Simscape Model - calculate inharmonicity in piano string.

SImscape models the flexural vibration of a piano string including the wire bending stiffness. Modal frequencies are a good match to theory.
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Updated 18 Oct 2023

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The vibrating “string” of a piano is a thin steel wire that is tensioned to tune it to the intended playing frequency. Sufficient tension in the wire gives it the properties approximately of a flexible string, with its multiple resonance frequencies approximately at harmonic intervals. However the wire bending stiffness modifies the resonance frequencies by a small amount. It is well known that the additional stiffness modifies the resonance frequencies f_n such that where alpha << one and f_0 is the fundamental frequency of a similar ideal flexible string. A Simscape model of the vibrating string demonstrates this behavior, and its solver has sufficient resolution to match this theoretical prediction.

Cite As

Steve Thompson (2024). Simscape Model - calculate inharmonicity in piano string. (https://www.mathworks.com/matlabcentral/fileexchange/136764-simscape-model-calculate-inharmonicity-in-piano-string), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2023b
Compatible with any release
Platform Compatibility
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Version Published Release Notes
1.0.1

Fix type in title

1.0.0