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Contemporary music composition is a highly creative and disciplined activity that requires free expression of ideas and sophisticated computer programming. This paper presents a technique for structured observation of expert creative behavior, as well as Polyphony, a novel interface for systematically studying all phases of computer-aided composition. Polyphony is a unified user interface that integrates interactive paper and electronic user interfaces for composing music. It supports fluid transitions between informal sketches and formal computer-based representations. We asked 12 composers to use Polyphony to compose an electronic accompaniment to a 20-second instrumental composition by Anton Webern. All successfully created a complete, original composition in an hour and found the task challenging but fun. The resulting dozen comparable snapshots of the composition process reveal how composers both adapt and appropriate tools in their own way.