A regularization algorithm for local key detection

In the field of music information retrieval, the detection of global key in both popular and classical music has been studied extensively, but local key detection has been studied to a lesser extent, even though modulation is an important component of compositional style. It is particularly challenging to identify key change boundaries correctly. We modeled this task as an optimization problem, that of finding out how to divide a piece into sections in different keys taking into consideration both the quality of the fit between the key and the section and the number of sections. We determined the optimal assignment of key to section using the Krumhansl–Schmuckler algorithm with a slightly modified version of the Krumhansl and Kessler key profile. We included a regularization algorithm in the formulation of our problem to balance the number of sections and avoid superfluous modulations. Using a dataset of 80 randomly chosen pieces of music in a variety of genres and levels of complexity, we compared our algorithm with a hidden Markov model (HMM) to determine which method is better for identifying local key. Our approach yielded significantly more accurate results and suggests future avenues of research.