ויאמר ה' אל משה ואל אהרן בארץ מצרים לאמר החדש הזה לכם ראש חדשים ראשון הוא לכם לחדשי השנה
God said to Moses and Aaron in the land of Egypt: This month shall mark for you the beginning of the months; it shall be the first of the months of the year for you.
החדש הזה — He showed him the moon in the first stage of its renewal, and He said to him, “The time when the moon renews itself thus, shall be unto you the beginning of the month”. (The translation therefore is: “This stage of renewal (חדש) shall be the moment of beginning the months”; cf. Mekhilta d'Rabbi Yishmael 12:2:2). But no Scriptural verse can lose its literal meaning, and He really spoke this in reference to the month Nisan: this month shall be the beginning in the order of counting the months, so that Iyar shall be called the second, Sivan the third.
החדש הזה לכם ראש חדשים מכאן ואילך יהיו החדשים שלכם, לעשות בהם כרצונכם, אבל בימי השעבוד לא היו ימיכם שלכם, אבל היו לעבודת אחרים ורצונם, לפיכך ראשון הוא לכם לחדשי השנה. כי בו התחיל מציאותכם הבחיריי:
from now on these months will be yours, to do with as you like. [you have My authority to organise your own calendar] This is by way of contrast to the years when you were enslaved when you had no control over your time or timetable at all. [Freedom, i.e. retirement from the “rat race,” means being able to formulate one’s own timetable. Ed.] While you were enslaved, your days, hours, minutes even, were always at the beck and call of your taskmasters.
(א) החדש הזה. ... והשנה באמת היא לשמש לבדו. כי הוא המוליד זמני קור וחום וקיץ וחורף, שהם ד' תקופות השנה...והוא ילך בגלגלו שס''ה ימים וקרוב מרביעית יום עד שובו פעם שנית ובעבור זה נקרא שנה. והנה אין ללבנה שנה כלל. כאשר אין לשמש חדש כלל.
דמפני שלשה דברים מעברין השנה שיהיו ב' אדרין, [פ'א'ת' סימן], מפני פירות, כשרואין בית דין שפירות האילן לא יתבשלו עדיין קודם עצרת, ולא יוכלו להביא אז בכורים, ויצטרכו הבעלי בתים לחזור ולעלות להביאן. ומפני אביב, כשרואין שהאביב רחוק, שלא תתבשל התבואה בפסח, להביא העומר, והרי כתיב בפסח שיהיה בחודש האביב [שמות י"ג]. ומפני תקופה. כשרואין ב"ד שתקופת החמה שבטבת, תמשך עד ט"ז בניסן, ויהיה א"כ הבאת העומר תוך תקופת טבת, או כשרואין שתמשך תקופת החמה שבתמוז, עד אחר סוכות, והרי נקרא חג האסיף. ולכל הנך צריך אומד ב"ד יפה [דגם ימי התקופה, אע"ג דידוע מספר ימיו, עכ"פ יש ג' מיני חשבונות בתקופה אם תקופת רב אדא, או תקופת שמואל, או תקופה אמצעית. כמו שנבאר במקום אחר בס"ד, להכי צריך אומדנת כ"ד על זה באיזה תקופה יחשבו]:
The Beginning of the Jewish Calendar By Bernard Dickman, Ḥakira, the Flatbush Journal of Jewish Law and Thought, Vol. 8
Historically, Sanhedrin decided when a month started and when a leap year should be added. Sometime after the destruction of the second Temple a fixed calendar was put in place... R. Avraham bar Chiyya in Sefer ha-Ibbur (1123) says that in 992 R. Hai Gaon claimed that the calendar was created in Eretz Yisrael under the leadership of Hillel II in 358/9. We do not have a copy of the cited R. Hai Gaon’s work. The earliest confirmed existence of our calendar dates to the 12th century... Many calendar historians question this dating and some say that the fixed calendar was not finalized until the 800s. A noted expert, Engineer Yaaqov Loewinger, reviews this controversy and argues that astronomical data are consistent with a 358/9 dating of the calendar.
A Short History of the Jewish Fixed Calendar: The Origin of the Molad By: J. Jean Ajdler, Ḥakira, the Flatbush Journal of Jewish Law and Thought, Vol. 20
The Letter of the Resh Galuta of 836 C.E.
J. Mann discovered an exceptional document from the Cairo Geniza and published it in 1922. This document was called the letter of the Resh Galuta, because its author appeared to be a very important and authoritative personality. This letter reveals that Passover (15 Nissan 4596) of the year 836 C.E. was due to occur on a Tuesday, March 21, 836 while according to the present-day calendar, it should have occurred on Thursday, March 23, 836.
The Dispute of R’ Sa’adia Gaon and Ben Meir
On Hoshana Rabbah 921 C.E. The Palestinian Gaon Ben Meir or his son proclaimed on the Mount of Olives that the months of Marheshvan and Kislev of 4682 would be defective. As a result Passover 922 would fall on Sunday instead of the following Tuesday if the year had been made full. And in fact, in 922 the Jews of Palestine and probably the communities in Egypt celebrated Passover on Sunday, two days before the Jews of Babylonia. This split between the communities of Palestine and Babylonia caused considerable agitation throughout world Jewry. References to this event can be found in non-Jewish documents. The Syrian Elias of Nissibis wrote that in the year 1232 of the Seleucid era dissension broke out between the Jews of the West (Palestine) and those of the East (Babylonia) with regard to the calculation of their holiday. The Jews of the West celebrated Rosh Hashanah 4683 on a Tuesday and those of the East celebrated it on the next Thursday. Similarly the Karaite Sahal ben Mazliah134 also referred this event and sought to prove from this controversy that the rabbinic calendar calculations were groundless....
The conclusion of the R’ Saadia-Ben Meir controversy at the advantage of the Babylonians had a tremendous consequence at the level of the unity of the Jewish people. Before 922 C.E, the Jewish calendar was communicated by the Palestinian Gaon on an annual or multi-annual basis. It appears that from about 838 onwards, the Babylonians were able to make their own calculations and during the period of about eighty years preceding 922 C.E. they always agreed with the keviyah sent from Palestine.... Only after the end of the dispute, did the rules of the calendar and the Four Gates Table became universally known and only then was the complete unity of the Jewish communities of the Diaspora achieved in the celebration of their festivals...
It is interesting to note that this important event of 922-924 remained unknown until the beginning of the twentieth century, until the discovery and the study of the documents of the Cairo Geniza. It is a fact that R’ Sherira Gaon and R’ Hai Gaon did not mention the event at all. At first glance we could think that the leaders of the Babylonian community did not want to leave a remembrance of this schism for posterity; it could have thrown a shadow on the authority of the Jewish calendar and on the doctrine of its Sinaïtic origin taught by R’ Sa’adia Gaon. This, however, is not the case. We know that R’ Sa’adia Gaon wrote two books: הזיכרון ספר and המועדים ספר .The first book was intended to be read publicly in order to recall the event. The second book was probably a treatise on the festivals and the Jewish calendar and it probably also mentioned the events of the famous dispute of 922- 924 in order to prevent the possibility of a new schism in the future. It was the fear of maḥaloquet that prompted him to write the first and probably the second book. R’ Sa’adia’s works on the calendar are lost, although they appear to have been well known in the middle ages (Rashi, R’ Tam and R’ Jacob ben Shimshon refer to it). It is a mystery why these two books did not survive.
By contrast, it is evident that the Palestinian side was not interested to speak about this event and indeed they never did mention this dispute again... The present day calendar was the calendar of the Babylonians since about 838 C.E. that emerged after the dispute of 922-924. This calendar did not change any more.
כי אתא עולא אמר עברוה לאלול אמר עולא ידעי חברין בבלאי מאי טיבותא עבדינן בהדייהו מאי טיבותא עולא אמר משום ירקיא רבי אחא בר חנינא אמר משום מתיא... מאי שנא לדידן אפילו לדידהו נמי לדידן חביל לן עלמא לדידהו לא חביל להו עלמא
§ It is related that when Ulla came from Eretz Yisrael to Babylonia, he said: This year they added an extra day to the month of Elul. Ulla continued and said: Do our Babylonian colleagues understand what benefit we did for them? We pushed off Rosh HaShana for a day, so that the Festival would not occur adjacent to Shabbat. The Gemara asks: What is the benefit in having a weekday between Shabbat and a Festival? Ulla said: Due to the vegetables that would not be picked for two days and those picked beforehand that would no longer be fresh. Rabbi Aḥa bar Ḥanina said: Due to the dead who would not be buried for two days and consequently would begin to decompose... The Gemara asks:... what is different about those who live in Babylonia and those who live in Eretz Yisrael? Why did Ulla specifically say that adding an extra day to Elul was beneficial to us, in Babylonia; it was beneficial to them as well. The Gemara answers: For us in Babylonia the weather is very hot, and so vegetables wither and corpses decompose quickly. But for them in Eretz Yisrael, the weather is not as hot, and vegetables and corpses can be kept for two days.
ערבה שבעה כיצד: ערבה בשביעי מ"ט דחיא שבת א"ר יוחנן כדי לפרסמה שהיא מן התורה... אי הכי האידנא נמי לידחי... כי אתא בר הדיא אמר לא איקלע
§ The mishna continues: The altar is encircled with the willow branch for seven days. How so? If the seventh day of performing the mitzva of the willow branch occurs on Shabbat, since on that day the mitzva of the willow branch is a mitzva by Torah law, it overrides Shabbat and the mitzva of the willow branch is then performed seven days. The Gemara asks: With regard to the mitzva of the willow branch on the seventh day, what is the reason that it overrides Shabbat? Rabbi Yoḥanan said: It is in order to publicize that it is a mitzva that applies by Torah law, since it is not written explicitly in the Torah. ... The Gemara asks: If so, i.e., if the mitzva of the willow branch is so significant that it overrides Shabbat, let it override Shabbat today as well, even though the Temple is not standing ...When bar Hedya came from Eretz Yisrael to Babylonia he said: That is not a practical question, as the seventh day does not coincide with Shabbat, since the Sages fixed the calendar to avoid that possibility.
לא אד״ו ראש
לא בד״ו פסח
Holidays based on first day of Pesach:
א=תשעה באב
ב=שבועות
ג=ראש השנה
ד=קריאת התורה
ה=צום כיפור
ו=פורים
ז=עצמאות
אלו הימי' שאין קובעי' בהם המועדי' לא אד"ו ר"ה ולא אג"ו י"ה לא זב"ד פורים לא בד"ו פסח ולא גה"ז עצרת והו"ר לא ג' חנוכ' ולא אג"ו צום אסתר ולא בד"ו צום תמוז ואב. לעולם ביום שיהיה פורים יהיה ל"ג לעומר וסימן פל"ג וביום שיהיה חנוכה יהיה עצרת:
These are the days on which the holidays may not fall: Rosh Hashanah not on Sunday, Wednesday or Shabbat; Yom Kippur - not on Sunday, Tuesday, or Friday; Purim - not on Shabbat, Monday or Wednesday; Pesach - not on Monday, Wednesday or Friday; Atzeret(Shavuot) and Hoshanah Rabbah - not on Tuesday, Thursday or Shabbat; Chanukah - not on Tuesday; Taanit Esther - not on Sunday, Tuesday or Friday; 17th Tammuz and Tisha b'Av - not on Monday, Wednesday and Shabbat; The day on which Purim is always the day of the week as Lag b'Omer, and the sign is P'LaG; and the day on which Chanukah falls will also fall Atzeret(Shavuot).
The Beginning of the Jewish Calendar By Bernard Dickman, Ḥakira, the Flatbush Journal of Jewish Law and Thought, Vol. 8
The Jewish calendar is a lunisolar calendar consisting of 12 months annually of 29 or 30 days. An extra leap month of 30 days is added every 2 or 3 years (7 leap months in 19 years) for a total of 235 lunar months in 19 years. This 19-year cycle is called the Metonic cycle and results in the 19 Jewish years approximating 19 solar years. In this way, the Jewish holidays are always in the same season and vary by less than a month in the solar calendar.
...
7 in 19
A key component of the Jewish calendar is the molad, or average conjunction, of each new month. The timing of the molad of Tishrei determines when Rosh Hashanah occurs. The molad is calculated by taking the molad of the Tishrei at creation... and adding the average time between months (29 days, 12 hours, 44 minutes and 3.33 seconds) for every month until we get to the desired month. This requires one to know how many years and months have passed since creation. The number of years we know based on our Jewish calendar. However, we do not know which years had a leap month. A basic assumption of the Jewish calendar is that it has averaged 7 leap months every 19 years. While there may have been 19-year periods with six or eight leap months, over the entire time span since creation, the Jewish calendar assumes that there have been exactly 7 leap months for every 19 years.
The 19-year cycle:
גו״ח א״ד ז״ט
Month Lengths
| Month | Length |
|---|---|
| Tishrei | 30 |
| Cheshvan | 29 or 30 |
| Kislev | 29 or 30 |
| Tevet | 29 |
| Shevat | 30 |
| Adar | 29 |
| (Adar I) | 30 |
| (Adar II) | 29 |
| Nisan | 30 |
| Iyar | 29 |
| Sivan | 30 |
| Tamuz | 29 |
| Av | 30 |
| Elul | 29 |
The Hebrew year can be one of six different lengths, depending on whether or not its a leap year and the length of Cheshvan and Kislev.
| Months | Cheshvan | Kislev | Type | Year Len. |
|---|---|---|---|---|
| 12 (Regular) | 29 | 29 | Chaser | 353 |
| 12 (Regular) | 29 | 30 | Kesidran | 354 |
| 12 (Regular) | 30 | 30 | Malei | 355 |
| 13 (Leap) | 29 | 29 | Chaser | 383 |
| 13 (Leap) | 29 | 30 | Kesidran | 384 |
| 13 (Leap) | 30 | 30 | Malei | 385 |
The Four Dechiyot
The Jewish Calendar and the Torah 4th Ed. by James Shneer
Rule 1
If the molad of Tishrei, the calculated new moon, occurs after hour 18 (noon), Tishrei 1, Rosh Hashanah, is postponed by one day. This is an artifact of the old days which required visual sighting of the lunar crescent . It is assumed that if the molad occurs after noon, the lunar crescent cannot be sighted until after 6 P.M., which will then be on the following day.
Rule 2
Tishrei 1, Rosh Hashanah, cannot begin on a Wednesday, a Friday or Sunday… After the other calculations, if Rosh Hashanah were to fall on Wednesday, Friday, or Sunday, it is postponed to the following day. Thus Rosh Hashanah can occur only on Monday, Tuesday, Thursday, or Saturday.
The Purpose of the Hebrew Calendar Rosh Hashanah Dehiyyot (Postponements of the First Day of Tishrei)
by Dr. Irv Bromberg (https://individual.utoronto.ca/kalendis/hebrew/postpone.htm)
Rule 3
For the fixed arithmetic traditional Hebrew calendar, if the molad of Tishrei of a non-leap year falls on Tuesday at or after 9h 204p then the next molad of Tishrei will be 12 molad intervals later, which will place it at or after noon on Shabbat (Saturday), which will be postponed to Sunday, but that weekday is not allowed, or if the molad falls at or after 15h 204p then the next molad of Tishrei will land directly on Sunday — either way Rosh Hashanah will be postponed to Monday. Either of these postponements would cause this year length to be 356 days, but the longest possible length of a non-leap year is 355 days (where Cheshvan and Kislev both are full 30-day months). Therefore Rosh Hashanah this year is postponed from Tuesday to Wednesday, and because Wednesday is not allowed (see rule #2, above) it is postponed again to Thursday, making this year an acceptable 354 days.
Rule 4
For the fixed arithmetic traditional Hebrew calendar, if the molad of Tishrei falls on Monday at or after 15h 589p and the prior year was a leap year, then the previous molad of Tishrei would have been 13 molad intervals earlier, which would have placed it at or after noon on Tuesday, which would have been postponed to Wednesday, but that weekday is not allowed, so it would have been again postponed to Thursday. This would have caused that prior year length to be only 382 days, but the shortest possible length of a leap year is 383 days (where Cheshvan and Kislev both are deficient 29-day months). Therefore Rosh Hashanah this year is postponed from Monday to Tuesday, making the prior year an acceptable 383 days.
A Short History of the Jewish Fixed Calendar: The Origin of the Molad By: J. Jean Ajdler, Ḥakira, the Flatbush Journal of Jewish Law and Thought, Vol. 20
The Four Gates Table is a Babylonian invention from the 9th century. It represents a higher degree of sophistication and knowledge of the rules of the calendar. It allows knowing the keviyah of a year by the knowledge of its Molad and its rank in the cycle of 19 years.
Maimonides did not describe this method in Hilkhot Kiddush haHodesh. He must find the day of 1 Tishrei of two consecutive years in order to find the characteristics of the first year. R’ Abraham ibn Ezra worked the same way in his Sefer ha-Ibbur.
The Four Gates Table is mentioned in a letter of R’ Sa’adia Gaon related to the dispute. He also gave the detailed rules of the Four Gates Table. We also have a description of the Four Gates Table in a poem of R’ Yose ben al-Naharwani. The Four Gates was thus well-established knowledge in Babylonia. The Four Gates Table was thoroughly examined by R’ Abraham bar Ḥiyya in Sefer ha-Ibbur and in R’ Isaac Israeli’s Yessod Olam. In the supplement at the end of the second volume of Maḥzor Vitry we find the table of the Four Gates according to the molad of the preceding Nissan.
