We would like something minimalist - so in that sense modern - but since the term (http://en.wikipedia.org/wiki/Siren) has classic origins, some classic touches would be nice. I'll leave it up to the designers - I don't want to stifle anyone's creativity. We think it's a fun, beautiful name, and the logo should be in keeping with that sense of it.
Wikipedia description (but I'd recommend visiting the page - pretty interesting):
In Greek mythology, the Sirens (Greek singular: Σειρήν Seirēn; Greek plural: Σειρῆνες Seirēnes) were three dangerous bird-women, portrayed as seductresses
Sailors who sailed near were compelled by the Sirens' enchanting music and voices to shipwreck on the rocky coast.
The sirens of Greek mythology are sometimes portrayed in later folklore as mermaid-like; in fact, some languages use the same word for both bird and fish creatures, such as the Maltese word 'sirena'.
The term "siren song" refers to an appeal that is hard to resist but that, if heeded, will lead to a bad result.