Repetition is a core principle in music. Many musical pieces are characterized by an underlying repeating structure over which varying elements are superimposed. This is especially true for pop songs where a singer often overlays varying vocals on a repeating accompaniment. On this basis, we present the REpeating Pattern Extraction Technique (REPET), a novel and simple approach for separating the repeating “background” from the non-repeating “foreground” in a mixture. The basic idea is to identify the periodically repeating segments in the audio, compare them to a repeating segment model derived from them, and extract the repeating patterns via time-frequency masking. Experiments on data sets of 1,000 song clips and 14 full-track real-world songs showed that this method can be successfully applied for music/voice separation, competing with two recent state-of-the-art approaches. Further experiments showed that REPET can also be used as a preprocessor to pitch detection algorithms to improve melody extraction.