HIdden Geometry Found In Music

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	HIdden Geometry Found In Music

m_a_d_d_i_

3-28-2007 10:10 PM

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tags:

music, maths, geometry, modelling

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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/a8411d57-9359-49c9-bf2d-5d932e8af6d3/C9407FB1-EBD7-4118-97FC-172B99D090FB/" 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://www.physorg.com/news71417403.html" href="http://www.physorg.com/news71417403.html" style="font-size: 11px;">www.physorg.com</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.physorg.com/news71417403.html"><DIV id="Preview"> 
Composers often speak of fitting chords and melodies together, as though sounds were physical objects with geometric shape -- and now a Princeton University musician has shown that advanced geometry actually does offer a tool for understanding musical structure.
</DIV></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://www.physorg.com/news71417403.html">His findings have resulted in the first paper on music theory that the journal <I>Science</I> has printed in its 127-year history, and may provide an additional theoretical tool for composers searching for that elusive next chord</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://www.physorg.com/news71417403.html">		
							"I'm not trying to tell people what style of music sounds good, or which composers to prefer," said Tymoczko</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://www.physorg.com/news71417403.html">"What I hope to do is provide a new way to represent the space of musical possibilities.</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://www.physorg.com/news71417403.html">One of Tymoczko's musical spaces resembles a triangular prism, in which points representing traditionally familiar harmonies such as major chords gather near the center of the triangle, forming neat geometric shapes with other common chords that relate to them closely.</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/C9407FB1-EBD7-4118-97FC-172B99D090FB/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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