Carry A Tune Meaning

(idiomatic) To produce music, especially to sing, with accurate relative pitch.

Example: 1903, Kate Douglas Wiggin, Rebecca Of Sunnybrook Farm, ch. 1,
  Jenny is named for a singer and Fanny for a beautiful dancer, but mother says they're both misfits, for Jenny can't carry a tune and Fanny's kind of stiff-legged.
1922, Jim Tully, Emmett Lawler, page 209:
  Emmett burst forth in song, but his comrade punched him in the side and said, “Lord Sakes, shut up, you can't carry a tune in a bucket.