We consider the problem of estimating the fundamental frequency of periodic signals such as audio and speech. A novel estimation method based on polynomial rooting of the harmonic MUltiple SIgnal Classification (HMUSIC) is presented. By applying polynomial rooting, we obtain two significant improvements compared to HMUSIC. First, by using the proposed method we can obtain an estimate of the fundamental frequency without doing a grid search like in HMUSIC. This is due to that the fundamental frequency is estimated as the argument of the root lying closest to the unit circle. Second, we obtain a higher spectral resolution compared to HMUSIC which is a property of polynomial rooting methods. Our simulation results show that the proposed method is applicable to real-life signals, and that we in most cases obtain a higher spectral resolution than HMUSIC.