Yes indeed. I used to do this precise thing that you are speaking of. I'm also a piano player, and whenever I would hear a melody, I'd find myself pretending to play it with my fingers. Drove me nuts.
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I(ntroverted) iN(tuitive) F(eeling) P(erceiving)
AQ = 35
EQ = 31
SQ = 48
Your Aspie score: 160 of 200
Your neurotypical (non-autistic) score: 53 of 200
You are very likely an Aspie