ICNCM 2026 – University of Toronto, Canada
25–27 June 2026
22nd International Conference on Nineteenth-Century Music
Undertones Unheard: Riemann’s Speculative Acoustics and its Collapse
Abstract
Following experiments on combination tones by Giuseppe Tartini and Hermann von Helmholtz, Hugo Riemann ventured into speculative territory once he started to believe in the objective existence of undertones. Since that moment he sought to substantiate his belief through various means. Different argumentations in his dissertation, followed by the article »Die objective Existenz der Untertöne in der Schallwelle«, and later reflections in the »Musikalische Syntaxis« failed to provide a satisfactory explanation. Nevertheless, Riemann built his means of notation and analysis, the »Unterklänge« as »Klangschlüssel« and »Leittonwechselklänge« in the »Funktionstheorie«. Despite the thorough reception of Helmholtz’ ideas by Riemann, both authors are divided by their use of scientific methods. Absolute objectivity in Helmholtz’ writing is contrasted by subjective perception in Riemann’s experiments. Inductive theory is combined with a deductive approach by the latter, whereas Helmholtz remains in his physical laboratory, detached from speculative musical thought—surrounded by resonators and a provisionally modified harmonium with just intervals. Riemann offered ingenious but empirically fragile explanations for the inaudibility of undertones: such as the merging of undertones with combination tones or destructive interference. Ultimately, his pursuit of undertones seems to have led him into a theoretical dead end—one he would later acknowledge himself, admitting in retrospect that he had been mistaken in believing in their objective existence. This rare moment of self-correction marks a turning point in his theoretical framework and its relation to empirical validation.
This presentation is supported by the ERASMUS+ Programme of the European Union.