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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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-09-14 20:48:09 UTC</tt>.<br>
| | | Color name = 3o6, tho 6th |
| : The original revision id was <tt>254165610</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 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 and 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¢.
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| See: [[Gallery of Just Intervals]]</pre></div>
| | '''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]]. |
| <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>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 3/2 and 7/4, 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 />
| | 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¢. |
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| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div> | | == Approximation == |
| | 13/8 is a fraction of a cent away from the neutral sixth found in the [[10edo|10''n''-edo]] family (7\10). |
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| | 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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| | == See also == |
| | * [[16/13]] – its [[octave complement]] |
| | * [[64/39]] – the greater tridecimal neutral sixth |
| | * [[Gallery of just intervals]] |
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| | [[Category:Sixth]] |
| | [[Category:Neutral sixth]] |
| | [[Category:Golden ratio approximations]] |