Consonance and Dissonance of Simultaneous Trichords in Western Music: A Listening Experiment to Test Models of Harmonicity and Roughness

Previous empirical studies have suggested that the perceived consonance/dissonance (C/D) of a musical chord depends on its psychoacoustic smoothness (lack of roughness), spectral harmonicity (perceptual fusion), and/or musical familiarity. We tested the dependence of C/D on smoothness and harmonicity in a hearing experiment that included all 19 possible trichords in musical pitch-class set theory. In each trial, a listener heard a chord (duration: 300 or 500 ms) and rated its C/D on an 11-point scale. Each trichord was presented 10 times: 4 times constructed from octave-complex tones (OCTs, sounding like an electronic organ) and 6 times from natural piano tones. Each OCT chord was presented in 4 different transpositions. The piano chords were in close or open position, and root position or 1st/2nd inversion (2 levels of spacing x 3 levels of inversion = 6 levels of voicing). We found no main effect of timbre (OCT versus piano) and no interaction between trichord and timbre. Results correlated closely with predictions of simple models of roughness and harmonicity. The roughness model performed better, and the predictions correlated with each other. A combined model was not superior to roughness alone. The results were consistent with a multifactorial model of the C/D of a musical chord, the main factors being roughness, harmonicity, and familiarity.