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This article investigates the role of interaction kinesics in human-robot interaction (HRI). We adopted a bottom-up, synthetic approach towards interactive competencies in robots using simple, minimal computational models underlying the robot's interaction dynamics. We present two empirical, exploratory studies investigating a drumming experience with a humanoid robot (KASPAR) and a human. In the first experiment, the turn-taking behaviour of the humanoid is deterministic and the non-verbal gestures of the robot accompany its drumming to assess the impact of non-verbal gestures on the interaction. The second experiment studies a computational framework that facilitates emergent turn-taking dynamics, whereby the particular dynamics of turn-taking emerge from the social interaction between the human and the humanoid. The results from the HRI experiments are presented and analysed qualitatively (in terms of the participants' subjective experiences) and quantitatively (concerning the drumming performance of the human-robot pair). The results point out a trade-off between the subjective evaluation of the drumming experience from the perspective of the participants and the objective evaluation of the drumming performance. A certain number of gestures was preferred as a motivational factor in the interaction. The participants preferred the models underlying the robot's turn-taking which enable the robot and human to interact more and provide turn-taking closer to 'natural' human-human conversations, despite differences in objective measures of drumming behaviour. The results are consistent with the temporal behaviour matching hypothesis previously proposed in the literature which concerns the effect that the participants adapt their own interaction dynamics to the robot's.