After Jesus’ Passover with His disciples, they leave singing for the Mount of Olives.  Last time they were on the Mount, Jesus predicted the destruction of a temple.  His return to the mountain marks the initial fulfillment of that prophecy: Jesus is the temple, torn down and raised again in three days; so too, the disciples are the temple, scattered and regathered in three days.

In all likelihood, they go out singing the Hallel, Psalms 113-118, which climaxes with the marvelous news that the rejected stone has become the chief cornerstone of the temple (118:22).  It’s a fitting song to be singing on Olivet.