17/15: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
'''17/15'''
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-08 15:09:17 UTC</tt>.<br>
: The original revision id was <tt>513253790</tt>.<br>
: 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">**17/15**
|0 -1 -1 0 0 0 1&gt;
|0 -1 -1 0 0 0 1&gt;
216.6867 cents
216.6867 cents
[[media type="file" key="jid_17_15_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_17_15_pluck_adu_dr220.mp3|sound sample]]


In [[17-limit]] [[Just Intonation]], 17/15 is the "septendecimal whole tone" measuring about 216.7¢. It is the [[mediant]] between [[9_8|9/8]] and [[8_7|8/7]], as it is (9+8)/(8+7). It is found in the [[OverToneSeries|harmonic series]] between the 17th and 15th overtones. [[11edo]]'s second degree, measuring approximately 218.2¢, is close in size to 17/15 -- indeed, the 11edo system has excellent approximations of the 15th and 17th harmonics, and so this harmonic function is plausible in 11edo.
[[File:jid_17_15_pluck_adu_dr220.mp3]] [[:File:jid_17_15_pluck_adu_dr220.mp3|sound sample]]
 
In [[17-limit|17-limit]] [[Just_intonation|Just Intonation]], 17/15 is the "septendecimal whole tone" measuring about 216.7¢. It is the [[mediant|mediant]] between [[9/8|9/8]] and [[8/7|8/7]], as it is (9+8)/(8+7). It is found in the [[OverToneSeries|harmonic series]] between the 17th and 15th overtones. [[11edo|11edo]]'s second degree, measuring approximately 218.2¢, is close in size to 17/15 -- indeed, the 11edo system has excellent approximations of the 15th and 17th harmonics, and so this harmonic function is plausible in 11edo.


√2/(17/15) is three cents flat of a 5/4 major third, and this or 17/15 itself can be used for a tuning for wizard and its various relatives (lizard, gizzard, etc.).
√2/(17/15) is three cents flat of a 5/4 major third, and this or 17/15 itself can be used for a tuning for wizard and its various relatives (lizard, gizzard, etc.).


See: [[Gallery of Just Intervals]]</pre></div>
See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]     [[Category:17-limit]]
<h4>Original HTML content:</h4>
[[Category:just_interval]]
<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;17_15&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;17/15&lt;/strong&gt;&lt;br /&gt;
[[Category:sound_example]]
|0 -1 -1 0 0 0 1&amp;gt;&lt;br /&gt;
216.6867 cents&lt;br /&gt;
&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_17_15_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_17_15_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_17_15_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_17_15_pluck_adu_dr220.mp3/513250008/jid_17_15_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_17_15_pluck_adu_dr220.mp3/513250008/jid_17_15_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
In &lt;a class="wiki_link" href="/17-limit"&gt;17-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 17/15 is the &amp;quot;septendecimal whole tone&amp;quot; measuring about 216.7¢. It is the &lt;a class="wiki_link" href="/mediant"&gt;mediant&lt;/a&gt; between &lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt; and &lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;, as it is (9+8)/(8+7). It is found in the &lt;a class="wiki_link" href="/OverToneSeries"&gt;harmonic series&lt;/a&gt; between the 17th and 15th overtones. &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;'s second degree, measuring approximately 218.2¢, is close in size to 17/15 -- indeed, the 11edo system has excellent approximations of the 15th and 17th harmonics, and so this harmonic function is plausible in 11edo.&lt;br /&gt;
&lt;br /&gt;
√2/(17/15) is three cents flat of a 5/4 major third, and this or 17/15 itself can be used for a tuning for wizard and its various relatives (lizard, gizzard, etc.).&lt;br /&gt;
&lt;br /&gt;
See: &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>