The natural frequencies of piano strings depart somewhat from the harmonic series and the degree of inharmonicity has important implications for tone quality, tuning and the electronic synthesis of piano sounds. Apart from effects due to the finite compliance of the supports, the stiffness of the steel wire from which piano strings are made accounts almost entirely for the inharmonicity of the plain wire strings. It has been shown, however that the string stiffness is not the only source of inharmonicity of the overwound piano strings. Not only the effects of wave-reflection at the terminations of the various copper covering layers of overwounds strings, but also the effects of nonuniformity may contribute. Weak partial cannot be explained by string stiffness alone. Some discussions on the stepped string have appeared over the last few years by Levinson, Sakata and Sakata, and Gottlieb, but their analyses have not incorporated the stiffness of the stepped string. In this thesis, an expression for the frequencies of vibration of a stepped overwound string was described, and numerical calculations have been undertaken to compute theoretical mode frequencies for strings with varying degrees of overwinding. The numerical results of the frequency equation were compared with data from the experiment. The experiments of the inharmonicities of overwound string on a rigid monochord have been measured. The rigid monochord has been designed in order to control the parameters and to reduce external effects disturbing the vibration of the strings. It is evident from the comparison that the theory presented here gives a better fit to measured inharmonicities than Fletcher's analysis for a uniform string. The original motivation for this study was to determine the extent to which the non-uniformity of the overwinding on a bass piano string affected the inharmonicity of its mode frequencies. To examine the extent to which this work was relevant to the behaviour of overwound piano strings with the end support conditions typical of normal use, a series of measurements was performed on the bass strings of a Broadwood grand piano. It is evident from the results that the major cause of the discrepancy between the Fletcher prediction and the measurement is indeed the non-uniformity of the winding.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:643167 |
| Date | January 1995 |
| Creators | Chumnantas, Pochaman |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/13393 |
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