During auditory perception, neural oscillations are known to entrain to acoustic dynamics but their role in the processing of auditory information remains unclear. As a complex temporal structure that can be parameterized acoustically, music is particularly suited to address this issue. In a combined behavioral and EEG experiment in human participants, we investigated the relative contribution of temporal (acoustic dynamics) and nontemporal (melodic spectral complexity) dimensions of stimulation on neural entrainment, a stimulus-brain coupling phenomenon operationally defined here as the temporal coherence between acoustical and neural dynamics. We first highlight that low-frequency neural oscillations robustly entrain to complex acoustic temporal modulations, which underscores the fine-grained nature of this coupling mechanism. We also reveal that enhancing melodic spectral complexity, in terms of pitch, harmony, and pitch variation, increases neural entrainment. Importantly, this manipulation enhances activity in the theta (5 Hz) range, a frequency-selective effect independent of the note rate of the melodies, which may reflect internal temporal constraints of the neural processes involved. Moreover, while both emotional arousal ratings and neural entrainment were positively modulated by spectral complexity, no direct relationship between arousal and neural entrainment was observed. Overall, these results indicate that neural entrainment to music is sensitive to the spectral content of auditory information and indexes an auditory level of processing that should be distinguished from higher-order emotional processing stages. NEW & NOTEWORTHY Low-frequency (<10 Hz) cortical neural oscillations are known to entrain to acoustic dynamics, the so-called neural entrainment phenomenon, but their functional implication in the processing of auditory information remains unclear. In a behavioral and EEG experiment capitalizing on parameterized musical textures, we disentangle the contribution of stimulus dynamics, melodic spectral complexity, and emotional judgments on neural entrainment and highlight their respective spatial and spectral neural signature.