Just perfect fifth: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 238830299 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
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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 /> | ||
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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 /> | ||
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...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> | ||