It is well accepted that the left and right hemispheres of the brain typically play separate and distinct roles in cognitive processing. Extensive research examining the lateralization of music and language processes has provided a clear and consistent demonstration of this division of processing across the cerebral hemispheres. However, in spite of this line of research examining population-level lateralization of these processes, little focus has been placed on examining the relationship between the two processes. Do these two processes share a common developmental origin that influences their pattern of lateralization, or do independent processes govern their lateralization? In this study we examined the relationship pattern in degree of lateralization between linguistic processing and melody recognition using dichotic-listening tasks. The expected right ear advantage was observed for the linguistic processing task. Additionally, the expected left ear advantage was not observed for the melody recognition task, precluding an informative assessment of complementarity between the two tasks. A positive correlation between the laterality scores on the two tasks suggests a shared processing network for linguistic and melodic processing.