If one wants to know what the ancient Jews believed, I have found it is better to consult Jewish writings.
[SIZE=-1]Jewish Encyclopedia - CALENDAR, HISTORY OF:
By : Joseph Jacobs Cyrus Adler
Bound Lunar Year.
Astronomers know this kind of year as a bound lunar year. The Greeks had a similar year. Even the Christian year, although a purely solar year, is forced to take account of the moon for the fixing of the date of Easter. The Mohammedans, on the other hand, have a free lunar year.
It thus seems plain that the Jewish year was not a simple lunar year; for while the Jewish festivals no doubt were fixed on given days of lunar months, they also had a dependence on the position of the sun. Thus the Passover Feast was to be celebrated in the month of the wheat harvest, and the Feast of Tabernacles, also called, took place in the fall. Sometimes the feasts are mentioned as taking place in certain lunar months (Lev. xxiii.; Num. xxviii., xxix.), and at other times they are fixed in accordance with certain crops; that is, with the solar year.
In post-Talmudic times Nisan, Siwan, Ab, Tishri, Kislew, and Shebaṭ had 30 days, and Iyyar, Tammuz, Elul, Ḥeshwan, Ṭebet, and Adar, 29. In leap-year, Adar had 30 days and We-Adar 29. According to Pirḳe Rabbi Eliezer, there was a lunar solar cycle of 48 years. This cycle was followed by the Hellenists, Essenes, and early Christians.
In the times of the Second Temple it appears from the Mishnah (R. H. i. 7) that the priests had a court to which witnesses came and reported. This function was afterward taken over by the civil court (see B. Zuckermann, "Materialien zur Entwicklung der Altjüdischen Zeitrechnung im Talmud, "Breslau, 1882).
The fixing of the lengths of the months and the intercalation of months was the prerogative of the Sanhedrin, at whose head there was a patriarch or. The entire Sanhedrin was not called upon to act in this matter, the decision being left to a special court of three. The Sanhedrin met on the 29th of each month to await the report of the witnesses.
From before the destruction of the Temple certain rules were in existence. The new moon can not occur before a lapse of 29½ days and ⅔ of an hour. If the moon could not be exactly determined, one month was to have 30 days and the next 29. The full months were not to be less than 4 nor more than 8, so that the year could not be less than 352 days nor more than 356. After the destruction of the Temple (70 C.E.) Johanan ben Zakkai removed the Sanhedrin to Jabneh. To this body he transferred decisions concerning the calendar, which had previously belonged to the patriarch. After this the witnesses of the new moon came direct to the Sanhedrin.
Empirical Determination of Leap-Year.
Every two or three years, as the case might be, an extra month was intercalated. The intercalation seems to have depended on actual calculation of the relative lengths of the solar and lunar years, which were handed down by tradition in the patriarchal family. Moreover, it was possible to judge by the grain harvest. If the month of Nisan arrived and the sun was at such a distance from the vernal equinox that it could not reach it by the 16th of the month, then this month was not called Nisan, but Adar Sheni (second).
On the evening before the announcement of the intercalation the patriarch assembled certain scholars who assisted in the decision. It was then announced to the various Jewish communities by letters. To this epistle was added the reason for the intercalation. A copy of such a letter of Rabban Gamaliel is preserved in the Talmud (Sanh. xi. 2).
The country people and the inhabitants of Babylonia were informed of the beginning of the month by fire-signals, which were readily carried from station to station in the mountain country. These signals could not be carried to the exiles in Egypt, Asia Minor, and Greece, who, being accordingly left in doubt, celebrated two days as the new moon.
Owing to the weather it was frequently impossible to observe the new moon. In order to remove any uncertainty with regard to the length of the year on this account, it was ordained that the year should not have less than 4 nor more than 8 full months. After the fixing of the calendar it was settled that the year should not have less than 5 nor more than 7 full months.
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