Except for the first mishnah (which really belongs in chapter 2), chapter 3 deals with the laws of the shofar. While the Torah calls the first of Tishrei "Yom teruah", the Sages were concerned about the lack of specificity concerning the nature and structure of the shofar. In these mishnayot, the Sages present their conclusions which then needed further refining in the Gemara. The Talmud, you might recall, consists of two parts: Mishnah and Gemara. The Mishnah is a collection of laws edited by Rabbi Yehudah HaNasi, circa 200 CE. The mishnayot were written in Hebrew and were debated by the Sages in the great study halls in Palestine (Yavneh) and the Babylonian diaspora. The "gemara", which means "completion" in Aramaic, is a running commentary (in Aramaic, not Hebrew!) on these discussions and was edited several hundred years later by Rav Ashi in Babylon. A separate Talmud (called the "Palestinian Talmud" or "Talmud Yerushalami") was developed as well. The "Babylonian Talmud" has been accepted by Ashkenazic Jews as the more authoritative.

Mishnah 1:

If the court itself and all Israel had seen it, or if the witnesses had been examined, but they did not manage to proclaim "It is sanctified", before it grew dark, then this is intercalated...If three persons saw it, and they compose the court, two of them must stand up and set their collegues besides a single one, and bear witness before them. and these must say "It is sanctified! It is sanctified!"; for a single person is not considered trustworthy by himself.

Mishnah 2:

All kinds of shaofar are valid except that of a cow because this is a "horn". Rabbi Yose says, But are not all shofars called horns? As it is said, "When they make a long blast with the ram's horn."

Mishnah 3:

The shofar for the New year was of a wild goat, straight, and its mouthpiece was overlaid with gold. And there were two trumpets at the sides. The shofar sounded a long note, but the trumpets a short one, for the duty of the day devolved on the shofar.

Mishnah 4:

On a fast day, they were of rams' horns, curved, their mouthpieces overlaid with silver. And there were two trumpets at the sides. The shofar sounded a short note but the trumpets prolonged, for the obligation of the day devolved upon the trumpets.

Commentary:

The first mishnah is leftover from chapter 2. If the court, which must consist of at least three people, includes the two witnesses, then they must excuse themselves from judging and testify before a new court selected for this purpose. The intercalation is due to the fact that the sanctification sets the new month not the observation. Thus, if the court neglected to sanctify Rosh Chodesh during the day, the month was extended (intercalated) to thirty days instead of twenty nine.

The remaining mishnayot in this grouping describe the shofar used in Temple times. Today, we only use the curved ram's horn for Rosh Hashanah. In Temple times, fast days were proclaimed with trumpets also. The use of the ram's horn is in commemoration of the 'akedah' in which a ram was sacrificed instead of Yitzchak. The opinion of Rabbi Yose in mishnah 2 is rejected as halachah. The horn of a bull or an ox is also invalid for use as a shofar.

The Rambam, comments on the shofar in his "Mishnah Torah":

"We are commanded in the Torah to hear the blasts of the shofar on Rosh Hashanah, as it is written (Bamidbar 29:1):'It is a day for you to blow (the shofar).' The shofar used on Rosh Hashanah and at the proclamation of a Jubilee must be the curved horn of the male sheep. All horns other than those of the male sheep are disqualified. Although the Torah does not expressly prescribe the blasting of the shofar on Rosh Hashanah, it does say so regarding the Jubilee:' You shall make proclamation with the blast of the shofar on the tenth day of the seventh month'(Vayikra 25:9). By way of tradition, it has been derived that just as the shofar is prescribed for proclaiming the Jubilee, so to ,the shofar must be sounded on Rosh Hashanah."

"In the Temple, on Rosh Hashanah, they used one shofar, flanked by two trumpets; the shofar sounding a long note and the trumpets a short note, since the duty of the day required the blast of the shofar. Why then were trumpets blown along with the shofar? Because it is written

(Tehillim 98:6):'With trumpets and the sound of the horn shout praise before the King, the Lord.' Elsewhere, only a shofar must be used on Rosh Hashanah."

In mishnah 4, the Priests used to sound the shofar on public fast days. During the Shemoneh Esrei, two Priests would sound the shofar and trumpets after the seventh benediction. The sound of the shofar is supposed to reach our inner soul and arouse us to seek "teshuvah." Starting on Rosh Chodesh Elul, the shofar is sounded in the daily morning service followed by a Pslam for "The Days of Awe". The shofar, we will learn, is not sounded on Shabbos.

Mishnah 5:

The Jubilee year was just like the New year regarding the blowing and the benedictions. Rabbi Yehidah says, On the New Year, they sounded on thise of rams, but on the Jubilee year, on those of goats.

Mishnah 6:

A shofar that split, and someone stuck it together, is unfit for use. If one cemented together the pieces of a shofar, this is invalid. If there is a hole in it and one stopped it up, if it hinders the blowing, it is not valid; but if not, it is valid.

Mishnah 7:

If someone blew in a well or in an underground masoned store room, or in a large cask, and one heard the sound of the shofar, he has fulfilled his obligation; but if he heard the sound of the echo, he has not fulfilled his obligation. And likewise, if one were passing behind a synagogue, or if his house was close to a synagogue, and he heard the sound of the shofar, or the reading of the megillah, if he concentrated his mind on it, he has fulfilled his obligation; but if not, he has not carried out his duty. Though the former heard and the latter heard, one directed his mind and the other did not direct his mind.

Mishnah 8:

"And it came to pass, when Moshe held up his hand, that Israel prevailed, etc." But could could the hands of Moshe wage a battle or lose a battle? This is rather to teach you that whenever Israel looked on high, and subjected their heart to their father in heaven, they prevailed; but ifnot, they fell. Likewise, you may explain the verse, "Make for thee a firey serpent and set it upon a pole, and it shall be that whosoever is bitten and looks at it, he shall live." But could the serpent kill or could the serpent keep alive? Only whenever israel looked on high, and subjected their heart to their Father in heaven, were they healed; but if not, they perished. A deaf mute, an imbecile, or a minor cannot assist the many to fulfill their duty. This is the general principle: Whoever is himself not liable to perform an act, cannot aid the many to carry out their obligation.

Commentary:

In mishnah 5, the ruling of rabbi Yehudah is rejected as halacha since only curved rams' horns are acceptable on Rosh Hashanah and the Jubilee year is no longer observed. In mishnah 6, the splitting of the shofar is lengthwise and it is still valid provided that the part spilt is clasped, with the mouthpiece protruding from the fist. Any damage cannot impair the tone of the shofar otherwise it is "possul"; disqualified.

Mishnah 7 discusses the concept of "kavannah" which means intention. One must hear the actual sound and not an echo (or a recording). The similarities between the hearing of the shofar and the hearing of the Megillah is interesting. In order to fulfill the mitzvah, one must be able to hear and understand what is involved. hence, a deaf person cannot technically, according to the mishnah, fulfill this obligation. It is unfortunate that the word "imbicile" is used in the translation, but the intent of the verse is that if a person is incapable of comprehending what is happening, then even if they hear the shofar (or the reading of the Megillah), they have not fulfilled the mitzvah.

We can compare this requirement to the reciting of the "Shema". Since the phrase uses the expression "Hear O Israel...", the Sages stated that in order to fulfill the mitzvah of the Shema, one must recite the words audibly enough so that he himself can hear them.

The concept of kavannah is an important one in Judaism. To concentrate our minds that what we are about to do is the fulfillment of a mitzvah from God, we usually say a "bracha". This transforms a mundane act, such as eating, into an act of Holiness. The blowing of the shofar and the reading of the Megillah are both preceded by a blessing. However, there is no explicit blessing before the reading of the Shema. By explicit, I mean a blessing that would involve the standard formula:

"Blessed are you, O lord, our God, King of the Universe, who has sanctified us and commanded us to recite the Shema".

This blessing is never said before the reading of the Shema (nor before the reading of the Pesach Haggadah). This formula is used before the blowing of the shofar (just change the last few words to "...comanded us to blow the shofar") and the reading of the Megillah. The formaul, as some of you may know, is silightly different before eating food, or washing hands, but it is similar. I think you get the point of this discussion. A mitzvah must be accompanied by a recognition that what you are doing has a purpose.

In mishnah 8 we see that the Sages did not take the verse from Shemot 17:11 literally. The Sages ask, could the act of Moshe raising or lowering hands decide the outcome of a battle? The intent of the verse, write the Sages, is that whenever Israel recognized that their battle and it's success rests with God, they prevailed. The second verse quoted in mishnah 8 comes from Bamidbar 21:8 and again the Sages question whether the image of the serpent can really cure a person. Rather, write the Sages, when Israel would concentrate their minds and undertsand that it was God who brought about the cure, then they were cured.

The last part of mishnah 8 discusses agency in Judaism. One cannot designate an agent to fulfill a ritual obligation if that agent is themselves ineligible to fulfill the obligation themselves. Minors cannot act on behalf of adults and, as we stated, a person who is incapable of understanding what they are doing, cannot act on behalf of someone else.

The Rambam has some interesting comments regarding the reading of the Megillah:

"Everyone is required to hear its reading: men, women, emancipated slaves, proselytes..."

"If a man read the megillah by heart, he has not fulfilled his obligation..."

"If a man read the Megillah without due intention, he has not discharged his duty..."

On the concept of agency and intention, the Rambam also writes:

"Anyone who is not required to perform a certain religious duty cannot act on behalf of another person who is so required...If one practices blowing the shofar, he does not discharge his duty; neither does the person hearing him practice. If a listener intends to fulfill his duty, but the one who blows the shofar does not intend to act on the listeners behalf, or if the latter has the proper intention and the listener does not, he has not discharged his duty. Both the listener and the one who blows the shofar must have proper intention.