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From the Holman Bible Dictionary:

Hebrew Lunar Calendar, of Feasts and Fasts

The Old Testament 
Mentions days,  months,  and years,  the basic elements of a calendar;  but it has no prescription for regulating one. It was in the rabbinical period that the written treatise on Jewish traditions,  Rosh Hashanah,  a part of the Mishna, organized the biblical data into the detailed calendrical system that the Jews observe today. 

The earliest practice was to use the Canaanite month-names, of which four survive in the Bible: 

Abib March-April
Ziv April-May
Ethanim September-October
Bul October-November

(Ex 13:4; 23:15; 34:18; 1 Kings 6:1,37-38; 8:3).  The other Canaanite months are known from Phoenician inscriptions.  These are all agricultural names and reflect a seasonal pattern of reckoning, as in the Gezer calendar.

The usual practice in the Old Testament is to simply number the months from first to twelfth. Some of these numbered months are found in the passages mentioned above, hence the practice must be at least as early as the time of the Israelite monarchy. Because the first month is always in the spring, we must trace this practice back to the patriarchs, who would have learned it in Mesopotamia (Gen 11:31).

When the Jews returned from Babylonian Exile, they brought with them the names of the Babylonian calendar, at the same time counting the new year from the spring. Although the rabbis returned to an autumnal new year, Judaism retains these Babylonian names as its own: 

Nisan March-April
Iyyar April-May
Sivan May-June
Tammuz June-July
Ab July-August
Elul August-September
Tishri  September-October
Marcheshvan October-November
Chislev November-December
Tebeth December-January
Shebat  January-February
Adar February-March
WeAdar (Adar) The intercalated year

The New Testament
We can assume that what the rabbis codified was in general practice among the Jews of the first century,  the time of Christ and the apostles,  but the New Testament offers little direct calendrical data.  Periods into which certain important events are dated mention not the day and month,  but the name of one or another of the ancient Jewish festivals: 

The Passover Usually in the passion pericopes, 
Matt 26; Mark 14:1; Luke 22:1; John 18:1-19:42; otherwise at Luke 2:41 and at seven passages in John preceding the passion
Day of Pentecost The Jewish feast of Weeks
Acts 2:1; 20:16; 1 Cor 16:8
Feast of Dedication  Jewish Hanakkah
John 10:22-23

The New Testament offers no evidence that the Jews inside or outside Palestine observed the Roman calendar commencing on January 1, but the apocryphal book 1 Maccabees and the Jewish historian Josephus do substitute Greek (Macedonian) month names for Jewish month names. We may assume that in business dealings Greek-speaking Jews made free use of them. This was little more than a linguistic convention, however, since the Greek months corresponded with the Jewish months, making little difference in the basis of calendrical reckoning.

(from Holman Bible Dictionary. (c) Copyright 1991 by Holman Bible Publishers. All rights reserved., Electronic Database)

Hebrew Lunar Calendar, of Feasts and Fasts

From the McClintock and Strong Encyclopedia:

The year of the Hebrews is composed of  twelve (and occasionally of thirteen) lunar months,  of thirty and twenty-nine days alternately.

The Civil Year begins in Autumn
The Sacred Year begins in Spring

The Jews had calendars anciently wherein were noted

All the Feasts
All the Fasts
All the Days

On which they celebrated the memory of any great event that had happened to the nation (Zech 8:19; Est 8:6, in Graec.)
These ancient calendars are sometimes quoted in the Talmud (Mishna, Taanith, 8),  but the rabbins acknowledge that they are not now in being (see Maimonides and Bartenora, in loc.). Those that we have now, whether printed or in manuscript, are not very ancient (see Genebrar. Bibliot. Rabinic. p. 319; Buxtorf, Levit. Talmnud. p. 1046; Bartolocci, Bibl. Rabbinic. 2:550; Lamy's Introduction to the Scripture; and Plantav. Isagog. Rabbin. ad fin.). 

That which passes for the oldest is  Megillath Taanith,  "the volume of affliction," which contains the days of feasting and fasting heretofore in use among the Jews,  which are not now observed,  nor are they in the common calendars.  

Abib or Nisan

The first month of the sacred year
The seventh month of the civil year
30 Days March/April
1st New moon A fast for the death of the sons of Aaron (Lev 10:1,2)
10th   A fast for the death of Miriam, sister of Moses (Num 20:1)
Also in memory of the scarcity of water that happened, after her death, to the children of Israel in the desert of Kadesh (Num 20:2)
On this day every one provided himself a lamb or a kid, preparatory to the following Passover.
14th Passover
Lamb killed
On the evening of this day they killed the paschal lamb; 
they began to use unleavened bread, 
and ceased from all servile labor.
15th Feast of
The solemnity of the Passover, with its octave
The first day of Unleavened Bread, a day of rest; 
they ate none but unleavened bread during eight days.
After sunset they gathered a sheaf of barley, which they brought into the Temple (Menachot. 6:3).
Supplication for the reign of the spring (Geneb.).
16th Feast of

Beginning of

On the second day of the feast they offered the barley which they had provided the evening before, as the First-Fruits of the harvest; after that time it was allowed to put the sickle to the corn.
The beginning of harvest.
From this day they began to count fifty days to Pentecost. 
21st End  of Passover The octave (8th day) of the feast of the Passover; 
the end of unleavened bread. 
This day is held more solemn than 'the other days of the octave, yet they did not refrain from manual labor on it.
26th   A fast for the death of Joshua (Josh 24:29)
30th   Alternate of the first new moon of the succeeding month.


The second month of the sacred year
The eighth month of the civil year
29 Days April/May
1st New moon  
6th   A fast of three days for excesses committed during the feast of the Passover That is, on the Monday, Thursday, and the Monday following.
(Calendar Barto locci).
7th   The dedication of the Temple, when the Asmonaeans consecrated it anew, after the persecutions of the Greeks (Meqill. Taanith, 100:2).
10th   A fast for the death of the high-priest Eli, 
and for the capture of the ark by the Philistines.
14th Second
The second Passover, in favor of those who could not celebrate the first, on the 15th of the foregoing month.
23rd   A feast for the taking of the city of Gaza by Simon Maccabaeus 
(Calend. Scalig.; 1 Macc. 13:43, 44); 
or for the taking and purification of the citadel of Jerusalem by the Maccabees (Calendar of Sigonius; 1 Macc. 13:49, 53; 16:7, 36); 
A feast for the expulsion of the Caraites out of Jerusalem by the Asmonseans or Maccabees (leg. Taanith; See TEBETH 28).
27th   A feast for the expulsion of the Galilseans, or those who attempted to set up crowns over the gates of their temples and of their houses, and even on the heads of their oxen and asses, and to sing hymns in honor of false gods. The Maccabees drove them out of Judea and Jerusalem, and appointed this feast to perpetuate the memory of their expulsion (Megill. Taanith).
28th   A fast for the death of the prophet Samuel (1 Sam 25:1)


The third month of the sacred year
The ninth month of the civil year
30 Days May/June
1st New moon  
6th Pentecost Pentecost, the fiftieth day after the Passover
Feast of Weeks Also the Feast of Weeks, because it happened seven weeks after the Passover.
15th &
  A feast to celebrate the victory of the Maccabees over the people of Bethsan (1 Macc. 5:52; 12:40, 41; Megill. Taanitm).
17th   A feast for the taking of Cesarea by the Asmonseans, who drove the pagans out, and settled the Jews there (Megill. Taanith).
22nd   A fast in memory of the prohibition by Jeroboam, son of Nebat, to his subjects, forbidding them to carry their first-fruits to Jerusalem (1 Kings 12:27).
25th   A fast in commemoration of the death of the rabbins Simeori, son of Gamaliel; Ishmael, son of Elisha; and Chanina, the high-priest's deputy.
A feast in honor of the solemn judgment pronounced in favor of the Jews by Alexander the Great against the Ishmaelites, who, by virtue of their birthright, maintain a possession of the land of Canaan; against the Canaanites, who claimed the same as being the original possessors; and against the Egyptians, who demanded restitution of the vessels and other things borrowed by the Hebrews when they left Egypt (see Mlegillath Taanith)
A feast for the expulsion of the Caraites out of Jerusalem by the Asmonseans or Maccabees (leg. Taanith; See TEBETH 28).
27th   A fast, because Rabbi Chanina, the son of Thardion, was burnt with the book of the law.


The fourth month of the sacred year
The tenth month of the civil year
29 Days May/June
1st New moon  
14th   A feast for the abolition of a perniciols book of the Sadducees and Bethusians, by which they endeavored to subvert the oral law and all the traditions (Megill. Taanith).
17th   A fast in memory of the tables of the law broken by Moses (Ex 32:19).


The fifth month of the sacred year
The eleventh month of the civil year
30 Days July/August
1st New moon A fast for the death of Aaron, the high priest.
5th   A commemoration of the children of Jethuel, of the race of Judah, who, after the return from the captivity, furnished wood to the temple (Megill. Taanith).
9th   A fast of the fifth month in memory of God's declaration to Moses, on this day, that none of the murmuring Israelites should enter the land of promise (Num 14:29,31).
18th   A fast, because in the time of Ahaz the evening lamp went out.
21st   Xylophoria - a feast on which they stored up the necessary wood in the Temple (Selden; see Josephus, Wir, 2:17). 
Scaliger places this festival on the 22nd of the next month.
24th   A feast in memory of the abolition of a law by the Asmonseans, or Maccabees, which had been introduced by the Sadducees, enacting that both sons and daughters should alike inherit the estates of their parents (MeOill. Tmnitlh).


The sixth month of the sacred year
The twelfth month of the civil year
29 Days August/September
1st New moon A fast for the death of Aaron, the high priest.
7th   Dedication of the walls of Jerusalem by Nehemiah (Ezra 12:27). 
17th   A fast for the death of the spies who brought an ill report of the land of promise (Num 14:36).
18th   A fast, because in the time of Ahaz the evening lamp went out.
21st   Xylophoria - 2nd feast on which they stored up the necessary wood  for keeping up the fire of the altar of burnt-sacrifices (see the 21st of the foregoing month - AB)
22nd   A feast in memory of the punishment inflicted on the wicked Israelites, whose insolence could not be otherwise restrained than by putting them to death; 
for then Judaea was in the possession of the Gentiles. They allowed these wicked Israelites three days to reform; but as they showed no signs of repentance, they were condemned to death (Megill. Taanith).
From the beginning to the end of this month, the cornet is sounded to warn of the approaching new civil year.


The seventh month of the sacred year
The first month of the civil year
30 Days September/October
1st New moon Beginning of the civil year.
Feast of
The Feast of Trumpets (Lev 23:24; Num 29:1,2).
8th   Fast for the death of Gedaliah (2 Kings 25:25; Jer 41:2).
10th Day of Atonement The tenth day of the seventh month was the Day of Atonement-
a day of abstinence, a day of holy convocation, in which all were to afflict themselves. Special offerings were made.
(Lev 23:26-32; 16:1,34; Num 29:7-11; Ex 30:10).
17th   A fast for the death of the spies who brought an ill report of the land of promise (Num 14:36).
The same day, the abolition of written contracts. 
The wicked kings having forbidden the Israelites to pronounce the name of God, when they were restored to liberty the Asmonmeans or Maccabees ordained that the name of God should be written in contracts after this manner: "In such a year of the high-priest N., who is minister of the most high God," etc. The judges to whom these writings were presented decreed they should be satisfied, saying, for example, "On such a day, such a debtor shall pay such a sum, according to his promise, after which the schedule shall be torn." But it was found that the name of God was taken away out of the writing, and thus the whole became useless and ineffectual; for which reason they abolished all these written contracts, and appointed a festival day in memory of it (Megill. Taanith, 100:7).
5th   Rabbi Akiba, son of Joseph, dies in prison.
7th   A fast on account of the worshipping the golden calf, and of the sentence God pronounced against Israel in consequence of that crime (Ex 32:6-8,34).
10th   A fast of expiation (making atonement)  (Lev 23:19, etc.).
15th Feast of
The Feast of Tabernacles, with its octave (8 days) (Lev 23:34).
21st Hosanna-
The seventh day of the Feast of Tabernacles, or the Feast of Branches.
22nd   The 8th day of the Feast of Tabernacles.
23rd   The rejoicing for the law; 
a solemnity in memory of the covenant that the Lord made with the Hebrews in giving them the law by the mediation of Moses. 
On this same day, the dedication of Solomon's Temple (1 Kings 8:65; 66).


The eighth month of the sacred year
The second month of the civil year
29 Days October/November
1st New moon Beginning of the civil year.
6th & 7th   A fast, because Nebuchadnezzar put out the eyes of Zedekiah, after he had slain his children before his face (2 Kings 25:7; Jer 52:10).
19th   A fast on Monday and Tuesday [Thursday?],  and the Monday following,  to expiate faults committed on occasion of the Feast of Tabernacles 
(Calendar, ed. Barto locci).
26th   A feast in memory of some places possessed by the Cuthites, which the Israelites recovered at their return from the captivity.


The ninth month of the sacred year
The third month of the civil year
30 Days November/December
1st New moon  
3rd   A feast in memory of the idols which the Asmonaeans threw out of the courts, where the Gentiles had placed them (Megill. Talanith).
6th   A fast in memory of the book of Jeremiah, torn and burnt by Jehoiakim (Jer 36:23).
21st   The feast of Mount Gerizim. 
The Jews relate that when their high-priest Simon, with his priests, went out to meet Alexander the Great, the Cutheans or Samaritans went also, and desired this prince to give them the Temple: of Jerusalem, and to sell them a part of Mount Moriah, which request Alexander granted. But the high-priest of the Jews afterward presenting himself, and Alexander asking him what he desired, Simon entreated him not to suffer the Samaritans to destroy the Temple. The king replied to him that he delivered that people into his hands, and he might do what he pleased with them. Then the high-priest and inhabitants of Jerusalem took the Samaritans, bored a hole through their heels, and, tying them to their horses' tails, dragged them along to Mount Gerizim, which they ploughed and sowed with tares, just as the Samaritans had intended to do to the Temple of Jerusalem. In memory of this event they instituted this festival 
24th   Prayers for rain (Calendar Bartolocci).
25th Feast of
The dedication or renewing of the Temple, profaned by order of Antiochus Epiphanes, and purified by Judas Maccabaeus (1 Macc. 4:52; 2 Mmfcc. 2:16; John 10:22). This feast is kept with its octave (8 days).
   Josephus says that in his time it was called the Feast of Lights; perhaps, he says, because this good fortune of restoring the Temple to its ancient use appeared to the Jews as a new day (Aif.12:11).
 But the Jewish authors give another reason for the name of lights. They report that when they were employed in cleansing the Temple, after it had been profaned by the Greeks, they found there only one small phial of oil, sealed up by the high. priest, which would hardly suffice to keep in the lamps so much as one night; but God permitted that it should last several days, till they had time to make more, in memory of which the Jews lighted up several lamps in their synagogues and at the doors of their houses. (See Selden, De Si'ned. lib. in, cap. 13.) 
Others affirm (as the Acholatical History, also Thomas Aquinas and Cardinal Hugo, on 1 Macc. 4:52) that the appellation of the Feast of Lights was a memorial of that the from heaven which inflamed the wood on the altar of burnt-offerings, as related in 2 Macc. 1:22.
Some think this feast of the dedication was instituted in memory of Judith. (See Sigon. De Reputbl. Hebr. lib. in, cap. 18.) But it is doubted whether this ought to be understood of Judith, daughter of Merari, who killed Holofernes, or of another Judith, daughter of Mattathias, and sister of Judas Maccabaeus, who slew Nicanor, as they tell us. (See Ganz, Zemach Dai'd; Millenar. 4, an. 622, et apud Selden, De Synedriis, lib. in, cap. 13, n. 11.) This last Judith is known only in the writings of the rabbins, and is not mentioned either in the Maccabees or in Josephus. But there is great likelihood that the Jews have altered the Greek history of Judith to place it in the time of Judas Maccabaeus. 
A prayer for rain.
Time of sowing begins in Judaea.


The tenth month of the sacred year
The fourth month of the civil year
29 Days December/January
1st New moon  
8th   A fast, because of the translation of the law out of Hebrew into Greek.
This day and the three following days were overcast by thick darkness.
The fast of the tenth month (Calend. Bartolocci).
9th   A fast for which the rabbins assign no reason.
10th   A fast in memory of the siege of Jerusalem by Nebuchadnezzar (2 Kings 25:1).
28th   A feast in memory of the exclusion of the Sadducees out of the Sanhedrim, where they had all the power in the time of King Alexander Jannasus. 
Rabbi Simeon, son of Shatach, found means of excluding them one after another, and of substituting Pharisees (Megillath Taanith). See IJAR 23.


The eleventh month of the sacred year
The fifth month of the civil year
30 Days January/February
1st New moon  
2nd   A rejoicing for the death of King Alexander Jannea us, a great enemy to the Pharisees (Mleill. Tasnith).
4th or 5th   A fast in memory of the death of the elders who succeeded Joshua 
(Judg 2:10).
15th   The beginning of the year of trees; 
that is, from hence they begin to count the four years during which trees were judged unclean, from the time of their being planted (Lev 19:23-25). 
Some place the beginning of these four years on the first day of the month.
22nd   A feast in memory of the death of one called Niscalenus, who had ordered the placing images or figures in tie Temple, which was forbidden by the law; but he died, and his orders were not executed. 
The Jews place this under the high-priest Simon the Just. It is not known who this Niscalenus was (Megill. Taan. 100:11).
23rd   A fast for the war of the ten tribes against that of Benjamin  (Judg 20).
They also call to remembrance the idol of Micah (Judg 18).
29th   A memorial of the death of Antiochus Epiphanes, an enemy of the Jews 
(1 Macc. 6:1; Megiil. Taanith).


The twelfth month of the sacred year
The sixth month of the civil year
29 Days February/March
1st New moon  
7th   A fast, because of the death of Moses (Deut 34:5).
8th & 9th   The trumpet sounded by way of thanksgiving for the rain that fell in this month, and to pray for it in future (Megillath Tal'raith). 
A fast in memory of the schism between the schools of Shammai and Hillel [called Taanith Tsadehim].
12th   A feast in memory of the death of two proselytes,  Hollianius and Pipus his brother,  whom one Tyrinus or Turianus would have compelled to break the law,  in the city of Laodicea;  but they chose rather to die than to act contrary to the law (Selden, De Synedr. lib. 3, cap. 13, ex Megfil!. lT-anith).
13th   Esther's fast;  probably in memory of that of  Est 4:16 
(Geneb. and Bartolocci);
A feast in memory of the death of Nicanor, an enemy of the Jews (1 Macc. 7:44; 2 Macc. 15:30, etc.). Some of the Hebrews insist that Nicanor was killed by Judith, sister of Judas Maccabaeus.
14th 1st Feast of
(Feast of
The first Purim, or lesser Feast of Lots (Est 9:21). The Jews in the provinces ceased from the slaughter of their enemies on Nisan 14, and on that day made great rejoicing; but the Jews of Shushan continued the slaughter till the 15th; therefore Mordecai settled the Feast of Lots on the 14th and 15th of this month.
15th Great Feast
of Purim
The great Feast of Pulrin or Lots; the second Purim. 
These three days, the 13th 14th, and 15th, are commonly called the days of Mordecai, though the feast for the death of Nicanor has no relation either to Esther or to Mordecai.
Tax The collectors of the half shekel, paid by every Israelite (Ex 30:13), received it on Adar 15 in the cities, and on the 25th in the Temple (Talmud, Shekmlim).
17th   The deliverance of the sages of Israel, who, flying from the persecution of Alexander Jannseus, king of the Jews, retired into the city of Koslik in Arabia; but, finding themselves in danger of being sacrificed by the Gentiles, the inhabitants of the place, they escaped by night (Mcgill. Taanith).
20th   A feast in memory of the rain obtained from God by one called Onias Ham-magel, during a great drought in the time of Alexander Janneaes 
(Meill. Taanith).
28th   A feast in commemoration of the repeal of the decree by which the kings of Greece had forbidden the Jews to circumcise their children, to observe the Sabbath, and to decline foreign worship (Megill. Taznith, et Gemar. Taanith, 100:2). -- Calmet, Append.


When the year consisted of thirteen lunar months, they place here, by way of intercalation, the " second month of Adar", or Ve-Adar. 

The intercalary month was added after the month of  'Adhar and was called the second  'Adhar (sheni, wa-'adhar, "and Adar"),  and,  as already indicated,  was added about once in 3 years. More exactly, 4 years out of every 11 were leap years of 13 months 
(Jewish Encyclopedia, article "Calendar")
(from International Standard Bible Encyclopaedia, Electronic Database Copyright (c)1996 by Biblesoft)

(from McClintock and Strong Encyclopedia, Electronic Database. Copyright (c) 2000 by Biblesoft)



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