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In this paper we propose a divergence measure which is applied to the analysis of the relationships between gesture and sound. Technically, the divergence measure is defined based on a Hidden Markov Model (HMM) that is used to model the time profile of sound descriptors. We show that the divergence has the following properties: non- negativity, global minimum and non-symmetry. Particularly, we used this divergence to analyze the results of experiments where participants were asked to perform physical gestures while listening to specific sounds. We found that the proposed divergence is able to measure global and local differences in either time alignment or amplitude between gesture and sound descriptors.