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This paper proposes a query by humming method based on locality sensitive hashing (LSH). The method constructs an index of melodic fragments by extracting pitch vectors from a database of melodies. In retrieval, the method automatically transcribes a sung query into notes and then extracts pitch vectors similarly to the index construction. For each query pitch vector, the method searches for similar melodic fragments in the database to obtain a list of candidate melodies. This is performed efficiently by using LSH. The candidate melodies are ranked by their distance to the entire query and returned to the user. In our experiments, the method achieved mean reciprocal rank of 0.885 for 2797 queries when searching from a database of 6030 MIDI melodies. To retrieve audio signals, we apply an automatic melody transcription method to construct the melody database directly from music recordings and report the corresponding retrieval results.