Accurate pitch perception of harmonic complex tones is widely believed to rely on temporal fine structure information conveyed by the precise phase-locked responses of auditory-nerve fibers. However, accurate pitch perception remains possible even when spectrally resolved harmonics are presented at frequencies beyond the putative limits of neural phase locking, and it is unclear whether residual temporal information, or a coarser rate-place code, underlies this ability. We addressed this question by measuring human pitch discrimination at low and high frequencies for harmonic complex tones, presented either in isolation or in the presence of concurrent complex-tone maskers. We found that concurrent complex-tone maskers impaired performance at both low and high frequencies, although the impairment introduced by adding maskers at high frequencies relative to low frequencies differed between the tested masker types. We then combined simulated auditory-nerve responses to our stimuli with ideal-observer analysis to quantify the extent to which performance was limited by peripheral factors. We found that the worsening of both frequency discrimination and F0 discrimination at high frequencies could be well accounted for (in relative terms) by optimal decoding of all available information at the level of the auditory nerve. A Python package is provided to reproduce these results, and to simulate responses to acoustic stimuli from the three previously published models of the human auditory nerve used in our analyses.