Sukkah, Chapter 5, Mishnah 5. After discussing the Simchas Beis HaSho'evah and mentioning that they would sound trumpet blasts during it, our Mishnah now teaches in a general way how they would sound the blasts in the Beis HaMikdash every single day, and how they would sometimes do so on Sukkos.
The basic rule:
"Ein pochasin me'esrim ve'achas teki'os bamikdash, ve'ein mosifin al arba'im ushmoneh" - they never sound fewer than twenty one blasts in the Beis HaMikdash, and never more than forty eight. The number given under the heading of "teki'os" actually includes the teru'os as well. Forty eight is the maximum number of blasts on any single day in the Beis HaMikdash, though we will see that this is not entirely precise, since there is an occasion on which they could sound even more.
The twenty one blasts of every day:
Three at the opening of the gates: teki'ah, teru'ah and teki'ah at the time they would open the gates of the Azarah in the morning.
Nine for the daily Tamid offering: at the time of the wine libation the Levi'im would sing the song of the day, the daily chapter of Tehillim, which is divided into three sections, and before each section they sounded teki'ah, teru'ah and teki'ah - that makes nine.
And nine more for the second Tamid offering: in exactly the same order.
So we have twenty one: three, nine and nine.
On days that have a Musaf offering: on any day with a Musaf, such as Shabbos, they would add nine blasts, since the Musaf offering also included a wine libation, and at that moment they sounded the blasts in the order described.
On Erev Shabbos - six additional blasts:
Three to separate the people from their work (and it appears that the first signal was a teki'ah):
The first - so that those working in the distant fields would stop their labor.
The second - so that the shops would close.
The third - so that they would remove the pots from the fire, put things away, and begin lighting the Shabbos candles.
And three to separate between holy and mundane: three blasts sounded as a signal that Shabbos was actually entering.
Erev Shabbos that falls during Sukkos - forty eight:
Three at the opening of the gates of the Azarah, as on every day.
Three at the upper gate leading out of the Azarah, when they had finished the celebration itself and began preparing to go out and draw the water.
Three at the bottom of the stairs descending from the Azarah, and they would continue sounding blasts until they reached the outer gate.
Three at the Water Gate, as they returned to the Beis HaMikdash with the water they had drawn - teki'ah, teru'ah and teki'ah.
Three upon the Mizbe'ach: some explain that this refers to the time when they took the willow branches and stood them up against the Mizbe'ach, and others explain that it refers to the blasts sounded at the time of the water libation itself.
Nine for the Tamid offering, in their usual daily order.
And nine more for the second Tamid offering.
Nine for the Musaf, since on Sukkos a Musaf offering is brought.
Three to separate the people from their work, since it is Erev Shabbos.
Three to separate between holy and mundane.
It is worth noting that our Mishnah omits a detail we mentioned in the previous chapter: they would also sound blasts on the tenth step, yet the Mishnah here does not count those blasts, for whatever reason.
Erev Pesach that falls on Shabbos: the Gemara explains that on that day they would sound even more blasts, because of the blasts sounded at the time the Korban Pesach was offered, bringing the total to fifty seven. However, since this is something that occurs only rarely, the Mishnah did not count it.