Information in speech and music is often conveyed through changes in fundamental frequency (f0), perceived by humans as "relative pitch". Relative pitch judgments are complicated by two facts. First, sounds can simultaneously vary in timbre due to filtering imposed by a vocal tract or instrument body. Second, relative pitch can be extracted in two ways: by measuring changes in constituent frequency components from one sound to another, or by estimating the f0 of each sound and comparing the estimates. We examined the effects of timbral differences on relative pitch judgments, and whether any invariance to timbre depends on whether judgments are based on constituent frequencies or their f0. Listeners performed up/down and interval discrimination tasks with pairs of spoken vowels, instrument notes, or synthetic tones, synthesized to be either harmonic or inharmonic. Inharmonic sounds lack a well-defined f0, such that relative pitch must be extracted from changes in individual frequencies. Pitch judgments were less accurate when vowels/instruments were different compared to when they were the same, and were biased by the associated timbre differences. However, this bias was similar for harmonic and inharmonic sounds, and was observed even in conditions where judgments of harmonic sounds were based on f0 representations. Relative pitch judgments are thus not invariant to timbre, even when timbral variation is naturalistic, and when such judgments are based on representations of f0.