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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 neutral third, Alpharabian artoneutral third |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-21 17:09:28 UTC</tt>.<br>
| | | Color name = 1o3, ilo 3rd |
| : The original revision id was <tt>256747890</tt>.<br>
| | | Sound = jid_11_9_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]], 11/9 is a neutral third of about 347.4¢, falling in between "major third" and "minor third" territory. It is the simplest neutral third in just intonation, but of course, only one of many (others include [[16_13|16/13]], [[27_22|27/22]], [[49_40|49/40]] and [[60_49|60/49]]). It is nearly halfway between two intervals of [[12edo]], implying that it is both very xenharmonic and well-represented in [[24edo]].
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| In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the harmonic 11th and the harmonic 9th. A triad can also be built with a 3/2 fifth and 11/9 third: this would be 18:22:27. This introduces a second neutral third, 27/22, which together make a perfect fifth. Many temperaments, including [[17edo]], [[24edo]] and [[31edo]], to name a few, conflate these two neutral thirds, allowing one neutral third interval to be stacked to generate a perfect fifth. 11/9 differs from 27/22 by 243/242, but also from 49/40 by 441/440 and 60/49 by 540/539, with varied consequences when one or more of them are tempered out. Tempering out all of them leads to the 11-limit rank three temperament [[Breed family#Jove, aka Wonder|jove]]. | | In [[11-limit]] [[just intonation]], '''11/9''' is a [[neutral third]] of about 347.4¢, falling in between "major third" and "minor third" territory. It is the simplest neutral third in just intonation, but it is only one of many, of which others include [[16/13]], [[27/22]], [[39/32]], [[49/40]] and [[60/49]]. As this is the smaller of the two [[11-limit]] neutral thirds obtained by modifying Pythagorean intervals by [[33/32]], it is dubbed the '''Alpharabian artoneutral third''' in [[Alpharabian tuning]]. Since it is nearly halfway between two intervals of [[12edo]], it implies that it is both very xenharmonic and well-represented in [[24edo]]. It is approximated even more closely in [[31edo]] and [[38edo]], where the slight flatness of the fifth creates two near perfect 11/9's when divided in half, making the neutral triad particularly stable sounding in these tunings. |
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| See: [[Gallery of Just Intervals]]</pre></div>
| | In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the 11th harmonic and the 9th harmonic. A triad can also be built with 3/2 and 11/9, and the chord formed is 18:22:27. This introduces a second neutral third, 27/22, which is the difference between 3/2 and 11/9. Many temperaments, including [[7edo]], [[10edo]], [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[Gamelismic clan#Miracle|miracle]], [[Breedsmic temperaments #Harry|harry]], and [[Schismatic family #Sesquiquartififths|sesquart]], conflate these two neutral thirds. The interval which represents both neutral thirds can then be stacked twice to generate a perfect fifth. 11/9 differs from 27/22 by [[243/242]], but also from 49/40 by [[441/440]] and 60/49 by [[540/539]], with varied consequences when one or more of them are tempered out. Tempering out all of these commas leads to the 11-limit rank three temperament [[Breed family #Jove, aka Wonder|jove]]. |
| <h4>Original HTML content:</h4>
| | == Approximation == |
| <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>11_9</title></head><body>In <a class="wiki_link" href="/11-limit">11-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 11/9 is a neutral third of about 347.4¢, falling in between &quot;major third&quot; and &quot;minor third&quot; territory. It is the simplest neutral third in just intonation, but of course, only one of many (others include <a class="wiki_link" href="/16_13">16/13</a>, <a class="wiki_link" href="/27_22">27/22</a>, <a class="wiki_link" href="/49_40">49/40</a> and <a class="wiki_link" href="/60_49">60/49</a>). It is nearly halfway between two intervals of <a class="wiki_link" href="/12edo">12edo</a>, implying that it is both very xenharmonic and well-represented in <a class="wiki_link" href="/24edo">24edo</a>.<br />
| | {{Interval edo approximation|11/9}} |
| <br />
| | == See also == |
| In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the harmonic 11th and the harmonic 9th. A triad can also be built with a 3/2 fifth and 11/9 third: this would be 18:22:27. This introduces a second neutral third, 27/22, which together make a perfect fifth. Many temperaments, including <a class="wiki_link" href="/17edo">17edo</a>, <a class="wiki_link" href="/24edo">24edo</a> and <a class="wiki_link" href="/31edo">31edo</a>, to name a few, conflate these two neutral thirds, allowing one neutral third interval to be stacked to generate a perfect fifth. 11/9 differs from 27/22 by 243/242, but also from 49/40 by 441/440 and 60/49 by 540/539, with varied consequences when one or more of them are tempered out. Tempering out all of them leads to the 11-limit rank three temperament <a class="wiki_link" href="/Breed%20family#Jove, aka Wonder">jove</a>.<br /> | | * [[7edo]] |
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| | * [[24edo]] |
| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div> | | * [[18/11]] – its [[octave complement]] |
| | * [[27/22]] – its [[fifth complement]] |
| | * [[12/11]] – its [[fourth complement]] |
| | * [[Gallery of just intervals]] |
| | * [[Iceface tuning]] |
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| | [[Category:Third]] |
| | [[Category:Neutral third]] |
| | [[Category:Alpharabian]] |
| | [[Category:Tritave-reduced harmonics]] |