Hi Nando,
I do hope to be able and tell with sufficient authority on the subject

that this indeed
is one of the earliest existing
handgonne barrels that I have ever seen.
It compares quite exactly to the sample in my collection
- see my thread, post #2:
http://www.vikingsword.com/vb/showth...ight=handgonne
which is obviously made of band iron folded around a hardened core.
Please also see
http://www.vikingsword.com/vb/showth...ight=handgonne
http://www.vikingsword.com/vb/showth...ighlight=berne
With their overall shapes, of round section throughout and with notable swamping at the rear as well as at the forward end, plus the fact that their touch holes are very close to the rear end, they represent the last stylistic extension of the Romanesque period, being very close in style to the famous Loshult gun (ca. 1330-50), and doubtlessly ranging among the earliest wrought iron barrels ever made.
If you look at it closely, holding it against broad daylight, you should be able to identify the characteristic structure of the wound band iron, which is clearly visible on my specimen.
And, once more in terms of style, it is significantly earlier than the earliest barrels adopting the new Gothic style and reflecting it by their multi-sided shapes: hexagonal and octagonal, both probably entering the war scene as late as ca. 1400, as some barrels in both your collection and mine denote
http://www.vikingsword.com/vb/showth...nd+cannon+1400
and as the earliest known existing and datable portable 'long arm'/'gun', which luckily is in my collection, proves because it exactly corresponds to an illustration dated 1411 (Cod.Vind. 3069, fol. 38v) - see:
http://www.vikingsword.com/vb/showth...andgun+1400-10
Please also search the surface in front of the touch hole carefully for a tiny
arrowhead mark, as it is struck on my barrel!
The measurements of my counterpart are:
overall length 13.8 cm, outer diameter at both the rear and forward end 4.5 cm, 'bore' ca. 25 mm; thus our barrels are nearly identical and doubtlessly were part of a series made by the same workshop!
Highly remarkable is the narrowing rear breech section you mentioned, as it is another early criterion typical of guns meant to fire limestone balls (German:
Steinbüchsen), before balls were cast of lead or, in the case of the smith Peter Pögl in the 1490's, were of wrought iron, made by order of King Maximilian.
I should closely examine my sample as well.
Best wishes
and congrats,
Michl