>I daresay I have done the same with similar use of physics and its principles. >It is a measure of the possible futility of this discussion that you seem to >unawares of this. I apparently am. I have read that if I had read anything about the more advanced aspects of vibration, I would understand your theory. I have, and I don't. That's why I asked for references. The references you have quoted haven't, that I have been able to tell, addressed it either. For instance the reference indicating that the string terminations are nodes, and since nodes don't theoretically move, the string can't move the bridge. Is that a serious attempt at explanation, and the level of specificity your theory is based on? > Believing, along with others as you do, that the string is pulling and >pushing the bridge and then moving the soundboard would you then agree >that the >string should move the bridge and board downward when the string is pressed >down, and similarly upwards when lifted? If you do agree, then would you also >agree that this is the mechanism, although perhaps simplified, that causes the >subsequent wave behavior in the board that results in acoustic radiation? You >have said so, essentially, many times. Yes, I have said so many times. That hasn't changed. > How do you suppose this can occur efficiently when the string is not >effectively clamped to the bridge by the bridge pins? The frequent >traveling up >the bridge pin by the strings on a grand piano indicates readily how >ineffective >is the function of the pin as a clamp. It can not effectively transfer the >supposed lifting motion of the string that you and others claim exists, >which, in >fact, does not exist, at least from my point of view. There must >necessarily be >an asymmetry of effect as the efficiency of lifting of the strings cannot >possibly be as great as that which exists when the strings are pushing >down on >the bridge. Such asymmetry must result in a clipping of the harmonic motion >imposed on the bridge by the string, which you and others, apparently, believe >exists at this point, another point of subtlety, and a "troublesome question" >which appears to be disregarded, along with numerous others by your camp. This point is built on the belief that strings climb up bridge pins in a properly set up piano. They don't, so the point is moot. There is almost certainly some asymmetry to the motion imposed on the bridge by the string, but that has nothing to do with whether or not the string moves the bridge. Nor does it seem to support your theory that the string does not move the bridge. Since it doesn't seem to pertain to the issue, why do you bring it up? Note please that I'm not asking you to quantify and integrate every conceivable manifestation of observed, reported, rumored, or mythologized bridge and soundboard effect in your theory. I am just asking for a realistic straightforward explanation, with some sort of reference material that explains the apparently non standard science involved in terms of actual science. How can the string move the soundboard without moving the bridge? What known science allows for the total disregard of the mass reactions involved? > In point of fact, I have a number of books on the subject of vibrations >and other pertinent subjects and have quoted from them when requested to do >so. >The quotes, their implications and other points I have made, you seem to have >found irrelevant and then simply disregarded, something, in the context of >intellectual enquiry, that is a mystery to me. It's a mystery to me too. The references you have quoted have been very elementary and very general. The implications drawn have been entirely yours, and considerably different than those drawn by others from an established physics standpoint. In the case I mentioned above, the theoretical labeling of a string termination as a node, and the extrapolation that since a node doesn't theoretically move, therefor the bridge doesn't move, is ignoring the physical reality that the bridge and soundboard in the real world are quite easily, and quite measurably deflected. You point out that I am ignoring "loading", though I'm still not sure what you are talking about or what it has to do with the question, while you continue to disregard the fundamental physical properties of matter in favor of a vague generality on node theory, stress transpondance, and the passing of longitudinal waves unabated through termination barriers, all without moving the bridge. What real science can you produce to back this stuff up? >> This entire controversy boils down to a few simple questions: Are the >> motions, if any, at the bridge, the direct result of the string driving the >> bridge and thence the board in the fashion of, as you have said, a >spring on >> spring system? If so, this would indeed be fantastic. Yes Robin, I understand the controversy. The question is quite simple. And yes, I am aware of your opinion that my stand is "fantastic". I am also aware that you repeatedly return to this point, though I fail to understand how it serves to your benefit in the discussion. >AND is the >motion, if >> any, of the bridge linearly related to the motion of the string? That is, >does >> a very slight excusion of the string result in a very slight bodily >> displacement of the bridge, and a somewhat greater excursion result in a >> somewhat greater excursion and so on? Are these motions proportional? If >not, >> then the pertinence of the example of the floating of valves in an engine is >> plain. It is simply not enough to say that something lags the other by a >> "computable phase angle" as this does not address what actually happens as >that >> lag develops. I have no way of measuring or knowing how proportional the movement is. I presume it is roughly linear, but can't say definitely one way or the other. The lag develops as the driving frequency rises above the fundamental harmonic frequency of the system, as I quoted. What actually happens as the driving frequency increases and the lag develops is that the amplitude of the reaction diminishes, but does not disappear. It is frequency dependant as to the amplitude of the reaction, but the reaction is at the same frequency as the driver, lagging behind the driver at that computable phase frequency. All this is in the physics books, has been covered, and is part of a system in which the driving force directly moves the driven object. In the case of a piano, that is the string directly moving the bridge. Since that notion is by your repeated declaration "fantastic", how can this example possibly support your theory that the bridge doesn't move? > I say any motions of string and bridge are not directly functions of each >other as the strings cannot move the bridge for numerous reasons in a way >sufficient to achieve what it is you and your coproponents claim to occur and >that the stress transduction method I have described is a much better model for >this and that this model also accounts for events occuring when a tuning >fork is >applied to bridge or board. Where is my physics reference for the stress transduction explanation? As nearly as I have been able to tell, this came out of thin air too since I have repeatedly asked for references on the effect and haven't yet seen any. As for the fork, I have described it's action in terms of established physics that doesn't leave anything out or violate any natural laws of which I am aware. Since everything connected with your theory requires a stress transduction that turns stress into movement without moving the stressed item, It's time you produced some actual references on this phenomenon. > Why is it so hard to believe that a string, when stretched by the standing >waves occuring upon it, will pulse a longitudinal wave faithfully rendering > the >periods of the standing waves across the terminations and that this will >refract >into the medium in contact with the string and then diffuse through this >medium, >developing through reflection and refraction imperfect longitudinal standing >waves which can then move, in the case of the soundboard, the bridge, if >necessary? This is a far simpler, at least mathematically speaking, >explanation than what you propose, notwithstanding, its evident conventional >standing. Fine, let's see the math. Let's see the references. The reason this is so hard for me to believe is that it doesn't correspond to empirical observation, measurement, and an established and accepted body of scientific principals. My stand that the strings move the bridge isn't based on belief, but on the connection of established principals of physics and mechanics, observable phenomena, and a firm conviction in the principal of Ocham's razor. What you propose is anything but simple, and can only be conceived of as simple by ignoring most of the established principals of physics. If either of these theories is based on faith and belief, it will be the one that can't be rationally explained with producible physics precepts. > To continue the wave analysis using your model. : Say the string is >at the >unstable equilibrium configuration of the fundamental. By the "Cyclic >Pressure" >method ( to take recourse to new terminology per your request) when the >string is >displaced above the bridge it is pulling upward on the bridge and soundboard. >This will occur for less than half of a period, as it must proceed through the >entire gamut of free resonances: the string will then cycle to the other phase, >pulling downard again for less than half a period. In the case of A-440 it >will >momentarily pull upwards for less than half the period, that is 1/880 of a >second as it must cycle through all of the other standing waves.and then >proceed >to the opposite phase still cycling through the other standing waves similarly, >and all this in the other half period which is 1/880th of a second. Held >down >by other strings, unable to remain effectively in contact with the bridge on >the >upstroke, and attached to a massive,stiff bridge and relatively massive >soundboard, the string simply is not able to operate as a force in the >manner >you defend so intently. >Regards, Robin Hufford This is again, based on the erroneous assumption that the string is not held to the bridge top by the pins. It is, though albeit not as perfectly as should be possible. The string does not normally slither up and down the pin during play. In those instances where front bearing is negative and the front bridge pin is near vertical, this will happen, and the audible effect is disastrous. Dispense with that false assumption, and yes - the bridge is moved by the string up and down at that 440cps rate, lagging somewhat behind the string phase, but still at the fundamental frequency. It is also being accelerated and retarded during this primary excursion by the varying pressures applied by the standing waves of the various string partials. If you look at a vibrating string, you won't see any part of the string between the terminations that appears not to be moving. There are nodes between upper partials, but they are moving transversely with the fundamental standing wave in the string. The mass reaction at the bridge to the force of moving string mass beyond the straight line between the terminations is the driver. The net velocity and direction of string movement at any given moment defines the force applied to the bridge. The reaction to this force directly moves the bridge. It is profoundly simple in principal. Ron N
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