The monks at St. John Monastery in California released this Hymn to the Theotokos a while back sung in an American idiom. They want to see how the Byzantine hymns could be sung in a way true to their musical meaning yet incorporating the tones and cadences that are unique to America and define our cultural legacy (think music scores for Westerns for example).
I think they succeed. It almost sounds like it could be sung around a campfire, yet at the same time it still has the Byzantine feel to it.