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Singing pitch estimation and singing voice separation are challenging due to the presence of music accompaniments that are often nonstationary and harmonic. Inspired by computational auditory scene analysis (CASA), this paper investigates a tandem algorithm that estimates the singing pitch and separates the singing voice jointly and iteratively. Rough pitches are first estimated and then used to separate the target singer by considering harmonicity and temporal continuity. The separated singing voice and estimated pitches are used to improve each other iteratively. To enhance the performance of the tandem algorithm for dealing with musical recordings, we propose a trend estimation algorithm to detect the pitch ranges of a singing voice in each time frame. The detected trend substantially reduces the difficulty of singing pitch detection by removing a large number of wrong pitch candidates either produced by musical instruments or the overtones of the singing voice. Systematic evaluation shows that the tandem algorithm outperforms previous systems for pitch extraction and singing voice separation.