Jean Baptist Fourier (1768–1830), a French mathematician and physicist, made discoveries in a number of fields, including the greenhouse effect. He developed mathematical tools known as Fourier series and transforms that are used in a wide variety of applications. The Fourier Theorem states that any repetitive waveform can be constructed from a series of waves of specific frequencies, a fundamental and higher harmonics. The reverse is also true—if you add together waves of frequencies f, 2f, 3f, etc., specifying their amplitudes, you can construct a complex waveform. Using Fourier analysis, then you can record the waveform of a musical instrument and determine the amplitudes of the harmonics of which it is made, that is, its spectrum.

Today Fourier analysis is very easy to do. Most computers either have built in microphones or can use an external microphone. Free software can be downloaded from the web that will display the spectrum.