The correct profile for early guns was determined by the way the blacksmiths forged them.
Traditionally there are five ways to do this...
Method the First
-Get a flat strip of wrought iron (not mild steel, it doesn't weld as well).
-Use a fuller and a grooved anvil to give it a U-shaped section, then gradually form it into a hollow tube with an overlapping seam.
-Carefully weld along the seam (forge welding, not arc!) using a polished steel rod (mandrel) to stop the tube collapsing unde the blows of the hammer
-True up the outside of the barrel as much as posible, to save filing. Using just a flatter and a hammer, it is easy to get an accurate square or octagon shape. If you have a set of fullers, you could make a round or octagon to round barrell. Some early gonnes had octagon to hexa-decagon (16-sided). Hexagons can also be made with just a flatter and hammer, but it is a LOT harder. I have only ever seen two hex-barreled guns - and one was japanese. They are rare.
-Of course, if you draw out your barrel on the mandrell, you can get a tapered or swamped barrel, but getting the flats on the swamped barrel without filing would be difficult
Method the Second
-Make several shorter tubes as detailed about, but each with a different wall thickness.
-Use the thickest as the breech, the thinest at the muzzle.
-Flair one end of each tube and weld them end to end.
-Finish as above
Method the Third
-Take two thick strips of wrought iron.
-Fuller a long grove down the middle of each
-Weld both pieces together to make a hollow tube, using the mandrel as above
-Finish the barrel as above
Method the Fourth
-Take a strip of iron (or damascus made from wrought iron mixed with steel)
-Wind it around the mandrell to make a spiral tube with overlapping edges.
-Carefully forge weld along the overlap
-Finish barrel as above
The fifth method is to cast the barrel in bronze, in which case you can have any weird shape you want
Back to the subject, tapered and swamped and octagon-round barrels were used for better balance and to save expensive iron. They look historically accurate (for post 1470-ish) but tend to be more expensive, and take a lot of skill to inlet into a stock.
I have seen a lot of "ordinary" matchlock muskets with tapered "rough round" barrels, but the finer decorated ones tend to have tapered octagon barrels, some with a raised ring or octagon on the muzzle
A bit of carefull filing should turn a big beefy barrel like the one you mentioned into anything you want... emphasis on the careful
