Dyad’s consonance and dissonance: combining the compactness and roughness approaches

At present, there are two approaches that aim at explaining on physical grounds the psychoacoustic perception of consonance and dissonance for dyads, whose pioneers have been, respectively, Galilei and Helmholtz: One is based on the “compactness” of the waveform of the combined signal, while the other on the absence of “roughness” due to possible beats. We perform a detailed study of each approach and find that none of the associated model versions, not even the more refined ones, is fully satisfactory when faced to perceptual data on dyads. We show that combining the two approaches results instead in a surprisingly successful agreement with perceptual data: This demonstrates that compactness and roughness are both necessary ingredients for a phenomenological description of consonance and dissonance. Graphical abstract