Tonality Induction and Probabilistic Modeling
How do listeners get a sense of the key of a piece of music? How do they intuit which notes are acceptable or unacceptable pitches on which a melody might end? Which pitches are stable or unstable within the hierarchical structure of music? This research seeks to answer these questions by separating two aspects of melodic structure: their pitch distributions and tonal melodic formulae (such as mi-re-do). Statistical pitch distributions were created for each key based on analysis of a corpus of music (counting the instances of each pitch class in each key) and converted to a probability function. New melodies were created quasi-randomly, taking into account the probabilites for each pitch but avoiding (except by chance) any typical tonal melodic patterning. Listeners (with and without absolute pitch) identified what they perceived to be the most stable pitch for each melody and these responses were compared with each melody’s generating key. Listeners identified the generating key a little over half the time, though well above chance performance. Future research will study the “wrong” judgments made by our listeners in an effort to refine the probabilistic models, will continue to explore the ability of humans to track pitch distributions in differing musical contexts, and will explore other strategies by which listeners make tonality judgments.