What question did this study set out to answer?

The aim is to explore the evolution of sine waves from a mathematical symbol to a fundamental acoustic signal.

April 10, 2026Open Access

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

Key Points

The aim is to explore the evolution of sine waves from a mathematical symbol to a fundamental acoustic signal.
Analysis of historical development of Fourier analysis in sound studies.
Examination of the works of Joseph Fourier, Ohm, and Helmholtz.
Discussion of the transition from symbolic to acoustic representations.
Sine waves are identified as both mathematical and acoustic entities.
The work reveals the historical contextualization connecting sound, music, and harmony.
It highlights the sine wave's lasting impact on our understanding of sound.

Abstract

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.

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