Joseph Fourier’s methods (and their variants) are omnipresent in audio signal processing. However, it turns out that the underlying ideas took some time to penetrate the field of sound analysis and that different paths were first followed in the period immediately following Fourier’s pioneering work, with or without reference to him. This illustrates the interplay between mathematics and physics as well as the key role played by instrumentation, with notable inventions by outsiders to academia, such as Rudolph Koenig and Édouard-Léon Scott de Martinville.