In the literature, there are various Markov models more parsimonious than full Markov chain models, such as Variable Length Markov Chains (VLMC), Partition Markov Models (PMM), and multivariate Markov process indexed by the structure of conditional dependence of the marginal processes (SCDMP). This work explains how the structure of conditional dependence of the marginal processes reduces the number of parameters needed to specify a multivariate Markov process. Then this methodology is applied to infer the interaction structure for three correlates of rhythm for each of three languages classified as having different rhythmics properties. We show that the structure is different for each language, showing that this structure can be used as a tool in discriminant computational linguistics.