The neural mechanisms of pitch coding have been debated for more than a century. The two main mechanisms are coding based on the profiles of neural firing rates across auditory nerve fibers with different characteristic frequencies (place-rate coding), and coding based on the phase-locked temporal pattern of neural firing (temporal coding). Phase locking precision can be partly assessed by recording the frequency-following response (FFR), a scalp-recorded electrophysiological response that reflects synchronous activity in subcortical neurons. Although features of the FFR have been widely used as indices of pitch coding acuity, only a handful of studies have directly investigated the relation between the FFR and behavioral pitch judgments. Furthermore, the contribution of degraded neural synchrony (as indexed by the FFR) to the pitch perception impairments of older listeners and those with hearing loss is not well known. Here, the relation between the FFR and pure-tone frequency discrimination was investigated in listeners with a wide range of ages and absolute thresholds, to assess the respective contributions of subcortical neural synchrony and other age-related and hearing loss-related mechanisms to frequency discrimination performance. FFR measures of neural synchrony and absolute thresholds independently contributed to frequency discrimination performance. Age alone, i.e., once the effect of subcortical neural synchrony measures or absolute thresholds had been partialed out, did not contribute to frequency discrimination. Overall, the results suggest that frequency discrimination of pure tones may depend both on phase locking precision and on separate mechanisms affected in hearing loss.