A little way down the hall from the climbing pole is an alcove. Pick up the wooden TORCH from the floor. Step on either round grate to light one of the braziers.
Carefully approach the brazier with torch in hand and press Action to light the torch.
Continue along the hallway and down the stairs...
...to a room with a wooden floor. Press the Draw Weapons button to toss the torch onto the wooden floor.
Then stand back to watch as it goes up in flames. If the torch slides off the wooden slats, pick it up and try tossing it again.
NOTE: The raised passageway on the east side of the room with the wooden floor leads to door J on the upper level of the MAIN HALL. It can only be opened from the other side, but you shouldn't need to go that way.
After a few moments, the wooden floor burns away leaving jagged opening. Lara won't grab the angled edges of the opening, so to avoid taking damage when you drop into the room below, move to the far (north) edge...
...and safety drop from there.
BUG NOTE: A few PlayStation users have found a bug here. After burning away the floor, they left the area, saved the game, then returned later only to find an invisible barrier preventing them from dropping through the floor. I recommend dropping through immediately after burning the floor.
In the ROOM BELOW WOODEN FLOOR, pick up the MUSIC SCROLL. (It's the one in the circle on the floor that Lara stares at intently when you walk past it.)
Shoot the vase to get some shotgun shells. Climb up into the doorway, turn left and push open the blue doors (marked F in the diagram) to emerge back in the MAIN HALL.