----- Original Message ----- From: Ron Nossaman <RNossaman@KSCABLE.com> To: <pianotech@ptg.org> Sent: June 17, 2000 7:46 AM Subject: Re: impedance and empericism > >Ric rites back > >Yeah, but you forgot to say how it can be measured. If impedance is to be > >defined at a useful level it should come from it measurements. The point of > >emperical science is that prediction is the same as measurement. Or the > >measured result should be the same as predicted by the formula---which is > >constructed from the measured results. This is what the inharmonicity > >formula appears to be, a formula based on measurements. However it doesn't > >appear to predict so good, since other variables are now being claimed to > >influence Ih. > > I didn't forget, I just don't have a means of doing so that puts a number > on it. Del explained how it's done. For my part, I have to rely on what I > can hear. Being able to generate the numbers and correlate them to > measurements would certainly be handy, but it's beyond my present capabilities. > ------------------------------------------------- A hundred or so years ago -- when most of scaling principles for pianos that, sadly, are still practiced today were initially worked out -- the math didn't exist to predict either the tension or the inharmonicity for wrapped strings. In fact, the idea of inharmonicity had not yet come along. That didn't mean it was impossible to calculate the tension of wrapped string, it only meant that they were unable to do so at the time. Nor does it mean that inharmonicity did not exist in the strings used in those days or that either of these parameters was unimportant in the development or the performance of the piano. Neither did it stop piano designers from designing pianos or piano builders from building them. I do suspect, though, that if such tools had existed then the pianos we see now would be some different. So time goes on and we build on what came before. What I described was a process to measure the mechanical impedance of structure such as a piano soundboard at a single frequency and at a single point on a soundboard bridge. The results of this test give us a complex number representing the mechanical impedance of the soundboard system at one single point along one of (usually) two bridges at one single, simple frequency (i.e., no harmonics, either in- or en-) and at one single power level. Yes, the process can be expanded to include a sweep of all practical audio frequency signals at that point. Doing so makes the result considerably more complicated. If we add in varying power levels -- i.e., more or less amplitude in the driving signal -- the result becomes even more complicated. Now, let's add some harmonics that are not quite harmonic? Oh, yes, let's give these in-harmonic signals varying power levels and varying decay rates. This is something of the complexity you would find in trying to quantify the mechanical impedance of a simple single string mono-chord using a simple test soundboard assembly. And, since the test soundboard is made of wood and the mechanical characteristics of wood change with its moisture content, let's vary the humidity level and take some more readings. Now, let's add in a few more strings -- say, 220 or so and let's give them all varying lengths, masses, tensions, fundamental vibrating frequencies, varying levels of downforce against the bridge(s), etc. -- and spread out along a couple of bridges contacting the soundboard over a widely varying area? And, yes -- to get back to the original question -- let's factor in those varying humidity levels as well. Now, let me understand the problem here. Given this mix of complex variables -- and let's just ignore the effect of a few additional variables such as the plate, rim, and a few more I've forgotten about or don't yet even know about -- we are supposed to define a mathematical relationship that will accurately predict the effect on the harmonic coefficient of a single string lying somewhere along the string scale that results from a change in relative humidity from, say, 40% to 60% and if we can not currently provide this formula then this cause and effect relationship does not exist? Stephan Birkett has proposed a research project that would just begin to look into some of these questions but I'm not sure even the project he envisions would provide accurate answers to this question. If anyone is interested enough, though, I'm sure he would welcome contributions. I hope I am wrong -- for his sake as well as ours -- but I suspect the condition of, and the attitude within, the piano industry today is such that there is very little interest in this type of basic research. And extensive basic research is just what is needed if we are going to even begin to understand these types of complex relationships fully. No, if this type of work is done at all it will probably be done by interested piano technicians and/or scientists who have a particular interest in the piano and who are willing to pursue the question on their own nickel. As may be, just because a certain causal relationship cannot be explained and quantified by today's science -- either empirical or theoretical -- does not mean it does not exist. No, I do not have a full understanding of the relationship between the vibrating string plane and the complex mechanical impedance of the soundboard system. Nor can I provide a mathematical expression defining it. But I do have enough knowledge of the relationship between a variety of single strings acting against simple test soundboards -- gained through empirical testing -- to understand at least some of the basic principles of mechanical impedance and string/soundboard relationships as they apply to the whole vibrating string plane and to the entire complex piano soundboard system to make some educated assumptions and guesses. Enough so, at least, to enable me to design and build soundboards that give better acoustical results than those of the past. Are these soundboards perfect? Of course not. Can they be improved through the development of better science? Certainly so. Should I stop stretching the limits of my knowledge and my understanding just because I cannot currently measure and define all of the inter-relationships that exist between the vibrating string and the soundboard/rim assembly. If I do that I am dead -- at least intellectually so and the physically so would soon follow. I have no idea what the relationship between varying humidity levels and measured string inharmonicity might be. Or between soundboard impedance and string inharmonicity. I have made no effort to either measure or to explain these things. Probably won't, although I think there are a few interesting possibilities to explore. But this question has essentially no bearing on how pianos are designed, which is my area of interest. At least I don't think it does. (I know this is heresy, but the whole concept of inharmonicity has very little to do with piano design. Well, ok, across the bass/tenor break...) I do it immensely interesting, however, to read what others are saying about it. The questions, the ideas... If a viable theory develops out of all of this then the drive to understand how the piano works will have taken one more small step forward. Keep at it, folks! Regards, Del Delwin D Fandrich Piano Designer & Builder Hoquiam, Washington USA E.mail: pianobuilders@olynet.com Web Site: http://pianobuilders.olynet.com/
This PTG archive page provided courtesy of Moy Piano Service, LLC