Just perfect fifth: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:~~genewardsmith~~|~~genewardsmith~~]] and made on <tt>2011-06-~~27 03~~:53:36 UTC</tt>.<br>

: This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2011-08-09 15:21:32 UTC</tt>.<br>

: The original revision id was <tt>~~238907361~~</tt>.<br>

: The original revision id was <tt>245081037</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">The **just perfect fifth** is the [[interval]] between the 2nd and 3rd ~~[[partial tone]]~~. ~~The~~ frequency ratio is 3:2~~, the~~ width is 701.955 cents. It's an interval with ~~a high~~ [[~~consonance~~]].

<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">The **just perfect fifth** is the [[superparticular]] [[interval]] 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.

~~Some sort~~ of fifth (whether just or not) ~~appears~~ in most music of the world. On a harmonic instrument, the third harmonic is 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]].

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]]...

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

<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>just perfect fifth</title></head><body>The <strong>just perfect fifth</strong> is the <a class="wiki_link" href="/~~interval~~">~~interval~~</a> ~~between the 2nd and 3rd~~ <a class="wiki_link" href="/~~partial%20tone~~">~~partial tone~~</a>. ~~The~~ frequency ratio is 3:2~~, the~~ width is 701.955 cents. It's an interval with ~~a high~~ <a class="wiki_link" href="/~~consonance~~">~~consonance~~</a>.<br />

<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>just perfect fifth</title></head><body>The <strong>just perfect fifth</strong> is the <a class="wiki_link" href="/superparticular">superparticular</a> <a class="wiki_link" href="/interval">interval</a> 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 <a class="wiki_link" href="/harmonic%20entropy">harmonic entropy</a>, and therefore high consonance.<br />

<br />

~~Some sort~~ of fifth (whether just or not) ~~appears~~ in most music of the world. On a harmonic instrument, the third harmonic is 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 />

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 />

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 />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-27 03:53:36 UTC</tt>.<br>
+: This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2011-08-09 15:21:32 UTC</tt>.<br>
-: The original revision id was <tt>238907361</tt>.<br>
+: The original revision id was <tt>245081037</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">The **just perfect fifth** is the [[interval]] between the 2nd and 3rd [[partial tone]]. The frequency ratio is 3:2, the width is 701.955 cents. It's an interval with a high [[consonance]].
+<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">The **just perfect fifth** is the [[superparticular]] [[interval]] 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.
-Some sort of fifth (whether just or not) appears in most music of the world. On a harmonic instrument, the third harmonic is 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]].
 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]]...
@@ Line 19: / Line 19: @@
 ...see also [[http://en.wikipedia.org/wiki/Perfect_fifth|Perfect fifth on Wikipedia]].</pre></div>
 <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;The &lt;strong&gt;just perfect fifth&lt;/strong&gt; is the &lt;a class="wiki_link" href="/interval"&gt;interval&lt;/a&gt; between the 2nd and 3rd &lt;a class="wiki_link" href="/partial%20tone"&gt;partial tone&lt;/a&gt;. The frequency ratio is 3:2, the width is 701.955 cents. It's an interval with a high &lt;a class="wiki_link" href="/consonance"&gt;consonance&lt;/a&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;The &lt;strong&gt;just perfect fifth&lt;/strong&gt; is the &lt;a class="wiki_link" href="/superparticular"&gt;superparticular&lt;/a&gt; &lt;a class="wiki_link" href="/interval"&gt;interval&lt;/a&gt; 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;
 &lt;br /&gt;
-Some sort of fifth (whether just or not) appears in most music of the world. On a harmonic instrument, the third harmonic is 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;
 &lt;br /&gt;
-Producing a chain of just perfect fifths yields Pythagorean tuning. Such a chain does not close at a circle, but continues infinitely. &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; 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 &lt;a class="wiki_link" href="/quarter-comma%20meantone"&gt;quarter-comma meantone&lt;/a&gt; (see &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;), identical. &lt;br /&gt;
+Producing a chain of just perfect fifths yields Pythagorean tuning. Such a chain does not close at a circle, but continues infinitely. &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; 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 &lt;a class="wiki_link" href="/quarter-comma%20meantone"&gt;quarter-comma meantone&lt;/a&gt; (see &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;), identical.&lt;br /&gt;
 &lt;br /&gt;
 Some better (compared to 12edo) approximations of the perfect fifth are &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;...&lt;br /&gt;