As someone who had to study Music History (ughh) Greylock is right on the button. Ancient Greek and Roman music was monophonic (meaning only one tone played at any one time - even if there were multiple instruments or voices, they played/sang the same notes. Monophony was considered the ONLY form of music and harmony or multiple instrumentation just wasn't allowed.
Even percussion, which by modern usage strikes the backbeat or the rhythm and sets the overall tempo, played in unison with the other instruments. The modern concept of an orchestral piece, such as those used for movies to set the 'ancient mood', are just plain wrong.
Also, the instruments they used were less than appealing, especially to modern ears. The lyra is NOT a harp and the cithara (pronounced gitarah) is NOT a guitar. They all have sound boxes and strings and you pluck them, but that's where the similarity ends. The tonality of the ancient instruments is shrill and the vibrato is unnerving. Also the aulos (a two headed flute like instrument) sounds something like strangling a snake while it's head is stuck in a trumpet. (think of a louder version of blowing on a blade of grass - if you've ever done that)
For examples go
here and click on the melodies - As you can tell, the MIDI is not helping, but the single note structure should be pretty grating to modern ears. I know I screamed internally every time I had to listen to it with the REAL instruments, trust me, they don't make it sound any better.