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Human-robot interaction is a key issue in order to build robots for everyone. The difficulty for people to understand how robots work and how they must be controlled will be one of the mains limit for broad robotics. In this paper, we study a new way of interacting with robots without needing to understand how robots work or to give them explicit instructions. This work is based on psychological data showing that synchronization and rhythm are very important features for pleasant interaction. We propose a biologically inspired architecture using rhythm detection to build an internal reward for learning. After showing the results of keyboard interactions, we present and discuss the results of real human-robots (Aibo and Nao) interactions. We show that our minimalist control architecture allows the discovery and learning of arbitrary sensorimotor associations games with expert users. With nonexpert users, we show that using only the rhythm information is not sufficient for learning all the associations due to the different strategies used by the human. Nevertheless, this last experiment shows that the rhythm is still allowing the discovery of subsets of associations, being one of the promising signal of tomorrow social applications.