The Vibrating String In Keyboard Instruments

Lincoln, John (1983). The Vibrating String In Keyboard Instruments. MPhil thesis The Open University.



In this thesis some aspects of the acoustics of the piano and harpsichord are discussed.

Initially the wave equation for the vibrating string is derived. Since the strings in the piano are not perfectly flexible the wave equation is extended to take into account the stiffness of the strings.

The wave equation thus modified affects the frequencies of the partials of the strings. The predicted frequencies are compared with the actual frequencies on a piano. The discussion is then continued to show how this affects the actual tuning of the instrument. Computer and programmable calculator programmes are used in these predictions.

The theoretical basis for the spectra of piano and harpsichord strings are discussed and brief notes included on the effects of hammer width and string stiffness.

The final experimental section deals with the reverberation times for piano and harpsichord strings, taking account of the effects of multiple stringing. Multiple stringing is found to affect the piano strings but not the harpsichord strings reverberation times. No accurate measurements of harpsichord reverberation times could be found in the literature, and the experiments were extended to include the effects of the buff stop.

The conclusions contain several suggestions for further study and stress the importance of piano scaling. It is noted that scaling is also of importance to the musician when selecting instruments for the performance of duets, especially with regard to tuning compatibility.

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