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Reference: V. E. Howle and Lloyd N. Trefethen, (1997). Eigenvalues and Musical Instruments. Unspecified.Citable link to this page:

 

Eigenvalues and Musical Instruments

Abstract: Most musical instruments are built from physical systems that oscillate at certain natural frequencies. The frequencies are the imaginary parts of the eigenvalues of a linear operator, and the decay rates are the negatives of the real parts, so it ought to be possible to given an approximate idea of the sound of a musical instrument by a single plot of points in the complex plane. Nevertheless, the authors are unaware of any such picture that has every appeared in print. This paper attempts to fill that gap by plotting eigenvalues for a guitar string, a flute, a clarinet, a kettledrum, and a musical bell. For the drum and the bell, simple idealized models have eigenvalues that are irrationally related, but as the actual instruments have evolved over the generations, the leading five or six eigenvalues have moved around the complex plane so that their relative positions are musically pleasing.

Bibliographic Details

Issue Date: 1997-08Identifiers

Urn: uuid:29211059-6206-4e1c-95e6-6a9eb515a996 Item Description

Type: Technical Report;

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Author: V. E. Howle - - - Lloyd N. Trefethen - - - - Bibliographic Details Issue Date: 1997-08 - Identifiers Urn: uuid:29211059-6206-4e1c

Source: https://ora.ox.ac.uk/objects/uuid:29211059-6206-4e1c-95e6-6a9eb515a996



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