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The Original World Calendar is the Moon!
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The Feasts are the keys to the Calendar

should two calendars be mixed?

Consider the following:

Let us see what the Scriptures say concerning the calendar in regards to the Feasts. (Right now, we are more concerned with the details of the calendar then the Feasts themselves.)

Leviticus
23.1 And the LORD spake unto Moses, saying, 23.2 Speak unto the children of Israel, and say unto them, Concerning the feasts of the LORD, which ye shall proclaim to be holy convocations, even these are my feasts. 23.3 Six days shall work be done: but the seventh day is the sabbath of rest, an holy convocation; ye shall do no work therein: it is the sabbath of the LORD in all your dwellings. 23.4 These are the feasts of the LORD, even holy convocations, which ye shall proclaim in their seasons. 23.5 In the fourteenth day of the first month at even is the LORD's passover. 23.6 And on the fifteenth day of the same month is the feast of unleavened bread unto the LORD: seven days ye must eat unleavened bread. 23.7 In the first day ye shall have an holy convocation: ye shall do no servile work therein. 23.8 But ye shall offer an offering made by fire unto the LORD seven days: in the seventh day is an holy convocation: ye shall do no servile work therein.

You will notice that the entire chapter 23 of Leviticus concerns the Feasts. They are not the "Feasts of the Jews" but rather the "Feasts of the LORD" (the Hebrew actually has his name, YHWH.) The chapter then goes to list the feasts, starting with the Creation Sabbath, and then listing them as they occur on the lunar calendar.

Is there any indication that a different calendar is used for the Sabbath and the other feast days which are all grouped together in Leviticus 23? Or is it just an assumption that there is?

Often the best way to see things is with an example. First, we will show the calendar of the Seventh Month. Then, we will show the Feast of Tabernacles for two different years, using the "Saturday Sabbath", and note the problems which occur, and the solution.

Feasts of the Seventh Month

The Feasts of the Seventh Month: Trumpets (first), Atonement (10th), and Tabernacles (15th to 21st).

(NM = New Moon,  W = Work day, S = Sabbath)

W W W W W W   NM
S
            New Moon - only a small sliver is visible 1
2 3 4 5 6 7 Right Half illuminated 8
9 10 11 12 13 14 Full Moon 15
16 17 18 19 20 21 Left Half illuminated 22
23 24 25 26 27 28 Last sliver 29
              (30)

Does the modern calendar support this principle in the keeping of the Feasts? Consider the Feast of Tabernacles. The feast begins on the 15th day of the month which is a Sabbath, lasts for seven days, and then the eighth day, the 22nd of the month is a Sabbath.

Leviticus 23
23:34 The fifteenth day of this seventh month shall be the feast of tabernacles for seven days unto the LORD. .... 23:39 Also in the fifteenth day of the seventh month, when ye have gathered in the fruit of the land, ye shall keep a feast unto the LORD seven days: on the first day shall be a sabbath, and on the eighth day shall be a sabbath.

Note that the Jews today, following Hillel's calendar inspired by Constantine's persecutions, have to add an extra day (a Sabbath at the end of the seven-day feast), to make this work, and they also will have a floating continuous-seventh day "Saturday Sabbath" somewhere in the middle of the Feast.

Problem with Mixed Calendar, Example 1:

14 15 16 17 18 19 20 21 22
Tue. Wed. Thu. Fri. Sat. Sun. Mon. Tue. Wed.
  Tab.
Day 1
Sab.
Tab.
Day 2
Tab.
Day 3
Tab.
Day 4
Tab.
Day 5
Tab.
Day 6
Tab.
Day 7
Tab.
Day 8
Sab.
Note: This example occurred in Oct., 2008.

Problem with Mixed Calendar, Example 2:

14 15 16 17 18 19 20 21 22
Sat. Sun. Mon. Tue. Wed. Thu. Fri. Sat. Sun.
 'Sat. Sab.' Tab.
Day 1
Sab.
Tab.
Day 2
Tab.
Day 3
Tab.
Day 4
Tab.
Day 5
Tab.
Day 6
Tab.
Day 7
Tab.
Day 8
Sab.
Note: This was Saturday, Oct. 3, to Sunday, Oct. 11, 2009.

The solution, of course, is that there is no "Saturday Sabbath", and that all feastdays, including the seventh day Sabbath, are based on the lunar calendar.

Solution, based on Example 2:

14 15 16 17 18 19 20 21 22
Sat. Sun. Mon. Tue. Wed. Thu. Fri. Sat. Sun.
  Tab.
Day 1
Sab.
Tab.
Day 2
Tab.
Day 3
Tab.
Day 4
Tab.
Day 5
Tab.
Day 6
Tab.
Day 7
Tab.
Day 8
Sab.
Note: This was Saturday, Oct. 3, to Sunday, Oct. 11, 2009.

A similar analysis could be made with respect to the First Month. The problems of the Saturday Sabbath clashing with the feast days will be seen. Of course, the solution is to use the same calendar, the lunar calendar, for both the feasts and seventh day Sabbath.

Feasts of the First Month

The Feasts of the First Month: Beginning of Year (first), Secure a Lamb (10th), Passover (14th), Unleavened Bread (15th to 21st), First Fruits (16th).

W W W W W W   NM
S
            New Moon - only a small sliver is visible 1
2 3 4 5 6 7 Right Half illuminated 8
9 10 11 12 13 14 Full Moon 15
16 17 18 19 20 21 Left Half illuminated 22
23 24 25 26 27 28 Last sliver 29
              (30)

Rules of Postponement

the "smoking gun" in the Rabbi's hand

Because they are now using the mixed calendar, the Rabbis have developed "Rules of Postponement" to avoid a clash. For example, they don't want the Day of Atonement to be adjacent to a "Saturday Sabbath". However, if a Lunar Sabbath is used, then the Day of Atonement is always five days from the Sabbath, and there is never a problem. Even though the Bible has many details about the feasts, it is silent on "postponements". Why? Because Moses and the Prophets didn't use a mixed calendar, and so they didn't need them.

We can see that, by calculating the seventh day Sabbath in the same way as the feast days (from the beginning of the lunar month), there are no "clashes", nor is there a need to add an extra day. The very fact that these Rabbinical "Rules of Postponement" exist is the "smoking gun" that indicates that the Rabbis are not using the Scriptural Calendar for the seventh day Sabbath!