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Simple Modeling of Soundboard Effect for Piano Transcription

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Partials of piano sounds are inharmonic. This inharmonicity is due either to string stiffness and to soundboard impedance. The last has not been widely documented. Two problems arise: to know the value of the impedance and to evaluate the frequency deviation the partial suffers. In this work, that deviation has been calculated either by using Morse’s equations and by using author’s proposed method. To validate results, deviations for some piano notes have been measured. Besides, the soundboard impedance has also been measured to verify relationship between deviation and impedance. Moreover, a method to evaluate impedance using measured deviations is also proposed. This last method can be useful during training stages in transcription systems and for parameter extraction schemes.

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