Commentary for Zevachim 10:1

כֹּל הַתָּדִיר מֵחֲבֵרוֹ, קוֹדֵם אֶת חֲבֵרוֹ. הַתְּמִידִים קוֹדְמִים לַמּוּסָפִין, מוּסְפֵי שַׁבָּת קוֹדְמִין לְמוּסְפֵי רֹאשׁ חֹדֶשׁ, מוּסְפֵי רֹאשׁ חֹדֶשׁ קוֹדְמִין לְמוּסְפֵי רֹאשׁ הַשָּׁנָה, שֶׁנֶּאֱמַר (במדבר כח), מִלְּבַד עֹלַת הַבֹּקֶר אֲשֶׁר לְעֹלַת הַתָּמִיד תַּעֲשׂוּ אֶת אֵלֶּה:

Anything that is [offered] more frequently than something else, precedes it [when both are offered]. The Tamid [communal burnt-offering brought twice daily in the Temple, once at dawn and once in the late afternoon] precede the Musaf offerings [additional sacrifices brought on Shabbat and holidays]; the Musaf offerings of Shabbat precede the Musaf offerings of Rosh Chodesh [the first day of the new month on which special prayers and sacrifices offered]; the Musaf offerings of Rosh Chodesh precede the Musaf offerings of Rosh HaShanah [the New Year's festival], as it says: "You shall offer these in addition to the Olah [an offering that is entirely burnt] of the morning, which is for a continual Olah" (Numbers 28:23).

Bartenura on Mishnah Zevachim

כל התדיר מחבירו קודם את חבירו – as it is written (Numbers 28:23): “[You shall present these] in addition to the morning portion of the regular burnt-offering.” Since it is written, “in addition to the morning portion,” it implies that it was already done, from it we hear/learn that the daily offerings precede the additional/Musaf offerings; “of the regular burnt offering,” why do I need this? It is obvious that the burnt offering of the morning is the regular daily burnt offering, but rather, that it suspended for you the reason of its preceding [the Musaf offering] through its frequency in order that you will learn the rest of the frequent things that should precede. For since this is its essence, it was not necessary to explain it.

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English Explanation of Mishnah Zevachim

Whatever is more frequent than another, takes precedence over the other.
The daily offerings precede the additional offerings;
The additional offerings of Shabbat precede the additional offerings of Rosh Hodesh;
The additional offerings of Rosh Hodesh precede the additional offerings of Rosh Hashanah.
As it is said, “You shall present these in addition to the morning portion of the regular burnt offering” (Numbers 28:23).
The first five mishnayot of this chapter deal with the order in which different sacrifices are offered. There are two general rules, one which we will see in this mishnah and one in the next mishnah.
Section one: This is a general principle that is today often invoked when determining which prayer, or which blessing is recited first (for instance over the matzah on Pesah). As is frequently the case, a principle that plays a large role in later halakhah, has its origins in sacrificial law.
Sections two-four: Here, the principle is invoked in connection to the daily offerings and the additional offerings (musaf). A more frequent sacrifice is offered first.
Section five: This is the proof text that the daily tamid, the morning offering, is offered before the other additional offerings for holidays. The verse implies that the morning offering has already been offered before the other sacrifices are offered. Hence, whatever is more frequent comes first.

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