Question: Why are the Teki'os of the tenth step not listed?

Answer: Our Mishnah is the opinion of R. Eliezer b. Yakov (who argues with the Tana Kama and holds that, rather than on the tenth step, the Teki'os were blown when the Aravos were arranged around the Mizbe'ach).

Question: What is R. Eliezer b. Yakov's rationale?

Answer: The tenth step is not a gate!

Question: What is Rabanan's rationale?

Answer: The Teki'os are for filling the water, to which the tenth step relates, while the Aravos are unrelated!

(Beraisa cited by R. Acha b. Chanina): Yiska'u teaches that the Teki'os go according to the Musafin.

(R. Acha b. Chanina): This means that we blow for each Musaf which is brought.

Question: If so, then the Mishnah should have listed Shabbos within Sukos as an example of 51 Teki'os!?

Answer (R. Zeira): The three Teki'os for opening the gates are not blown on Shabbos.

Questions (Rava, astonished by R. Zeira's suggestion):

The Mishnah says they blew for the opening of the gates ever day!?

If it were true that Erev Shabbos during Sukos is the same (48 Teki'os) as Shabbos during Sukos, then the Mishnah would surely have listed Shabbos, given that we could then learn both the rulings of R. Eliezer b. Yakov (1.b. above) as well as that of R. Acha b. Chanina (Teki'os for each Musaf)!?

Answer: Rather, there were none of the Teki'os associated with filling the water on Shabbos (which was done Erev Shabbos).

Question (on R. Acha): The Mishnah should have listed Rosh ha'Shanah (48 Teki'os, owing to three Musafim)!?

Answer: We would still opt for Erev Shabbos during Sukos (as the example of 48) since it teaches us the Din of R. Eliezer b. Yakov.

Question: The question implied that the Mishnah should list both!?

Answer: The Mishnah does not provide an exhaustive list of days with 48 Teki'os.

Question: What other instances were omitted?

Answer: Erev Pesach (given the three Teki'os for the Halel said three times by each group).

Question: But Erev Pesach could, if we follow the assertion of R. Yehudah (that the third group did not even finish the first Halel), have only 42 (and not be an omitted example at all)!?

Question: But we said (53b) that the Mishnah is not the view of R. Yehudah!?

Answer: Perhaps this Tana subscribes to one view of R. Yehudah (regarding the completion of Halel by the third group) and argues with the other (regarding how to figure a group of Teki'os)!?

Question: Then, all in all, which other instance was left out of our Mishnah?

Answer: Erev Pesach which falls on Erev Shabbos (48 Teki'os, after we remove the six which R. Yehudah would have us delete, and add the six of Erev Shabbos).

Question: What about Erev Pesach which falls on Shabbos (even following R. Yehudah there would be 51, and according to Rabanan there would be 57)!?

Answer: We list those instances which occur annually.

Question: Then what of Erev Shabbos in Sukos, given that there is not necessarily an Erev Shabbos during Sukos (if the first day of Yom Tov is Erev Shabbos)!?

Answer: There is always an Erev Shabbos during Sukos because we adjust the calendar to prevent the first day of Yom Tov from falling on Erev Shabbos (which meant that Yom Kipur would have occurred directly after the previous Shabbos - two days of Shabason!).

Question: But the Mishnah speaks of the Chalavim of Shabbos being brought on the Yom Kipur which follows it (and R. Zeira taught Halachos regarding Yom Kippur on Erev and Motzei Shabbos)!?

Answer: Our Mishnah is Rabanan (according to whom we adjust to calendar to prevent Yom Kippur falling next to Shabbos) while Acherim allow for this occurrence (as the Beraisa indicates that Acherim let the days fall where they will, four or five days further than their occurrence on the previous year).

Question: The Beraisa speaks of one Shir (Rosh Chodesh) overriding another (Shabbos), whereas, according to R. Acha, they should be saying both, just as they are Tokei'a for each Musaf!?

Answer (R. Safra): The overriding means that it is placed first, before the Shir of Shabbos.

Question: But Tadir should place Shabbos first!?

Answer (R. Yochanan): It is done so as a Heker to assert our confidence in the setting of Rosh Chodesh.

Question: But we already have a Heker in the higher placement of the Rosh Chodesh Musaf on the Kevesh!?

Answer: There are indeed two Hekerim.