Hey Alan, Hope this email finds you well. Your answer points in the right direction. The single answer is summed up as stiffness. Unlike an ideal flexible string (a theoretical string) piano wire has stiffness and so does not vibrate (or "hinge") exactly between its termination points of, say, the agraffe and bridge pin. Imagine, in a gross way, that instead of the vibrating wire hinging exactly at the agraffe and bridge it effectively terminates and hinges 1mm short of the exact points established by the agraffe and bridge. There are some technical problems with this simplistic model (so I believe I have heard somewhere) because inharmonicity is usually referred to regarding the partials and not the fundamental. But the visual works for me. In any event, all the resultant partials do not segment at exact theoretical points but rather at very short zones of string length. Also, all ascending partials are relatively stiffer than their lower neighbors causing all partials to vibrate at frequencies which are faster than their theoretical values. An orderly curve of increasingly faster-than-theoretically exact partials has been plotted over the years, one famously named the Railsback Curve, although this curve resulted from plotting deviations of aurally tuned string partials to theoretical values. It is for this reason that a natural piano tuning stretch is built into a careful tuning. Imagine a diving board (a cantilever). It does not flex or hinge all the way back to its support due to stiffness. But reduce the stiffness and the effective hinge of the diving board will move back closer to its support. If you now imagine a piano string exiting the agraffe for a few inches under tension, and then cut it off (in your imagination!) and pretend it is a diving board, the same conditions obtain. Interestingly, a bowed string, where the delivery device (the bow strands rather than a rebounding hammer) remains in constant contact with the string, exhibits a marked absence of inharmonicity. For a given string length a larger diameter wire (more stiffness) yields higher inharmonicity. The latest Journal (Feb 2009) article by Hans Velo will make interesting reading for your faculty colleague. See you soon in CA? Nick Gravagne, RPT Piano Technicians Guild Member Society Manufacturing Engineers Voice Mail 928-476-4143 _____ From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf Of reggaepass at aol.com Sent: Thursday, February 05, 2009 9:32 AM To: pianotech at ptg.org Subject: [pianotech] inharmonicity in piano wire List, I just received a query from a science faculty member at the art institute where I work. He asks how can it be that partials of piano wire are sharp of what they "should" be? I told him that my very pedestrian understanding is that this phenomenon is due to the high tension of piano wire up to pitch, but that is just me repeating what I have heard "somewhere." Is this response even close to being correct? Any further clarification as to why this is would be much appreciated all the way around. Thanks, Alan Eder CalArts _____ Carnations mean admiration, Tulips mean love - what do Roses mean? <http://shopping.aol.com/articles/2009/02/02/flowers-by-meanings/?ncid=AOLCO MMshopdrspwebf0001> Find out now! -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/pianotech_ptg.org/attachments/20090205/c42b6589/attachment.html>
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