The NMED-H dataset contains scalp EEG responses recorded from 48 adults as they heard intact and scrambled versions of full-length vocal works (Hindi pop songs). Sixteen stimuli were included in the experiment: Four songs in four conditions per song. Twelve participants were assigned to each stimulus, and each participant heard their assigned stimuli twice (24 trials total per stimulus). Dense-array EEG was recorded using the Electrical Geodesics, Inc. (EGI) GES 300 platform. Data are published in Matlab format. The dataset contains (1) raw EEG (individual recordings, 97 files), (2) clean EEG (aggregated by stimulus and listen, 32 files), (3) spatially filtered EEG (aggregated by stimulus condition, four files), (4) behavioral responses (grouped by listen, two files), and (5) participant-stimulus assignment file. Items (1) - (3) are compressed in .zip archives (500 MB - 2 GB each); an example file from each archive can be downloaded separately. Items (4) and (5) are < 1 KB each. This dataset can be used in combination with the Naturalistic Music EEG Dataset - Tempo (NMED-T).