This paper introduces the Common Prosody Platform (CPP), a computational platform that implements major theories and models of prosody. CPP aims at a) adapting theory-specific assumptions into computational algorithms that can generate surface prosodic forms, and b) making all the models trainable through global optimization based on automatic analysis-bysynthesis learning. CPP allows examination of prosody in much finer detail than has been previously done and provides a means for speech scientists to directly compare theories and their models. So far, four theories have been included in the platform, the Command-Response model, the AutosegmentalMetrical theory, the Task Dynamic model, and the Parallel Encoding and Target Approximation mod...