12/11
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author spt3125 and made on 2014-06-07 16:01:40 UTC.
- The original revision id was 513195536.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
**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 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]].
Original HTML content:
<html><head><title>12_11</title></head><body><strong>12/11</strong><br />
|2 1 0 0 -1><br />
150.63706 cents<br />
<!-- ws:start:WikiTextMediaRule:0:<img src="http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_12_11_pluck_adu_dr220.mp3?h=20&w=240" class="WikiMedia WikiMediaFile" id="wikitext@@media@@type=&quot;file&quot; key=&quot;jid_12_11_pluck_adu_dr220.mp3&quot; width=&quot;240&quot; height=&quot;20&quot;" title="Local Media File"height="20" width="240"/> --><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><!-- ws:end:WikiTextMediaRule:0 --> <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 />
<br />
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>. 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 />
<br />
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>