While others have done a good job explaining how the vocal folds are different in many ways, I would argue this is not the final answer! According to the same logic, all dogs and birds would have different barks/tweets, but at least to me most dogs (of the same breed ofc) sound basically the same.
So it’s the other way around: human voices are quite similar to one another when “objectively” studied, but we humans simply are excellent at picking up on the small differences. The human ear is most accurate near the frequency of human speech, even more accurate than that of e.g. dogs and other animals with “good hearing”. In addition to our anatomical ability, we learn from a young age to differentiate between the voices of different people: we all have a lot of practice at this. If I spent several years learning to recognize individual dogs, I would most likely manage it, but the start would be ruff.
So the reason our voices sound different is because we are incredibly good at listening to speech and trained in recognizing voices.
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