Mystery horn.
Yer guess is as good as mine.
Well, if my guess is as good as yours. . . 
then I´m Dick Whittington´s Cat. . . 
That mouthpiece is for a single tongue reed. . .I can´t really see if the bore is tapered. I´d guess an early saxophone 
Bob
Why is it square? 
So it can be made without a lathe? Contrabass recorders are square.
It’s got a one-off/bespoke/enthusiasts look about it. If done to be sold in a shop then after all that work I think they would have plated the metalwork.
Square or rectangular like the Craig Fischer U.P. Chanter
Ole, where the bleep do you even find this stuff? I Googled “square woodwind” and on Images got absolutely zilch.
That is one bizarre mouthpiece. Or I assume that’s what it is. Looks more like a weapon.
The Flute History Channel on defacebook.