7 Biblical Feasts of the Lord / Israel per Lev.23: A Historical Prophecy & Eschatology

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CALENDAR   METHODOLOGIES  And

CALENDAR of  Hebrew & Arabic MONTH NAMES

Of The7 Biblical Feasts of The Lord

                               Aka 7 JEWISH FESTIVALS Of ISRAEL


Reconciliation of various Hebrew and Arabic calenders and methods of measurement such as:  Solar, Lunar, Gregorian, Jewish, Christian and Prophetic Calendar methodologies, and there respective correlations to the 7 Feasts of the Lord, related to Bible Prophecy of the Biblical 7 Feasts of the Lord, aka the 7 Jewish Festivals of Israel, reflecting prophecy fulfilled and yet to come at the End of the Age, Last Days Tribulation Period, as prophesied by Daniel 9:24-27, in relation to the Feast of Trumpets to the Feast of Atonement Days of Awe, culminating with the Year of Jubilee aka the Millennial Kingdom.

                                                                 By   Feasts Of The Lord.Net

EARTH : TYPOLOGY  and  SOLAR  VIEWS:

CLICK  HERE

A Biblical year is a Lunar (moon) Calendar 354 days long.  The Biblical Calendar for feasts is initiated by the first sliver of a new moon, and marks the beginning of a month, which is always a sabbath, and the 1st day of the month (even when a leap month is added) ; thereby determining when the feasts will be held per Leviticus Chapter 23. Consequently, the feasts always fall on the same day of the week every year.  See Feasts Calendars file.  Note: The Biblical calendar year spans the Gregorian calendar years from the first month of Nissan; in approximately April or May.


In contrast to the Jewish Calendar Year averages  363.3 days per year; comprised of 12 lunar months with 29.530573496 astronomical days per month; for a 354 day year; except on leap years where an extra month is added in to adjust to solar reckoning:  To approximately adjust to a solar calendar, a leap month called Adar II comprised of 30 days, is added on: the 3rd, 6th, 8th, 11th, 14th , 17th and 19th year based upon a 19 year cycle. . This calendar is often called a “lunar /solar” calendar. 


In contrast to a Solar Calendar of 365.2422 days per year; today’s Gregorian Calendar of 30.43685 astronomical days, per month, average.  Note: the Gregorian calendar replaced the earlier, less accurate Julian calendar.


Current Jewish Calendar of Feasts:
 Today’s Jewish calendars superimpose a 354 day lunar calendar (Including a leap month Adar II) onto the Gregorian calendar of 365.2422 days per year.  Consequently the feasts then fall on a different day each year; rather than on the same day when based on a lunar calendar; as God had ordained in Leviticus 23. 


Christian Calendaring of feasts
, such as the “Feast of Passover”; aka Crucifixion of Jesus”, or the “Feast of Weeks”; aka “Easter, or the “Feast of Weeks”; aka Pentecost:  The Christian calendaring of these feasts is also inaccurate; this is due to the overlaying of a lunar calendar, on top of a modern Gregorian calendar, then purposefully adjusting the feasts to fall on predetermined days;  i.e. the Crucifixion on Passover to be on a Friday.


The B
iblical Prophetic Calendar is 360 days per year.  See Rev. 11:2-3, 12:6, 13:5 and Dan. 12:7-12 which indicate 42 months as equivalent to 3.5 years or 1260 days; 360 days per year (also used by Babylonians)  This is the calendar used in prophecy of Jesus 1st coming in Daniel 9:24-26,  then reconciled with the other calendaring methods mentioned

                        ===================================

Primary ESCHATOLOGY LINKS:

DANIEL  9: 24-27  PROPHECY   file link

LAST DAYS DATA    file link

INTERPRETATIVE CHART   file link

BIBLICAL MATHEMATICS   file link

"END OF THE AGE"   –   SIGNS OF JESUS COMING   file link

ESCHATOLOGY SUMMARY   file link

=================================================================================  

 

BC / AD  DATE CONVERSION CALCULATOR

CALENDAR of  Hebrew & Arabic MONTH NAMES

Mo.

No.

Common

Name

Hebrew

Name

Arabic

Name

Arabic

Cognate

Scripture

Reference

Days

Gregorian

Month

FEAST

1

NISSAN

ABIB / AUL

X

X

EX. 12:2

ESTHER 3:7

30

03 / 04

PASSOVER

UNLEAVENED BREAD

FIRST FRUITS / EASTER

2

IYAR

ZIF / ZIV

 

 

1 KG. 6:1

29

04 / 05

 

3

SIVAN

SIVAN

 

 

ESTHER 8:9

30

05 / 06

FEAST OF WEEKS / PENTECOST / Shavuot

4

TAMMUZ

 

X

X

 

29

06 /07

 

5

AV / AB

 

 

X

 

30

07 / 08

 

6

ELUL

 

 

X

 

29

08 / 09

 

7

TISHRI

ETHANIM

 

 

X

1 KG. 8:2

30

09 / 10

TRUMPETS / Rosh Hashanah

ATONEMENT / Yom Kippur

TABERNACLES/ Sukkot

8

HESHVAN

BUL

 

 

 

29 / 30

10 / 11

 

9

KISLEV / CHISLEV

 

 

 

ZECH. 7:1

30 / 29

11 / 12

Hanukkah

10

TEVET

 

X

 

ESTHER 2:16

29

12 / 01

 

11

SHEVAT / SHEBAT

 

 

X

 

30

01 / 02

 

12

ADAR

 

X

X

 

29

02 / 03

Purim

13

ADAR II

 

X

X

 

30

03 / 04

 

The HEBREW / JEWISH / BIBLICAL  CALENDAR

 Reconciling the

Hebrew Biblical / Lunar Calendar

With the Solar Calendar

By FEASTS OF THE LORD. Net

 

ROSH CHODESH:  ADAR SHENI - The Intercalary Month

Intercalation is the insertion of a leap day, week or month into some calendar years to make the calendar follow the seasons or moon phases. Lunisolar calendars may require intercalations of both days and months.  The solar year does not have a whole number of days (it's about 365.24 days), but a calendar year must have a whole number of days. The only way to reconcile the two is to vary the number of days in the calendar year.  The Jewish calendar is a lunisolar calendar predominantly used for religious observances, but is also employed as an agricultural framework.  It is used to reckon the Jewish New Year and dates for Jewish holidays, and also to determine appropriate public reading of Torah portions, Yahrzeits (dates to commemorate the death of a relative), and daily Psalm reading, among many ceremonial uses.  The principles of the Hebrew calendar are found in the Torah.  During Temple times and through the Tannaitic period, the Hebrew calendar was observational, with the beginning of each month determined by the high court based on the testimony of witnesses who had observed a new crescent moon. Periodically, the court ordered an extra month added to keep Passover in the spring, again based on observation of natural events. Through the Amoraic period and into the Geonic period, the purely empirical calendar was displaced by calendarical rules, which finally became systematically arranged into a computed calendar. The principles and rules of the current calendar are fully described by Maimonides in the Mishneh Torah.

Because of the 11.24 day difference between twelve lunar months at 354 days per year, and one solar year at 365.24 days per year, the year lengths of the Hebrew calendar vary in a repeating 19-year Metonic cycle of 235 lunar months.  Consequently a intercalary lunar month of 30 days is added according to defined rules every two or three years, for a total of 7 times per 19 years. Seasonal references in the Hebrew calendar reflect its development in the region east of the Mediterranean Sea and the times and climate of the Northern Hemisphere. The Hebrew calendar's year is longer by about 6 minutes and 25+25/57 seconds than the present-day mean solar year, so that every 224 years, the Hebrew calendar will fall a full day behind the modern fixed solar year, and about every 231 years it will fall a full day behind the Gregorian calendar year.

The Jewish calendar is a lunisolar calendar, or "fixed lunar year," based on twelve lunar months of twenty-nine or thirty days, with an intercalary  a 30 day lunar month added seven times every nineteen years (once every two to three years) to synchronize the twelve lunar cycles with the slightly longer solar year. Each Jewish lunar month starts with the new moon. Although originally the new lunar crescent had to be observed and certified by witnesses, the timing of the new moon is now determined mathematically.

Concurrently there is a weekly cycle of seven days, mirroring the seven-day period of the Book of Genesis in which the world is created. The names for the days of the week, like those in the Creation story, are simply the day number within the week, with Shabbat being the seventh day. The Jewish day always runs from sunset to the next sunset; the formal adjustments used to specify a standard time and time zones are not relevant to the Jewish calendar.

The twelve regular months are: Nisan (30 days), Iyar (29 days), Sivan (30 days), Tammuz (29 days), Av (30 days), Elul (29 days), Tishrei (30 days), Cheshvan (29 or 30 days), Kislev (29 or 30 days), Tevet (29 days), Shevat (30 days), and Adar (29 days). In the leap years an additional month, Adar I (30 days) is added after Shevat, and the regular Adar is referred to as "Adar II".

The first month of the festival year is Nisan.  Nisan 15 is the start of the festival of Passover / Pesach, corresponding to the full moon of Nisan. Pesach is a spring festival associated with the barley harvest,[3] so the leap-month mentioned above is intercalated periodically to keep this festival in the northern hemisphere's spring season. Since the adoption of a fixed calendar, intercalations in the Hebrew calendar have been at fixed points in a 19-year cycle. Prior to this, the intercalation was determined empirically:

The year may be intercalated on three grounds: 'aviv [i.e.the ripeness of barley], fruits of trees, and the equinox. On two of these grounds it should be intercalated, but not on one of them alone.[4]  The solar year is 11.24 days longer than twelve lunar months. The Bible does not directly mention the addition of "embolismic" or intercalary months. However, without the insertion of embolismic months, Jewish festivals would gradually shift outside of the seasons required by the Torah. This has been ruled as implying a requirement for the insertion of embolismic months to reconcile the lunar cycles to the seasons, which are integral to solar yearly cycles.

When the observational form of the calendar was in use, whether or not an embolismic month was announced after the "last month" (Adar) depended on whether "the barley was ripe".[citation needed] It may be noted that in the Bible the name of the first month, Aviv, literally means "spring" but originally it probably meant "the ripening of barley". Thus, if Adar was over and the barley was not yet ripe, an additional month was observed. However, according to some traditions, the announcement of the month of Aviv could also be postponed depending on the condition of roads used by families to come to Jerusalem for Passover, adequate numbers of lambs to be sacrificed at the Temple, and on the ripeness of the barley that was needed for the first fruits ceremony.[citation needed]

Under the codified rules, the Jewish calendar is based on the Metonic cycle of 19 years, of which 12 are common years (12 months) and 7 leap years (13 months). The leap years are years 3, 6, 8, 11, 14, 17, and 19 of the Metonic cycle. Year 19 (there is no year 0) of the Metonic cycle is a year exactly divisible by 19 (when the Jewish year number, when divided by 19, has no remainder). In the same manner, the remainder of the division indicates the year in the Metonic cycle (years 1 to 18) the year is in.

During leap years, a month, Adar II is added before Nisan.  (Although not directly stated this concept is implied in Num 9:11; 2 Chron 30:2-3, and 1 Kings 12:32-33.)  During leap years Adar I (or Adar Aleph — "first Adar") is actually considered to be the extra month, and has 30 days. Adar II (or Adar Bet — "second Adar") is the "real" Adar, and has the usual 29 days. For this reason, during a leap year, holidays such as Purim are observed in Adar II, not Adar I.  The Jewish calendar is based on the Metonic cycle of 19 years, of which 12 are common years (12 months) and 7 leap years (13 months). A Metonic cycle equates to 235 lunar months in each 19-year cycle. This gives an average of 6939 days, 16 hours and 595 parts for each cycle.

But due to the Rosh Hashanah postponement rules (see below), a cycle of 19 Jewish years can be either 6939, 6940, 6941, or 6942 days in duration. Since none of these values is evenly divisible by seven, the Jewish calendar repeats exactly only following 36,288 Metonic cycles, or 689,472 Jewish years. There is a near-repetition every 247 years, except for an excess of 50 minutes (905 parts).  The Jewish leap years are years 3, 6, 8, 11, 14, 17, and 19 of the Metonic cycle. To determine whether a year is a leap year, find the remainder when dividing the Jewish year number by 19. If the remainder is 3, 6, 8, 11, 14 or 17, the year is a leap year and an extra month, Adar I, is added, preceding Adar II (sometimes called "the real Adar"). If the remainder is zero, the year is also a leap year since year 19 of the Metonic cycle is a year exactly divisible by 19. Another way to check a specific year is to find the remainder in the following calculation: ( 7 x the Jewish year number + 1 ) / 19. If the remainder is less than 7, the year is a leap year.

[Source: http://en.wikipedia.org/wiki/Intercalation]


The Jewish Leap Year – Adar II

By Nachum Mohl

Torah has fixed the Jewish month based on the moon – not on the sun. The moon begins at the beginning of each Jewish month as a thin crescent and gradually grows fuller each night until it is perfectly full and round. This marks the middle of the Jewish month. Then the moon begins it gradual reduction until it disappears only to reappear again at the beginning of the new month. When the moon first appears as a narrow crescent it is called the New Moon or the beginning of a new month, in Hebrew: Rosh Chodesh.

It takes the moon a little over 29 ½ days for the moon to complete its monthly cycle. Since we cannot have part of a day belonging to one month and part of the day belonging to another, the calendar is arranged so that some days are 29 days long and some days are 30 days long. A month is never more than 30 days nor less than 29 days.

This explains why we sometimes two days Rosh Chodesh (the beginning of the month) and some times only one day Rosh Chodesh. When we have one day Rosh Chodesh it means that the out going month had 29 days; when there is two days Rosh Chodesh it means that the first day of Rosh Chodesh is the last day of the out going month and the second day is the first day of the incoming month. The only except to this rule is the month of Tishre when the Rosh Chodesh is Rosh Hashanah; then the first two days of Rosh Chodesh are Rosh Hashanah which are the first and second days of the New Year.

Now although the months go according to the moon's cycle, the year must be reckoned in consideration to the sun's cycle. The reason is that Torah was particular that the holiday of Passover should fall in the spring. The moon's cycle has no relation to the seasons, but the sun's cycle is related. In the summer the sun is high in the noonday sky, in the winter it is low. During spring and fall the sun's height as measured by the noon day position is in an intermediate position.

Since the holiday of Passover must be observed in the spring, we must reckon the counting of the months in a manner that the month of Nisan (in which Passover comes) is always in the spring. Now the four seasons take up 365 ¼ days, yet the moon's cycle is only 29 ½ days. If we multiply 29 ½ days by twelve months we get 354 days which leaves us some 11.24 days short of a solar year. That means that every year the months move back about one third of a month and in nine years the Jewish holidays would fall behind the solar year and seasons by about three months. If we allowed this to happen, Passover would be in the summer and then in a few more years in the winter! Yet the Torah explicitly stated that Passover should be celebrated in the spring.

Therefore to keep the festivals on track an extra month is added once in about every three years when the 11 day difference grows into a month. This extra month is added after the month of Sh'vat and before the month of Adar that has in it Purim. We call this month Adar I and the Adar that has in it Purim, we call Adar II. In this manner Nissan, the month that has Passover, is pushed back into its rightful place in the sequence of the seasons. Once Nissan is in its proper place, then all the subsequent months and their festivals, Shavuot and Succot, fall into their proper places.

During the time of the Temples, the months were declared according to visual testimony in the Jewish Supreme court, the Sanhedrin. Since the destruction of the Temple, and the demise of the Sanhedrin, we rely on the fixed calendar for all of our months and festivals. The following is their method of calculation:  A leap year cycle is a nineteen year cycle. During this period of time there are seven leap years: the 3rd, 6th, 8th, 11th, 14th, 17th, and 19th years in the cycle are the leap years. We can figure out if the year is a leap year by dividing the present Hebrew year by 19. If the remainder number is one of the above numbers or zero (in the place of 19) then it is a leap year. For example, this year is 5768; if we divide it by 19, we get 305 with a remainder of 11, which tells us that this is the 11th year in the 19 year cycle. The next leap year will be in the 14th year (in three more years).

If a person was born in Adar, in which Adar does he celebrate his birthday? The usual custom is to celebrate the birthday in the same Adar in which Purim falls, meaning Adar II. However if he was born in Adar I in a leap year, then he would celebrate his birthday in Adar I. Conversely, if someone was born in Adar II, he celebrates his birthday in regular years in the only Adar that comes, regular Adar. This can present a small problem, if one person was born in the twentieth of Adar I and his friend was born in the next month on the third of Adar II, if their bar mitzvah is in a plain year (with only one Adar), the younger boy (born in Adar II) will celebrate his bar mitzvah on the third of Adar before his older friend (born in Adar I) on the third of Adar. Ah, such is the irony of the Jewish calendar!

During a leap year, the date in Adar I of Purim is not celebrated as Purim, however it has become a festive day in that certain prayers are not said, and the custom is to eat in a more festive manner. It is called Purim Katan, meaning the small Purim.

The rule is that we increase joy, never decrease, therefore a year with two Adars in it is considered a happy year.                [Source: http://www.jewishmag.com/121mag/jewish_month/jewish_month.htm]

Astronomy:

In Astronomy, there is a natural 19-year cycle between the sun and the moon.

Every 19 years, the month and day of the year will be the same.

For the lunar calendar, the 19-year cycle requires that 235 months be used in order to equal to the 19-year solar calendar.

 

Since we use 12-months in a year, 19 years of 12 months gives us 228 total months. This is easy to show by using your calculator and multiplying 19 x 12 as follows:

 

19 x 12 = 228.  Consequently, the 228 months are 7 months less than the required 235 months. Thus, an additional 7 "leap" months are inserted into the 19-year cycle. 

 [Source: http://www.harvardhouse.com/prophetictech/new/19-year_cycles.htm]

 

Solar Year:

The solar year does not have a whole number of lunar months.  In lunar calendars, a lunar month is the time between two identical syzygy. There are many variations. In Middle-Eastern and European traditions, the month starts when the new moon becomes first visible at evening after Astronomical conjunction with the Sun 1 or 2 days before that evening.  A lunar month is about 12.37 lunations (i.e. the mean time for one lunar phase cycle; average 29.530589 days, or 29 d 12 h 44 min 3s; length of this cycle is linked to many phenomena in nature), so a lunisolar calendar must have a variable number of months in a year. This is usually 12 months, but a 13th month (an intercalary or embolismic month) is added to the year every two or three years.  The month is a unit of time, used with calendars, which is approximately as long as some natural Orbital period related to the motion of the Moon; month and Moon are cognates....
[Source: http://www.absoluteastronomy.com/topics/Intercalation]

 

Astronomical Phenomena:

The Jewish calendar is based on three astronomical phenomena: the rotation of the Earth about its axis (a day); the revolution of the moon about the Earth (a month); and the revolution of the Earth about the sun (a year). These three phenomena are independent of each other, so there is no direct correlation between them. On average, the moon revolves around the Earth in about 29½ days. The Earth revolves around the sun in about 365¼ days, that is, about 12.4 lunar months.

The civil calendar used by most of the world has abandoned any correlation between the moon cycles and the month, arbitrarily setting the length of months to 28, 30 or 31 days.

The Jewish calendar, however, coordinates all three of these astronomical phenomena. Months are either 29 or 30 days, corresponding to the 29½-day lunar cycle. Years are either 12 or 13 months, corresponding to the 12.4 month solar cycle.

The lunar month on the Jewish calendar begins when the first sliver of moon becomes visible after the dark of the moon. In ancient times, the new months used to be determined by observation. When people observed the new moon, they would notify the Sanhedrin. When the Sanhedrin heard testimony from two independent, reliable eyewitnesses that the new moon occurred on a certain date, they would declare the rosh chodesh (first of the month) and send out messengers to tell people when the month began.

There are approximately 12.4 lunar months in every solar year, so a 12-month lunar calendar is about 11 days shorter than a solar year and a 13-month lunar is about 19 longer than a solar year. The months drift around the seasons on such a calendar: on a 12-month lunar calendar, the month of Nissan, which is supposed to occur in the Spring, would occur 11 days earlier in the season each year, eventually occurring in the Winter, the Fall, the Summer, and then the Spring again. On a 13-month lunar calendar, the same thing would happen in the other direction, and faster.

To compensate for this drift, the Jewish calendar uses a 12-month lunar calendar with an extra month occasionally added. The month of Nissan occurs 11 days earlier each year for two or three years, and then jumps forward 30 days, balancing out the drift. In ancient times, this month was added by observation: the Sanhedrin observed the conditions of the weather, the crops and the livestock, and if these were not sufficiently advanced to be considered "spring," then the Sanhedrin inserted an additional month into the calendar to make sure that Pesach (Passover) would occur in the spring (it is, after all, referred to in the Torah as Chag he-Aviv, the Festival of Spring!).

A year with 13 months is referred to in Hebrew as Shanah Me'uberet (pronounced shah-NAH meh-oo-BEH-reht), literally: a pregnant year. In English, we commonly call it a leap year. The additional month is known as Adar I, Adar Rishon (first Adar) or Adar Alef (the Hebrew letter Alef being the numeral "1" in Hebrew). The extra month is inserted before the regular month of Adar (known in such years as Adar II, Adar Sheini or Adar Beit). Note that Adar II is the "real" Adar, the one in which Purim is celebrated, the one in which yahrzeits for Adar are observed, the one in which a 13-year-old born in Adar becomes a Bar Mitzvah. Adar I is the "extra" Adar.

In the fourth century, Hillel II established a fixed calendar based on mathematical and astronomical calculations. This calendar, still in use, standardized the length of months and the addition of months over the course of a 19 year cycle, so that the lunar calendar realigns with the solar years. Adar I is added in the 3rd, 6th, 8th, 11th, 14th, 17th and 19th years of the cycle. The current cycle began in Jewish year 5758 (the year that began October 2, 1997).

[Source: http://www.jewfaq.org/calendar.htm]

 

Moses:

Moses used terms moon & month interchangeably (e.g. Ex.19:1).  Per Josephus (Ant.I,iii,3) Moses ordered year of holy feasts begin with Nisan (month the Exodus occurred); however he retained the old order of year for commerce and secular affairs.  The lunar year of feasts, fasts & agriculture was linked to the divine order of heavenly bodies “for signs and for seasons and for days and years: (Gen. 1:14) & God’s promise of Gen.8:22.

Hillel probably introduced the constant calendar.

Early Israelites designated months by names borrowed from Canaanites or Phoenicians indicating seasonal connotations. (e.g. Ex.13:4, Deut. 16:1, 1 Kg.6:1,38 & 8:2

By end of Kingdom period calendar reformed, replacing old names of months with ordinary numbers and changing the year’s beginning to spring (see 1 Kg.6:1, 8:2)

By 6th century B.C., minor-prophets used numeral designations without any refs. to earlier naming (e.g. Haggai 1:1; 2:1,10); exception: Zechariah, who relates numeral month to Babylonian names (1:7).

Post-Exilic month names were adopted from Babylonian, but weren’t used for civil/historic purposes.

Jewish calendar contained 2 concurrent years: the sacred year, beg. in Spring with Nisan, and civil year, beginning in the fall with Tishri.  Sacred yr., instituted by Moses following the Exodus, consists of 12 or 13 lunar months of 29.5 days ea.  Civil yr. came into use c. 3rd cent. A.D.

Babylonians & Egyptians devised the intercalary month in order to reconcile the lunar & solar years.  It was determined as follows:  if on the 16th of the month Nisan, the sun had not reached the vernal equinox, the month was declared to be the 2nd Adhar; thus the month following was called Nisan.  The Jewish leap years in their Metonic cyc le of 19 years were fixed, adding an intercalary month to the 3rd, 6th, 9th, 11th, 14th, 17th & 19th years.   Julius

Caesar’s calendar, developed in 46 B.C. contained 365.5 days, but had a discrepancy of 11 min. in excess of the solar year.  So it was superseded by the Gregorian calendar in 1582 A.D., which gained one day in 3,325 yrs. 

[Source: “Calendaring” by Dr. Guy Funderberk, Pictorial Bible Dictionary, M.C. Tenney, Gen.Ed. 1973]

 
The Metonic Cycle:                From Wikipedia, the free encyclopedia

 

The Metonic cycle or Enneadecaeteris in astronomy and calendar studies is a particular approximate common multiple of the tropical year (also known as a solar year) is the length of time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice) and the synodic (lunar) month. The Greek astronomer Meton of Athens observed that a period of 19 tropical years is almost exactly equal to 235 synodic months, and rounded to full days counts 6940 days. The difference between the two periods (of 19 tropical years and 235 synodic months) is only 2 hours.

Taking a year to be 1/19th of this 6940-day cycle gives a year length of 365 + 1/4 + 1/76 days (the unrounded cycle is much more accurate), which is slightly more than 12 synodic months. To keep the 12-month lunar year in pace with the solar year, an intercalary 13th month would have to be added on seven occasions during the nineteen-year period. Meton introduced a formula for intercalation in circa 432 BC.

The cycle's most significant contemporary use is to help in flight planning (trajectory calculations and launch window analysis) for lunar spacecraft missions as well as serving as the basis for the Hebrew calendar's 19 year cycle. Another use is in computus, the calculation of the date of the Christian feast of Easter.

 

Mathematical basis:

19 tropical years differ from 235 synodic months by about 2 hours. The Metonic cycle's error is one full day every 219 years, or 12.4 parts per million.

19 tropical years = 6939.602 days

235 synodic months = 6939.688 days

This cycle is an approximation of reality. The period of the Moon's orbit around the Earth and the Earth's orbit around the Sun (ignoring also exact definition of the year) are independent and have no known physical resonance. Examples of a real harmonic lock would be Mercury, with its 3:2 spin-orbit resonance or other orbital resonance.

A lunar year of 12 synodic months is about 354 days on average, 11.24 days short of the 365-day solar year. Therefore, in a lunisolar calendar, every 3 years or so there is a difference of more than a full lunar month between the lunar and solar years, and an extra (embolismic) month should be inserted (intercalation). The Athenians appear not to have had a regular means of intercalating a 13th month; instead, the question of when to add a month was decided by an official.

 

Application in traditional calendars

Traditionally (in the ancient Attic and Babylonian calendars, as well as in the Hebrew calendar), the years 3, 6, 8, 11, 14, 17, and 19 are the long (13-month) years of the Metonic cycle. This cycle can be used to predict eclipses, forms the basis of the Greek and Hebrew calendars, and is used in the computation of the date of Easter each year.

The Chaldean astronomer Kidinnu (4th century BC) knew of the 19-year cycle, but the Babylonians may have learned of it earlier. They measured the moon's motion against the stars, so the 235:19 relation may originally have referred to sidereal years, instead of tropical years as it has been used in various calendars.  The Bahá'í calendar, established in the middle of the 19th century, is also based on cycles of 19 years.

The Metonic cycle incorporates two less accurate subcycles, for which 8 years = 99 lunations (an Octaeteris) to within 1.5 days, i.e. an error of one day in 5 years; and 11 years = 136 lunations within 1.5 days, i.e. an error of one day in 7.3 years. Adding the 11 year cycle to 17 or 18 Metonic cycles creates the more accurate cycles of 334 years in 4131 lunations and 353 years in 4366 lunations (see lunisolar calendar).

Meton of Athens approximated the cycle to a whole number (6940) of days, obtained by 125 long months of 30 days and 110 short months of 29 days. In the following century Callippus developed the Callippic cycle of four 19-year periods for a 76-year cycle with a mean year of exactly 365.25 days.

The 19-year cycle is also close (to somewhat more than half a day) to 255 draconic months, so it is also an eclipse cycle, which lasts only for about 4 or 5 recurrences of eclipses.

Sources: Mathematical Astronomy Morsels, Jean Meeus, Willmann-Bell, Inc., 1997 (Chapter 9, p. 51, Table 9.A Some eclipse Periodicities)

See also: http://en.wikipedia.org/wiki/Metonic_cycle

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