Learning Harmonic Relationships in Digital Audio with Dirichlet-Based Hidden Markov Models

Harmonic analysis is a standard musicological tool for understanding many pieces of Western classical music and making comparisons among them. Traditionally, this analysis is done on paper scores, and most past research in machine-assisted analysis has begun with digital representations of them. Human music students are also taught to hear their musical analyses, however, in both musical recordings and performances. Our approach attempts to teach machines to do the same, beginning with a corpus of recorded Mozart symphonies. The audio files are first transformed into an ordered series of normalized pitch class profile (PCP) vectors. Simplified rules of tonal harmony are encoded in a transition matrix. Classical music tends to change key more frequently than popular music, and so these rules account not only for chords, as most previous work has done, but also for the keys in which they function. A hidden Markov model (HMM) is used with this transition matrix to train Dirichlet distributions for major and minor keys on the PCP vectors. The system tracks chords and keys successfully and shows promise for a real-time implementation.