<html> <body> Robin, Very well said.  I was hoping that we would eventually get back to the discussion of the Modulus of Reslience, having not felt that it was dealt with very well at the time. Thank you very much. Best. Horace At 10:38 AM 1/25/2005, you wrote: <blockquote type=cite class=cite cite="">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    <a href="mailto:Erwinspiano@aol.com">Erwinspiano@aol.com</a> wrote: <blockquote type=cite class=cite cite="">  = Ron      Yes & I happen to agree with you. Mysteries= are  after all............still mysteries?   Dale <dl> <dd>I strongly suspect that there is some sort of important relationship= <dd>between mass/stiffness/soundboard area which fundamentally influences= <dd>the tonal qualities of an instrument. Please don't ask me to <dd>elaborate on this matter at this time. This theory remains just that,= <dd>at present. <dd>Ron O. </dl> </blockquote></blockquote></body> </html>