Pitch discrimination is better for complex tones than pure tones, but how pitch discrimination differs between natural and artificial sounds is not fully understood. This study compared pitch discrimination thresholds for flat-spectrum harmonic complex tones with those for natural sounds played by musical instruments of three different timbres (violin, trumpet, and flute). To investigate whether natural familiarity with sounds of particular timbres affects pitch discrimination thresholds, this study recruited non-musicians and musicians who were trained on one of the three instruments. We found that flautists and trumpeters could discriminate smaller differences in pitch for artificial flat-spectrum tones, despite their unfamiliar timbre, than for sounds played by musical instruments, which are regularly heard in everyday life (particularly by musicians who play those instruments). Furthermore, thresholds were no better for the instrument a musician was trained to play than for other instruments, suggesting that even extensive experience listening to and producing sounds of particular timbres does not reliably improve pitch discrimination thresholds for those timbres. The results show that timbre familiarity provides minimal improvements to auditory acuity, and physical acoustics (e.g., the presence of equal-amplitude harmonics) determine pitch discrimination thresholds more than does experience with natural sounds and timbre-specific training.