B737 CREW HEARD THE ZTL RADAR CTLR; CLRED TO TURN L. THE CREW COMPLIED. AFTER QUESTIONING THE CREW THE CTLR TOLD THEM TO TURN R INSTEAD.

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CTLR WAS WORKING 2 FREQS. HE CALLED US AND SAID; 'ACR #1; TURN L 5 DEGS FOR TFC.' WE BOTH HEARD HIM SAY 'L' AND CONFIRMED MY ACTION OF A L TURN. NEITHER ONE OF US WAS DOING ANYTHING EXCEPT FLYING. NO OTHER DISTRS AT THAT TIME. THE CTLR CAME BACK AND SAID; 'ACR #1 TURN FURTHER L 10 DEGS.' WE COMPLIED AGAIN AND ROLLED OUT ON A HDG OF 040 DEGS. I RECEIVED A SHORT CALL FROM THE FLT ATTENDANTS IN THE BACK AT THAT TIME AND WAS PREOCCUPIED WITH THAT FOR ABOUT A MIN. WHEN I CAME BACK; I SAW THE FO TURNING THE ACFT TO THE R HDG 090 DEGS. I ASKED HIM WHAT WAS GOING ON; AND HE SAID THAT THE CTLR CAME BACK AND SAID 'ACR #1 YOU MADE A TURN TO THE L DIDN'T YOU!' THE FO REPLIED YES AND THAT THE NEW HDG WAS 040 DEGS. THE CTLR REPLIED; 'WELL; I TOLD YOU TO MAKE A R TURN. TURN NOW TO 090 DEGS.' THE CTLR APPARENTLY WENT ON TO CHANGE ANOTHER ACFT'S ALT; 2000 FT ON THE OTHER FREQ; WE THINK TO AVOID OURS. HOWEVER; WE SAW NO CONFLICT ON TCASII. WE BELIEVE THAT WE ACCURATELY HEARD AND COMPLIED WITH THE CTLR'S INITIAL INSTRUCTIONS TO TURN L. I SUSPECT THAT DUE TO HIS PERSONAL TFC SATURATION (WORKING 2 FREQS) THAT HE SAID L WHEN HE MEANT R. SUPPLEMENTAL INFO FROM ACN 622391: ZTL CALLED BACK AND ASKED IF WE HAD TURNED L? I REPLIED; 'YES; WE TURNED L AND OUR HDG WAS 040 DEGS' (ACTUALLY IT WAS 042 DEGS). THE CTLR THEN STATED THAT HE HAD INSTRUCTED US TO TURN R. HE THEN SAID ABRUPTLY; 'TURN R NOW TO HDG 090 DEGS.' I COMPLIED. I BELIEVE THERE MIGHT HAVE BEEN A TFC CONFLICT BECAUSE THE CTLR; WHO WAS WORKING 2 FREQS AT THE SAME TIME; ASKED SOME TYPE OF CPR ACFT ON THE OTHER FREQ IF IT WAS CAPABLE OF FL390. EVIDENTLY; IT WAS UNABLE AND THE CTLR THEN ISSUED A DSCNT CLRNC TO FL350.