Effect of boundary conditions on string inharmonicity

Chien-Yu Chen, Rama B. Bhat

Abstract


In studying the vibration of and sound from stringed musical instruments, the string is always considered to be completely fixed. However, this does not reflect the reality, especially for instruments such as guitar and violin where the player presses the strings with fingers. From the results obtained, it is clear that a partially fixed string will produce inharmonicity which will introduce some degree of beat phenomenon. This indicates an important aspect that has not been discussed extensively previously. In this paper, a simple mathematical model has been developed to represent a fixedpartially fixed string. The parameters that cause inharmonicity are discussed and the beat phenomenon between fundamental and inharmonic partials is studied.

Keywords


Boundary conditions; Mathematical models; Musical instruments; Parameter estimation; Beat; Guitars; Inharmonicity; Violins

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