Looking at this hammer/string interaction for even a short while indicates to me that no amount of elementary physics will reveal very much about the process of energy transfer. I believe arguments based on momentum, energy, square pulses, fourier analysis etc. are all doomed to fail...sorry to say it again...primarily because of inherent non-linearity, but also because there are too many inter-related parameters. For instance, the hammer is effectively stiffer at higher velocities which will affect tonal spectra, efficiency of energy transfer, and many other things. Therefore a fast light hammer is fundamentally different from a slow heavier hammer. Energy efficiency is less for a heavy hammer as the energy required to push the hammer away from the string is greater. In at least one of the references inharmonicity was seen to influence the harmonic sprectrum. because of the response of the hammer head while in contact with the string etc. There are so many parameters involved here and they are quite interdependent, so it's unlikely that a situation exists where a pair of parameters may be changed so as to create no overall change. I think we could all contribute to this research by suggesting parameters that may influence tone, say those between the shank pivot to the string (since it is the hammer/string interaction that is in question)...I suggest the following list: shank geometry (length, cross-section, driving force and direction) mass pivot compliance hammer mass geometry compliance string length dia density (overspun?) compliance (inharmonicity) bridge coupling (for reflections) Each of these parameters is measurable, although not all are easy. Each of these is independently variable. The problem then becomes: what are the sprectral energies imparted to the string when a hammer shank is driven by a given force from the action. And how does this harmonic structure change as a particular parameter is varied. Such a problem is more meaningful than random `what-if' scenarios. But I don't believe such a problem can be solved with ordinary physics, or even at all analytically...which is true for similar problems in robotics. Any more suggestions for parameters that you think are important?? Stephen Birkett (Fortepianos) Authentic Reproductions of 18th and 19th Century Pianos Waterloo, Ontario, Canada tel: 519-885-2228 fax: 519-763-4686
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