King Charles's father, Prince Philip, was raised in the Greek Orthodox church. He was received into the Church of England in 1947, the month before he wed Princess Elizabeth, according to Wikipedia.
My guess is that that family background was behind the Byzantine chant at the coronation today, but maybe it was just an ecumenical gesture.
Psalm 71 in the Orthodox reckoning is 72 for everyone else, I believe. The Orthodox join what everyone else has as Psalm 9 and 10 together into Psalm 9, so the count gets off by one after that.
This Psalm is fitting for a coronation:
