In a choir I was in a couple years ago we would sing a C at the start of each rehearsal, and we always got it at least very close, usually right, because we knew what it should sound like and what it felt like. I think perfect pitch through Heightenings would help you know what each note you heard was, like seeing all the shades of color but for sound instead, and because of that knowing what it sounds like you'd know how to replicate it when you needed to.