Hi folks. Hope this isnt dead because its actually full of good stuff. I think one of the main points with this mathematical model of Dr. Andersen is being missed in the rush to discount the whole thing. I'm assuming the model he built was based on a piano string isolated from outside influences... such as a soundboard. If this is so then the question about validity and how all this in turn fits into the piano, then things are not quite as straightforward as the discussion so far has required. First there is the matter of whether or not <<a string>> will vibrate longer if kept virbrating in a vertical direction by the terminations as opposed to changing over to the horizontal mode. I'm assuming for the moment that its possible to actually control vibrational direction to some degree thus. In order to find out whether the nett sustain of the string actually is longer for same input force one is going to have to isolate the string from all driven systems... like a soundboard. i.e. maximize the impeadance in all directions at the terminations. If a string in iself does then actually have longer sustain when forced to vibrate vertically --- or rather in the same direction as the input force (which is the actual heart of the matter me thinks) then we can move on to the next bit. A few facts have been thrown into the mesh here already. Most notably the effect of mass on sustain and the fact that the soundboard is more easily driven up and down rather then sideways. This second used to assert that if the (installed) string did actually vibrate longer in the vertical direction then the board would just more readily suck up its energy and sustain would decrease... ie the opposite of the <<claim>>. But if it was established in the first place that a string in itself will indeed vibrate longer if its vibrational direction stays in the same direction as the input force... then suddenly we have an entirely puppy we are dealing with. And this puppy, as it were, would have to be correctly designed into the rest of the piano. One scenario I can imagine is that Stuart and his team KNEW that he would have to exploit this sustaining string correctly BECAUSE of the problem with soundboard impeadance.... and that the mass of the aggraffes could be used along with other soundboard design issues to create an appropriate impedance to a string vibrating thus. Just a thought. btw... this is why I thought it interesting to hear the Steingræaber in comparison. No doubt Udo came up with some different combination of things and it would be real cool to know what those were and listen to the differences. Cheers RicB
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