Harmonic sinusoidal models are a fundamental tool for audio signal analysis. Bayesian harmonic models guarantee a good resynthesis quality and allow joint use of learnt parameter priors and auditory motivated distortion measures. However inference algorithms based on Monte Carlo sampling are rather slow for realistic data. In this paper, we investigate fast inference algorithms based on approximate factorization of the joint posterior into a product of independent distributions on small subsets of parameters. We discuss the conditions under which these approximations hold true and evaluate their performance experimentally. We suggest how they could be used together with Monte Carlo algorithms for a faster sampling-based inference.