<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <meta content="text/html;charset=ISO-8859-1" http-equiv="Content-Type"> <title></title> </head> <body bgcolor="#ffffff" text="#000000"> Cy and others. I can not see that this paper says the same thing as has been conveyed on this list the last few years. The similarity stops with the description of the symptoms of a loose bridge pin and a recessed notch.  The paper does not claim beat rates that are compatible with the ones claimed here on pianotech.   The beat rates accounted for are quite slow in comparison.  The paper is right on the same track as the massy/springy comments I made the last time this was up. <a class="moz-txt-link-freetext" href="https://www.moypiano.com/ptg/pianotech.php/2005-December/182440.html">https://www.moypiano.com/ptg/pianotech.php/2005-December/182440.html</a>.  Nor does the paper claim that the cause of this kind of false beat is solely because of loosepins/recessed notch edge alone. In fact it states that  the loose pins/recessed notch can be a contributing factor... only.  This is also exactly what I said last time this was up.  The paper, which echoes Weinreich, echoes Ellis, and others, points to the complexity of any local anisotropic boundary conditions at the bridge.   In other words. There are many factors which contribute to the degree the boundary the bridge is massy / springy.  Some of these factors can no doubt be in opposition to one another.  Which would explain why many times false beats do not occur given a loose pin and a recessed edge and can also explain the wide range of beat rate speeds observed. <blockquote>Cy writes: > Capleton's paper > (<a class="moz-txt-link-freetext" href="http://www.amarilli.co.uk/academic/acoustics/false_beats.pdf">http://www.amarilli.co.uk/academic/acoustics/false_beats.pdf</a>) notes > that once the string no longer touches the bridge cap, the bridge pin is > effectively a cantilevered termination. > </blockquote> It says cantilevered support not cantilevered termination. An important distinction. <blockquote> > Isn't it possible that when the string touches the pin above the bridge > its leverage makes for a less-secure termination, effectively increasing > the speaking length? </blockquote> This is again exactly what I said the last time this came up.  Again.. I cited effective speaking length changes that are related to the massyness/springiness of the string/bridge interface. The pins role in this is that it no longer provides a secure termination in the horizontal direction, placing the effective termination longer back on the bridge. As such the pin is not really the termination for the string in the horizontal vibration direction. <blockquote></blockquote> <blockquote>Ron N: Which is exactly what I've been saying repeatedly for, what, seven or eight years now? Since it's been published now by someone official, I suppose it might finally be taken seriously. </blockquote> It has been previously claimed the pin is the sole termination, the pin flagpoles sideways and increases the speaking length.   It was stated that sideways movement of the pin would be enough to account  for as much as a 0.001 inch increase in length and implied that this would be enough for the beat rates we see.   Its just that there is no increase in the real length if the pin is seen as the sole and effective termination for the string and a 0.001 increase in length (real or effective) can not account for a noticeable beat rate in the first place. For even a string so short as 50 mm long and 0.8 mm diameter given  the 0.001 inch variation at the same tension (for example 150 lbs -- 68 kgs) will only yeild a 1.3 hz difference.   Thats barely more then 1 bps at C88.  The rates given in Capleton's paper are based on a 0.1 mm increase in effective length... which is a MILE compared to the 0.001 inch (roughy 0.025mm) cited earlier here on pianotech.  And even that do not result in beat rates above 1.6 bps for the shortest strings in the usual false beat affected area.  Formula used is from McFerrin  T= (Lfd)^2/398*10^6.   Solve for f. <blockquote>> And why can't a .003mm increase in speaking length happen by a .003mm > movement of the bridge pin? > > --Cy-- </blockquote> It can if the pin moves forward and backwards in the direction of the string... but not if it moves sideways.   It has been claimed here on pianotech that the sideways movement of the pin caused two speaking lengths with the pin terminating both. It cant work that way. The thing is, false beats are caused by variety of things. Torsional stress, non uniformity in the string, rust, and others are ofte times given as specific causes.  Anisotropic boundary conditions come about because of a convergence any and all factors that can influence the massyness/springiness of the bridge. As (false) beat rates are presumably connected to the degree of anisotropy there needs to be more at work then just a wobbly pin to account for both the beat rates we see, the variation there are in beat rates, and the fact that they very often simply do not occur despite the presence of a loose pin and/or recessed notch edge Cheers RicB </body> </html>