Jean-François Paiement

Probabilistic melodic harmonization

We propose a representation for musical chords that allows us to include domain knowledge in probabilistic models. We then introduce a graphical model for harmonization of melodies that considers every structural components in chord notation. We show empirically that root notes progressions exhibit global dependencies that can be better captured with a tree structure related to the meter than with a simple dynamical HMM that concentrates on local dependencies. However, a local model seems to be sufficient for generating proper harmonizations when root notes progressions are provided. The trained probabilistic models can be sampled to generate very interesting chord progressions given other polyphonic music components such as melody or root note progressions.

Predictive models for music

Modelling long-term dependencies in time series has proved very difficult to achieve with traditional machine-learning methods. This problem occurs when considering music data. In this paper, we introduce predictive models for melodies. We decompose melodic modelling into two subtasks. We first propose a rhythm model based on the distributions of distances between subsequences. Then, we define a generative model for melodies given chords and rhythms based on modelling sequences of Narmour features. The rhythm model consistently outperforms a standard hidden markov model (HMM) in terms of conditional prediction accuracy on two different music databases. Using a similar evaluation procedure, the proposed melodic model consistently outperforms an input/output HMM. Furthermore, these models are able to generate realistic melodies given appropriate musical contexts.

Probabilistic models for melodic prediction

Chord progressions are the building blocks from which tonal music is constructed. The choice of a particular representation for chords has a strong impact on statistical modeling of the dependence between chord symbols and the actual sequences of notes in polyphonic music. Melodic prediction is used in this paper as a benchmark task to evaluate the quality of four chord representations using two probabilistic model architectures derived from Input/Output Hidden Markov Models (IOHMMs). Likelihoods and conditional and unconditional prediction error rates are used as complementary measures of the quality of each of the proposed chord representations. We observe empirically that different chord representations are optimal depending on the chosen evaluation metric. Also, representing chords only by their roots appears to be a good compromise in most of the reported experiments.