There were two series of psalms so called. Jahn tells us in the Feast of Tabernacles the series consisted of Psalms cxiii. to cxviii. both included (Archæologica Biblica, p. 416). Psalm cxxxvi. was called the Great Hallel. And sometimes the songs of degrees sung standing on the fifteen steps of the inner court seem to be so called (i.e. cxx. to cxxxvii. both included).
“Along this [path] Jesus advanced, preceded and followed by multitudes with loud cries of rejoicing, as at the Feast of Tabernacles, when the Great Hallel was daily sung in their processions.” —Geikie: Life of Christ, vol. ii. chap. 55, p. 397.
In the following quotation the Songs of Degrees are called the Great Hallel.
“Eldad would gladly have joined in praying the Great Hallel, as they call the series of Psams from the cxx. to the cxxxvi., after which it was customary to send round the [paschal] cup a fifth time, but midnight was already too near.” —Eldad the Pilgrim, chap. ix.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894