Your analogy is invalid, just FYI. It is impossible for a human to produce a tone that lacks overtones/harmonics, which is what make people singing the same note sound different.
Interesting, thank you. So what you are saying is that there would be a measure that could explain the differences between what we hear. But this measure would not be the note or the fundamental tone at 440Hz. Would there be measures that could explain the differences between DACs chips? Because when I look into the specs of Wolfson DAC chips for example http://www.wolfsonmicro.com/products/dacs/
it seems to me that the differences in SNR ratio for example are quite substantial and possibly audible (i.e not all DAC will sound the same since I think that 20-30 dB differences should be easily audible to the ear no?).