>The hammer that stays on the string longer actually mutes partials that >would otherwise be vibrating while the hammer is on the string. If the >hammer stayed on the string 1 second it would be muting all vibration >(blocking). If it stayed on the string only 1 _micro_, second all audible >partials would be heard. Right?? >David M. Porritt, RPT >SMU - Dallas My Reply----------- I slept on this one. That doesn't mean that my answer is even necessarily in the right direction. My own belief is that the energy in the higher partials are not absorbed. A string vibrates with a potential to produce all of its natural frequency partials. The only variable that will change its partial spectrum from its natural setting is the shape of the waveform that is imprinted to the string at the actual moment the hammer leaves the string following impact. This is opposed to the view from Mr. Porritt in which he would expect the pulses corresponding to certain partial frequncies traveling down the string to be absorbed by the hammer and thus eliminating their strength. My own view has certain pulses of energy that have been reflected from from the termination points or boundaries being absorbed also to some degree but more importantly these arriving pulses will change the shape of the string as it flexes around the impact of the hammer. To do true Fourier Analysis for this problem you would have to solve a Three dimensional wave equation (find the equation that will predict the amplitude for each partial frequency). To do this we would need to know the boundary conditions (no problem the string position is fixed at either end) and the shape of the wave on the string at the exact moment the hammer leaves the string. Since it is a three dimensional problem we would need to know that shape in two independent planes (shape of the string moving in up and down, the shape of the string moving sideways). As you can imagine that is nearly impossible to do. You also need the velocity of string in each direction. So Fourier Analysis will not work here and thus we can not predict from this method the spectrum of a given note (relative strength of partial frequencies). What we are left with is analyzing empirically what is produced with different types of blows. We can record signals then statistically scope them to determine the spectrum distribution. I believe that is what Mr. Davis meant when he referred to Fourier Analysis. I'm not sure, but people have computer programs that run off of spread sheets which will take the information and manipulate it mathematically to get this result. I think it is called a Fast Fourier Transform. Mr. Davis wrote: Yes [well, except for the ones which are multiples of the inverse of the strike point fraction -- i.e., if the string is struck at 1/7 of its length, the 7th, 14th, etc. partials will be missing]. My Reply-------------- Why would this be true? Do you have any idea as to what its physical explanation would be? Michael Wathen
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