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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox Interval |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | Name = (greater) tridecimal neutral third, octave-reduced 13th subharmonic |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-07 23:21:20 UTC</tt>.<br>
| | | Color name = 3u3, thu 3rd |
| : The original revision id was <tt>513215274</tt>.<br>
| | | Sound = jid_16_13_pluck_adu_dr220.mp3 |
| : 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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| <h4>Original Wikitext content:</h4>
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| <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">**16/13**
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| 359.47234 cents
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| [[media type="file" key="jid_16_13_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_16_13_pluck_adu_dr220.mp3|sound sample]]
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| In [[13-limit]] [[Just Intonation]], 16/13 is a tridecimal (13-based) neutral third measuring about 359.5¢. It is the inversion of [[13_8|13/8]], the 13th harmonic. It differs from [[5_4|5/4]] by [[65_64|65/64]], about 26.8¢. It differs from the undecimal neutral third [[11_9|11/9]] by [[144_143|144/143]], about 12¢. A [[List of root-3rd-P5 triads in JI|root-3rd-P5 triad]] featuring 16/13 is 26:32:39, which introduces another tridecimal neutral third, [[39_32|39/32]], which measures about 342.5¢. The interval between these two intervals is 512/507, about 17¢. While 16/13 is utonal, 39/32 is otonal, as it is the 39th overtone of the [[OverToneSeries|harmonic series]]. | | In [[13-limit]] [[just intonation]], '''16/13''', the '''(greater) tridecimal neutral third''', is a 13-limit-based interval measuring about 359.5¢. It is the inversion of [[13/8]], the 13th harmonic. |
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| See: [[Gallery of Just Intervals]]</pre></div>
| | 16/13 differs from the Pythagorean major third [[81/64]] by [[1053/1024]], about 48¢, from the classic major third [[5/4]] by [[65/64]], about 27¢, from the undecimal neutral third [[11/9]] by [[144/143]], about 12¢, and from the rastmic neutral third [[27/22]] by [[352/351]], about 4.9¢. A [[List_of_root-3rd-P5_triads_in_JI|root-3rd-P5 triad]] featuring 16/13 is 26:32:39, which introduces another tridecimal neutral third, [[39/32]], which measures about 342.5¢. The interval between these two intervals is [[512/507]], about 17¢. While 16/13 is utonal, 39/32 is otonal, as it is the 39th harmonic of the [[harmonic series]]. |
| <h4>Original HTML content:</h4>
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| <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>16_13</title></head><body><strong>16/13</strong><br />
| | 16/13 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos. |
| |4 0 0 0 0 -1&gt;<br />
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| 359.47234 cents<br />
| | 16/13 is near the border-region between neutral thirds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds, while still sounding slightly darker than a major third like [[5/4]]. |
| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_16_13_pluck_adu_dr220.mp3?h=20&amp;w=240&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;jid_16_13_pluck_adu_dr220.mp3&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;20&quot; width=&quot;240&quot;/&gt; --><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_16_13_pluck_adu_dr220.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed><!-- ws:end:WikiTextMediaRule:0 --> <a href="http://xenharmonic.wikispaces.com/file/view/jid_16_13_pluck_adu_dr220.mp3/513215244/jid_16_13_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_16_13_pluck_adu_dr220.mp3/513215244/jid_16_13_pluck_adu_dr220.mp3');">sound sample</a><br />
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| | == See also == |
| In <a class="wiki_link" href="/13-limit">13-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 16/13 is a tridecimal (13-based) neutral third measuring about 359.5¢. It is the inversion of <a class="wiki_link" href="/13_8">13/8</a>, the 13th harmonic. It differs from <a class="wiki_link" href="/5_4">5/4</a> by <a class="wiki_link" href="/65_64">65/64</a>, about 26.8¢. It differs from the undecimal neutral third <a class="wiki_link" href="/11_9">11/9</a> by <a class="wiki_link" href="/144_143">144/143</a>, about 12¢. A <a class="wiki_link" href="/List%20of%20root-3rd-P5%20triads%20in%20JI">root-3rd-P5 triad</a> featuring 16/13 is 26:32:39, which introduces another tridecimal neutral third, <a class="wiki_link" href="/39_32">39/32</a>, which measures about 342.5¢. The interval between these two intervals is 512/507, about 17¢. While 16/13 is utonal, 39/32 is otonal, as it is the 39th overtone of the <a class="wiki_link" href="/OverToneSeries">harmonic series</a>.<br />
| | * [[13/8]] – its [[octave complement]] |
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| | * [[39/32]] – its [[fifth complement]] |
| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div> | | * [[Gallery of Just Intervals]] |
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| | [[Category:Third]] |
| | [[Category:Neutral third]] |
In 13-limit just intonation, 16/13, the (greater) tridecimal neutral third, is a 13-limit-based interval measuring about 359.5¢. It is the inversion of 13/8, the 13th harmonic.
16/13 differs from the Pythagorean major third 81/64 by 1053/1024, about 48¢, from the classic major third 5/4 by 65/64, about 27¢, from the undecimal neutral third 11/9 by 144/143, about 12¢, and from the rastmic neutral third 27/22 by 352/351, about 4.9¢. A root-3rd-P5 triad featuring 16/13 is 26:32:39, which introduces another tridecimal neutral third, 39/32, which measures about 342.5¢. The interval between these two intervals is 512/507, about 17¢. While 16/13 is utonal, 39/32 is otonal, as it is the 39th harmonic of the harmonic series.
16/13 is a fraction of a cent away from the neutral third found in the 10n family of edos.
16/13 is near the border-region between neutral thirds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds, while still sounding slightly darker than a major third like 5/4.
See also