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<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Good morning folks,<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>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. ½, 1/3, ¼,
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></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Any thoughts?<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Georgia><span style='font-size:12.0pt;
font-family:Georgia'>Allan<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Georgia><span style='font-size:12.0pt;
font-family:Georgia'>Allan L. Gilreath, RPT<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=1 face=Georgia><span style='font-size:8.0pt;
font-family:Georgia'>Registered Piano Technician<o:p></o:p></span></font></p>
<p class=MsoNormal><b><font size=3 face=Georgia><span style='font-size:12.0pt;
font-family:Georgia;font-weight:bold'>Allan Gilreath & Associates, Inc.<o:p></o:p></span></font></b></p>
<p class=MsoNormal><i><font size=3 face=Georgia><span style='font-size:12.0pt;
font-family:Georgia;font-style:italic'>The Piano Experts<o:p></o:p></span></font></i></p>
<p class=MsoNormal><st1:address w:st="on"><st1:Street w:st="on"><font size=2
face=Georgia><span style='font-size:10.0pt;font-family:Georgia'>PO Box 1133</span></font></st1:Street><font
size=2 face=Georgia><span style='font-size:10.0pt;font-family:Georgia'> - <st1:City
w:st="on">Calhoun</st1:City>, <st1:State w:st="on">GA</st1:State> <st1:PostalCode
w:st="on">30703</st1:PostalCode></span></font></st1:address><font size=2
face=Georgia><span style='font-size:10.0pt;font-family:Georgia'><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Georgia><span style='font-size:10.0pt;
font-family:Georgia'>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></span></font></p>
<p class=MsoNormal><font size=2 face=Georgia><span style='font-size:10.0pt;
font-family:Georgia'>allan@allangilreath.com - www.allangilreath.com<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Georgia><span style='font-size:10.0pt;
font-family:Georgia'>phone 706 602-7667 - fax 706 602-0979<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
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