Music as Math: A Time-Dependent Markov Model for Irish Folktune Melodies
Markov chains have been used extensively to model melodic and harmonic structures in music theory, but these fail to take into account the time-dependent nature of music. As a result, these methods isolate sequences without respect to their relative positions within a piece of music. We propose a time-dependent Markov model to analyze note-to-note movement of Irish folk songs. In this model, the probability of note-to-note transition at a particular position within the composition is dictated by the position itself. The model can then generate melodies derived from its learning and describe tendencies in movement at different points in time. When applied to this and other collections of music, this approach provides a novel way to analyze melodies within corpora, serves as a descriptive tool for analyzing a composer’s or genre’s melodies, and may be utilized as an effective creative aide.
Daniel Q Naiman