<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><meta http-equiv=Content-Type content="text/html; charset=us-ascii"><meta name=Generator content="Microsoft Word 12 (filtered medium)"><style><!--
/* Font Definitions */
@font-face
{font-family:SimSun;
panose-1:2 1 6 0 3 1 1 1 1 1;}
@font-face
{font-family:SimSun;
panose-1:2 1 6 0 3 1 1 1 1 1;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:Tahoma;
panose-1:2 11 6 4 3 5 4 4 2 4;}
@font-face
{font-family:"\@SimSun";
panose-1:2 1 6 0 3 1 1 1 1 1;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman","serif";}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
span.EmailStyle17
{mso-style-type:personal-reply;
font-family:"Calibri","sans-serif";
color:#1F497D;}
.MsoChpDefault
{mso-style-type:export-only;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>I think a good introductory outline that relates the traditional music theoretic terminology to the corresponding group theory terminology is Chapter 9 ("Symmetry in music") of David Benson's book, <i>Music: a mathematical offering</i>. With the cooperation of Cambridge UP, he has put the entire book (all 400+ pages) up on the web for free. It can be downloaded here: <a href="http://www.maths.abdn.ac.uk/~bensondj/html/maths-music.html">http://www.maths.abdn.ac.uk/~bensondj/html/maths-music.html</a>.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>I don't think I've ever heard of any good historical overview of how symmetry has been used in music (Western or non), but, since you say her overall interest is the relationship between symmetry and beauty (not just of the musical kind), I've never read a better "cross-disciplinary" discussion than Hermann Weyl's beautiful little book, <i>Symmetry</i> (<a href="http://www.amazon.com/Symmetry-Hermann-Weyl/dp/0691023743">http://www.amazon.com/Symmetry-Hermann-Weyl/dp/0691023743</a> -- not much in it about music per se though).<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Steve Soderberg<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Stephen Soderberg<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Senior Specialist<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> for Contemporary Music<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Music Division<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Library of Congress<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Washington, DC<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><div style='border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> smt-talk-bounces@lists.societymusictheory.org [mailto:smt-talk-bounces@lists.societymusictheory.org] <b>On Behalf Of </b>Laurel Parsons<br><b>Sent:</b> Thursday, December 09, 2010 1:55 PM<br><b>To:</b> smt-talk@societymusictheory.org<br><b>Subject:</b> [Smt-talk] Symmetry and Musical Aesthetics<o:p></o:p></span></p></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Dear colleagues,<o:p></o:p></p><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>An upper-level undergraduate student at our liberal arts and sciences university is embarking on a long-term interdisciplinary study of the relationship between symmetry and beauty. She is an accomplished violinist, but is not a music major and has no post-tonal theory background as yet; however, she is both well-versed and interested in calculus, statistics, and other mathematical forms so could pick it up fairly easily. While there are hundreds of scholarly articles on various kinds of compositional symmetry in the music of Western composers to which I could refer her, I'm wondering if anyone can recommend:<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>1) a good historical overview of how symmetry has been used in Western music, and/or<o:p></o:p></p></div><div><p class=MsoNormal>2) scholarly writing that addresses the <i>aesthetics</i> of musical symmetry rather than (")simply(") the compositional mechanics of its usage in the works of specific composers. <o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Any suggestions would be greatly appreciated.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Best wishes,<o:p></o:p></p></div><div><p class=MsoNormal style='margin-bottom:12.0pt'>Laurel Parsons<br clear=all><br>-- <br>Laurel Parsons, Ph.D.<br>Co-ordinator, Humanities Division<br>Quest University Canada<br>3200 University Blvd.<br>Squamish, BC<br>VB8 0N8<br><a href="mailto:laurel.parsons@questu.ca" target="_blank">laurel.parsons@questu.ca</a><br><a href="http://www.questu.ca" target="_blank">www.questu.ca</a><o:p></o:p></p></div></div></body></html>