The modern Hebrew calendar has been designed to ensure that certain holy days and festivals do not fall on certain days of the week. As a result, there are only four possible patterns of days on which festivals can fall. (Note that Jewish days start at sunset of the preceding day indicated in this article.) Hebrew week days Hebrew name Abbreviation Translation English equivalent Yom Rishon (יום ראשון) First day Sunset on Saturday to sunset on Sunday Yom Sheni (יום שני) Second day Sunset on Sunday to sunset on Monday Yom Shlishi (יום שלישי) Third day Sunset on Monday to sunset on Tuesday Yom Revii (יום רביעי) Fourth day Sunset on Tuesday to sunset on Wednesday Yom Hamishi (יום חמישי) Fifth day Sunset on Wednesday to sunset on Thursday Yom Shishi (יום שישי) Sixth day Sunset on Thursday to sunset on Friday Yom Shabbat (יום שבת) Sabbath day Sunset on Friday to sunset on Saturday

Reasons The modern Hebrew calendar has been arranged so that Yom Kippur does not fall on a Friday (Yom Shishi) or Sunday (Yom Rishon), and Hoshana Rabbah does not fall on Shabbat.This is the reason given by most halachic authorities, based on the Talmud, Rosh Hashanah 20b and Sukkah 43b. Maimonides (Mishneh Torah, Kiddush Hachodesh 7:7), however, writes that the arrangement was made (possible days alternating with impossible ones) in order to average out the difference between the mean and true lunar conjunctions. These rules have been instituted because Shabbat restrictions also apply to Yom Kippur, and if Yom Kippur were to fall on Friday (Yom Shishi), it would not be possible to make necessary preparations for Shabbat, including candle lighting, because the preceding day is Yom Kippur. Similarly, if Yom Kippur fell on a Sunday (Yom Rishon), it would not be possible to make the necessary preparations for Yom Kippur, including candle lighting, because the preceding day is Shabbat.The Talmud (Rosh Hashanah 20b) puts it differently: over two consecutive days of full Shabbat restrictions, vegetables would wilt (since they can't be cooked), and unburied corpses would putrefy. Also, the laws of Shabbat override those of Hoshana Rabbah (the seventh day of Sukkot), so that if Hoshana Rabbah were to fall on Shabbat certain rituals that are a part of Hoshana Rabbah services (such as carrying willows, which is work) could not be performed in that year.

As a consequence, in the case of Yom Kippur, which falls on 10 Tishrei and cannot fall on a Friday or Sunday, the days in Cheshvan and/or Kislev are adjusted so that Rosh Hashanah, which falls on 1 Tishrei, does not fall on a Wednesday (Yom Revii) or Friday (Yom Shishi). And, in the case of Hoshana Rabbah, which falls on 21 Tishrei and cannot fall on a Saturday, Rosh Hashanah cannot be on a Sunday. This leaves only four days on which Rosh Hashanah is allowed to fall: Monday, Tuesday, Thursday and Saturday (i.e. the first, second, or fourth days of the week, or Shabbat), which are also referred as the "four gates" ().

The four gates Since three arrangements cannot occur within the fixed calendar, most holidays can each occur on one of four possible days.

All the major holy days and festivals fall in the months of Nisan through Tishrei, months one to seven. These months always have the same number of days, alternating 30 and 29. The next two months are Cheshvan and Kislev, months eight and nine. Both or either of these months can have either 29 or 30 days, allowing for adjustments to be made and the schedule in the coming year to be manipulated. (On a regular year, Cheshvan has 29 days and Kislev has 30 days). The months of Tevet and Shevat, months ten and eleven, have 29 and 30 days respectively. Finally, in a regular year the month of Adar has 29 days, while in a leap year Adar I of 30 days is added before the regular Adar, which becomes Adar II of 29 days. The result is that the period from 1 Tevet to 29 Cheshvan is fixed, except that in a leap year Adar I of 30 days is added; and all adjustments are made using 29/30 Cheshvan and/or 29/30 Kislev.

The period from 1 Adar (or Adar II, in leap years) to 29 Cheshvan contains all of the festivals specified in the Bible - Purim (14 Adar), Pesach (15 Nisan), Shavuot (6 Sivan), Rosh Hashanah (1 Tishrei), Yom Kippur (10 Tishrei), Sukkot (15 Tishrei), and Shemini Atzeret (22 Tishrei). This period is fixed, during which no adjustments are made. The result is that all dates from 1 Nisan through 29 (or 30) Cheshvan can each fall on one of four days of the week. Dates during Kislev can fall on any of six days of the week; during Tevet and Shevat, five days; and dates during Adar (or Adar I and II, in leap years) can each fall on one of four days of the week.

GateFrequencyPurimPassover(first day)Yom HaZikaronYom Ha'atzmautShavuot(first day)17 Tammuz/Tisha B'AvRosh Hashanah/Sukkot/Shmini Atzeret/(first day)Yom KippurHanukkah(first day)10 TevetTu BishvatPurim Katan (only in leap years)Gate that follows131.9%SunTueMon*Tue*WedTueThuSatWed or ThuWed, Thu, or FriTue, Wed, or ThuWed or FriGates 1, 3, or 4228.6%TueThuTueWedFriThuSatMonFri or SatFri or SunThu or SatFri or SunGates 1, 2, or 4328.0%ThuSatWed†Thu†SunSun*MonWedSun or MonSun or TueSat or MonSun or TueGates 1, 2, or 3411.5%FriSunWed‡Thu‡MonSunTueThuMonTueMonTueGates 2 or 3 †Pushed back from Thu/Fri‡Pushed back from Fri/Sat *Postponed from Shabbat

With each gate, some unusual effects occur.

Gate 1 (31.9%) Neither the Three Pilgrimage Festivals nor Rosh Hashanah coincide with the Sabbath nor fall on Sunday, therefore no additions to the Yom Tov kiddush (i.e. the Sabbath additions and havdalah) are said during the course of the year. Since Purim falls on Sunday, the 13th of Adar, known as the Fast of Esther, falls on Saturday. Usually, fasts other than Yom Kippur are postponed to the following Sunday. But as this Sunday is Purim, and fasts are usually not observed on Friday, the fast is advanced to the prior Thursday (the 11th of Adar). Vayehi Noam, Psalm 91 and the "verses of blessing" are recited at Maariv on Purim, due to it immediately following the Sabbath. (V'Ata Kadosh is recited at Maariv on Purim even on weeknights.) This is the only instance in which there is a Sabbath of Chol HaMoed for both Passover and Sukkot. Yom HaZikaron is postponed from Sunday to Monday, and Yom Ha'atzmaut is postponed from Monday to Tuesday, so that preparations cannot interfere with Shabbat. No leniencies are made for the observance of Tisha B'Av nor the Tenth of Av. During Tishrei, three holidays start on Thursday. In the diaspora, the eruv tavshilin is prepared thrice. (In Israel, it is only made on the eve of Rosh Hashanah.) In Israel, this is the only occasion with a "three-day holiday" (the two days of Rosh Hashanah followed by the Sabbath). This is the only gate in the Diaspora to contain multiple "three-day holidays." Due to immediately following Rosh Hashanah, an abridged form of Kabbalat Shabbat is recited at Maariv on Shabbat Shuvah. The Fast of Gedaliah falls on Saturday. Since fasts other than Yom Kippur are not observed on Saturday, this is observed on the following Sunday. This leaves an interval of just five days between fasts, the shortest ever on the Jewish Calendar (other than the Fast of Behav). Vayehi Noam, Psalm 91 and V'Ata Kadosh are recited on Motza'ei Shabbat Shuvah, due to their occurrence being exactly one week before Yom Kippur. Ashkenazim recite Avinu Malkeinu on the eve of Yom Kippur, due to it largely being omitted on Yom Kippur itself. Yom Kippur occurs on Saturday. This is the only occurrence in which a fast is ever observed on Saturday. Ashkenazim do not recite Avinu Malkeinu except during Ne'ila. This is also the only case in which the following Torah reading (in this case, V'Zot HaBerachah) is not read on Saturday afternoon and in which a haftarah is read on Saturday afternoon. The "verses of blessing" are recited on the expiry of Yom Kippur, due to it coinciding with the Sabbath. (Vayehi Noam, Psalm 91 and V'Ata Kadosh are not recited, because Sukkot falls before the upcoming Sabbath.) This is the only instance in which Bereshit is not read during the Torah reading on the preceding Thursday. If the previous gate was also 1, this is a leap year; and, the following occur: Vayakhel is read as it does not coincide with Parshat Shekalim. (Parshat Shekalim instead coincides with Pekudei.) This is one of three cases in which Vayakhel'''s proper haftarah is read. (The others are during a Gate 4 leap year and during Gate 2 on the last day of Hanukkah when both Cheshvan and Kislev have 30 days.)Chukat coincides with Rosh Chodesh Tammuz (rather than Korach in other Gate 1 years). Due to the lack of yom tov sheni shel galuyot, this is the only case in Israel in which the haftarah of Chukat is omitted. (It is also omitted in the Diaspora during Gate 2 due to being paired with Balak.)Pinechas falls on 14 Tammuz (meaning that its proper haftarah is read), and Matot and Masei are read separately. This also means that Nitzavim-Vayelech are the only doubled-up parshiot during the year (Tishrei-Elul). If this is a leap year and the previous gate was 2, the following occur: According to the custom that the haftarah of Acharei Mot is read for Kedoshim whenever Acharei Mot is pre-empted by a special haftarah, the haftarah of Kedoshim is read (the rarest-read haftarah). This is because Acharei Mot-Kedoshim are doubled up in non-leap years; and, in other leap years, either Kedoshim coincides with Rosh Chodesh Iyar (Gate 2), Acharei Mot (or Kedoshim in Israel) falls on the eve of Rosh Chodesh Iyar (Gate 3), or Acharei Mot coincides with Shabbat HaGadol (Gate 1-1 and Gate 4).Tazria's proper haftarah is read. If the previous gate was 3, this is not a leap year. If Cheshvan has 29 days, then Kislev will have either 29 or 30 days. This is the only occurrence in which it happens. If both Cheshvan and Kislev have 30 days, then the Tenth of Tevet will occur on Friday, one of two public fasts that can possibly be observed on a Friday (the other being the Fast of the Firstborn). The fast is not broken until nightfall, after the Sabbath begins. If both Cheshvan and Kislev have 30 days, then Purim Katan, the holiday that only occurs in leap years, will occur on Friday.

Gate 2 (28.6%) The eruv tavshilin is prepared prior to the first day Passover in the diaspora and prior to Shavuot in both the diaspora and Israel.Yom HaZikaron and Yom Ha'atzmaut are actually observed on 4 Iyar and 5 Iyar respectively.Yom tov sheni shel galuyot for Shavuot falls on Saturday, which results in the weekly Torah portion between Israel and the diaspora to be out of sync between Naso and Balak. To compensate for this, Chukat-Balak are doubled up in the diaspora. (In Israel, these two parshiot are always read separately.) In the diaspora, the usual Torah reading of the second day of Shavuot (Deuteronomy 15:19–16:17) is extended to its length on Shemini Atzeret (Deuteronomy 14:22–16:17) to accommodate the seven readings on the Sabbath.Vayehi Noam, Psalm 91, V'Ata Kadosh and the "verses of blessing" are recited on the expiry of Shavuot in the Diaspora, due to it coinciding with the Sabbath. Following Tisha B'Av, bathing, laundering, shaving, and taking a haircut are all permitted immediately after the fast, in preparation for the Sabbath. These, along with the rest of the restrictions of the Nine Days, are normally postponed until midday on the Tenth of Av. Rosh Hashanah, Sukkot, and Shemini Atzeret begin on Saturday. On Rosh Hashanah, since blowing the Shofar is prohibited on the Sabbath, the shofar is blown only on the second day. Ashkenazim do not recite Avinu Malkeinu on Saturday. In Ashkenazic communities, Tashlich is also postponed to the second day. On Sukkot, the Four Species, which are not taken on the Sabbath, are unused on the first day.