partial answers

[Alan Barnard]

I don't know exactly why, but I do know that the motions of a chord (string) under tension are e x t r e m e l y complex. We always picture it moving  up and down, like a jump rope or something, but it also whips around on it's own longitudinal axis with the same wild motions.



Any time you set up a standing wave, in air or a solid medium, the sound, itself, divides into it's natural partials. The medium, itself, tends to reinforce or quash some of the partials. This, of course, is what makes the oboe sound different from the clarinet and, in fact, shapes the timbre, or unique sound, of every musical instrument. (And more subtly, the difference between a factory violin and a Strad)



So ... my theory (and it's only a guess, really) is that since the struck string naturally generates a fundamental and its overtone series, the sound energy of each partial actually feeds, or loops back to, the string energy at that frequency, thus the sound energy and mechanical energy reinforce each other until both are damped out by the resistance of the mediums of steel (and copper), wood, air, etc.



If I'm right, it would be like striking a tuning fork, then placing it on a resonator, maybe a guitar bridge. Both sound AND mechanical energy are transferred to a more obliging medium for producing sound--especially in the overtones, resulting in much louder partials. The trade-off, of course, is that the inefficiency of energy transfer to a medium that was just, after all, sitting there minding its own business, results in substantial diminution of sustain.



Hope that made sense. Love to hear from the scientific community ...



Alan Barnard

Salem, MO









Original message

From: "Allan Gilreath, RPT" 

To: "Pianotech List" 

Received: 6/29/2007 8:41:14 AM

Subject: partial answers





Good morning folks,



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.”



Any thoughts?



Allan

Allan L. Gilreath, RPT

Registered Piano Technician

Allan Gilreath & Associates, Inc.

The Piano Experts

PO Box 1133 - Calhoun, GA 30703 

2612 Hwy 41 S - Calhoun, GA 30701

allan at allangilreath.com - www.allangilreath.com

phone 706 602-7667 - fax 706 602-0979
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