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This paper presents a novel content-based music retrieval system that accepts a query containing multiple tags with multiple levels of preference (denoted as an MTML query) to retrieve music from an untagged music database. We select a limited number of popular music tags to form the tag space and design an interface for users to input queries by operating the scroll bars. To effect MTML content-based music retrieval, we introduce a tag-based music aspect model that jointly models the auditory features and tag-based text features of a song. Two indexing methods and their corresponding matching methods, namely pseudo song-based matching and tag co-occurrence pattern-based matching, are incorporated into the pre-learned tag-based music aspect model. Finally, we evaluate the proposed system on the Major Miner dataset. The results demonstrate the potential of using MTML queries to retrieve music from an untagged music database.