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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 second |
| : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-09-16 19:10:42 UTC</tt>.<br>
| | | Color name = 3o2, tho 2nd |
| : The original revision id was <tt>254920096</tt>.<br>
| | | Sound = jid_13_12_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">In [[13-limit]] [[Just Intonation]], 13/12 is a neutral second of about 138.6¢. It is also a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th overtone (between [[13_8|13/8]] and [[3_2|3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12_11|12/11]] by [[144_143|144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14_13|14/13]] by [[169_168|169/168]] (about 10.3¢).
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| The neutral second in [[17edo]] is about 141.2¢, about 2.6¢ sharp of 13/12. Thus, if 10\17edo (ten degrees of 17edo) is taken to approximate 3/2 and 12\17edo taken to approximate 13/8, you can generate a 13-limit harmonic triad that approximates an 8:12:13 chord with a good 13/12.
| | In [[13-limit]] [[just intonation]], '''13/12''' is the '''(lesser) tridecimal neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢). |
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| See: [[Gallery of Just Intervals]]</pre></div>
| | == Temperaments == |
| <h4>Original HTML content:</h4>
| | {{Todo|expand|inline=1}} |
| <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_12</title></head><body>In <a class="wiki_link" href="/13-limit">13-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 13/12 is a neutral second of about 138.6¢. It is also a <a class="wiki_link" href="/superparticular">superparticular</a> interval, as it is found in the harmonic series between the 13th and the 12th overtone (between <a class="wiki_link" href="/13_8">13/8</a> and <a class="wiki_link" href="/3_2">3/2</a> in the octave). It is flat of the <a class="wiki_link" href="/11-limit">11-limit</a> lesser neutral second of <a class="wiki_link" href="/12_11">12/11</a> by <a class="wiki_link" href="/144_143">144/143</a> (about 12.1¢), and sharp of the 13-limit large semitone of <a class="wiki_link" href="/14_13">14/13</a> by <a class="wiki_link" href="/169_168">169/168</a> (about 10.3¢).<br />
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| | == Approximation == |
| The neutral second in <a class="wiki_link" href="/17edo">17edo</a> is about 141.2¢, about 2.6¢ sharp of 13/12. Thus, if 10\17edo (ten degrees of 17edo) is taken to approximate 3/2 and 12\17edo taken to approximate 13/8, you can generate a 13-limit harmonic triad that approximates an 8:12:13 chord with a good 13/12.<br />
| | It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]]. |
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| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
| | == See also == |
| | * [[24/13]] – its [[octave complement]] |
| | * [[18/13]] – its [[fifth complement]] |
| | * [[Gallery of just intervals]] |
| | * [[List of superparticular intervals]] |
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| | [[Category:Second]] |
| | [[Category:Neutral second]] |
In 13-limit just intonation, 13/12 is the (lesser) tridecimal neutral second of about 138.6¢. It is a superparticular interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between 13/8 and 3/2 in the octave). It is flat of the 11-limit lesser neutral second of 12/11 by 144/143 (about 12.1¢), and sharp of the 13-limit large semitone of 14/13 by 169/168 (about 10.3¢).
Temperaments
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Todo: expand
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Approximation
It is approximated to within about 0.11 cents by the 3-step interval of 26edo.
See also
