Just perfect fifth: Difference between revisions
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Wikispaces>xenwolf **Imported revision 238801853 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 238830299 - 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: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-26 16:03:50 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>238830299</tt>.<br> | ||
: The revision comment was: <tt></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> | ||
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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 [[http://en.wikipedia.org/wiki/Quarter_comma_meantone|quarter-comma meantone]] (see [[31edo]]), identical. | 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 [[http://en.wikipedia.org/wiki/Quarter_comma_meantone|quarter-comma meantone]] (see [[31edo]]), identical. | ||
Some better (compared to 12edo) approximations of the perfect fifth are | Some better (compared to 12edo) approximations of the perfect fifth are [[29edo]], [[41edo]], [[53edo]]... | ||
(see all at [[http://oeis.org/ | (see all at [[http://oeis.org/A060528|The On-Line Encyclopedia of Integer Sequences (OEIS)]]; also relevant are the [[http://oeis.org/A060528|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". | 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". | ||
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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_ext" href="http://en.wikipedia.org/wiki/Quarter_comma_meantone" rel="nofollow">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_ext" href="http://en.wikipedia.org/wiki/Quarter_comma_meantone" rel="nofollow">quarter-comma meantone</a> (see <a class="wiki_link" href="/31edo">31edo</a>), identical. <br /> | ||
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Some better (compared to 12edo) approximations of the perfect fifth are | 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/ | (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/A060528" rel="nofollow">denominators of the convergents to log2(3)</a>.<br /> | ||
<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 /> | 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 /> | <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></pre></div> | ...see also <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Perfect_fifth" rel="nofollow">Perfect fifth on Wikipedia</a>.</body></html></pre></div> | ||
Revision as of 16:03, 26 June 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2011-06-26 16:03:50 UTC.
- The original revision id was 238830299.
- 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:
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]]. 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]]. 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 [[http://en.wikipedia.org/wiki/Quarter_comma_meantone|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/A060528|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>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 /> <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 /> <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_ext" href="http://en.wikipedia.org/wiki/Quarter_comma_meantone" rel="nofollow">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/A060528" rel="nofollow">denominators of the convergents to log2(3)</a>.<br /> <br /> 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".<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>