That's fairly common and the simplest explanation I know about is that you can "memorize" a sound if you train for it and then when you hear it you recall the m

That's fairly common and the simplest explanation I know about is that you can "memorize" a sound if you train for it and then when you hear it you recall the memory without going through the whole "pipeline" for understanding what it is. Your memory or "cache" for what C is indexes with the specific harmonics that make the timbre of a piano. On another instrument it's a different sound, the main harmonic is the same one but the timbre is so different that you need to go through the "let's use perfect pitch for this" part of your brain. It's the same thing mechanics use to identify engine sounds quickly or why some people can tell who's walking on a hallway because of how the steps sound. Repeated exposition to a stimulus that then gets associated with something etches a memory. This not only happens with perfect pitch. To for example know how to tell a major third from a minor third on all keys you can "memorize" all the sounds and know which one they are. I think my brain kinda did that and now I sometimes get confused with M3 and P5 because of how "similar" they sound even though you can like totally fit another tone comfortable between the root and the fifth and the root and the third don't have enough air for that.