Neural networks and recurrent neural networks have been employed to learn, generalize, and generate musical examples and pieces. Yet, these models typically suffer from an inability to characterize and reproduce the long-term dependencies of musical structure, resulting in products that seem to wander aimlessly. We describe and examine three novel hierarchical models that explicitly operate on multiple structural levels. A three layer model is presented, then a weighting policy is added with two different methods of control attempting to maximize global network learning. While the results do not have sufficient structure beyond the phrase or section level, they do evince autonomous generation of recognizable medium-level structures.