<DIV><STRONG><FONT face="comic sans ms" color=#c00000>Hi, Allan!</FONT></STRONG></DIV> <DIV><STRONG><FONT face="Comic Sans MS" color=#c00000></FONT></STRONG> </DIV> <DIV><STRONG><FONT face="Comic Sans MS" color=#c00000>No, I don't have a definitive anwer as to the "why," BUT...you're a fellow trombone player. Don't you have the ability...with some effort...of getting to the 12th partial, and don't they line up exactly the same way, at least theoretically? And for that matter, ANY vibrating body, even speaker cones (though the designers try hard to damp most of them way down) has above every pitch the same order of partials. (And air columns, too, in flutes or organ pipes.) Alan Barnard is quite correct when he says that the relative strength or weakness of various numbered partials produces the tone color we expect in various instruments. Trouble is, as my elementary understanding goes, we just don't always fathom the "why" with laws of
physics. Axiomatic, maybe. It's just a little like the formula for combinations...n(factorial), or however that's supposed to be expressed.</FONT></STRONG></DIV> <DIV><STRONG><FONT face="Comic Sans MS" color=#c00000></FONT></STRONG> </DIV> <DIV><STRONG><FONT face="Comic Sans MS" color=#c00000>Cheers!</FONT></STRONG></DIV> <DIV> </DIV> <DIV>Good morning folks,</DIV> <DIV> </DIV> <DIV>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.”</DIV> <DIV> </DIV> <DIV>Any thoughts?</DIV> <DIV> </DIV> <DIV>Allan</DIV> <DIV>Allan L. Gilreath, RPT</DIV> <DIV>Registered Piano Technician</DIV> <DIV>Allan Gilreath & Associates, Inc.</DIV> <DIV>The Piano Experts</DIV> <DIV>PO Box 1133 - Calhoun , GA 30703</DIV> <DIV>2612 Hwy 41 S - Calhoun , GA 30701</DIV> <DIV><A href="mailto:allan@allangilreath.com">allan@allangilreath.com</A> - <A href="http://www.allangilreath.com/">www.allangilreath.com</A></DIV> <DIV>phone 706 602-7667 - fax 706 602-0979<BR></DIV><BR><BR><DIV>Stan Ryberg <BR>Barrington IL <BR><U>jstan40@sbcglobal.net</U></DIV>