Some additional thoughts: 1. Producing identical sound loudness probably requires equal energy transfer from the hammer to the string. Energy is not equivalent to momentum. Energy is mass times the square of the velocity. 2. To ask the question the way it has been phrased, assumes that the motion of the key is the same in both A and B. I think this is unlikely, as the inertia seen by the finger at keystick B is significantly less than in A, so the same pianist will produce different velocity profiles in the two keys. 3. A slower heavier hammer transferring the same amount of energy to the string will probably have a different dwell time at the string. Will that affect how much of the hammer's kinetic energy actually gets transferred to the string? Not a simple answer, since we're talking about energy distributed across a spectrum of partials. Perhaps you could equalize dwell time through voicing. Perhaps you'd rather make them sound as similar to each other as possible through voicing. In either case, it's starting to look a lot like apples and oranges. Mike John Delacour wrote: > At 19:47 -0700 23/3/10, David Love wrote: > >> Forgive the awkward formulation of the question. Let's put it a >> different >> way. > > But why?! I have answered the question and the question you have > re-put at length in different words. > > momentum = velocity x mass. > > It is momentum that leads to the transfer of energy on impact between > the hammer and the string. The resistive potential of the string is > constant no matter what you do to the action, and so the calculation > is simple. By the simplest of algebra, if you halve the velocity you > must double the mass to get the same momentum. > > I don't see how it can be put more clearly. > > JD > > >
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