Bob et al.: Yes, all of these effects exist to a greater or lesser extent. Engineers and physicists are the people who exercise informed judgement about which effects might be significant in the case at hand, make predictions (take action) based on those judgements, and reconcile the results obtained with the predicted behavior. This eventually lends a degree of confidence to the model that is directly related to the agreement between theory and observation, and suggests what elements of the model might need to be refined. My fingers raise varying tidal bulges on Betelgeuse when I type, but the magnitude of the effect isn't big enough be of much practical interest. The TWANGY!! sound of Indian instruments like sitars and tambouras results from the fact that they have rounded bridges (the string passes over an arc rather than a ridge) with a radius of curvature of about 1-2 inches, and when a vibrating string ascends it lengthens, while when it descends it gets shorter. This one I *have* simulated, and with no trouble at all what emerges is a sound just like that of the real instrument. If such bridge effects were significant on a piano, we would hear them loud and clear (and sometimes do in a sick piano). The point is that you only need to push a model as far as measurable random (not systematic!) discrepancies from the model predictions remain, and no farther, because once there are no measurable discrepancies there is no way to test the validity of the model any further. Before we worry seriously about vibrating bridges, mode coupling, large-amplitude vs. small-amplitude vibrations, and a host of other plausible physical complications, we need to apply simple modeling predictions (such as cubic stiffness terms, which give rise to most of the observed inharmonicity -- conventional stretching) to one or more real pianos, measure the residual errors in partial frequencies that remain after these predictions are taken into account, and decide (1) whether the residuals are systematic, and (2) whether they are acceptably small. This of course is the question I asked about a week ago (Can we consistently measure random deviations from smooth stretching?), and the discussion so far has been terrific. Marc Damashek Hampstead, MD BobDavis88@AOL.COM wrote: > Engineers, > Doesn't the moving bridge cause the terminus of the string to "appear" > farther away than it is? And the string therefore to act longer? And wouldn't > the stiffness of the sbd vary the apparent length, and therefore the > inharmonicity of the string? > Thanks > Bob Davis ____________________________________________________________________ Get your own FREE, personal Netscape WebMail account today at http://webmail.netscape.com.
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