idea
Fourier's idea
In the early 1800s Joseph Fourier showed that any wave that repeats, however complicated its shape, can be built by adding simple sine waves. The frequencies of these sine waves are whole-number multiples of how often the wave repeats. For sound, this means that the shape of the wave over time and the list of its harmonics describe the same thing in two ways. A spectrum, the picture that shows how strong each harmonic is, is the second way of looking at it.