Lunar/Solar Calendar Sources

(2) גרש ירחים — there are some fruits which the moon brings to maturity, these are cucumbers and melons (Sifrei Devarim 353:3).

(1) The four new years are: On the first of Nisan, the new year for the kings and for the festivals; On the first of Elul, the new year for the tithing of animals; Rabbi Eliezer and Rabbi Shimon say, on the first of Tishrei. On the first of Tishrei, the new year for years, for the Sabbatical years and for the Jubilee years and for the planting and for the vegetables. On the first of Shevat, the new year for the trees according to the words of the House of Shammai; The House of Hillel says, on the fifteenth thereof.

(11) On your new moons you shall present a burnt offering to the LORD: two bulls of the herd, one ram, and seven yearling lambs, without blemish. (12) As meal offering for each bull: three-tenths of a measure of choice flour with oil mixed in. As meal offering for each ram: two-tenths of a measure of choice flour with oil mixed in. (13) As meal offering for each lamb: a tenth of a measure of fine flour with oil mixed in. Such shall be the burnt offering of pleasing odor, an offering by fire to the LORD. (14) Their libations shall be: half a hin of wine for a bull, a third of a hin for a ram, and a quarter of a hin for a lamb. That shall be the monthly burnt offering for each new moon of the year. (15) And there shall be one goat as a sin offering to the LORD, to be offered in addition to the regular burnt offering and its libation. (16) In the first month, on the fourteenth day of the month, there shall be a passover sacrifice to the LORD,

This is the general principle: Any day on which work is permitted and prolonging the prayer service would delay the masses from doing their work (e.g., a public fast day and Tisha B'Av), only three people read from the Torah, so as not to lengthen the prayer service unnecessarily. But any day on which prolonging the prayer service would not constitute a deprivation of labor for the masses, (e.g., Rosh Chodesh and Chol Hamoed) four people read from the Torah.

(10) Come now, and let us go up against them, and destroy the covenant their God has made with them, their Sabbaths, new-moon [festivals], and circumcision.”...

(33) And seeing that this royal decree was issued in haste, they soon found a man who circumcised his son. And the man and his wife were brought before them, and they hung them opposite the child.

(34) There was also a woman who bore a son after the death of her husband, and she circumcised him when he was eight days old. And she went up on the wall of Jerusalem, bearing her circumcised son.

(35) And she cried out and said, “To you Bagris, the wicked, be it said ‘You plan to destroy the covenant that has been made with us, the covenant of our forefathers. Sabbath and the new-moon [festivals] and circumcision we will not abandon, neither we nor our children’s children.’ And she cast her son to the ground, and leaped down after him, and both died together. Many of the children of Israel did thus in those days rather than violate the covenant of their fathers.

(4) Aaron said to himself: If I tell Israel, Give me your gold and silver, they will bring it immediately; but if tell them, Give me the earrings of your wives, and your sons, the matter will fail, as it is said, "And Aaron said to them, Break off the golden rings" (ibid. 2). The women heard (this), but they were unwilling to give their earrings to their husbands; they responded: Ye desire to make abominations and images without any power to deliver. The Holy One gave the women their reward in this world and in the world to come. What reward did He give them in this world? That they should observe the New Moons more stringently than the men, and what reward will He give them in the world to come? They are destined to be renewed like the New Moons, as it is said, "Who satisfieth thy years with good things; so that thy youth is renewed like the eagle" (Ps. ciii. 5).

[The Talmud's reference to not working on Rosh Chodesh] is about women not working on Rosh Chodesh as we see (1) the Yerushalmi acknowledges the tradition of women not working on Rosh Chodesh as a valid minhag; (2) Pirkei D'Rebbi Eliezer attributes this to women's refusal to contribute their jewelry to the Eigal and (3) I heard from my brother that the holidays were established to correspond to the forefathers--Abraham, baked cakes (Gen. 18), hence Pesach, Isaac, is associated with the ram's horn of the Akeida, which sounded at matan torah, hence Shavuout, Jacob, made booths for his flock (Gen. 34) hence, Sukkot and the twelve days of Rosh Chodesh corresponded to the twelve tribes...but when the twelve tribes sinned at the Eigal it was taken from the men of the tribes and given to the women, because they did not participate.

“Rabbi Shimon ben Pazzi queries: ‘And God made the two great lights; as it reads ‘The large light, and the small light.’ The moon said to the Holy One, Blessed Be He, ‘Master of the Universe, How can two kings share one crown?’ He said to her, ‘Go and diminish yourself!’ She said to him: ‘Master of the universe, because I said a logical thing before you, I should diminish myself?’ He said to her, ‘Go and you will rule by day and by night’. She said to him, ‘What is the greatness in that, How does a lamp help in the daytime?’ He said to her: ‘Go! Israel will count through you the days and the years.’ She said to him, ‘Day is the primary unit of time, and I can’t be used to count for days, as it says “And let them be for signs of the seasons and days and years”.’ He said, “Go! And great people will be called by your name: ... Yaakov the Small, Shmuel the Small, David the Small." God saw that the moon was still not happy at the time. The Holy One said, “Bring an atonement on Me for I have diminished the moon.” And so that is what is meant when Rabbi Shimon ben Lakish said, “What is the difference in how the New Moon offering is written, “A he-goat on the new moon, FOR THE LORD?’ Because the Holy One is saying, ‘Let this he-goat be an atonement FOR ME, for the diminishment of the moon.”

(1) And the LORD spoke unto Moses and Aaron in the land of Egypt, saying: (2) ’This month shall be unto you the beginning of months; it shall be the first month of the year to you.

R. Aha b. Hanina also said in the name of R. Assi in R. Johanan's name: Whoever pronounces the blessing over the new moon in its due time welcomes, as it were, the presence of the Shechinah: for one passage states, "This month;" while elsewhere it is said, "This is my God, and I will glorify Him."

(1) Observe the month of Aviv, and keep Pesach unto the LORD your God; for in the month of Aviv the LORD your God brought you forth out of Egypt by night.

(1) A leap year is a year in which another month has been added. And we only ever add an Adar and make two Adars, an Adar Rishon (first Adar) and an Adar Sheini (Second Adar). And why do we add this month? Because of the spring time, so that the Passover will fall at that time, as it is said (Deuteronomy 16:1) "Guard the month of the spring", that this month should be in the spring. And if it wasn't for the addition of this month, Passover would sometimes come in the days of the sun (the summer) and sometimes in the days of the rain (the winter).

(1) שמור את חודש האביב, make sure that the month of Nissan always occurs in the spring, by manipulating the calendar, if necessary and inserting an extra month of Adar. By doing this the solar orbit (year) and the lunar orbits, (12 moons equaling a year) can be brought into line with each other.

ON the fourth day He connected together the two luminaries, of which one was not greater (in size) than the other. They were equal as regards their height, qualities, and illuminating powers, as it is said, "And God made the two great lights" (Gen. i. 16). Rivalry ensued between them, one said to the other, I am bigger than you are. The other rejoined, I am bigger than you are.

(2) What did the Holy One, blessed be He, do, so that there should be peace between them? He made the one larger and the other smaller, as it is said, "The greater light to rule the day,” and the lesser light to rule the night and the stars he also made"

The Sages taught in another baraita: When the sun is eclipsed, it is a bad omen for the other nations. When the moon is eclipsed, it is a bad omen for the enemies of the Jewish people. This is due to the fact that the Jewish people calculate their calendar primarily based on the moon, and the other nations calculate based on the sun.

(20) And Mordechai wrote these things, and sent letters to all the Jews that were in all the provinces of the king Achashverosh, both near and far, (21) to enjoin them that they should keep the fourteenth day of the month Adar, and the fifteenth day of the same, yearly, (22) the days wherein the Jews had rest from their enemies, and the month which was turned unto them from sorrow to gladness, and from mourning into a good day; that they should make them days of feasting and gladness, and of sending portions one to another, and gifts to the poor.