Non-metric music means that there is no specific meter that is being followed. There are instances when the rhythm method is 2/4 then it will be changed to 4/4 depending on what is required. The Gregorian chant is known to be monophonic.
This type of sacred song is unaccompanied by any type of music. It follows that it does not follow a certain rhythmic method when it is being sung. The modern Gregorian chant may already have a few changes that are done to it but they can still be separated into two. The first is the recitative melody and the second category is free melody.