Consonance in the carillon

Previous psychological studies have shown that musical consonance is not only determined by the frequency ratios between tones, but also by the frequency spectra of those tones. However, these prior studies used artificial tones, specifically tones built from a small number of pure tones, which do not match the acoustic complexity of real musical instruments. The present experiment therefore investigates tones recorded from a real musical instrument, the Westerkerk Carillon, conducting a "dense rating" experiment where participants (N = 113) rated musical intervals drawn from the continuous range 0-15 semitones. Results show that the traditional consonances of the major third and the minor sixth become dissonances in the carillon and that small intervals (in particular 0.5-2.5 semitones) also become particularly dissonant. Computational modelling shows that these effects are primarily caused by interference between partials (e.g., beating), but that preference for harmonicity is also necessary to produce an accurate overall account of participants' preferences. The results support musicians' writings about the carillon and contribute to ongoing debates about the psychological mechanisms underpinning consonance perception, in particular disputing the recent claim that interference is largely irrelevant to consonance perception.