Triad's consonance and dissonance: a detailed analysis of compactness models

Theories of consonance and dissonance based on the "compactness" approach include the two sub-categories of periodicity and harmonicity. In a previous work, we discussed the related consonance and dissonance indicators for dyads; as they are given by discontinuous functions of the dyad frequency ratio, we proposed a method to extend them to the continuum, based on the auditory discrimination limen. Here, we generalize the compactness indicators to describe the consonance and dissonance for triads and discuss their extension to the continuum. We compare our model predictions with perceptual data from a recent psychoacoustic test by means of a Chi-square analysis. The result is that compactness indicators provide a quite effective, but not fully satisfactory, description of consonance, and dissonance for triads.