> >>The frequency of vibrating piano strings is not stable, but tends to > >>lower as the string continues to sound. I would like to see a reference to support this. Studies done in 1943 as reprinted in _Piano Technician's Journal_ Jan. 1964 studied the "measurement of the frequencies of the partials and their amplitudes as functions of time." They did not report a lowering of freq as the string continued to sound ( ie function of time.) This was reprinted from "Observations on the Vibrations of Piano STrings" by OH Schuck and R. W. Young of C.G. Conn Ltd., Elkhart, Indiana. Journal of American Acoustical Society ,(JASA) Vol 15, Nol 1, 1-11, July 1943. The interesting parts of this article was proposing that the variance of the partial from true harmonic was proportional between a constant and the square of the partial number. Also the actual methods they used to produce and record their data. An interesting observation that goes contrary to what some say today was that the method of striking the key did not influence the frequencies of the partials, "as it was found that variations in the strength of the blow produced negligible effects on the modal frequencies, the key was struck manually." FWIW the "vibration pickup" was a "crystal vibration pick-up fastened to a rib of the sounding board". that was "fed through an analyzer to a chromatic stroboscope". The analyzer I think was one that filters out all frequencies but a small band. If a "chromatic stroboscope" is like an oscilliscope, I don't know. As with all scientific investigations, the scene repeats itself, but with newer and better and glitzier equipment, making it that much more exciting. Might be interesting to repeat these experiments with a state of the art oscilliscope. The crystal pickup might be compared to a magnetic pickup or a pzm. A vibrating piano wire clamped between two points on a railroad rail might be photographed with a strobe at each of the partial freq, or simply observed with a hi-tech strobe light. If the frequency really does lower in time, a strobe light should tell beyond all doubt. It is probable inharmonicity really can't be measured. Such concerns soon get scrutinized for practicality and point of view. What is the need for a mathematical formula to predict inharmonicity.? I am curious, that's enough. Now what about that grant? ---ric
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