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A simple answer is the mathematical relationship between the characteristics of the instrument and the sound. The sound scale is log linear, but there may be more than one harmonic frequency also present as is the case for the violin. I am not a musician, but I am quite interested in the mathematics of music, and the log plot of the piano key fundamental frequencies form a straight line plot. There may also be other frequencies present for a given tone that produce narrow side frequencies. These sound signals can be viewed in real time on an oscilloscope or a spectrum analyzer.
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