Harmonic Analysis Using Neural Networks

This thesis describes a system of neural networks that performs harmonic analysis on musical compositions. The system is split into four groups of Networks: Key Network, Root Network A (used to detect secondary functions), Root Network B, and Quality Network. The system is trained on 20 J.S. Bach chorales and tested on another 18 Bach chorales. Accuracies of over 90% were obtained for all four groups of Networks. Comparison with a modified version of Krumhansl's key-finding algorithm indicates Key Network outperforms it by more than 16% in overall accuracy. This work has potential for extension into music of other composers or genres. Also, this work can be used by a computer accompanist to determine the key of an improvising soloist. ii Acknowledgement First of all, I wish to thank gratefully Prof. James MacLean for supervising me for the entirety of this thesis. His suggestions have impacted this work very much. I also thank my fellow graduate schoolmates in the SF lab for making me feel I am not alone in this seemingly neverending world of graduate studies. I would like to thank University of Toronto for all the forms of financial support it had provided me. I would like to thank my brothers and sisters in Paul Fellowship for praying for me, my cousin Alan Wong for his continual encouragement to go on, my parents and grandmother for encouraging me to pursue graduate school, and Brenda Chan for keeping me sane in the days and nights when work is much but progress is few. Finally, I give thanks to my Lord Jesus Christ for leading me through this earthly travail. Without Him, nothing is possible.