The five sela of a first-born must be made in maneh Tzori.
The thirty shekels of a slave (Shemot21:32) and likewise the fifty shekels of one who violates a woman (22:29), the indemnity for seduction (Shemot 22:16) and the one hundred shekels of one who spreads an evil name ( 22:19), in all these cases the holy shekel is meant, paid in maneh Tzori.
Generally speaking, during the time of the Talmud there were two types of coins. Matbe’ah Tzori was a silver-based coin that was viewed as being biblical money. Kesefmedinah were coins that had the same names as the more valuable matbe’ah Tzori, but were made of cheaper metals and were worth one-eighth the value of kesef Tzori. These coins were used for payments whose obligations were of Rabbinic origin. Different values for coins with identical names were not uncommon in the ancient world and this phenomenon still exists in some places today, where paper money may have the same name as a gold coin, for example, but is worth significantly less. It is therefore essential to determine which coin is being discussed.
According to the Gemara, all of the payments listed in our Mishnah had to be made using the value of a holy shekel. The Melekhet Shlomo suggests that the Mishnah separates the case of the firstborn from the other cases because it does not want to mix the case of a mitzvah with the cases of payment for violent or anti-social acts. He also quotes the Ritva as teaching that there is a distinction between the cases. Whereas the payment of five shekalim for redeeming the firstborn remains at the original value even in the event of currency fluctuation, the other cases will depend on the value of the coin at a given time.
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