that anecdote fills me with an insatiable sense of envy.
That orchestra conductor probably spent a large part of their life studying music. Part of learning music is ear training: the ability to name/write chords by hearing them, and conversely to "hear" them in one's imagination given the name (or from written music). No different than the way many people "hear" words in their head when reading.
I haven't used it personally, but from what I heard a few years ago it wasn't very accurate.