A series of experiments investigated the influence of harmonic resolvability on the pitch of, and the discriminability of differences in fundamental frequency (F0) between, frequency‐modulated (FM) harmonic complexes. Both F0 (62.5 to 250 Hz) and spectral region (LOW: 125–625 Hz, MID: 1375–1875 Hz, and HIGH: 3900–5400 Hz) were varied orthogonally. The harmonics that comprised each complex could be summed in either sine (0°) phase (SINE) or alternating sine‐cosine (0°–90°) phase (ALT). Stimuli were presented in a continuous pink‐noise background. Pitch‐matching experiments revealed that the pitch of ALT‐phase stimuli, relative to SINE‐phase stimuli, was increased by an octave in the HIGH region, for all F0’s, but was the same as that of SINE‐phase stimuli when presented in the LOW region. In the MID region, the pitch of ALT‐phase relative to SINE‐phase stimuli depended on F0, being an octave higher at low F0’s, equal at high F0’s, and unclear at intermediate F0’s. The same stimuli were then used in three measures of discriminability: FM detection thresholds (FMTs), frequency difference limens (FDLs), and FM direction discrimination thresholds (FMDDTs, defined as the minimum FM depth necessary for listeners to discriminate between two complexes modulated 180° out of phase with each other). For all three measures, at all F0’s, thresholds were low (<4% for FMTs, <5% for FMDDTs, and <1.5% for FDLs) when stimuli were presented in the LOW region, and high (≳10% for FMTs, ≳7% for FMDDTs, and ≳2.5% for FDLs) when presented in the HIGH region. When stimuli were presented in the MID region, thresholds were low for low F0’s, and high for high F0’s. Performance was not markedly affected by the phase relationship between the components of a complex, except for stimuli with intermediate F0’s in the MID spectral region, where FDLs and FMDDTs were much higher for ALT‐phase stimuli than for SINE‐phase stimuli, consistent with their unclear pitch. This difference was much smaller when FMTs were measured. The interaction between F0 and spectral region for both sets of experiments can be accounted for by a single definition of resolvability.