Neural oscillations synchronize with auditory stimuli and support rhythmic movements. This study investigated the role of auditory feedback in producing variations in temporal precision during rhythmic tapping and melody production. Participants performed two rhythmic tasks: a spontaneous motor tempo task (with no auditory feedback) and a spontaneous production rate task (with auditory feedback), while tapping rates, temporal variability, and electroencephalography (EEG) were recorded. Participants' tapping rates differed with and without auditory feedback. Furthermore, results showed EEG power spectral density peaks at the produced beat frequency. In the presence of sound, power spectral density (PSD) peaked at simple ratio frequencies (2:1). PSD amplitudes were person-specific in each task: PSD was greater at each participant's production rate than at others' rates. In the presence of auditory feedback, tapping variability and PSD at performance frequency were uncorrelated. Conversely, in the absence of auditory feedback, individuals with higher peaks in spectral power showed reduced temporal variability: tapping variability and PSD at performance frequency were negatively correlated in the motor-only task. Behaviourally, lag-1 autocorrelations suggested sound facilitates error correction. Auditory feedback allowed performers to flexibly adjust their tapping rate, reflected in their temporal variability. Together, these findings suggest that power spectral density peaks support increased temporal regularity in the motor task and reflect coupled oscillations in the presence of musical feedback.