In Keilim 19:4 and 28:6, we see an unusual (to me) way of describing av hatumah and rishon l'tumah:

נִשָּׂא הַזָּב עַל הַמִּטָּה וְעַל הַמִּזְרָן, מְטַמֵּא שְׁנַיִם וּפוֹסֵל אֶחָד, דִּבְרֵי רַבִּי מֵאִיר. רַבִּי יוֹסֵי אוֹמֵר, נִשָּׂא הַזָּב עַל הַמִּטָּה וְעַל הַמִּזְרָן, עֲשָׂרָה טְפָחִים, מְטַמֵּא שְׁנַיִם וּפוֹסֵל אֶחָד. מֵעֲשָׂרָה וְלַחוּץ, מְטַמֵּא אֶחָד וּפוֹסֵל אֶחָד. נִשָּׂא עַל הַמִּזְרָן, מֵעֲשָׂרָה וְלִפְנִים, טָמֵא. מֵעֲשָׂרָה וְלַחוּץ, טָהוֹר.

If a zav was carried on a bed and on its mattress, the latter causes an uncleanness of two grades and an unfitness of one grade, the words of Rabbi Meir. Rabbi Yose says: if a zav was carried on a bed and on its mattress the part that is shorter than ten handbreadths causes an uncleanness of two grades and an unfitness of one grade, but that which is over the ten handbreadths causes only an uncleanness of one grade and an unfitness of one grade. If he was carried on the mattress, [on the overhanging part] that was shorter than ten handbreadths, it becomes unclean, but if on the part that was longer than ten handbreadths it remains clean. [from Sefaria]

We see similar language to the bolded text in 28:6 as well (as well as in Tosefta Keilim B"K 4:10). Why use this roundabout language of describing an av hatumah and rishon l'tumah?

Oftentimes, weird turns of phrases are helpful as a memory aide, but here, one is likely to misremember the numbers, whereas av hatumah and rishon l'tumah are hard to mix up. Thus it would appear that "a memory aide" is not the answer here.

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    Are you sure the Mishnah is describing an Av and Rishon, and not a Rishon and Sheini! – DonielF Jul 14 '19 at 4:18
  • @DonielF Tumah becomes pasul, so the מטמא שנים ופוסל אחד is probably av hatumah causing rishon, sheni, and making terumah pasul (and similarly for the other). (This is also what Kehati explained.) You reminded me of another question I had, though: why isn't קדשים included here? – magicker72 Jul 14 '19 at 4:38
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    It's not really an unusual phrase - we find it multiple times in Taharos and Zovim. But your question still stands: Why sometimes use this way of defining the level of Tumah? – Danny Schoemann Jul 14 '19 at 8:19

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