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Musicians well trained in music theory can correctly sing intervals given a first reference note (relative pitch). Then a small portion of them also have the ability to not need a reference note to find the correct pitch, it's called absolute pitch (there's a debate if it's an innate ability, and it is a superpower with downsides).
So the answer is yes, at least with a first reference note. But it may take years of practice. I think all professional classical musicians have this ability.
What are the downsides?
Choirs are really good at being in tune with one another, but not necessarily in tune with absolute pitch. So if you’re a singer with absolute pitch, your life is looking at a note on a page, knowing what that note SHOULD sound like, but then singing a slightly off-pitch note to be in tune with everyone else. Or even a completely different note if the group has shifted enough.
Or if a group decides that a piece isn’t in a good range for someone, and they decide to sing in a different key, for most people it’s really easy. Take the new starting note and go. But if you have absolute pitch you have to transpose on the fly if you’re sight reading.
That said, I think given the choice I’d take absolute pitch. My wife has it and she can sight read so much better than I can.
That’s super interesting. A blessing and a burden
Baroque musique for example is often played at A = 415 Hz as opposed to 440 Hz, so someone who has their absolute pitch set on A = 440 Hz, because it is the current international standard, may be very disturbed.
More details: https://en.wikipedia.org/wiki/Absolute_pitch#Possible_problems
Also yes. My wife says that to her, Baroque tuning sounds basically like a half-step below what’s written (which is pretty close).
This explains, IMO, why so much well-loved Baroque music is in D major. D♭ major is such a beautiful key, after all! 🙂