The French mathematician Fourier discovered that you could build any repeating waveform by adding enough sine and/or cosine waves. This is called Fourier synthesis. It is also possible to analyze a repeating waveform to find out how much of each frequency is present. This is called Fourier analysis. For a repeating wave the extra frequencies present are all multiples of the fundamental and are called harmonic frequencies. The timbre of a musical instrument depends on the amount of each harmonic that is present.
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