A Frequency Error Model for Fretted String Instruments

    Authors

    J. Lane;T. Kasparis

    Comments

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    Abbreviated Journal Title

    Acta Acust. United Acust.

    Keywords

    Acoustics

    Abstract

    A mathematical model, quantifying frequency error due to string displacement and the process of fretting a note on a string instrument, is presented. The model is developed starting with the standard relationship between length, tension, density, and frequency of a perfect string. The change in string length, as a result of displacing the string to a point behind a fret, is modeled by a set of parameters approximating the resulting shape of the fretted string. The string length model is then combined with an inharmonicity model which approximates the frequency deviation of the series of partials contained in the string's frequency spectrum. Inharmonicity is weakly dependent on the change in string tension due to fretting, but to first order, inharmonicity frequency errors of a string with finite bending stiffness are independent of the process of fretting a string.

    Journal Title

    Acta Acustica United with Acustica

    Volume

    98

    Issue/Number

    6

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    936

    Last Page

    944

    WOS Identifier

    WOS:000311839300010

    ISSN

    1610-1928

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