“ The further extension so as to include Pss. cxv. to cxviii. probably dates from the first half of the 2nd century A.D., and these four psalms were recited after the pouring out of the fourth cup, the two earlier ones being taken at the beginning of the meal. From the 3rd century the use of the Hallel was extended to other occasions, and was gradually incorporated into the liturgy of eighteen festal days.
The “Great Hallel” (Ps. cxxxvi. and its later extension to cxx.-cxxxvi.) always served the wider purpose of a more general thanksgiving. ”

“ All of these Hallels (except cxlvii. and cxlix. which are Maccabean) belong to the Greek period, forming a collection of sixteen psalms composed for public use by the choirs, especially at the great feasts. Their distribution into four groups was the work of the final editor of the psalter. ”