp;lt; &lt;a class="wiki_link" href="/96_95"&gt;96:95&lt;/a&gt; &amp;gt;&amp;gt;&lt;br /&gt;
 .1¢&lt;br /&gt;
 &lt;/td&gt;