Let me start out by questioning the very supposition in the above title: did the angels in the Christmas story actually do any singing at all?
Here’s the relevant text from the translation I know best, the King James Version:
And there were in the same country shepherds abiding in the field, keeping watch over their flock by night. And, lo, the angel of the Lord came upon them, and the glory of the Lord shone round about them: and they were sore afraid. And the angel said unto them, Fear not: for, behold, I bring you good tidings of great joy, . . . And suddenly there was with the angel a multitude of the heavenly host praising God, and saying, Glory to God in the highest, and on earth peace, good will toward men. (Luke 2:9-10, 13-14)