NMAC BTWN 2 DEPARTING ACR ACFT CLBING TO ALT.

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DURING A BUSY DEP FROM NASHVILLE ARPT (BNA); RWY 2L; OUR MLG-A WAS ASSIGNED A HDG OF 015 DEGS AND 5000 FT. AFTER TKOF; WE CHANGED OUR RADIO OVER TO DEP CTL. WE NOTICED THAT WE WERE OVERTAKING AN LGT WHICH HAD DEPARTED JUST PRIOR TO US. THE DEP CTLR ASKED IF WE HAD THE LGT IN VISUAL CONTACT; WE SAID YES. HE WAS LEVEL AND IN OUR 1 O'CLOCK POS. WE WERE TOLD TO MAINTAIN VISUAL SEPARATION FROM THAT ACFT. THERE WERE NUMEROUS RADIO XMISSIONS TO VARIOUS ACFT; AND SHORTLY WE WERE TOLD TO TURN TO A HDG OF 290 DEGS (85 DEGS TO OUR L). THE LGT STILL SEEMED TO BE AHEAD AND TO OUR R FRONT. WE PROCEEDED TO TURN L TO THAT HDG. SHORTLY; WE NOTICED THAT THE LGT WAS IN A L TURN. I ASKED THE CTLR 'WHAT HDG IS THE (NAME OF AIRLINE) TURNING TO?' AS I COULD SEE A PROB DEVELOPING IF THE LGT CONTINUED HIS TURN. THE CTLR DID NOT RESPOND AND CLRED THE LGT TO 13000 FT. I AGAIN ASKED THE CTLR 'WHAT HDG IS THE (AIRLINE) TURNING TO.' MOMENTARILY; THE LGT QUERIED THE CTLR AS TO WHAT ALT HE WAS CLRED TO. THE CTLR RESPONDED 13000 FT. ABOUT THIS TIME OUR TCASII WAS SOUNDING A 'TFC; TFC' WARNING AS THE LGT KEPT TURNING TOWARDS US. THE LGT ROGERED THE ALT AND SAID HE HAD 'TFC' IN SIGHT. HOWEVER WE WERE STILL ON WHAT LOOKED LIKE A COLLISION COURSE AT PROBABLY 400 KTS! THE MLG CAPT DECIDED TO DSND TO AVOID FURTHER CONFLICT; BUT JUST THEN THE MLG TCASII BEGAN AN RA OF 'CLB; CLB.' SINCE THE LGT HAD BEEN CLRED TO A HIGHER ALT; THE MLG CONTINUED ITS DSCNT. JUST AS THE LGT PASSED BEHIND AND ABOVE IT; THE MLG TCASII WAS CALLING 'INCREASE CLB; INCREASE CLB.' I BELIEVE THAT THIS CLOSE CALL OCCURRED BECAUSE THE DEP CTLR AND THE LGT CREW DID NOT UNDERSTAND EACH OTHER. THE CTLR ASSUMED THAT THE MLG WOULD TURN BEHIND THE LGT TO THE WESTERLY HDG. HOWEVER; THE MLG CREW WAS NOT AWARE OF THE HDG CHANGE GIVEN TO THE LGT (WHICH BASICALLY WAS A COURSE REVERSAL HDG FOR THE LGT); AND THE MLG TURNED TO THE 290 DEG HDG WHEN INSTRUCTED TO. THE NEW HDG GIVEN TO THE MLG SHOULD HAVE BEEN GIVEN AFTER THE LGT HAD PASSED TO THE SW OF THE MLG. 4 PROBS WERE APPARENT: 1) VISUAL SEPARATION INSTRUCTIONS WERE GIVEN TO AN 'EXPANDING' DEP SIT (HOW LONG DO YOU KEEP WATCHING THE OTHER ACFT TO 'KEEP VISUAL SEPARATION?' WHAT DO YOU DO WHEN; ON AN IFR CLRNC; YOU ARE GIVEN A HDG THAT PUTS YOU CONVERGING WITH ANOTHER ACFT ON AN IFR CLRNC THAT YOU WERE TOLD TO KEEP SEPARATION FROM)? 2) ALL PLAYERS NOT LISTENING TO THE 'NECESSARY' OR PERTINENT RADIO CALLS. 3) TCASII NOT KNOWING WHAT ATC HAD INSTRUCTED THE CONVERGING ACFT TO DO. 4) ATC NOT KNOWING WHAT TCASII WAS INSTRUCTING THE CONVERGING ACFT TO DO.