Difference limens for complex tones (DLCs) that differ in F0 are widely regarded as a measure of periodicity-pitch discrimination. However, because F0 changes are inevitably accompanied by changes in the frequencies of the harmonics, DLCs may actually reflect the discriminability of individual components. To test this hypothesis, DLCs were measured for complex tones, the component frequencies of which were shifted coherently upward or downward by ΔF = 0%, 25%, 37.5%, or 50% of the F0, yielding fully harmonic (ΔF = 0%), strongly inharmonic (ΔF = 25%, 37.5%), or odd-harmonic (ΔF = 50%) tones. If DLCs truly reflect periodicity-pitch discriminability, they should be larger (worse) for inharmonic tones than for harmonic and odd harmonic tones because inharmonic tones have a weaker pitch. Consistent with this prediction, the results of two experiments showed a non-monotonic dependence of DLCs on ΔF, with larger DLCs for ΔF’s of ±25% or ±37.5% than for ΔF’s of 0 or ±50% of F0. These findings are consistent with models of pitch perception that involve harmonic templates or with an autocorrelation-based model provided that more than just the highest peak in the summary autocorrelogram is taken into account.