DISPUTED DIRECTION OF TURN ON THE TEXOMA DEP FROM DFW; TX.

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DEP RWY 17R. ON DEP; ASSIGNED HDG OF 170 DEGS. WE WERE DIRECTED TO TURN R (I THINK) HDG 350 DEGS TO INTERCEPT. WE STARTED A R TURN. (I READ BACK HDG TO CTLR STATING 'UNDERSTAND R TURN TO 350 DEGS.') AFTER APPROX 30 DEGS OF TURN; THE CTLR SAID; 'ACR; I SAID L TURN; TURN L HDG 350 DEGS.' I RECOLLECT THAT HE ASKED FOR A TIGHT TURN. WE SAW NO CONFLICT; AND TCASII DIDN'T INDICATE ANY ACFT CLOSE TO US. WE IMMEDIATELY EXECUTED A TIGHT L TURN. PERFORMANCE: I WAS USING AN ANR HEADSET TO HELP OFFSET B727 NOISE PROBS. I BELIEVE I HEARD R TURN AND REPEATED 'UNDERSTAND R TURN.' THE PF WAS AN ACR LINE CHK CAPT (IN R SEAT) AND HE ALSO THOUGHT HE HEARD R TURN. THE TEX7.FUZ DEP REQUIRES HDGS AND EXPECT VECTORS. IF THE SID; UNDER 'JETS TKOF BROKE DOWN THE RWYS INTO SOUTHERLY RWYS; OR INDIVIDUAL RWYS IE; RWY 17L/C/R FLY HDG 174 DEGS (N VECTORS EXPECT L TURN) AND RWY 18L/R FLY HDG 174 DEGS (N VECTOR AREA EXPECT R TURN); THEN THIS WOULD BE MORE CLR AND PREDISPOSE US TOWARDS THE CORRECT TURN OR QUESTION A TURN GIVEN IN THE OPPOSITE DIRECTION.