The Morph Table is a new music interface designed for collaborative music making. It comprises a software system that generates transitions and variations (morphs) between MIDI-based musical material, and a table-top hardware design on which cubes representing algorithmic parameters are moved around to control generative music. Like other table-top interfaces the size and multiple objects afford social interaction. The generative music system of the Morph Table makes it particularly suited to installations and use by inexperienced users. This paper outlines the design and usage features of the Morph Table.