> Instead of thinking about speaking length, you could also look at a > vibrating string as a spring/mass resonant system. The resonant > frequency of such a system is determined by the mass of the vibrating > member (the string) and the spring constant of the spring that is acting > to return the mass to its central position. If we can model the loose > bridge pin (and the wood that is holding it) as a spring, then its > springiness adds to the springiness due to string tension. This causes > a slight decrease in the spring constant, which is the ratio of > restoring force to deflection distance. Therefore the pitch is > different when the bridge pin is loose. With the system further affected by how far back on the crushed bridge cap the string is unsupported (this is where string stiffness would have the most effect), and the unsupported length of the bridge pin between where it is pushed (by side bearing) against the hole it's installed in, and the string. The speaking length correlation was just one indication of why we don't find loose pin induced false beats in the lower half of the scale. The differences between the resonant frequencies of springing pin and vibrating strings is the other, and I did state that I was ignoring that to illustrate the speaking length relationship. > Of course there are other mechanisms for producing false beats. Loose > bridge pins is just one of them. > > Robert Scott Yes there are, none of which are are nearly as common as the loose pin beat, and none are cured by seating either strings or bridge pins any more than is the loose pin beat - which has been my point all along. Ron N
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