This appeared in rmmp. back in December. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Bob Scott wrote: An easy way to understand false beats is to imagine the piano string just after it is struck. It is vibrating essentially up and down. But it doesn't continue to vibrate that way. It begins drifting towards a side-to-side vibration. When it vibrates like that there is less coupling to the sound board. Then the vibration continues to drift to an up and down motion - this time upside down from the original motion. Now it is producing sound 180 degrees out of phase with what it was doing originally. If it goes through this cycle once per second you will hear a once per second fluctuation in the loudness of the note. It is not like vibrato, which is a fluctuation in the pitch of a note. Now what makes the string decide to start vibrating sideways? Lots of various imperfections in the string or its seating can cause that. But the effect is a cyclic fluctuation in the loudness of the note which is indistinguishable from the sound made from two strings tuned slightly off from each other. -Bob Scott (rscott@wwnet.com) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ At 03:39 AM 4/13/97 +0000, you wrote: >Ron & list: > >I'm on my way out of town for two weeks, but this was an interesting thread, >and I wanted to at least give a swag, in case the thread has died by the time I >get back. >Frictional force is equal to the normal force times the coefficient of >friction (Ff=Fn x u). I'm not a piano technician, so I will assume some >values for discussion purposes, but I think the logic will hold. The >downbearing force is a function of >the angle across the bridge versus the string tension. The side force >against the bridge pin is a function of the side angle against the pin and >the string tension. >The string tension being a constant for a particular string the forces >involved (down >force versus side force against the bridge pin) are a ratio of the angles >down and sideways on the pin. I looked at my piano and it looks like >typical ratios would be: >down force .1 inch down over a 30 inch length or a tangent of 1/300 versus a >side angle force of .1 inch sideways over a .75 inch length or a tangent of >1/7.5 (depending of course on what note you are looking at). Please >note that I am just wildly estimating, but the differences are so great that >the argument will hold with a large estimation error. Anyway..... the >sideward force on >the bridge pin relative to the down force will be a ratio of the above numbers. >In our hypothetical example above, down force would only be 7.5/300 of the >side force on the pin. With a friction coefficient of approximately .1 to >.15 for lubricated copper alloy versus steel, it looks like the bridge pins >could definitely hold a displaced string off of the bridge, even with the >negative angle the bridge pins have. If this thread is still going when I >get back I'll take some measurements, and can calculate the angle a bridge >pin would have to be at to prevent this from happening. Of course a >microscopic burr or imperfection on the pin will also lead towards causing >the string to stay up off of the bridge when displaced. > >As to this causing false beats, I don't pretend to know the answer; but will >ask a >naive question (I don't have any acoustic background knowledge): When the >string is seated against the bridge it has one degree of freedom (it can >move up and down, it seems sideways would be rapidly damped). If it is held >off the bridge up on the pin it can vibrate in a more 360 degree mode - >could this cause false beats?) > >Well, I've got to run - please forgive me for the above "off the top of my >head" >comments; I like to think things through more thoroughly, but wanted to >answer before I left! > > Regards, Mike >At 05:46 PM 4/12/97 +0000, you wrote: >>Hi John, >> >>Ambrose Beirce defined apology as "laying the groundwork for a future >offense". With this in mind, and looking toward the future, I'm reluctant to >accept apologies where there was no offense. This being the case, I'm >returning your apology (unused) so you may save it for a more worthy cause. >> >>Doggone you John, I was hoping to get cheap answers without having to do my >own R&D. Now I'm going to have to go out in the shop and try your experiment >for myself. <G> I can see where the "stagger" and resulting side bearing >would have some bearing (sorry) on the phenomenon as it would vector the net >bearing more toward the horizontal. With little to no side bearing, the net >bearing vector would be vertical, straight down on the bridge. Maybe there's >still hope of clarification. Mike Imbler posted on another topic stating >that he was a mechanical engineer. Mike help, please! Is the coefficient of >friction between music wire and copper plated mild steel high enough to >account for this phenomenon with the forces and angles involved here in >pianos? In other words, does the math fit the model? What is the high limit >of angle at a given tension before the string slides on the pin? >> >>While Mike is deciding whether or not to play, I have more questions. >> >>A hard hammer blow (from below) will cause a string to slide up a bridge >pin. We seem to have a consensus on this one, yes? Since the hammer blow >isn't delivered anywhere near the bridge, isn't it the wave in the string >caused by the blow that propagates down to the bridge that does the deed? >Isn't the excursion of a string above the rest position balanced by an equal >(average-diminishing) excursion below? Why, then, doesn't the excursion >below the plane pull the string back down, especially with all the help it's >getting from down and side bearing???? >> >>Lastly, how would a string stuck up on a bridge pin cause a false beat in >the first place? If it's hanging in there good enough to withstand all the >above mentioned forces to the contrary, the string termination is as solid >as one could hope for! If it's because the bridge pin is loose, we are back >to my original premise that most of the false beats found in pianos are the >result of loose bridge pins and aren't curable by seating strings to >bridges. I don't mean this to look like I'm trying to lead the discussion >with a bull whip, but this is where the logic process brought me. All >enlightenment, clarification, pertinent random musings, empirical >observations and universal truths cheerfully entertained. >> >> >>Expectantly, >> Ron Nossaman >> >> >><******* History beyond this point *********> >> >> >> >>At 09:17 PM 4/11/97 -0600, you wrote: >>>Hi Ron, >>> >>>My apologies for misinterpreting your question. I understand now what >your asking, and I have tried a very un-scientific, but possibly >enlightening experiment this evening. >>> >>>I am currently doing some work on my personal piano in my shop. I rebuilt >this piano (a Bradbury 5'6" reproducer grand) about six years ago, and it >happened to be my first bridge recapping job. Because of this some of the >bridge pin placement is, well, pretty embarasingly wacky. A few pins are >placed in such a way that there is very little, if any side bearing. The >rest of the job is fine: good downbearing, nice tight well angled bridge >pins etc. I took some strings off and checked bridge pins and found no >*visible* notching in them. >>> >>>I got to thinking that this would be a great situation to test if side >bearing played a major role keeping the strings off the bridge. >>> >>>Here's what I did: With the piano up to pitch, I simply pulled up on the >speaking lenght side of a couple of strings until they lifted off the >bridge, then let go and watched what happened. The strings that had no side >bearing went right back down to the bridge. The strings that had decent >side bearing stayed up! I did several in the sixth octave of the piano (this >is where the misplaced pins are) and the strings rode up above the bridge >anywhere from 10 to 15 thousandths according to my feeler gauge. >>> >>>This little test, while not very controlled, would seem to point to side >bearing, and its attendant friction as one of the major contributing factors >in keeping those suckers up in the air. >>> >>>Comments anyone? >>> >>>John McKone, RPT >>>St. Louis Park, Minnesota >>>(612) 280-8375 >>> >>>----------------------------------------------- >>>>From : Ron Nossaman <nossaman@southwind.net> >>>Sent : 04/11/97 >>>To : pianotech@byu.edu >>>Subject: Re: bridges/seating >>> >>>At 08:58 PM 4/10/97 -0600, you wrote: >>>>Ron, >>>> >>>>If you're asking why the string can creep up against the pressure of >downbearing and friction, you need look no further than the impact of the >hammer (on a grand anyway) Especially on a hard use piano. >>>> >>>>John McKone, RPT >>>>St. Louis Park, Minnesota >>>>(612) 280-8375 >>>> >>> >>> >>>Nope, nope, not at all. It's quite obvious that a string can be knocked up >hill against tension, friction, or anything else you care to name. You can >here it happening if you work at it. It's quite clear to me how a string >GETS up a bridge pin. I'm saying that it's not possible for it to STAY up >off the bridge, AT REST, against tension and side/down bearing and pin >angle, unless there is something physically wrong with the bridge pin. What >else would hold it up there magically???? David Copperfield plating? There >has to be a real reason for an observable physical phenomenon. I get enough >mysticism and "have faith, trust me" metaphysics from Government. >Demonstrations can illustrate that it's possible (I'm still working on that >one), but I don't think anyone can realistically champion a fix without a >clear understanding of what's broke. Let's talk "mechanism". I'm willing to >accept the notion that this happens only in the context of a rational >explanation as to WHY it is possible. Wouldn't you like to know too? >>> >>> >>> Ron Nossaman >>> >>> >>> Ron Nossaman
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