From roughness to coincidence—Concepts of dissonance and consonance

150 years after the first English translation of Hermann von Helmholtz's opus “On the Sensations of Tone,” we review existing consonance theories that have emerged from this seminal work: According to Helmholtz, the degree of roughness between the partials of two simultaneously sounding tones determines the degree of consonance of an interval (the rougher the more dissonant). For chords, on the other hand, Helmholtz saw the difference tones as a way of determining consonance (the more the difference tones correspond to pitches already present in the chord, the more consonant it is). Based on these two psychoacoustic phenomena (roughness and difference tones), a whole series of consonance theories were formed. However, these psychoacoustic explanations proved to be limited in the course of the 20th century. Coincidence theories offered an alternative here, according to which the more matching partials (frequency domain) or periods (time domain) existing in the sounds of an interval, the greater the sensation of consonance. This perspective has been supported since the 1960s by perception experiments on intervals with compressed and stretched partial series. Within the scope of the article, an Internet application is introduced with which such sounds and intervals can be generated easily and intuitively.