Thesis (Ph.D.) - Indiana University, University Graduate School/Luddy School of Informatics, Computing, and Engineering, 2020Score following is an AI technique that enables computer programs to “listen to” music: to track a live musical performance in relation to its written score, even through variations in tempo and amplitude. This ability can be transformative for musical practice, performance, education, and composition. Although score following has been successful on monophonic music (one note at a time), it has difficulty with polyphonic music. One of the greatest challenges is piano music, which is highly polyphonic. This dissertation investigates ways to overcome the challenges of polyphonic music, and casts light on the nature of the problem through empirical experiments. I propose two new approaches inspired by two important aspects of music that humans perceive during a performance: the pitch profile of the sound, and the timing. In the first approach, I account for changing timbre within a chord by tracking harmonic amplitudes to improve matching between the score and the sound. In the second approach, I model tempo in music, allowing it to deviate from the default tempo value within reasonable statistical constraints. For both methods, I develop switching Kalman filter models that are interesting in their own right. I have conducted experiments on 50 excerpts of real piano performances, and analyzed the results both case-by-case and statistically. The results indicate that modeling tempo is essential for piano score following, and the second method significantly outperformed the state-of-the-art baseline. The first method, although it did not show improvement over the baseline, still represents a promising new direction for future research. Taken together, the results contribute to a more nuanced and multifaceted understanding of the score-following problem.