A probabilistic model of melody perception

Abstract

This study presents a probabilistic model of melody perception, which infers the key of a melody and also judges the probability of the melody itself. The model uses Bayesian reasoning: For any "surface" pattern and underlying "structure," we can infer the structure maximizing P(structure surface) based on knowledge of P(surface, structure). The probability of the surface can then be calculated as ∑P(surface, structure), summed over all structures. In this case, the surface is a pattern of notes; the structure is a key. A generative model is proposed, based on three principles: (a) melodies tend to remain within a narrow pitch range; (b) note-to-note intervals within a melody tend to be small; and (c) notes tend to conform to a distribution (or key profile) that depends on the key. The model is tested in three ways. First, it is tested on its ability to identify the keys of a set of folksong melodies. Second, it is tested on a melodic expectation task in which it must judge the probability of different notes occurring given a prior context; these judgments are compared with perception data from a melodic expectation experiment. Finally, the model is tested on its ability to detect incorrect notes in melodies by assigning them lower probabilities than the original versions.