Among the very few reported observations of singing angels, the account given by the shepherds of the angelic choir on Christmas night records some of the words but gives no account of the music, even though shepherds are much celebrated as pipe players and so form an unusually musical profession. But in which key did the angels sing? This question could only have been answered for us by a shepherd with perfect pitch, that is, an unusually good ear for pitch (how high or low the music is). However, the question also contains the hidden assumption that the angels based their music on the key system, which was not known on earth until the sixteenth century AD, so the question should be changed to “Which musical system did the angels use?”. Clearly, as angels are perfect, the system must be the best available, so we may be able to answer the question theoretically.