Five things are brought in tumah but may not be eaten in tumah: the Omer, the two loaves, the Lechem HaPanim, the communal peace offerings [Kisvei Atzeres], and the Rosh Chodesh goats. The Pesach offering brought in tumah — may be eaten in tumah, since it came originally only for eating.
Fuchsia — Rule
Green — Positive ruling
Black — Case
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The five — brought in tumah, not eaten in tumah
Korban
Brought in tumah?
Eaten in tumah?
הָעֹמֶר
✓ Yes
✗ No
שְׁתֵּי הַלֶּחֶם
✓ Yes
✗ No
לֶחֶם הַפָּנִים
✓ Yes
✗ No
זִבְחֵי שַׁלְמֵי צִבּוּר
✓ Yes
✗ No
שְׂעִירֵי רָאשֵׁי חֳדָשִׁים
✓ Yes
✗ No
The Pesach offering — the exception that explains the rule
הַפֶּסַח שֶׁבָּא בְטֻמְאָה — נֶאֱכָל בְּטֻמְאָה
The Pesach offering is unique: if brought in communal tumah, it may also be eaten in tumah. The reason: the Pesach's essence is its eating — the altar service is instrumental to the meal. Since the eating defines the Korban, the tumah that permitted the bringing also permits the eating. The five items above are different: their essence is the service itself (the Omer's waving, the Shtei HaLechem's tenufah) — eating is secondary, and so tumah permission does not extend from bringing to eating.
Position in the Omer to Shavuos arc — 43 mishnayos
Preceding · Mishnah 19
Menachos 6:1
The Omer among the nikmazos — its sacrificial structure is standard
Current · Mishnah 20
Pesachim 7:4 — Brought in Tumah, Not Eaten in Tumah
Movement II·D opens
Movement II·D is the Omer's legacy — what the Omer does to the world after it is brought. This mishnah shows one facet: the Omer belongs to a cluster of five Korbanos that are so essential — so fixed in time — that tumah cannot prevent them. They are brought even in communal impurity. But their permission does not extend to eating in tumah: the bringing is the mitzva; eating is secondary.
Following · Mishnah 21
Menachos 10:5
The Omer is sacrificed — Jerusalem's market fills with new grain