StumbleUpon brought me this video from youtube. It's a track from a CD compiled by a group who recreates early Etruscan and Roman music. It includes not just musicians, but archeologists as well. Apparently the do spend a fair amount of time on period instruments, and have even contributed to films such as Gladiator, and the short lived HBO series Rome.
This appears to be their web page, or the closest approximation I could find. Their wikipedia article is just as helpful. I suppose a bunch of Roman archeologists probably don't have much in the webhosting skills.
Of course much of their work is speculation given their knowledge of the instruments of the period and speculation work given what we know of ancient Greek music. Even less Roman music is extant than Greek music, which is kind of surprising when you consider that Rome at one point controlled the entire Mediterranean, including most of Europe, North Africa, and a sizable chunk of the Middle East. But when you often keep records on papyrus and wax tablets, I suppose permanency isn't a great strength in your society.
Nevertheless, much of Roman music was said to have been Greek in nature. (Not surprising when you consider the Latin tribes came to power after conquering the Etruscans, a people themselves influenced by the Greeks.) My understanding is that Synaulia has tried to incorporate likely influences of some of the peoples Rome conquered and culturally absorbed, and I'd like to think I can hear it in the music.
I have to say, some of the dissonances in the second one are really appealing. I'm not sure why. But it's a sound that I can't say I've really heard replicated elsewhere.
They are apparently the main Roman Music society of sorts, along with Musica Romana, who's English website can be found here. That must be where all the youngins are - easy to navigate, very helpful, and professional, webpage.