Sparse coding and its related theories have been successful to explain various response properties of early stages of sensory information processing such as primary visual cortex and peripheral auditory system, which suggests that the emergence of such properties results from adaptation of the nerve system to natural stimuli. The present study continues this line of research in a higher stage of auditory processing, focusing on harmonic structures that are often found in behaviourally important natural sound like animal vocalization. It has been physiologically shown that monkey primary auditory cortices (A1) have neurons with response properties capturing such harmonic structures: their response and modulation peaks are often found at frequencies that are harmonically related to each other. We hypothesize that such relations emerge from sparse coding of harmonic natural sounds. Our simulation shows that similar harmonic relations emerge from frequency-domain sparse codes of harmonic sounds, namely, piano performance and human speech. Moreover, the modulatory behaviours can be explained by competitive interactions of model neurons that capture partially common harmonic structures.