cellio | daf bit: Shevuot 10

The torah commands specific offerings for special days. Rosh Chodesh (new moon), festivals, and Yom Kippur all require the offering of a goat. The torah tells us that the goat for Yom Kippur atones for the people's sins; do the other goats atone for anything, or are they just offerings? The mishna seems clear that they atone, but the rabbis disagree on what they atone for. R. Shimon b. Yehudah describes a sort of "stacking", saying the Rosh Chodesh goat atones for improperly eating sanctified food, the festival goat atones for that and also unknown transgressions, and the Yom Kippur goat atones for those and known transgressions. The g'mara appears to disagree, arguing that the goats have designated, non-overlapping atonement roles to play. (10b)

(That offerings bound to particular days, rather than to events, would specifically atone for anything, other than the special case of Yom Kippur, came as a surprise to me. I thought they were tribute.)