Just perfect fifth: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 163257805 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 238801853 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
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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]]. | 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. | 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/A005664|The On-Line Encyclopedia of Integer Sequences (OEIS)]]) | |||
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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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 /> | 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 /> | ||
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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. | 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 (<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/A005664" rel="nofollow">The On-Line Encyclopedia of Integer Sequences (OEIS)</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> | ||