In this paper, a computationally efficient method for the estimation of the parameters of harmonic sinusoidal signals, including the order, which is of particular importance, for speech and audio signals is presented. The signal is modeled as a sum of harmonically related sinusoids in colored Gaussian noise. Aside from the order, the proposed method estimates the noise parameters, the fundamental frequency and the phase and amplitude of the individual harmonics. For the special case of white Gaussian noise, the method becomes particularly simple. The application of the proposed estimator to analysis of voiced speech and music signals is illustrated using real-life signals.