Encyclopaedia Britannica, 11th Edition, "Gyantse" to "Hallel" Volume 12, Slice 7
x. 5) the custom of its recitation at the paschal meal was still of
recent innovation. While the school of Shammai advised only Ps. cxiii., the school of Hillel favoured Pss. cxiii. and cxiv.[2] 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. According to Rabbi Johanan it derived its name from the allusion in v. 25 to the Holy One who sits in heaven and thence distributes food to all bis creatures.
FOOTNOTES:
[1] _International Critical Commentary_, "Psalms," Intro. lxxviii.
[2] The reference to a hymn at the institution of the Eucharist (Matt. xxvi. 30, Mark xiv. 26) must be interpreted in the light of this inceptive stage of the Hallel.