Robin Wonderful posting ! Dispassionate with regards to personal preferences as is your want, and strictly informative. I particularilly enjoyed your comments on the nature of structure born sound, your comments on the impedance perspective (which provide new thought for my evening ponderings) and read with fascination where your comments and quotes relative to Seeley seemed to be going. These kinds of posts usually take me a few three four readings to digest adequately. I would recommend anyone who is interested in the many opinions offered about the nature of soundboard functioning to do the same. Thanks muchly Cheers RicB > >> Dale >> There is just such a relationship and it is no a mystery, >> although, as far as I can tell it is neither comprehended nor taken >> into account in the flexural view of soundboard function. This >> factor is precisely what I suggested be taken into account in a post >> put up three years ago during the debate on the behavior of >> soundboards, entitled Rocking Bridges, Dec 30, 2001, in commentary >> on the Modulus of Resilience, which was ignored, or misunderstood as >> an impedance matter which is not the case. In my opinion, one >> should view the soundboard, as I have repeatedly urged, not through >> the prism of deflection mechanics or cyclic static pressures but, >> rather, as an energy absorbtive, concentrating and transmitting >> medium, the energy absorbed being the output of the string, which is >> a pressure excitation at the terminations. >> In my opinion, (and, I am going to drop this phrase through the >> remainer of this post although it all should be taken with this >> qualification) the soundboard should be seen as a device which has >> several functions. These functions themselves are not necessarily >> complementary and, in fact, are perhaps somewhat contradictary. How >> they are adjusted, vis a vis, one another is the particular solution >> found by any given design approach. At one and the same time, the >> board, bridge and ribs together, must be stiff enough to ensure >> loop stability on the strings which motion of the terminations past >> certain limits would preclude; at the same time, it must absorb this >> energy, which is just sound, another problem in and of itself;, it >> must then concentrate the sound in ways that build up the amplitude >> and, finally, transfer momentum out of the system as acoustic >> radiation. >> I will not repeat here the many arguments I have made for the >> nature of motion at the bridge and the energy loading that occurs >> there, they are, likely, well known. >> What follows will be a synoptic treatment of this entire >> question which will be published in substantially greater detail >> later this year, elsewhere. >> There are critical distinctions that arise, as I said in the >> post referred to above, from the nature of loading. These were >> dismissed as mere impedance issues. Not so. >> The absorption by the soundboard of this energy is a function of >> its energy resistance. Quoting from the post referred to above, >> which I will then elaborate upon: >> "The approach taken by your school of thought is generally, as >> far as I can tell, expressed in terms of mass and stiffness, flexion, >> and the ratio of stress to strain, that is the modulus of >> elasticity.(here I can't render appropriate notation due to the >> limitations of the keyboard I am using); These are the terms of >> deflection mechanics, among others. When applied to the transfer >> relations between string and bridge they are inadequate. A better >> measure of the relations is the one used in energy loading and that >> is the modulus of resilience which is half the quotient of the square >> of the stress to the modulus of elasticity. Although the modulus of >> resilience is in fact a measure of how much energy is absorbed per >> unit volume of the material when the material is stressed to the >> proportional limit, its implications for the design and manufacture >> or remanufacture of soundboards are profound as it can be used as a >> predictor for the absorbion of energy or energy resistance of a >> member and therefore models the transfer relations between string and >> bridge, among others. >> Critical implications of the modulus of resilience and energy >> loading arise in comparison to those of static loading. Static >> loading, whether flexion or axial depends upon the maximum stress >> developed, energy loading is substantially different, (quoting from >> Seely) " the resistance... of the bar((bridge, rh) to an energy >> load......depends not only the maximum unit-stress, s, but also, (1) >> on the distribution of stress through the body, since the energy >> absorbed by a given unit volume is ((the modulus of resilience is >> quoted, rh)), and hence depends upon the degree to which that VOLUME >> (caps mine, rh) is stressed, and (2), >> and on the number of units of volume of material in the bar ((bridge, >> rh)). What this means to those that have not grasped it is that the >> transfer relations between string and bridge/soundboard are a >> function of the VOLUME and the DISTRIBUTION of stress in the bridge >> itself, and not simply the stiffness and mass. The undercutting of >> the bridge, thinning of soundboards, tapering of ribs, inner rib >> angles, etc. are in fact methods of volume and stress control the >> purpose of which is to equalize the stress distribution in the >> material and thereby optimize its energy absorptive capacity or >> control its energy resistance. As far as I can see, this should be a >> matter dear to the heart of anyone attempting to design, >> remanufacture, or otherwise modify a piano soundboard. >> To further quote from Seely, "...show that the material in a >> beam having a constant cross-section is inefficient in absorbing >> energy. For example,........a rectangular beam, when loaded at >> mid-span with a concentrated load, can absorb only one-ninth as much >> energy as the same beam could absorb if all the material in the beam >> were stressed to the same degree." The requirement for >> stress-equalization, hence control of energy resistance, can be >> expressed as taper of ribbing, undercutting of bridges, notching of >> struts, etc. >> It is absolutely critical to understand that energy absorption >> under dynamic loading, as indicated above, is functionally different >> from that of static loading, one being dependant upon the maximum >> stress developed, the other the nature of the stress distribution, a >> more complex formulation requiring cognizance of the volume and >> stress together. This is, at the least, one important relationship >> between mass/stiffness/soundboard area which fundamentally influences >> the tonal qualities of an instrument, to use Ron O.'s words. >> It is often maintained, erroneously in my view, that the >> loudness or softness of a given note is some function of an >> "impedance" problem, and that, generally, this is true for the entire >> system. A much better view would be to see the entire piano >> structure as part of a completely whole, organic system, coupled in a >> dynamic manner, loaded with acoustic energy, and subjected to a >> forced vibration. The energy of these vibrations may find sinks >> where it is lost through excessive damping, or, it may superpose in >> ways which build it up in the soundboard which, itself, is the >> greatest sink of all. One can evaluate the soundfield in a piano >> soundboard, the rim, or the plate through various means. A simple >> way is to use the mechanic's stethoscope I suggested several years >> ago and explore the distribution of sound. The sound produced by >> the string is distributed to a greater or lesser degree, throughout >> the entire piano structure, which itself is also coupled to the >> floor, air, and, generally, the world. Piano design has attempted to >> control the distribution and superposition of these forced >> vibrations, particularly by attempting to control energy absorption, >> or its inverse, energy resistance, in the soundboard, bridge, ribs >> and rim, using just the principles described above, whether conscious >> or not. >> The sound does indeed traveld, as structure-borne-sound, >> through the entirety of the system, that is all components of the >> piano but, particularly through the soundboard, rim and plate. Good >> design will attempt to direct sound back into the soundboard where it >> may assist in building up the sound pressure level. The acoustic >> dowel is a design feature that attempts to facilitate this process. >> This is, regardless of any outlandish sales claims arising from this >> process, the dreaded "Circle of Sound", and, as such, is a real >> process. That such things will happen is a commonplace notion, just >> taken for granted, a complete given, and is the norm in sonic >> analysis. It is astonishing that technicians, who really should know >> better, confuse this process, one indubitably real, with their >> antagonism for what may be exaggerated claims by certain factories. >> The modulus of resilience is a measure, as I have indicated >> before, of the amount of energy a structure may absorb up to the >> proportional limit and is, in a way, inadequate for the >> structure-borne- sound found in a piano, as we are not looking to >> take the energy level to such a point. Its usefulness, however, lies >> in the perspective it affords. That is, what are the capabilties of >> a medium which influence its ability to absorb and transmit energy, >> in this case, acoustic energy and how does one maximize this. >> The soundboard can be made more effective at acquiring energy >> from the string, and, further, reacquiring it numerous times from the >> rim and plate by control of energy resistance and stress >> distribution, and, in particular, the equality of stress >> distribution. Consider an unribbed soundboard: it has a kind of >> moisture induced stress to some degree or the other. Dry it to some >> point and rib it, either by rib crowning or compression crowning, a >> new level of stress, glue it in, now a different distribution and >> then press it down by string bearing a further change in stress. I >> think it plainly evident piano design has evolved methods to impart >> certain stresses into the system for several reasons, for example, >> equalization for purposes of acoustic absorption, but also mechanical >> reasons such as the need to maintain tuning stability, and string >> termination. >> Crown, downbearing pressure, board thinning, ribbing, >> rib-tapering and inner rim angling achieve a number of these >> objectives simultaneously. That is, they can all be made to work >> together to give the best chance for equality of stress >> distribution. If terminations are to be secure there must be some >> offset allowed, were there no need for it acoustically, to counteract >> the relaxation, some degree of compression set, in my opinion much >> smaller than generally claimed, and plastic reponse of the board >> after loading by the strings. This is an utterly paramount, >> particularly as regards terminations, but, nevertheless mechanical >> consideration in a new soundboard, but which, as most know, must be >> accomplished effectively if there is to be a functional soundboard >> for any length of time after manufacture. This is another >> consideration in design discussions, which seems to have been >> generally disregarded here on the list. >> As I have said above these factors convienently serve control of >> energy resistance, itself the heart of acoustic function, which >> modulates the nature, along with reflection and superposition, of the >> coupled string/soundboard/ rim/case system as well. Where energy >> resistance is lessened the system easily absorbs energy from the >> string and feeds this energy right back into the vibrating string >> itself, the two become a dynamic whole. This, again, is a kind of >> circle of sound. It is easily seen that it differs entirely from >> attributing power and sustain solely to the degree of transmittivity >> and reflectivity resulting from wave activity at an impedance >> discontinuity which is expressed by the impedance ratio of the two >> media. Obviously, the interplay of these variables, alone, affords >> a considerable range of design flexibility, as long as energy >> resistance is controlled, which, again, requires equalization of >> stress distribution, that is manipulation of both volume and stress >> levels in a coordinated fashion. As volume varies as the cube >> slight changes in dimension, for example, the soundboard, ribbing, or >> rib taper, may cause substantial effects, equalities or >> inequalities, in the stress distribution, for better or worse >> insofar as absorption is concerned. >> The board, of course is highly anistropic, which requires >> structural alterations the purposes of which are also those of energy >> control, such as board thinning, ribs and rib tapering. These, along >> with downbearing pressure allow for some level of equalization of >> stress. It is entirely possible, as crown lessens, where such does >> occur, over time, that these changes actually result in more, rather >> than less, equalization, with a probable result being a better sound, >> and this may account for the better sound some find in old boards. I >> don't urge this as a mechanism I am certain of but, merely, a >> possible explanation. Ribbing, with or without crown, lessens the >> anistropy of the board. As the speed of sound is much greater >> along the grain the ribs, crossing the grain as they do, in at least >> one functional sense, lessen this anistropy by providing a sound path >> which allows the sound to more effectively travel into the board, >> where it does it's superpositional thing, than it could do by simply >> crossing the grain, arriving late and attenuated. As it is >> late, I will not, at the moment take up the last of the functions I >> indicated, which is acoustic radiation from the board itself. >> Regards, Robin Hufford >> >> <mailto:Erwinspiano@aol.com> >
This PTG archive page provided courtesy of Moy Piano Service, LLC