The acoustic origins of harmonic analysis

In music, harmony refers to a pleasant combination of sounds. In mathematics, a harmonic function is a sine function obtained by projecting a circular motion on a diameter, and harmonic analysis is the theory of the development of periodic functions into harmonic components, or the theory of similar developments. The occurrence of the same word in musical and mathematical contexts is neither a coincidence nor a purely metaphorical effect. As is well known, in the mid-nineteenth century Hermann Helmholtz connected the two meanings through the idea that the ear functions as a harmonic analyzer in a physico-mathematical sense.1 This formulation of Helmholtz’s achievement suggests that harmonic analysis preceded its acoustic and musical application. So does too the fact that Joseph Fourier’s foundation of this kind of analysis had to do with heat rather