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This paper proposes a music accompaniment system capable of catching the tempo of music. The original signal is first reduced to a detection function revealing the pulses of music. To induce the tempo and locate beats, a Fourier analysis-based algorithm with high practicality and generality is designed that it is robust to beat strength and not restricted to specific music genres. The regularity and periodicity of music beats are extracted and even the missing beats are recovered. The performance is validated using a comprehensive testing data set, and results in both formal objective experiments and subjective listening evaluations show convincible performance. Moreover, an interactive interface is designed that users are allowed to select an instrument to accompany the music based on the obtained tempo.