Not that this matters from a "current practice" standpoint. Our liturgy is not intended to be a historical/musicological exploration of first century worship or a diorama illustrating the historical circumstances of Jesus' cultural surroundings.
"The first reference to singing in the Bible comes after the crossing of the Red Sea. Israel has risen out of slavery. It has climbed up from the threatening depths of the sea. It is as it were reborn. It lives and it is free. The Bible describes the people’s reaction to this great event of salvation with the verse: "The people … believed in the Lord and in Moses his servant" (Ex 14:31). Then comes the second reaction which, with a kind of inner necessity, follows from the first one: "Then Moses and the Israelites sang this song to the Lord …" At the Easter Vigil, year after year, we Christians intone this song after the third reading, we sing it as our song, because we too, through God’s power, have been drawn forth from the water and liberated for true life."
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