UC San Diego

Though music is an art form with tremendous expressive capacity, the underlying frameworks of most musical compositions are highly structured and organized. As such, musical pieces are commonly studied by analyzing their melodic and harmonic structures. Two important concepts in any such analysis are the key and tonic. The key of a musical piece identifies a principal set of pitches that the composer uses to build its melodies and harmonies; the tonic is the most stable pitch in this set. Each musical piece is characterized by one overall key. However, the key can be shifted within a piece by a compositional technique known as modulation. Notwithstanding the infinite number of variations possible in music, most pieces can be analyzed in these terms. In this dissertation, we propose novel methods for modeling a corpus of musical pieces in terms of its harmonic structure. We describe several different models for symbolic and audio musical input, as we find both to be valuable data formats to perform harmonic analysis on. Our models are based on Latent Dirichlet Allocation (LDA), a popular probabilistic model traditionally used for discovering latent semantic topics in large collections of text documents. In our variant of LDA, we model each musical piece as a random mixture of keys. Each key is then modeled as a key-profile -- a distribution over a set of pitch classes. Using this representation, we show how to accomplish the tasks of key-finding and modulation- tracking, the first steps to any kind of harmonic analysis. Our approach to such tasks is unlike that of previous studies, which depend on extensive prior music knowledge or supervision by domain experts. Based on a model of unsupervised learning, our approach bypasses the need for manually key-annotated musical pieces, a process that is both expensive and prone to error. As an additional benefit, it can also discover correlations in the data of which the designers of rule-based approaches are unaware. Since we do not rely on extensive prior knowledge, our model can also be applied in a straightforward way to other, non-western genres of music with different tonal systems