A two-dimensional representation of musical chords using the simplicity of frequency and period ratios as coordinates

Musical chords play an essential role, especially in Western music, and the corresponding consonance–dissonance contrasts and emotional continua are still the targets of investigation in psychoacoustics and neurophysiology. In the present study, we define the simplicity of frequency ratios Sf and simplicity of period ratios Sp for the constituents of a chord and propose that those measures should be used as the two coordinate axes in the plane for plotting chords. In this plane, the major and minor chords are reflections of each other with respect to the diagonal Sf=Sp. The other chord pair in the same relationship is the major–minor seventh (dominant seventh) and the half-diminished seventh chords. The other triads and seventh chords do not make such pairs of different categories of chords. It was also found that at least for triads, the sum Sp+Sf and the difference Sp−Sf seem to correspond to subjective consonance and the melancholic/sad emotional ratings, respectively. Implications of these findings are discussed. The proposed simple presentation may help interpret and model psychoacoustic and neurophysiological results on musical chords.