music, fibonnacci, golden mean, bartok


	music, fibonnacci, golden mean, bartok

mikejn

7-2-2008 3:23 AM

120 views

mikejn says:

So Bartok is cerebral not just emotional, his music comes out of the conflict between the Dionysian and Appolonian

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<div style="margin: 12px 0px; font-family: arial; color: #333333; background: #ffffff; border: solid 4px #e5e5e5; width: 100%; clear: left;"><div class="CM_CTB_Content_Wrap" style="margin: 0px; padding: 0px;background-color: #ffffff;"><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content.clipmarks.com/blog_embed/d023855b-5e5b-4480-ae51-54a6c3b2510d/A07183D7-3170-4288-9BDF-02F85C26C985/" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://en.wikipedia.org/w/index.php?title=Music_and_mathematics&oldid=215396350" href="http://en.wikipedia.org/w/index.php?title=Music_and_mathematics&oldid=215396350" style="font-size: 11px;">en.wikipedia.org</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://en.wikipedia.org/w/index.php?title=Music_and_mathematics&oldid=215396350"><SPAN class="mw-headline">The Golden Ratio and Fibonacci Numbers</SPAN></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://en.wikipedia.org/w/index.php?title=Music_and_mathematics&oldid=215396350"><P>It is believed that some composers wrote their music using the <A title="Golden ratio" href="http://en.wikipedia.org/wiki/Golden_ratio">golden ratio</A> and the <A title="Fibonacci number" href="http://en.wikipedia.org/wiki/Fibonacci_number">Fibonacci numbers</A> to assist them.<SUP class="reference" id="cite_ref-2"><A title="" href="#cite_note-2">[3]</A></SUP></P></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://en.wikipedia.org/w/index.php?title=Music_and_mathematics&oldid=215396350"><P><A title="James Tenney" href="http://en.wikipedia.org/wiki/James_Tenney">James Tenney</A> reconceived his piece "For Ann (Rising)", which consists of up to twelve computer-generated tones that <A title="Glissando" href="http://en.wikipedia.org/wiki/Glissando">glissando</A> upwards (see <A title="Shepard tone" href="http://en.wikipedia.org/wiki/Shepard_tone">Shepard tone</A>), as having each tone start so each is the golden ratio (in between an <A title="Equal tempered" class="mw-redirect" href="http://en.wikipedia.org/wiki/Equal_tempered">equal tempered</A> <A title="Minor sixth" href="http://en.wikipedia.org/wiki/Minor_sixth">minor</A> and <A title="Major sixth" href="http://en.wikipedia.org/wiki/Major_sixth">major sixth</A>) below the previous tone, so that the combination tones produced by all consecutive tones are a lower or higher pitch already, or soon to be, produced.</P></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://en.wikipedia.org/w/index.php?title=Music_and_mathematics&oldid=215396350"><A title="Ernő Lendvai" class="mw-redirect" href="http://en.wikipedia.org/wiki/Ern%C5%91_Lendvai">Ernő Lendvai</A> analyzes <A title="Béla Bartók" href="http://en.wikipedia.org/wiki/B%C3%A9la_Bart%C3%B3k">Béla Bartók's</A> works as being based on two opposing systems: those of the golden ratio and the acoustic scale. In Bartok's <A title="Music for Strings, Percussion, and Celesta" class="mw-redirect" href="http://en.wikipedia.org/wiki/Music_for_Strings%2C_Percussion%2C_and_Celesta">Music for Strings, Percussion, and Celesta</A>, the <A title="Xylophone" href="http://en.wikipedia.org/wiki/Xylophone">xylophone</A> progression occurs at the intervals 1:2:3:5:8:5:3:2:1. French composer <A title="Erik Satie" href="http://en.wikipedia.org/wiki/Erik_Satie">Erik Satie</A> used the golden ratio in several of his pieces, including <I>Sonneries de la Rose Croix</I>.</blockquote></div><div style="margin: 0px 6px 6px 4px;"><table style="font-size: 11px;border-spacing: 0px;padding: 0px;" cellpadding="0" cellspacing="0" width="100%"><tr><td style="background:transparent;border-width:0px;padding:0px;">&nbsp;</td><td align="right" style="background:transparent;border-width:0px;padding:0px;width:107px" width="107"><a href="http://clipmarks.com/share/A07183D7-3170-4288-9BDF-02F85C26C985/blog/" title="blog or email this clip"><img src="http://content6.clipmarks.com/images/c2b-foot.png" border="0" alt="blog it" width="107" height="17" style="border-width:0px;padding:0px;margin:0px;" /></a></td></tr></table></div></div>

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