We begin the seventh chapter of Maseches Menachos, which is devoted to the loaves of the todah - the bread that accompanies the thanksgiving offering. The todah is an offering of thanks, a kind of sub-category of shelamim, and its status is therefore that of kodashim kalim. It is brought at any time while a person is still alive, and it may come from any type of animal: cattle, goat or sheep, male or female, old or young.
The todah differs from ordinary shelamim in two fundamental ways:
The time for eating it: only the day it is offered and the following night.
The bread: the todah is brought with forty loaves - four different types, ten loaves of each type. They too are eaten within that very same time frame.
Since the bread belongs to the category of menachos, the loaves of the todah are discussed here, in the seventh chapter of Maseches Menachos.
The recipe for preparing the forty loaves:
Our Mishnah enters into the details of the mathematical calculations, so let us first lay out the idea clearly and only afterward return to the numbers. The basis of the recipe: two eifos of flour are required. The isaron, which we have dealt with throughout the maseches, is a tenth of an eifah, so two eifos come to twenty esronos.
Half the flour is designated for the ten loaves that are chametz, and the other half for the thirty loaves that are matzah - that is, one eifah for the chametz and one eifah for the matzah. Since the very same amount of flour produces thirty matzah loaves as against ten chametz loaves, it turns out that the chametz loaves are three times the size of the matzah loaves.
Midbar measures and Yerushalayim measures:
Originally, in the midbar, the measures were as we have described. A convenient way to picture it: the eifah is equal in volume to three six-packs of two-liter water bottles stacked one on top of the other. Each six-pack is a se'ah, and each bottle inside it is a kav. These are approximately the true volumes.
In the era of the second Beis HaMikdash, the Jewish people adjusted their weights and measures, adding a sixth (shtus) - this is the "sixth" that the Mishnah speaks of - to the volume of the measuring vessels. The names remained as they were: kav, se'ah and eifah; but every measuring vessel became larger. The amount of flour that the Torah's recipe calls for does not change at all, only that the measuring vessels grew, and therefore fewer vessels are needed for that very same amount.
If previously six kabin went into one se'ah, now five enlarged bottles suffice to fill that same se'ah. The enlarged measures are called the Yerushalayim measures, as opposed to the original measures, which are called the midbar measures.
The calculation in midbar measures:
The recipe calls for two eifos of flour for the forty loaves: one eifah for the chametz loaves and one eifah for the three types of matzah. There are ten issaron in an eifah, and therefore:
The chametz loaves: ten issaron for ten loaves - one issaron per loaf.
The matzah loaves: ten issaron for thirty loaves - a third of an issaron per loaf.
The calculation in Jerusalem measures:
In the Jerusalem measures the measuring cup is larger: instead of six kabin to a se'ah, only five kabin hold that same quantity of flour. Three desert se'ah make up one eifah, so instead of eighteen kabin to an eifah there are fifteen Jerusalem kabin (three times five). Two eifos for the entire recipe - thirty kav.
One can reach the same result from the other direction as well: two eifos are six se'ah, and each se'ah holds six desert kabin - thirty six kav according to the desert measures. But once the containers are enlarged, only five kabin go into each se'ah, and six se'ah times five - thirty kav.
The chametz loaves: fifteen kav for ten loaves - a kav and a half per loaf.
The matzah loaves: fifteen kav for thirty loaves - half a kav per loaf, that is, two loaves for every kav of flour.
The four types of bread:
Chametz bread: flour and water that were allowed to leaven and rise, with no oil at all. In chapter five we already discussed the process of leavening in connection with the se'or.
Challos: something like Sephardic matzah - it is not crisp like a cracker; the oil is kneaded together with the flour and water into the dough, it does not rise, and it is baked in an oven.
Rekikin: something like Ashkenazic matzah - flour and water alone without oil, they are baked, and the oil is smeared on them after the baking.
Revuchin: "murbeches" comes from the word for scalding - first the flour is scalded by pouring boiling water over it, then it is baked for a short time, and finally it is fried.
The language of the Mishnah:
In its first part the Mishnah establishes the conversion ratio: whatever was six units in the desert is five units in Jerusalem - six desert se'ah in two eifos are five Jerusalem se'ah, and six kabin to a se'ah are five Jerusalem kabin.
"HaTodah haysah ba'ah chamesh se'in Yerushalmiyos, shehen shesh midbariyos" - the total quantity of flour that accompanies the forty loaves is five se'ah by the Jerusalem measure, which are six se'ah by the original desert measure.
"Shtei eifos" - this is the total quantity. "VehaEifah shalosh se'in" - three se'ah to a single eifah.
"Esrim isaron" - twenty issaron measures. Each eifah is divided into ten issronos (an issaron means a tenth part), so two eifahs come to twenty issronos.
"Asarah lechametz va'asarah lematzah" - ten for the leavened and ten for the unleavened. The twenty issronos are split into two equal halves, an eifah for each half: ten issronos for the leavened loaves, and ten issronos for the thirty unleavened loaves.
"Ve'isaron lachalah" - and an issaron for each loaf. Ten issronos for ten leavened loaves, which comes out to one issaron per loaf.
"Uvamatzah shloshah minim: chalos urekikin urevuchah" - and in the unleavened there are three types: loaves, wafers, and revuchah. The ten issronos of the unleavened are divided among the three types of bread: the loaves, in which the oil is kneaded into the dough and which are then baked; the wafers, which are baked without oil and the oil is spread on them afterward; and the revuchah, which is scalded, baked, and then fried.
"Nimtze'u shloshah esronim ushlish lechol min, shalosh chalos la'isaron" - so there are three and a third issronos for each type, three loaves per issaron. Ten issronos divided among three types comes to three and a third issronos for each type; and every three loaves take one issaron of flour. This is the calculation according to the original desert measures.
"Uvamidah Yerushalmis hayu shloshim kav" - and by the Jerusalem measure they were thirty kav. By the Jerusalem measures, in which the measuring vessels were enlarged and only five kav fit into a se'ah, the total comes to thirty Jerusalem kav.
"Chamishah asar lechametz vachamishah asar lematzah" - fifteen for the leavened and fifteen for the unleavened. The thirty kav are divided in half: fifteen for the ten leavened loaves, and fifteen for the thirty unleavened loaves.
"Chamishah asar lechametz - kav vachetzi lachalah" - fifteen for the leavened, a kav and a half per loaf. Fifteen kav for ten loaves, so each loaf comes to a kav and a half.
"Vachamishah asar lematzah... nimtze'u chameishes kabin lechol min, shtei chalos lakav" - and fifteen for the unleavened... so there are five kav for each type, two loaves per kav. The fifteen kav are divided equally among the three types of unleavened bread: loaves, wafers, and revuchah - five kav for each type. And since ten loaves are made from each type, each loaf comes to half a kav, that is, two loaves for every kav of flour.
In summary: In this chapter we learned the recipe for the todah breads: two eifahs of flour for forty loaves, half for the ten leavened loaves and half for the thirty unleavened loaves in their three types - loaves, wafers, and revuchah. By the desert measures this comes to an issaron for each leavened loaf and a third of an issaron for each unleavened loaf, and by the enlarged Jerusalem measures - a kav and a half for each leavened loaf and half a kav for each unleavened loaf.