This paper presents a fast implementation of the MUlti- ple SIgnal Classification (MUSIC) estimation criterion for fundamental frequency estimation of harmonic signals with known or unknown model orders. First, we reformulate the MUSIC estimator such that the MUSIC estimate can be computed directly from the signal subspace or just an ar- bitrary basis thereof. We also discuss the selection of a sub- space tracker based on the known or unknown rank of the signal and noise subspaces. Second, we introduce an imple- mentation of the MUSIC estimator that only involves one FFT for known model orders, and we extend it to the case of unknown model orders. The performance gain in terms of computation times obtained by the efficient implementation is significant which is demonstrated through simulations.