The nature of acoustic instruments and voice make them sound slightly different over a range, changing timbre (other harmonic content) with different notes, strings, octaves, comfortable ranges, etc., and if you're used to the sound of the instrument in question, you can tell when the sound has been altered because the instrument playing in that range normally (if possible) would have a different timbre.
If you take a synth making some set waveform, adjusting the frequency (pitch) doesn't effect the timbre, so anything you notice would be limiting effects of the system, caused by uneven response in the electronics or, more likely, the speakers. It's also worth mentioning that the frequency response of the human ear plays a significant role - a 1kHz square wave will sound different from a 4kHz square wave because we're able to hear much more of the odd harmonic content that characterizes the composition of the wave - the 1kHz we hear clearly 1,3,5,7,9,11,13,15,17kHz harmonics (well, you probably can't discern the last few given the power relative to the primary tone, but those can be discerned with the normal 20Hz to 20kHz range of hearing), but a 4kHz square, 2 octaves up, we can really only hear the 4kHz, 12kHz, and maybe 20kHz tones that comprise the odd harmonics of the fundamental. The ear's low pass filtering cuts out the higher harmonics, thus changing the profile of the sound being perceived, though this is not likely to be noticeable unless fairly high in range for most musical instruments or singing.