Sooie-Hoe Loke (Mathematics)
Hidden Markov and hidden semi-Markov models are utilized to predict structures of American jazz standard repertoire. Two separate relationships are explored. First, the 24 major and minor keys of the Western musical canon are designated as hidden states. Pairs of consecutive chord symbols represent observable emissions from those keys. HMM initial, emission, and transition parameters are defined by previous work on tonal relations, and optimized. Second, the bisectional nature of American jazz standards is parsed into two hidden states. Melodic pitch is used as an observable indicator. HMM and HSMM parameters (including duration) are semi-uniformly initiated, and optimized. The functionality of this project’s components are evaluated using ten jazz standards with key modulation and ten with bisectional form. Varying levels of accuracy are achieved. Discussion of use in digital cataloging/retrieval and for composition software is included, as well as an appendix of hidden-Markov statistical methods.
Keywords: Music, Probability, Optimization