Chord progressions are the building blocks from which tonal music is constructed. Inferring chord progressions is thus an essential step towards modeling long term dependencies in music. In this paper, three different representations for chords are designed. In a first representation, Euclidean distances roughly correspond to psychoacoustic dissimilarities between chords. Estimated probabilities of chord substitutions are then derived from these distances and are used to introduce smoothing in graphical models observing another chord representation. Finally, a third representation where we model directly each chord components leads to a probabilistic model considering the interaction between melodies and chord progressions. Parameters in the graphical models are learnt with the EM algorithm and the classical Junction Tree algorithm is used for inference. Various model architectures are compared in terms of conditional out-of-sample likelihood. Both perceptual and statistical evidence show that binary trees related to meter are well suited to capture chord dependencies.