You've just got to hear it. The Romans must have thought it was a reed instrument. They had their own kind of twin-pipe instrument which looked similar but it was evidently much more difficult to blow. They often used a leather strap around the musician's face to hold their cheeks in. Evidently, Dizzy Galespie wasn't the first person to inflate his entire neck by blowing too hard.
Some references even suggest that the Roman pipers suffered lung damage as a result.
Look at the Greek though, the relaxed face and posture. Even Glen Miller couldn't look as relaxed as those ancient Greeks.