There is a perfectly normal way of phrasing the line in the chorus of "The Holly and The Ivy", with all the stresses in the conventional places.
"The PLAYing of-the MERRy ORgan"
So why has it become the fashion to sing,
"The PLAYing of THER merry-orGAN"?
In the immortal words of Winnie the Pooh, "Don't you know what 'Ther' means?"
It's a minor irritation, but I do wonder where it comes from- possibly from John Rutter, introducer of musical obscurities into other Christmas carols.
Cheers
Dave