In the West, singing by the congregation faded away 5th-10th centuries nromh handed over to trained clerics. Coinciding with the development of Western music in general, European polyphony (combining several voice parts on top of and surrounding a melody) began appearing in Holy Mass during the 12th century. Apparently, things were getting out of hand by the 1300s when we read from Jacob of Liege:
There are some who although they contrive to sing a little in the modern manner, nevertheless, they have no regard for quality; they sing too lasciviously, they multiply voices superfluously some of them employ the hocquetus too much, breaking, cutting and dividing their voices into too many consonants; in the most inopportune places they dance, whirl and jump about on notes, howling like dogs.
This type of part-singing was eventually banned by Rome. Some styles of music simply do not fit the spirit of Holy Mass. However, church musicians continued to advance the art of part-singing in Mass settings, letting go of the specific hocket technique against which the Church ranted.
By the 1500s great Masters e.g. Palestrina, Byrd, Josquin des Prez, were creating beautiful music works with multiple harmonies for Holy Mass, Masters which today the Vatican encourages us to use. These type works are often sung by our choir at St. Joseph. However, the harmonies and rhythms were far too complicated for the common person to sing on the spot, thus they were sung by trained singers only.