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In this work, we propose to break this bottleneck using generative modeling. By pipelining a generative model of notes (Coconet trained on Bach Chorales) with a structured synthesis model of chamber ensembles (MIDI-DDSP trained on URMP), we demonstrate a system capable of producing unlimited amounts of realistic chorale music with rich annotations including mixes, stems, MIDI, note-level performance attributes (staccato, vibrato, etc.), and even fine-grained synthesis parameters (pitch, amplitude, etc.). We call this system the Chamber Ensemble Generator (CEG), and use it to generate a large dataset of chorales from four different chamber ensembles (CocoChorales). 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