Harmonising Chorales by Probabilistic Inference

We describe how we used a data set of chorale harmonisations composed by Johann Sebastian Bach to train Hidden Markov Models. Using a prob- abilistic framework allows us to create a harmonisation system which learns from examples, and which can compose new harmonisations. We make a quantitative comparison of our system's harmonisation perfor- mance against simpler models, and provide example harmonisations.