  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.
