I like to define it as follows.
Mellophone, Noun - A trumpet(not capitalized) with a bigger penis. Used by those who either play Horn in symphony or have realized in all of their infinite wisdom that trumpets suck at life.
Mark: "I'm a trumpet player and that makes me a horrible person, I'm stupid, annoying, and ugly, no one will ever love me genuinley, and pain and misery will haunt my pathetic life for all eternity"
mellophone player: good. that means we are doing our job!
Non Bandgeek: What's that?
Mellophone player: It's a trumpet looking object in the key of F which a huge bell the size of a French horn bell.
Trumpet Player 2: It's a mellophone. AKA a trumpet on steroids.
Trumpet Player 1: Ohhh! That's funny!
Mello Player: Really??? 'Cause I heard you play an anorexic Mello??
trumpet player thinks: ahh, i wish i could be a mellophone. they look so cool.