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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 = (lesser) tridecimal neutral sixth |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-07 22:24:46 UTC</tt>.<br>
| | | Color name = 3o6, tho 6th |
| : The original revision id was <tt>513213338</tt>.<br>
| | | Sound = jid_13_8_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">**13/8**
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| |-3 0 0 0 0 1> | |
| 840.52766 cents
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| [[media type="file" key="jid_13_8_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_13_8_pluck_adu_dr220.mp3|sound sample]]
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| 13/8 is a neutral sixth measuring about 840.5¢, falling between the categories of minor sixth and major sixth. In [[13-limit]] [[Just Intonation]], 13/8, as an octave-reduced 13th harmonic, is treated as a basic component of harmony. In the harmonic series and in chords based on it, 13/8 sits between the more familiar consonances of [[3_2|3/2]] and [[7_4|7/4]], separated from each by the [[superparticular]] ratios [[13_12|13/12]] and [[14_13|14/13]], respectively. It differs from the 11-limit neutral sixth [[18_11|18/11]] by 144/143, about 12.1¢. | | '''13/8''' is the '''(lesser) tridecimal neutral sixth''', which measures about 840.5¢, falling between the categories of minor sixth and major sixth. In [[13-limit]] [[just intonation]], 13/8, as an octave-reduced 13th harmonic, is treated as a basic component of harmony. In the harmonic series and in chords based on it, 13/8 sits between the more familiar consonances of [[3/2]] and [[7/4]], separated from each by the [[superparticular]] ratios [[13/12]] and [[14/13]], respectively. The word "lesser" is added when necessary to differentiate it from [[64/39]], another tridecimal neutral sixth. It may also be treated as a type of augmented fifth, as the sum of [[5/4]] and [[13/10]]. |
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| See: [[Gallery of Just Intervals]]</pre></div>
| | 13/8 differs from the Pythagorean minor sixth [[128/81]] by [[1053/1024]], about 48¢, from the classic minor sixth [[8/5]] by [[65/64]], about 27¢, from the undecimal neutral sixth [[18/11]] by [[144/143]], about 12¢, and from the rastmic neutral sixth [[44/27]] by [[352/351]], about 4.9¢. |
| <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>13_8</title></head><body><strong>13/8</strong><br />
| | == Approximation == |
| |-3 0 0 0 0 1&gt;<br />
| | 13/8 is a fraction of a cent away from the neutral sixth found in the [[10edo|10''n''-edo]] family (7\10). |
| 840.52766 cents<br />
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| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_13_8_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_13_8_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_13_8_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_13_8_pluck_adu_dr220.mp3/513213282/jid_13_8_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_13_8_pluck_adu_dr220.mp3/513213282/jid_13_8_pluck_adu_dr220.mp3');">sound sample</a><br />
| | This interval is a ratio of two consecutive Fibonacci numbers, therefore it approximates the [[golden ratio]]. In this case, 13/8 is ~7.4 [[cent|¢]] sharp of the golden ratio. |
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| 13/8 is a neutral sixth measuring about 840.5¢, falling between the categories of minor sixth and major sixth. In <a class="wiki_link" href="/13-limit">13-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 13/8, as an octave-reduced 13th harmonic, is treated as a basic component of harmony. In the harmonic series and in chords based on it, 13/8 sits between the more familiar consonances of <a class="wiki_link" href="/3_2">3/2</a> and <a class="wiki_link" href="/7_4">7/4</a>, separated from each by the <a class="wiki_link" href="/superparticular">superparticular</a> ratios <a class="wiki_link" href="/13_12">13/12</a> and <a class="wiki_link" href="/14_13">14/13</a>, respectively. It differs from the 11-limit neutral sixth <a class="wiki_link" href="/18_11">18/11</a> by 144/143, about 12.1¢.<br /> | | == See also == |
| <br />
| | * [[16/13]] – its [[octave complement]] |
| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
| | * [[64/39]] – the greater tridecimal neutral sixth |
| | * [[Gallery of just intervals]] |
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| | [[Category:Sixth]] |
| | [[Category:Neutral sixth]] |
| | [[Category:Golden ratio approximations]] |
13/8 is the (lesser) tridecimal neutral sixth, which measures about 840.5¢, falling between the categories of minor sixth and major sixth. In 13-limit just intonation, 13/8, as an octave-reduced 13th harmonic, is treated as a basic component of harmony. In the harmonic series and in chords based on it, 13/8 sits between the more familiar consonances of 3/2 and 7/4, separated from each by the superparticular ratios 13/12 and 14/13, respectively. The word "lesser" is added when necessary to differentiate it from 64/39, another tridecimal neutral sixth. It may also be treated as a type of augmented fifth, as the sum of 5/4 and 13/10.
13/8 differs from the Pythagorean minor sixth 128/81 by 1053/1024, about 48¢, from the classic minor sixth 8/5 by 65/64, about 27¢, from the undecimal neutral sixth 18/11 by 144/143, about 12¢, and from the rastmic neutral sixth 44/27 by 352/351, about 4.9¢.
Approximation
13/8 is a fraction of a cent away from the neutral sixth found in the 10n-edo family (7\10).
This interval is a ratio of two consecutive Fibonacci numbers, therefore it approximates the golden ratio. In this case, 13/8 is ~7.4 ¢ sharp of the golden ratio.
See also