Wikispaces>Andrew_Heathwaite |
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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 = undecimal major third, pentacircle major third |
| : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-01 16:25:08 UTC</tt>.<br>
| | | Color name = 1uz4, luzo 4th |
| : The original revision id was <tt>260509872</tt>.<br>
| | | Sound = jid_14_11_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 [[11-limit]] [[Just Intonation]], 14/11 is a supermajor third of about 417.5¢. It represents the difference between the 11th and 14th overtones of the [[OverToneSeries|harmonic series]] and appears in chords such as 8:11:14, the principal triad of [[Orgonia|Orgone]] temperament. 14/11 can also function as a [[Neo-Gothic]] major third, as it falls between [[5_4|5/4]] and [[9_7|9/7]]. Indeed, it is the [[mediant]] ratio between those simpler intervals, as it is (5+9)/(4+7). Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5+14)/(4+11) = [[19_15|19/15]], about 409.2¢) and between 14/11 and 9/7 (which is (14+9)/(11+7) = [[23_18|23/18]], about 424.4¢. Also in this region is the Pythagorean ([[3-limit]]) major third of [[81_64|81/64]] (about 407.8¢), which can be generated by stacking four [[3_2|3/2]] perfect fifths and [[octave-reduce|octave-reducing]].
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| See: [[Gallery of Just Intervals|Gallery of Just Intonation Intervals]], [[gentle chords]], [[List of root-3rd-P5 triads in JI]], [[http://dkeenan.com/Music/NobleMediant.txt|The Noble Mediant]]</pre></div>
| | In [[11-limit]] [[just intonation]], '''14/11''' is an '''undecimal major third''', specifically the '''pentacircle major third''', a major or supermajor third of about 417.5 [[cent]]s. It represents the difference between the 11th and 14th harmonics 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>14_11</title></head><body>In <a class="wiki_link" href="/11-limit">11-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 14/11 is a supermajor third of about 417.5¢. It represents the difference between the 11th and 14th overtones of the <a class="wiki_link" href="/OverToneSeries">harmonic series</a> and appears in chords such as 8:11:14, the principal triad of <a class="wiki_link" href="/Orgonia">Orgone</a> temperament. 14/11 can also function as a <a class="wiki_link" href="/Neo-Gothic">Neo-Gothic</a> major third, as it falls between <a class="wiki_link" href="/5_4">5/4</a> and <a class="wiki_link" href="/9_7">9/7</a>. Indeed, it is the <a class="wiki_link" href="/mediant">mediant</a> ratio between those simpler intervals, as it is (5+9)/(4+7). Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5+14)/(4+11) = <a class="wiki_link" href="/19_15">19/15</a>, about 409.2¢) and between 14/11 and 9/7 (which is (14+9)/(11+7) = <a class="wiki_link" href="/23_18">23/18</a>, about 424.4¢. Also in this region is the Pythagorean (<a class="wiki_link" href="/3-limit">3-limit</a>) major third of <a class="wiki_link" href="/81_64">81/64</a> (about 407.8¢), which can be generated by stacking four <a class="wiki_link" href="/3_2">3/2</a> perfect fifths and <a class="wiki_link" href="/octave-reduce">octave-reducing</a>.<br />
| | In many notation systems based on the [[5L 2s|diatonic]] [[chain-of-fifths notation]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), it is an imperfect fourth, as it is a [[4/3|perfect fourth (4/3)]] minus an instance of [[22/21]], which is a stack consisting of an [[33/32|undecimal quartertone (33/32)]] and a [[64/63|septimal comma (64/63)]], neither of which changes the [[scale|scale degree]] or [[interval quality|quality]]. It functions as such in voicings of the harmonic eleventh chord, [[4:5:6:7:9:11]]. |
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| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intonation Intervals</a>, <a class="wiki_link" href="/gentle%20chords">gentle chords</a>, <a class="wiki_link" href="/List%20of%20root-3rd-P5%20triads%20in%20JI">List of root-3rd-P5 triads in JI</a>, <a class="wiki_link_ext" href="http://dkeenan.com/Music/NobleMediant.txt" rel="nofollow">The Noble Mediant</a></body></html></pre></div> | | However, it is only sharp of the Pythagorean ([[3-limit]]) major third of [[81/64]] (about 407.8{{c}}) by a [[896/891|pentacircle comma (896/891)]], which makes it function sometimes as a major third, hence the names. Indeed, 14/11 is the simplest [[neogothic major and minor|neogothic major third]]. It falls between [[5/4]] and [[9/7]], and is the [[mediant]] ratio between those simpler intervals, as it is (5 + 9)/(4 + 7). It is [[56/55]] sharp of [[5/4]], and [[99/98]] flat of [[9/7]]. As such, it is used to form the gentle major triad, [[22:28:33]]<ref group="note">This is a [[minor minthmic chords|minor minthmic chord]] where 14/11 and [[13/11]] sum to a perfect fifth. Shown here is the simplest JI representation. </ref>. Compare this to 22:28:32 ([[11:14:16]]), which has the much more dissonant [[16/11]] as the outside interval in place of [[3/2]]; 11:14:16 can be voiced as 8:11:14 however, which is less dissonant. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5 + 14)/(4 + 11) = [[19/15]], about 409.2{{c}}) and between 14/11 and 9/7 (which is (14 + 9)/(11 + 7) = [[23/18]], about 424.4{{c}}). The fact that 14/11 functions as a type of third is one of the reasons why [[7/4]], the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth" – a cross between a sixth and a seventh – as opposed to merely a subminor seventh. |
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| | == Approximation == |
| | {{Interval edo approximation|14/11}} |
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| | == See also == |
| | * [[11/7]] – its [[octave complement]] |
| | * [[33/28]] – its [[fifth complement]] |
| | * [[Gallery of just intervals]] |
| | * [[Gentle chords]] |
| | * [[List of root-3rd-P5 triads in JI]] |
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| | == External links == |
| | * [http://dkeenan.com/Music/NobleMediant.txt ''The Noble Mediant''] by Margo Schulter and David Keenan |
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| | == Notes == |
| | <references group="note"/> |
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| | [[Category:Third]] |
| | [[Category:Major third]] |
| | [[Category:Supermajor third]] |
| | [[Category:Over-11 intervals]] |
| | [[Category:Pentacircle]] |
| | [[Category:Gentle]] |
| | [[Category:Neo-gothic]] |