This article is concerned with the estimation of fundamental frequencies, or F0s, in polyphonic music. We propose a new method for jointly evaluating multiple F0 hypotheses based on three physical principles: harmonicity, spectral smoothness and synchronous amplitude evolution within a single source. Based on the generative quasiharmonic model, a set of hypothetical partial sequences is derived and an optimal assignment of the observed peaks to the hypothetical sources and noise is performed. Hypothetical partial sequences are then evaluated by a score function which formulates the guiding principles in a mathematical manner. The algorithm has been tested on a large collection of artificially mixed polyphonic samples and the results show the competitive performance of the proposed method.