Consonance and dissonance for dyads: combining compactness and roughness

There are basically two types of approaches that aim to explain on physical grounds the psychoacoustic perception of consonance and dissonance in music. One is based on the “compactness” of the waveform of the combined signal, while the other on the absence of “roughness” induced by beats. In a previous detailed study of each approach for dyads, we found that none of the associated model versions is fully satisfactory when faced to perceptual data, while a surprisingly successful agreement is found by combining the two approaches. In the present contribution, we extend our analysis by exploring how compactness models for dyads can be related to the early arguments by GB Benedetti.