Temporal and spectral auditory processing abilities are required for efficient and unimpaired processing of speech and might thus be associated with the development of phonological and literacy skills in children. Indeed, studies with unselected children have found links between these basic auditory processing abilities and the development of phonological awareness, reading, and spelling. Additionally, associations between the processing of temporal or spectral/tonal information in music and phonological awareness/literacy have been reported, but findings concerning relations between music processing and spelling are rather sparse. To gain more insights into the specific, potentially age-dependent relevance of various temporal (e.g., rhythm, tempo) and tonal (e.g., pitch, melody) musical subdomains for phonological awareness and literacy, we adapted five music-processing tasks (three temporal, two tonal) for use with tablet computers and used them in two cross-sectional studies with German children from two age groups: Study 1 was conducted with preschool children (about 5 years of age; without formal reading and spelling instruction) and focused on associations between music processing and phonological awareness. In Study 2, third-graders (about 8 years of age) were investigated concerning relations between music processing, phonological awareness, reading comprehension, and spelling. In both studies, rhythm reproduction and pitch perception turned out to be significant predictors of phonological awareness in stepwise regression analyses. Although various associations between music processing and literacy were found for third-graders in Study 2, after phonological awareness was accounted for, only rhythm reproduction made a unique contribution to literacy skills, namely, to alphabetic spelling skills. Hence, both studies indicate that temporal (i.e., rhythm reproduction) and spectral/tonal (i.e., pitch perception) musical skills are distinctly and uniquely related to phonological awareness in children from different age groups (preschool vs. Grade 3). The finding that rhythm reproduction, an auditory temporal processing skill integrating perceptual and motor aspects of rhythm processing, was especially tightly linked to phonological awareness and literacy corroborates other findings on associations between rhythm processing and literacy development and is of interest from the viewpoint of current theories of developmental dyslexia. The potential relevance of our results for applied research concerning early diagnosis and training of literacy-related skills is discussed.