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Annotating music items with music genres is crucial for music recommendation and information retrieval, yet challenging given that music genres are subjective concepts. Recently, in order to explicitly consider this subjectivity, the annotation of music items was modeled as a translation task: predict for a music item its music genres within a target vocabulary or taxonomy (tag system) from a set of music genre tags originating from other tag systems. However, without a parallel corpus, previous solutions could not handle tag systems in other languages, being limited to the English-language only. Here, by learning multilingual music genre embeddings, we enable cross-lingual music genre translation without relying on a parallel corpus. First, we apply compositionality functions on pre-trained word embeddings to represent multi-word tags.Second, we adapt the tag representations to the music domain by leveraging multilingual music genres graphs with a modified retrofitting algorithm. Experiments show that our method: 1) is effective in translating music genres across tag systems in multiple languages (English, French and Spanish); 2) outperforms the previous baseline in an English-language multi-source translation task. We publicly release the new multilingual data and code.