Algorithmic composition of music has a long history and with the development of powerful deep learning methods, there has recently been increased interest in exploring algorithms and models to create art. We explore the utility of Hidden Markov Models in composing classical piano pieces from the Romantic era and consider the models’ ability to generate new pieces that sound like they were composed by a human. We find that Hidden Markov Models are fairly successful at generating new pieces that have largely consonant harmonies, especially when trained on original pieces with simple harmonic structure. However, we conclude that the major limitation in using Hidden Markov Models to generate music that sounds like it was composed by a human is the lack of melodic progression in the composed pieces. Classical Music Composition Using State Space Models