Taanit, Chapter Four, Mishnah Four
This mishnah teaches that on certain days they wouldnt do the special maamad prayers at certain services.
1) On any day when there is Hallel there was no maamad at Shaharit;
a) [On the day when] there is a Musaf-offering, there was no [maamad] at Ne’ilah.
b) [On the day of] the wood-offering, there was no [maamad] at Minhah, the words of Rabbi Akiva.
2) Ben Azzai said to him: Thus did Rabbi Joshua learn:
a) [On the day when] there is a Musaf-offering, there was no [maamad] at Minhah;
b) [On the day of] the wood-offering, there was no [maamad] at Neilah.
c) Rabbi Akiva retracted and learned like Ben Azzai.
Section one: According to Rabbi Akiva, on days when there is Hallel but no Musaf, such as Hannukah, they wouldnt do the maamad at Shacharit, but they would do it at Minhah and Neilah. On days when there is a Musaf offering, they wouldnt do the maamad at Neilah. This is understood to mean that even at Neilah they wouldnt do the service, all the more so at Shacharit, Musaf and Minhah.
Most commentators explain that this mishnah refers to those people of the maamad who were in Jerusalem. They were so busy on these days that they didnt have time to take care of their duties and recite all of the maamad prayers. The previous mishnah, according to which maamad prayers were recited on days which have Musaf, refers to those people of the maamad who were outside of Jerusalem.
The wood-offering refers to the bringing of wood to the Temple by certain families who would volunteer to do so. On this day they would offer a special sacrifice and they would make it into a holiday. According to Rabbi Akiva on these special days there was no maamad at Minhah but there was at Neilah. The next mishnah will discuss this at greater length.
Section two: Ben Azzai tells Rabbi Akiva that Rabbi Joshua disagrees with him concerning two of the three halakhot which he stated. On days with Musaf, there is no maamad at Minhah but there is at Neilah. However, on days when there was a wood-offering, there was no maamad even at Neilah. Upon hearing Rabbi Joshuas tradition, Rabbi Akiva retracted his statement.