Unsupervised Learning of Harmonic Analysis Based on Neural HSMM with Code Quality Templates

This paper presents a method of unsupervised learning of harmonic analysis based on a hidden semi-Markov model (HSMM). We introduce the chord quality templates, which specify the probability of pitch class emissions given a root note and a chord quality. Other probability distributions that comprise the HSMM are automatically learned via unsupervised learning, which has been a challenge in existing research. The results of the harmonic analysis of the proposed model were evaluated using existing labeled data. While our proposed method has yet to perform as well as existing models that used supervised learning and complex rule design, it has the advantage of not requiring expensive labeled data or rule elaboration. Furthermore, we also show how to recognize the tonic without prior knowledge, based on the transition probabilities of the Markov model.