Why don’t any of these Tannaim hold of 1:60?

Question

Terumos 10:8:

דָּג טָמֵא שֶׁכְּבָשׁוֹ עִם דָּג טָהוֹר, כָּל גָּרָב שֶׁהוּא מַחֲזִיק סָאתַיִם, אִם יֶשׁ בּוֹ מִשְׁקַל עֲשָׂרָה זוּז בִּיהוּדָה שֶׁהֵן חָמֵשׁ סְלָעִים בַּגָּלִיל דָּג טָמֵא, צִירוֹ אָסוּר. רַבִּי יְהוּדָה אוֹמֵר, רְבִיעִית בְּסָאתָיִם. וְרַבִּי יוֹסֵי אוֹמֵר, אֶחָד מִשִּׁשָּׁה עָשָׂר בּוֹ

The following summary of the Mishnah is based on the Yachin’s commentary.

If one pickled a non-Kosher fish with a Kosher one, then the Tanna Kamma requires a 1:960 ratio to permit the non-Kosher fish’s brine; R’ Yehudah requires a 1:192 ratio; and R’ Yose requires a 1:16 ratio.

The Tiferes Yisrael notes that the Tanna Kamma requires such a high number because fish brine has such a strong taste that it requires that much to dilute it.

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To this I ask: Why should this be any different than all other cases of Nosen Ta’am LaShevach (improving the taste of the food - Avodah Zarah 39a classifies spicy foods likewise) which are just 1:60? Where does he get 1:960 as the magical number to be nullified? (It looks like the Boaz addresses this, but I can’t understand what he’s saying.)

Likewise, according to R’ Yehudah and R’ Yose (especially R’ Yose): why do they not require 1:60?

This question may be strengthened by the Yachin’s final note on the Mishnah, that we indeed pasken 1:60 in this case, against all of these Tannaim (based on YD 3).

Answer 1

A berya, a whole being, is not bateil beshishim. (Nullified in a 1:60 r maybe 1/60 mixture. There is a dispute whether we mean 1 part problematic item vs 60 parts of other, or 1/60 of the total mix, which would be 1 part vs 59 parts of other.) What we actually hold in practice for bitul of a berya is more complicated, with opinions ranging from there never is bitul (Shulchan Arukh YD 100:1) to Issur veHeter haArukh (quoted by the Taz ad loc) saying once the berya is lost in the mixture, it's no longer a berya and the usual 1:60 applies. The Gra gives two possibilities -- 1:960 and the Rambam's 1:1000.

The Rosh (on Terumos 10:5, our 10:8) says that this is why bitul beshishim doesn't work in the case you ask about, and you instead need the greater ratio.

A more popular opinion is to focus on the fact that we're talking about tzir, brine, rather than the whole fish. This is the tack taken by Rambam and the Bartenura. Eg, the Bach quotes a mishnah's "ad shishah asar -- until 16" as saying brine's taste is 16 times stronger than most tastes, which is why the gemara requires 1:960 -- 16 times as much as 1:60.

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As for why 960... The mishnah works with established units of measure, not a ratio; 10 Judean zuz or 5 Galilean sela per 2 se'ah container. The Bartenura ad loc says it's simply close enough to the 1:1000 we find elsewhere to be sure there is no ta'am (roughly: taste; more like an expectation of taste, but it's a hard-to-define concept related to taste, perception and psychology).

But this is only the first opinion. Ralbach (in the Frankel Rambam on Maakhalos Asuros 15:34) says the other opinions map to Rabbi Yehudah requiring 1:192 and Rabbi Yosi -- 1:16 (!). Rabbi Yosi's opinion is less startling if you compare to finding a non-kosher cricket in your cricket pickling barrel, where you just pick out the non-kosher one and move on. Halakhah (see the Rambam ad loc) follows the Yerushalmi on our mishnah, requiring 1:200.