12/11: Difference between revisions

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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 second, Alpharabian tendoneutral second

~~: This revision was by author [[User:spt3125~~|~~spt3125]] and made on <tt>2014-06-07 16:01:40 UTC</tt>.<br>~~

| Color name = 1u2, lu 2nd

~~: The original revision id was <tt>513195536</tt>.<br>~~

| Sound = jid_12_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>~~

~~<h4>Original Wikitext content:</h4>~~

~~<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">**12/11**

|~~2 1 0 0 -1>~~

~~150.63706 cents~~

~~[[media type~~=~~"file" key="jid_12_11_pluck_adu_dr220.mp3" width="240" height="20"]] [[file:xenharmonic/~~jid_12_11_pluck_adu_dr220.mp3|~~sound sample]]~~

~~The~~ (lesser) neutral second is ~~a strangely exotic~~ interval found between the 11th and 12th partials of the harmonic series. In ~~Just Intonation~~ it is represented by the [[superparticular]] ratio 12/11, and is about 150.6 [[cent~~|cents~~]] large. One step of [[8edo]] is an excellent approximation of the just neutral second, and eight of them exceed the octave by the comma (12/11)^8/2 = |15 8 0 0 -8~~>~~. It follows that EDOs which are multiples of 8, such as [[16edo]] and [[24edo]], will also represent this interval well.

'''12/11''', the '''undecimal neutral second''' or '''(lesser) neutral second''', is an interval found between the 11th and 12th partials of the [[harmonic series]]. In [[just intonation]] it is represented by the [[superparticular]] ratio 12/11, and is about 150.6 [[cent]]s large. One step of [[8edo]] is an excellent approximation of the just neutral second, and eight of them exceed the octave by the comma [[Undecimal_octatonic_comma|(12/11)<sup>8</sup>/2 = {{Monzo|15 8 0 0 -8}}]]. It follows that EDOs which are multiples of 8, such as [[16edo]] and [[24edo]], will also represent this interval well. In [[Alpharabian tuning]] it is known as the '''Alpharabian tendoneutral second'''.

12/11 differs from the larger undecimal neutral second 11/10 (~165 cents) by 121/120 (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include [[15edo]], [[22edo]], [[31edo]], [[orwell]], [[porcupine]], [[mohajira]] ~~and~~ [[valentine]].~~</pre></div>~~

12/11 differs from the larger undecimal neutral second [[11/10]] (~165 cents) by [[121/120]] (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include [[15edo]], [[22edo]], [[31edo]], [[orwell]], [[porcupine]], [[mohajira]], [[valentine]], etc.

~~<h4>Original HTML content:</h4>~~

<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>12_11</title></head><body><strong>12/11~~</strong><br />~~

Many Western listeners might describe 12/11 as sounding "exotic".

~~|2 1 0 0 -1&gt;<br />~~

~~150.63706 cents<br />~~

== See also ==

<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_12_11_pluck_adu_dr220.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed> <a href="http://xenharmonic.wikispaces.com/file/view/jid_12_11_pluck_adu_dr220.mp3/513195200/jid_12_11_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_12_11_pluck_adu_dr220.mp3/513195200/jid_12_11_pluck_adu_dr220.mp3');">sound sample</a><br />

* [[11/6]] – its [[octave complement]]

~~<br~~ /~~>~~

* [[11/8]] – its [[fifth complement]]

The (lesser) neutral second is a strangely exotic interval found between the 11th and 12th partials of the harmonic series. In Just Intonation it is represented by the <a class="wiki_link" href="/superparticular">superparticular</a> ratio 12/11~~, and is about 150.6 <a class="wiki_link" href="~~/~~cent">cents</a> large. One step of <a class="wiki_link" href="/8edo">8edo</a> is an excellent approximation~~ of ~~the~~ just ~~neutral second, and eight~~ of them exceed the octave by the comma (12/11)^8/2 = |15 8 0 0 -8&gt;. It follows that EDOs which are multiples of 8, such as <a class="wiki_link" href="/16edo">16edo</a> and <a class="wiki_link" href="/24edo">24edo</a>, will also represent this interval well.<br />

* [[11/9]] – its [[fourth complement]]

~~<br />~~

* [[Iceface Tuning]]

~~12/11 differs from the larger undecimal neutral~~ second 11/10 (~165 cents) by 121/120 (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include <a class="wiki_link" href="/15edo">15edo</a>, <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/31edo">31edo</a>, <a class="wiki_link" href="/orwell">orwell</a>, <a class="wiki_link" href="/porcupine">porcupine</a>, <a class="wiki_link" href="/mohajira">mohajira</a> and <a class="wiki_link" href="/valentine">valentine</a>.</body></html></pre></div>

* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

[[Category:Second]]

[[Category:Neutral second]]

[[Category:Over-11 intervals]]

@@ Line 1: / Line 1: @@
-<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 second, Alpharabian tendoneutral second
-: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-07 16:01:40 UTC</tt>.<br>
+| Color name = 1u2, lu 2nd
-: The original revision id was <tt>513195536</tt>.<br>
+| Sound = jid_12_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>
+{{Wikipedia|Neutral second}}
-<h4>Original Wikitext content:</h4>
-<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">**12/11**
-|2 1 0 0 -1&gt;
-.63706 cents
-[[media type="file" key="jid_12_11_pluck_adu_dr220.mp3" width="240" height="20"]] [[file:xenharmonic/jid_12_11_pluck_adu_dr220.mp3|sound sample]]
-The (lesser) neutral second is a strangely exotic interval found between the 11th and 12th partials of the harmonic series. In Just Intonation it is represented by the [[superparticular]] ratio 12/11, and is about 150.6 [[cent|cents]] large. One step of [[8edo]] is an excellent approximation of the just neutral second, and eight of them exceed the octave by the comma (12/11)^8/2 = |15 8 0 0 -8&gt;. It follows that EDOs which are multiples of 8, such as [[16edo]] and [[24edo]], will also represent this interval well.
+'''12/11''', the '''undecimal neutral second''' or '''(lesser) neutral second''', is an interval found between the 11th and 12th partials of the [[harmonic series]]. In [[just intonation]] it is represented by the [[superparticular]] ratio 12/11, and is about 150.6 [[cent]]s large. One step of [[8edo]] is an excellent approximation of the just neutral second, and eight of them exceed the octave by the comma [[Undecimal_octatonic_comma|(12/11)<sup>8</sup>/2 = {{Monzo|15 8 0 0 -8}}]]. It follows that EDOs which are multiples of 8, such as [[16edo]] and [[24edo]], will also represent this interval well.  In [[Alpharabian tuning]] it is known as the '''Alpharabian tendoneutral second'''.
-/11 differs from the larger undecimal neutral second 11/10 (~165 cents) by 121/120 (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include [[15edo]], [[22edo]], [[31edo]], [[orwell]], [[porcupine]], [[mohajira]] and [[valentine]].</pre></div>
+/11 differs from the larger undecimal neutral second [[11/10]] (~165 cents) by [[121/120]] (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include [[15edo]], [[22edo]], [[31edo]], [[orwell]], [[porcupine]], [[mohajira]], [[valentine]], etc.
-<h4>Original HTML content:</h4>
-<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;12_11&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;12/11&lt;/strong&gt;&lt;br /&gt;
+Many Western listeners might describe 12/11 as sounding "exotic".
-|2 1 0 0 -1&amp;gt;&lt;br /&gt;
-.63706 cents&lt;br /&gt;
+== See also ==
-&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_12_11_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_12_11_pluck_adu_dr220.mp3&amp;amp;quot; width=&amp;amp;quot;240&amp;amp;quot; height=&amp;amp;quot;20&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_12_11_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_12_11_pluck_adu_dr220.mp3/513195200/jid_12_11_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_12_11_pluck_adu_dr220.mp3/513195200/jid_12_11_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;
+* [[11/6]] – its [[octave complement]]
-&lt;br /&gt;
+* [[11/8]] – its [[fifth complement]]
-The (lesser) neutral second is a strangely exotic interval found between the 11th and 12th partials of the harmonic series. In Just Intonation it is represented by the &lt;a class="wiki_link" href="/superparticular"&gt;superparticular&lt;/a&gt; ratio 12/11, and is about 150.6 &lt;a class="wiki_link" href="/cent"&gt;cents&lt;/a&gt; large. One step of &lt;a class="wiki_link" href="/8edo"&gt;8edo&lt;/a&gt; is an excellent approximation of the just neutral second, and eight of them exceed the octave by the comma (12/11)^8/2 = |15 8 0 0 -8&amp;gt;. It follows that EDOs which are multiples of 8, such as &lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt; and &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;, will also represent this interval well.&lt;br /&gt;
+* [[11/9]] – its [[fourth complement]]
-&lt;br /&gt;
+* [[Iceface Tuning]]
-/11 differs from the larger undecimal neutral second 11/10 (~165 cents) by 121/120 (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;, &lt;a class="wiki_link" href="/orwell"&gt;orwell&lt;/a&gt;, &lt;a class="wiki_link" href="/porcupine"&gt;porcupine&lt;/a&gt;, &lt;a class="wiki_link" href="/mohajira"&gt;mohajira&lt;/a&gt; and &lt;a class="wiki_link" href="/valentine"&gt;valentine&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
+* [[Gallery of just intervals]]
+* [[List of superparticular intervals]]
+[[Category:Second]]
+[[Category:Neutral second]]
+[[Category:Over-11 intervals]]