[atto]

I can also do this, don't have perfect pitch, was also a cello player, and have a guess.

Instruments have fairly unique timbres at different pitches, and our brain can pattern match that more effectively than pitch itself. So, you can actually "burn in" the correct timbre, which makes it easier to find. Since I was so used to an A reference note for tuning, I got to where I could get pretty close.

Years later, I saw this video, with someone who seems to have brute forced it to approximate perfect pitch using a similar method: https://www.youtube.com/watch?v=oT22zqg0jvE