There's no exact way to describe the sound of The Fall Of Troy. Wikipedia describes it as, "experimental rock/prog-rock with mathcore tendencies". What's mathcore? Good question. Mathcore is a style of music recognized for it's technical musicianship. It's filled with complicated notes, rhythms, and time signatures, and is usually composed using computers and other technical devices. The Fall Of Troy isn't well known if their name is dropped in the middle of a conversation, but the song "F.C.P.R.E.M.I.X." can be heard on the soundtracks of many video games such as Saint's Row, and MLB 2K6.
http://www.myspace.com/thefalloftroy