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Music tagging and content-based retrieval systems have traditionally been constructed using pre-defined ontologies covering a rigid set of music attributes or text queries. This paper presents MuLan: a first attempt at a new generation of acoustic models that link music audio directly to unconstrained natural language music descriptions. MuLan takes the form of a two-tower, joint audio-text embedding model trained using 44 million music recordings (370K hours) and weakly-associated, free-form text annotations. Through its compatibility with a wide range of music genres and text styles (including conventional music tags), the resulting audio-text representation subsumes existing ontologies while graduating to true zero-shot functionalities. We demonstrate the versatility of the MuLan embeddings with a range of experiments including transfer learning, zero-shot music tagging, language understanding in the music domain, and cross-modal retrieval applications.