CLEARED FOR TKOF RWY 27L; LGT TOOK OFF ON RWY 22L.

Narrative

PRIOR TO DEP AT A MAJOR ARPT THE ATIS RPTED RWY 22L AND 27L WERE DEP RWYS. WE WERE DEPARTING S SO WE ASSUMED RWY 22L WOULD BE OUR ASSIGNED RWY. THE RWYS ARE IN CLOSE APPROXIMATION TO ONE ANOTHER AT POINT OF TKOF AND TAXIING INSTRUCTIONS IN MANY CASES ARE THE SAME. WHEN WE RECEIVED THE TAXI INSTRUCTIONS WE EXPECTED RWY 22L (OBVIOUSLY A MINDSET). THE GND CTLR CLRED US TO RWY 27L; AND WE UNDERSTOOD IT TO BE 22L. WE TAXIED (SAME ROUTING) TO AND BEFORE ARRIVING AT RWY 22L; TWR CLRED US FOR TKOF; RWY 27L; TURN LEFT 230 DEGS. WE REPEATED BACK THE CLRNC AS WE UNDERSTOOD IT; 'CLRED FOR TKOF; 22L; TURN LEFT 230 DEGS.' I QUESTIONED THE TURN LEFT TO 230 DEGS TO THE F/O. HE VERIFIED FROM THE TWR THE HDG WAS 230 DEGS AND WE PROCEEDED TO TKOF ON RWY 22L. AFTER WE WERE AIRBORNE THE TWR BECAME CONFUSED AS TO WHO WAS AIRBORNE AND WHO WAS NOT. IT WAS THEN DETERMINED THAT WE HAD INDEED TAKEN OFF ON THE WRONG RWY. THE PROB ON OUR PART WAS OBVIOUSLY MINDSET. THE PROB ON THE CTLR'S PART WAS PROBABLY NOT HEARING OUR REPEAT OF THE CLRNC; 'CLRED FOR TKOF 22L; LEFT TURN 230 DEGS.' ALSO; POSSIBLE HE WAS NOT WATCHING WHO WAS ENTERING WHICH RWY FOR TKOF WHEN THE CLRNC WAS ISSUED. I'M STILL BEWILDERED TO THINK IT HAPPENED BUT IT DID; AND WE ARE LEFT WITH THE QUESTION; HOW COULD 3 CREW MEMBERS AND ONE CTLR MISINTERPRET AND MISUNDERSTAND ONE ANOTHER TO THE POINT OF ALLOWING A VERY DANGEROUS SITUATION TO MATERIALIZE?