Consonance in the carillon

Abstract

Recent research has confirmed that musical consonance is not only determined by the frequency ratios between tones, but also by the frequency spectra of the underlying tones (Marjieh et al., 2024). However, this prior research was limited to artificial tones, specifically tones built from a small number of pure tones, producing sounds that do not match the acoustic complexity of real musical instruments. Here we therefore investigate 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. We show that the traditional consonances of the major third and the minor sixth become dissonances in the carillon, and we show that small intervals (in particular 0.5-2.5 semitones) also become particularly dissonant in the carillon. Through computational modelling we show that these effects are primarily caused by interference between partials (e.g. beating), but we also show 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.