Just perfect fifth: Difference between revisions

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**Imported revision 513181966 - Original comment: added audio example**
Wikispaces>spt3125
**Imported revision 513196684 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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>2014-06-07 11:35:24 UTC</tt>.<br>
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-07 16:26:28 UTC</tt>.<br>
: The original revision id was <tt>513181966</tt>.<br>
: The original revision id was <tt>513196684</tt>.<br>
: The revision comment was: <tt>added audio example</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>
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>
<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">[[media type="file" key="jid_3_2_pluck_adu_dr220.mp3"]]
<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">[[media type="file" key="jid_3_2_pluck_adu_dr220.mp3" width="240" height="20"]] [[file:xenharmonic/jid_3_2_pluck_adu_dr220.mp3|sound sample]]


The **just perfect fifth** is the largest [[superparticular]] [[Gallery of Just Intervals|interval]] spanning the distance between the 2nd and 3rd harmonics. It has a frequency ratio of 3:2 with a width is 701.955 cents. It's an interval with low [[harmonic entropy]], and therefore high consonance.
The **just perfect fifth** is the largest [[superparticular]] [[Gallery of Just Intervals|interval]], spanning the distance between the 2nd and 3rd harmonics. It has a frequency ratio of 3:2, with a size of approximately 701.96 cents. It is an interval with low [[harmonic entropy]], and therefore high consonance.


Variations of the fifth (whether just or not) appear in most music of the world. On a harmonic instrument, the third harmonic is usually the loudest which is not an octave double of the fundamental. Treatment of the perfect fifth as consonant historically precedes treatment of the major third (see [[5_4|5:4]]) as consonant. 3:2 is the simple JI interval best approximated by [[12edo]], after the [[octave]].
Variations of the fifth (whether just or not) appear in most music of the world. On a harmonic instrument, the third harmonic is usually the loudest which is not an octave double of the fundamental. Treatment of the perfect fifth as consonant historically precedes treatment of the major third (see [[5_4|5:4]]) as consonant. 3:2 is the simple JI interval best approximated by [[12edo]], after the [[octave]].
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...see also [[http://en.wikipedia.org/wiki/Perfect_fifth|Perfect fifth on Wikipedia]].</pre></div>
...see also [[http://en.wikipedia.org/wiki/Perfect_fifth|Perfect fifth on Wikipedia]].</pre></div>
<h4>Original HTML content:</h4>
<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;just perfect fifth&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_3_2_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_3_2_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_3_2_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;br /&gt;
<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;just perfect fifth&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_3_2_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_3_2_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_3_2_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_3_2_pluck_adu_dr220.mp3/513181952/jid_3_2_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_3_2_pluck_adu_dr220.mp3/513181952/jid_3_2_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The &lt;strong&gt;just perfect fifth&lt;/strong&gt; is the largest &lt;a class="wiki_link" href="/superparticular"&gt;superparticular&lt;/a&gt; &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;interval&lt;/a&gt; spanning the distance between the 2nd and 3rd harmonics. It has a frequency ratio of 3:2 with a width is 701.955 cents. It's an interval with low &lt;a class="wiki_link" href="/harmonic%20entropy"&gt;harmonic entropy&lt;/a&gt;, and therefore high consonance.&lt;br /&gt;
The &lt;strong&gt;just perfect fifth&lt;/strong&gt; is the largest &lt;a class="wiki_link" href="/superparticular"&gt;superparticular&lt;/a&gt; &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;interval&lt;/a&gt;, spanning the distance between the 2nd and 3rd harmonics. It has a frequency ratio of 3:2, with a size of approximately 701.96 cents. It is an interval with low &lt;a class="wiki_link" href="/harmonic%20entropy"&gt;harmonic entropy&lt;/a&gt;, and therefore high consonance.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Variations of the fifth (whether just or not) appear in most music of the world. On a harmonic instrument, the third harmonic is usually the loudest which is not an octave double of the fundamental. Treatment of the perfect fifth as consonant historically precedes treatment of the major third (see &lt;a class="wiki_link" href="/5_4"&gt;5:4&lt;/a&gt;) as consonant. 3:2 is the simple JI interval best approximated by &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, after the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt;.&lt;br /&gt;
Variations of the fifth (whether just or not) appear in most music of the world. On a harmonic instrument, the third harmonic is usually the loudest which is not an octave double of the fundamental. Treatment of the perfect fifth as consonant historically precedes treatment of the major third (see &lt;a class="wiki_link" href="/5_4"&gt;5:4&lt;/a&gt;) as consonant. 3:2 is the simple JI interval best approximated by &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, after the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt;.&lt;br /&gt;

Revision as of 16:26, 7 June 2014

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 16:26:28 UTC.
The original revision id was 513196684.
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:

[[media type="file" key="jid_3_2_pluck_adu_dr220.mp3" width="240" height="20"]] [[file:xenharmonic/jid_3_2_pluck_adu_dr220.mp3|sound sample]]

The **just perfect fifth** is the largest [[superparticular]] [[Gallery of Just Intervals|interval]], spanning the distance between the 2nd and 3rd harmonics. It has a frequency ratio of 3:2, with a size of approximately 701.96 cents. It is an interval with low [[harmonic entropy]], and therefore high consonance.

Variations of the fifth (whether just or not) appear in most music of the world. On a harmonic instrument, the third harmonic is usually the loudest which is not an octave double of the fundamental. Treatment of the perfect fifth as consonant historically precedes treatment of the major third (see [[5_4|5:4]]) as consonant. 3:2 is the simple JI interval best approximated by [[12edo]], after the [[octave]].

Producing a chain of just perfect fifths yields Pythagorean tuning. Such a chain does not close at a circle, but continues infinitely. [[12edo]] is a system which flattens the perfect fifth by about 2 cents so that the circle close at 12 tones. Meanwhile, meantone temperaments are systems which flatten the perfect fifth such that the major third generated by four fifths upward be closer to 5:4 -- or, in the case of [[quarter-comma meantone]] (see [[31edo]]), identical.

Some better (compared to 12edo) approximations of the perfect fifth are [[29edo]], [[41edo]], [[53edo]]...
(see all at [[http://oeis.org/A060528|The On-Line Encyclopedia of Integer Sequences (OEIS)]]; also relevant are the [[http://oeis.org/A005664|denominators of the convergents to log2(3)]]).

In composition, the presence of perfect fifths can provide a "ground" upon which unusual intervals may be placed while still sounding structurally coherent. Systems excluding perfect fifths can thus sound more "xenharmonic".

...see also [[http://en.wikipedia.org/wiki/Perfect_fifth|Perfect fifth on Wikipedia]].

Original HTML content:

<html><head><title>just perfect fifth</title></head><body><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_3_2_pluck_adu_dr220.mp3?h=20&amp;w=240&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;jid_3_2_pluck_adu_dr220.mp3&amp;quot; width=&amp;quot;240&amp;quot; height=&amp;quot;20&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;20&quot; width=&quot;240&quot;/&gt; --><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_3_2_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_3_2_pluck_adu_dr220.mp3/513181952/jid_3_2_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_3_2_pluck_adu_dr220.mp3/513181952/jid_3_2_pluck_adu_dr220.mp3');">sound sample</a><br />
<br />
The <strong>just perfect fifth</strong> is the largest <a class="wiki_link" href="/superparticular">superparticular</a> <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">interval</a>, spanning the distance between the 2nd and 3rd harmonics. It has a frequency ratio of 3:2, with a size of approximately 701.96 cents. It is an interval with low <a class="wiki_link" href="/harmonic%20entropy">harmonic entropy</a>, and therefore high consonance.<br />
<br />
Variations of the fifth (whether just or not) appear in most music of the world. On a harmonic instrument, the third harmonic is usually the loudest which is not an octave double of the fundamental. Treatment of the perfect fifth as consonant historically precedes treatment of the major third (see <a class="wiki_link" href="/5_4">5:4</a>) as consonant. 3:2 is the simple JI interval best approximated by <a class="wiki_link" href="/12edo">12edo</a>, after the <a class="wiki_link" href="/octave">octave</a>.<br />
<br />
Producing a chain of just perfect fifths yields Pythagorean tuning. Such a chain does not close at a circle, but continues infinitely. <a class="wiki_link" href="/12edo">12edo</a> is a system which flattens the perfect fifth by about 2 cents so that the circle close at 12 tones. Meanwhile, meantone temperaments are systems which flatten the perfect fifth such that the major third generated by four fifths upward be closer to 5:4 -- or, in the case of <a class="wiki_link" href="/quarter-comma%20meantone">quarter-comma meantone</a> (see <a class="wiki_link" href="/31edo">31edo</a>), identical.<br />
<br />
Some better (compared to 12edo) approximations of the perfect fifth are <a class="wiki_link" href="/29edo">29edo</a>, <a class="wiki_link" href="/41edo">41edo</a>, <a class="wiki_link" href="/53edo">53edo</a>...<br />
(see all at <a class="wiki_link_ext" href="http://oeis.org/A060528" rel="nofollow">The On-Line Encyclopedia of Integer Sequences (OEIS)</a>; also relevant are the <a class="wiki_link_ext" href="http://oeis.org/A005664" rel="nofollow">denominators of the convergents to log2(3)</a>).<br />
<br />
In composition, the presence of perfect fifths can provide a &quot;ground&quot; upon which unusual intervals may be placed while still sounding structurally coherent. Systems excluding perfect fifths can thus sound more &quot;xenharmonic&quot;.<br />
<br />
...see also <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Perfect_fifth" rel="nofollow">Perfect fifth on Wikipedia</a>.</body></html>
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