<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML xmlns="http://www.w3.org/TR/REC-html40" xmlns:v = "urn:schemas-microsoft-com:vml" xmlns:o = "urn:schemas-microsoft-com:office:office" xmlns:w = "urn:schemas-microsoft-com:office:word" xmlns:st1 = "urn:schemas-microsoft-com:office:smarttags"><HEAD> <META http-equiv=Content-Type content="text/html; charset=iso-8859-1"> <META content="MSHTML 6.00.2800.1543" name=GENERATOR><o:SmartTagType name="PostalCode" namespaceuri="urn:schemas-microsoft-com:office:smarttags"></o:SmartTagType><o:SmartTagType name="Street" namespaceuri="urn:schemas-microsoft-com:office:smarttags"></o:SmartTagType><o:SmartTagType name="address" namespaceuri="urn:schemas-microsoft-com:office:smarttags"></o:SmartTagType><o:SmartTagType name="State" namespaceuri="urn:schemas-microsoft-com:office:smarttags"></o:SmartTagType><o:SmartTagType name="City" namespaceuri="urn:schemas-microsoft-com:office:smarttags"></o:SmartTagType><o:SmartTagType name="place" namespaceuri="urn:schemas-microsoft-com:office:smarttags"></o:SmartTagType> <STYLE>  </STYLE> </HEAD> <BODY lang=EN-US vLink=purple link=blue bgColor=#ffffff> <DIV>!/3 is not a multiple of 2</DIV> <DIV>The really weird divisions of the string are reserved for the longitudional vibtation</DIV> <DIV>Joe Goss RPT Mother Goose Tools <A href="mailto:imatunr@srvinet.com">imatunr@srvinet.com</A> <A href="http://www.mothergoosetools.com">www.mothergoosetools.com</A></DIV> <BLOCKQUOTE dir=ltr style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <DIV style="FONT: 10pt arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black">From: <A title=allan@allangilreath.com href="mailto:allan@allangilreath.com">Allan Gilreath, RPT</A> </DIV> <DIV style="FONT: 10pt arial">To: <A title=pianotech@ptg.org href="mailto:pianotech@ptg.org">'Pianotech List'</A> </DIV> <DIV style="FONT: 10pt arial">Sent: Friday, June 29, 2007 7:41 AM</DIV> <DIV style="FONT: 10pt arial">Subject: partial answers</DIV> <DIV> </DIV> <DIV class=Section1> Good morning folks,<o:p></o:p> <o:p> </o:p> I had a question from my apprentice that someone on the list may be able to help me with. We all know that vibrating strings divide up into segments with lengths approximately equal to fractional portions, i.e. ˝, 1/3, Ľ, 1/5, 1/6, etc. (we’re not even taking inharmonicity into account at this level.) His question is, “Why does the string divide into all of the different available fractional segments and not just even multiples of two?” I was hoping for a much better answer than just, “Because it does” but Benade, Helmholtz and Rayleigh, the best I can tell, all assume this to be a fact and I don’t really find the “why.”<o:p></o:p> <o:p> </o:p> Any thoughts?<o:p></o:p> <o:p> </o:p> Allan<o:p></o:p> Allan L. Gilreath, RPT<o:p></o:p> Registered Piano Technician<o:p></o:p> Allan Gilreath & Associates, Inc.<o:p></o:p> The Piano Experts<o:p></o:p> <st1:address w:st="on"><st1:Street w:st="on">PO Box 1133</st1:Street> - <st1:City w:st="on">Calhoun</st1:City>, <st1:State w:st="on">GA</st1:State> <st1:PostalCode w:st="on">30703</st1:PostalCode></st1:address><o:p></o:p> 2612 Hwy 41 S - <st1:place w:st="on"><st1:City w:st="on">Calhoun</st1:City>, <st1:State w:st="on">GA</st1:State> <st1:PostalCode w:st="on">30701</st1:PostalCode></st1:place><o:p></o:p> allan@allangilreath.com - www.allangilreath.com<o:p></o:p> phone 706 602-7667 - fax 706 602-0979<o:p></o:p> <o:p> </o:p></DIV></BLOCKQUOTE></BODY></HTML>