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Who invented music? A legend relates that Pythagoras discovered its mathematical and acoustic laws. It is often said that his discovery furnished a rational explanation of music by its harmony, that is to say, by numerical ratios. But is it impossible that music has a natural or cultural explanation, beyond its mathematical structure? Pythagoras inherits a tradition, which has strong religious and mythological resonances. He bases himself a rational approach to musical problems, which affect posterity. He is not alone in this long history, so the question of the invention allows to study an explanatory model that marks the history of music until today.