Consonance perception of complex-tone dyads and chords

Sensory consonance and dissonance are perceptual attributes of musical intervals conveying pleasantness, tension, and harmony in musical phrases. For complex-tone dyads, corresponding to two musical notes played simultaneously, consonance is known to vary with the ratio in fundamental frequency (F0) between the two tones in the dyad. While such a relationship is well established for dyads, the subjective consonance of chords containing three or more simultaneous notes, that form the basis of most musical pieces, remains to be explored. The present study aimed at comparing consonance judgments for dyads and 3-note chords as a function of the F0 ratio between their element tones. Dyads and chords were generated by adding two or three complex tones containing 6 harmonics with equal amplitude and random phase. The base F0 of the first tone was randomly selected from an interval spanning ±3/4 of a semitone centered at 440 Hz. The second tone F0 varied between 0–12 semitones above the base F0. For chords, the third tone F0 was fixed either at 5 (Perfect 4th, P4) or at 7 (Perfect 5th, P5) semitones above the base F0. Ten normal-hearing listeners were presented with all possible dyad/dyad, dyad/chord, and chord/chord combinations in random order and were asked to judge which interval was most consonant in each paired comparison. The results for dyad/dyad comparisons were consistent with earlier findings, with the unison, octave, P5, and P4 intervals being perceived as the most consonant. For dyad/chord comparisons, dyads were more consonant in the intervals around the fixed third tone. Overall, chords were not found to be more dissonant than dyads. This suggests that the hypothesis according to which consonance decreases with the amount of interaction between present harmonics, arguing for a potential role of frequency selectivity for consonance perception of dyads, might not hold for chords.