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Harmonic structure can be easily recognized in the time-frequency representation of speech signals even in diverse environment. The harmonicity is a measure of the completeness of harmonic structure. This paper extends the use of conventional harmonicity measure to the tasks of pitch estimation and voice activity detection. A set of hierarchical harmonicities, including grid, temporal, spectral and segmental harmonicities, is derived for this purpose. A series of experiments are conducted to show the effectiveness of using harmonicities in speech processing.