[Hermann von Helmholtz and Carl Stumpf on consonance and dissonance]

The article juxtaposes Hermann von Helmholtz's work in the experimental physiology of hearing and Carl Stumpf's tone psychology, focusing on the problem of consonance and dissonance in music. It argues that the experimental set-up plays a major role in the approaches to hearing of both Helmholtz and Stumpf, shaping their redefinition of the musical concepts of consonance and dissonance. Helmholtz, however, explains dissonance as resulting from the beats that are heard when sound waves interfere, while Stumpf explains consonance from the fusion (Verschmelzung) of sounds, noting that two tones, depending on their distance cannot always be recognized as two but are heard as one single tone. Helmholtz's definition of dissonance eventually threatens his own theory of hearing, which is based on the mechanical principle of resonance and considers sound to be composed of sinusoidal waves. Both the physical and the mathematical tools he uses cannot easily be brought into accordance with his experimental findings on beats, which ask for a discrimination of fast changes in intensity. Dissonance thus becomes "unrecomendable" for Helmholtz, because it overstrains the ear. Stumpf's research, in contrast, has its point of departure in the historically given set of intervals and tries to find a principle that would explain this choice. His tests with experimental subjects who have no conscious knowledge of musical harmony and prove incapable to follow or reproduce music reveals to him a difference between the unity and multiplicity of tones.