We propose a representation for musical chords allowing to include domain knowledge in probabilistic models. We then introduce a graphical model for harmonization of melodies by considering every structural components in chord notation. We will use this opportunity to present the Junction Tree Algorithm in detail. We show empirically that root 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 to generate proper harmonizations when root progressions are provided. The developed probabilistic models can be sampled to generate very interesting chord progressions given other polyphonic music components such as melody or root progressions.