This study introduces Mean Averaging Smoothed Product (MASP) Spectrum, which is a modified version of the Harmonic Product Spectrum, designed to enhance pitch estimation for many algorithm-wise deceptive frequency spectra that still lead clear pitches, for both harmonic and inharmonic cases. By introducing a global mean based smoothing for spectrum, the MASP algorithm diminishes the unwanted sensitivity of HPS for spectra with missing partials. The method exhibited robust pitch estimations consistent with perceptual expectations. Motivated upon the strong correlation between consonance and periodicity, the same algorithm is extended and, with the proposition of a harmonicity measure (H), used to evaluate musical consonance for two and three tones; yielding consonance hierarchies that align with perception and practice of music theory. These findings suggest that perception of pitch and consonance may share a similar underlying mechanism that depend on spectrum.