Melody harmonisation with interpolated probabilistic models

Stanislaw Raczynski 1 Satoru Fukayama 2 Emmanuel Vincent 1
1 METISS - Speech and sound data modeling and processing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : Automatic melody harmonisation aims to create a matching chordal accompaniment to a given monophonic melody. Several methods have been proposed to this aim, which are generally based on musicological expertise or on unsupervised probabilistic modelling. Among the latter category of methods, most systems use the generative hidden Markov model (HMM), in which the chords are the hidden states and the melody is the observed output. Relations to other variables, such as the tonality and scale or the metric structure, are handled by training multiple HMMs or are often simply ignored. In this paper, we propose a means of combining multiple probabilistic models of various musical variables into a versatile harmonisation system by means of model interpolation. The result is a joint model belonging to the class of discriminative models, which in recent years have proven to be capable of outperforming generative models in many tasks. We first evaluate our models in terms of their normalized negative log-likelihood, or cross-entropy. We observe that log-linear interpolation offers lower cross-entropy than linear interpolation and that combining several models by means of log-linear interpolation lowers the cross-entropy compared to the best of the component models. We then perform a series of harmonisation experiments and show that the proposed log-linearly interpolated model offers higher chord root accuracy than a reference musicological rule-based harmoniser by up to 5% absolute.
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Stanislaw Raczynski, Satoru Fukayama, Emmanuel Vincent. Melody harmonisation with interpolated probabilistic models. [Research Report] RR-8110, INRIA. 2012. ⟨hal-00742957⟩

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