Music. Short for COUNTER-TENOR; also app. any voice part set in contrast to a principal melody or part.

1

1869.  Mrs. Stowe, Oldtown Folks, 60. Uncle Fliakim … tuning up in a high, cracked voice, a weird part, in those days called ‘counter.’ Ibid. (1878), Poganuc P., vii. 56. Ben … beating and roaring, first to treble and then to counter and then to bass.

2