ENGELSKA - översättning, fakta och frågeställning [Sammanfogad tråd]

"Picking out a melody [or tune] at the piano" implies above all hunt-and-peck style trial-and-error, ordinarily for a known tune but also conceivably when making one up. It would not apply to including harmonies.

"Playing by ear" implies greater assurance and ability, and on a keyboard generally includes more than just melody.

I have a character in a chapter (not yet published) who tells another that her pianistic career began around age 7, after her mother's death, with sitting at the piano and picking out melodies of pieces her mother had used to play.