“Secret Science” and Piano Experiments: The Discovery of Harmonics

Harmonics straddle the frontier between experimental science, instrumental technique, music theory, and compositional practice. Named by Joseph Sauveur as a central element of his new science of acoustics, a harmonic subtracts from the complex sound of a vibrating string all but a single mode of vibration, analogous to Newton’s decomposition of white light into its spectral colors. Though French science legitimized string harmonics, musical practice elsewhere resisted them until Paganini showed their virtuosic power. In contrast, Hermann von Helmholtz’s piano experiments demonstrated an additive account of timbre through the superposition of harmonics and paved the way almost singlehandedly for piano harmonics, previously unknown. Ernst Mach’s popularization of Helmholtz and a controversy between Hugo Riemann and Georg Capellen brought piano experiments further recognition. After that, Arnold Schoenberg pondered piano experiments during his marital crisis (1908) and then began using piano harmonics in compositions. In the process, Schoenberg aligned his “secret science” of musical composition and the emancipation of dissonance with the counterintuitive discoveries of modern science.