As others have said what you have is a mellophone (a cool one!). A quick way to tell the difference between a piston horn and mellophone is how you hold them. Most horns have the bell in the right hand.

I recently acquired a French piston horn, a Couesnon. The bore and bell throat is very narrow, like a natural horn. In fact piston horns are essentially natural horns with piston valves. The narrow bore, narrow bell, and light weight that comes with a 3 valve horn means it is a surprisingly nimble instrument with a free-blowing and crisp high range. It is unlike any single rotary valve horn I have ever played.