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This article presents a frame-based system for estimating multiple fundamental frequencies (F0s) of polyphonic music signals based on the STFT (short-time Fourier transform) representation. To estimate the number of sources along with their F0s, it is proposed to estimate the noise level beforehand and then jointly evaluate all the possible combinations among pre-selected F0 candidates. Given a set of F0 hypotheses, their hypothetical partial sequences are derived, taking into account where partial overlap may occur. A score function is used to select the plausible sets of F0 hypotheses. To infer the best combination, hypothetical sources are progressively combined and iteratively verified. A hypothetical source is considered valid if it either explains more energy than the noise, or improves significantly the envelope smoothness once the overlapping partials are treated. The proposed system has been submitted to MIREX (Music Information Retrieval Evaluation eXchange) 2007 and 2008 contests where the accuracy has been evaluated with respect to the number of sources inferred and the precision of the F0s estimated. The encouraging results demonstrate its competitive performance among the state-of-the-art methods.