Probabilistic harmonization with fixed intermediate chord constraints

During the last decades, several methodologies have been proposed for the harmonization of a given melody with algorithmic means. Among the most successful are methodologies that incorporate probabilistic mechanisms and statistical learning, since they have the ability to generate harmonies that statistically adhere to the harmonic characteristics of the idiom that the training pieces belong to. The current paper discusses the utilization of a well–studied probabilisticmethodology, the hiddenMarkovmodel (HMM), in combination with additional constraints that incorporate intermediate fixed–chord constraints. This work is motivated by the fact that some parts of a phrase (like the cadence) or a piece (e.g. points of modulation, peaks of tension, intermediate cadences etc.) are characteristic about the phrase’s or piece’s idiomatic identity. The presented methodology allows to define and isolate such important parts/functions and include them as constraints in a probabilistic harmonization methodology. To this end, the constrained HMM (CHMM) is developed, harnessed with the novel general chord type (GCT) representation, while the study focuses on examples that highlight the diversity that constraints introduce in harmonizations.