"Tones That Have Lasted for Eternities" The Ideal Sine Wave between Symbol and Signal

As part of an extensive study of the nineteenth-century development of Fourier analysis as an important tool for the physical study of sound, this paper investigates the epistemological status of sine waves in between mathematical symbol and acoustic signal. The notion of the sine wave originally emerged as a result of Joseph Fourier's Analytical Theory of Heat conceived in 1807. The paper examines how, with the generalisation of Fourier analysis to apply to the physical study of sound by Ohm and Helmholtz, the notion of the sine wave was reconceptualised from a purely symbolic mathematical representation of a single frequency to a sonic object often conceived as the 'basic elements' of sound. Because it provides a seemingly empirical basis for the age-old discursive connection between music, harmony and regularity going as far back as Pythagoras' celestial harmony, as an idealised acoustic object, the sine wave is part of our sonic imagination up to this present day.