This article introduces the Projective Orchestral Database (POD), a collection of MIDI scores composed of pairs linking piano scores to their corresponding orchestrations. To the best of our knowledge, this is the first database of its kind, which performs piano or orchestral prediction, but more importantly which tries to learn the correlations between piano and orchestral scores. Hence, we also introduce the projective orchestration task, which consists in learning how to perform the automatic orchestration of a piano score. We show how this task can be addressed using learning methods and also provide methodological guidelines in order to properly use this database.