Some Days Get the Whole Song, Others Get Half

Hallel is not recited identically on every occasion it applies to: on some festival days the complete six psalms are sung in full, called the Whole Hallel, while on others, notably the latter six days of Passover and on Rosh Chodesh, the new moon, a shortened version omitting certain verses, called Half Hallel, is recited instead. The traditional explanation for this specific reduction during the later days of Passover draws on a well known rabbinic teaching that God rebuked the ministering angels for wanting to sing in celebration as the Egyptians drowned in the sea, on the grounds that these too were God's creatures, so full, unrestrained joy is considered inappropriate on those particular days precisely because Israelite deliverance and Egyptian death happened together, a moral reservation about celebrating a victory that necessarily involved another people's suffering built directly into how much of this prayer is said and when.

The Talmud itself does not present a single settled account of Hallel's institution, with different rabbinic opinions recorded across tractates disputing who first instituted its recitation and on precisely which occasions it was originally required, evidence that the practice's exact liturgical boundaries were still being worked out and debated among the rabbis well after the psalms themselves had long been part of scripture, rather than fixed from a single clear original source alongside the psalms' own composition.