11/9: Difference between revisions

: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-07 15:36:33 UTC</tt>.<br>

: The original revision id was <tt>513194466</tt>.<br>

[[media type="file" key="jid_11_9_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_11_9_pluck_adu_dr220.mp3|sound sample]]

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]].

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]], [[31edo]], [[41edo]], [[58edo]], [[72edo]], [[130edo]], [[202edo]], [[Gamelismic clan#Miracle|miracle]], [[Breedsmic temperaments#Harry|harry]], and [[Schismatic family#Sesquiquartififths|sesquart]], 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,%20aka%20Wonder|jove]].

&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_11_9_pluck_adu_dr220.mp3?h=20&amp;amp;w=240&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;jid_11_9_pluck_adu_dr220.mp3&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;20&amp;quot; width=&amp;quot;240&amp;quot;/&amp;gt; --&gt;&lt;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_11_9_pluck_adu_dr220.mp3?file_extension=mp3&amp;autostart=false&amp;repeat=false&amp;showdigits=true&amp;showfsbutton=false&amp;width=240&amp;height=20"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt; &lt;a href="http://xenharmonic.wikispaces.com/file/view/jid_11_9_pluck_adu_dr220.mp3/513194394/jid_11_9_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_11_9_pluck_adu_dr220.mp3/513194394/jid_11_9_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;

In &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, &lt;strong&gt;11/9&lt;/strong&gt; is a neutral third of about 347.4¢, falling in between &amp;quot;major third&amp;quot; and &amp;quot;minor third&amp;quot; territory. It is the simplest neutral third in just intonation, but of course, only one of many (others include &lt;a class="wiki_link" href="/16_13"&gt;16/13&lt;/a&gt;, &lt;a class="wiki_link" href="/27_22"&gt;27/22&lt;/a&gt;, &lt;a class="wiki_link" href="/49_40"&gt;49/40&lt;/a&gt; and &lt;a class="wiki_link" href="/60_49"&gt;60/49&lt;/a&gt;). It is nearly halfway between two intervals of &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, implying that it is both very xenharmonic and well-represented in &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;.&lt;br /&gt;

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 &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt;, &lt;a class="wiki_link" href="/130edo"&gt;130edo&lt;/a&gt;, &lt;a class="wiki_link" href="/202edo"&gt;202edo&lt;/a&gt;, &lt;a class="wiki_link" href="/Gamelismic%20clan#Miracle"&gt;miracle&lt;/a&gt;, &lt;a class="wiki_link" href="/Breedsmic%20temperaments#Harry"&gt;harry&lt;/a&gt;, and &lt;a class="wiki_link" href="/Schismatic%20family#Sesquiquartififths"&gt;sesquart&lt;/a&gt;, 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 &lt;a class="wiki_link" href="/Breed%20family#Jove,%20aka%20Wonder"&gt;jove&lt;/a&gt;.&lt;br /&gt;