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The role of expectation in listening and composing music has drawn much attention in music cognition since about half a century ago. In this paper, we provide a first attempt to model some aspects of musical expectation specifically pertained to short-time and working memories, in an anticipatory framework. In our proposal Anticipation is the mental realization of possible predicted actions and their effect on the perception of the world at an instant in time. We demonstrate the model in applications to automatic improvisation and style imitation. The proposed model,based on cognitive foundations of musical expectation, is an active model using reinforcement learning techniques with multiple agents that learn competitively and in collaboration. We show that compared to similar models, this anticipatory framework needs little training data and demonstrate complex musical behavior such as long-term planning and formal shapes as a result of the anticipatory architecture. We provide sample results and discuss further research.