1. The Chazon Ish (OC 141:7 DH v'Ha) writes that the reason why most years Elul was not 30 days is that it was common that the two months that follow Tishrei (Cheshvan and Kislev) were full months of 30 days. This is because Cheshvan and Kislev are the time of the early rains, the "Yoreh" (as we mention twice daily in the second paragraph of the Shema, in Devarim 11:14), and as a result of the clouds it was often difficult for the witnesses to see the moon on time so an extra day was added to the month. Similarly, Nisan is the time of "Malkosh," the late rains, and again because of the clouds it usually was a 30-day month. Then, in the summer, since the days in Tammuz and Av are very long and the nights are short it was hard for the witnesses to see the new moon immediately after it first appeared, and consequently Tammuz and Av usually contained 30 days. In contrast, the beginning of Tishrei is not usually cloudy, nor are the days long. Since there was a build-up of full months before Tishrei it followed that the new moon of Tishrei appeared early which is why Elul was usually only 29 days long.

2. Rashi in Sanhedrin (13a, DH Chag) writes that the months preceeding Elul were arranged by the Sanhedrin so that Rosh Hashanah should not fall on Sunday, Wednesday, or Friday ("Lo AD'U Rosh"), and they established the calendar in such a way that it would not be necessary to make Elul 30 days.

In order to understand this better, I am going to give some background for the way that Kidush ha'Chodesh works:

3. The Rashba (Teshuvos 4:254) writes that even in the times when Beis Din was empowered to establish Rosh Chodesh according to the testimony of witnesses who saw the new moon, the chief method of determining Rosh Chodesh was still the astronomical calculations that Chazal were capable of making in order to know when the new moon would appear. While it was a Mitzvah for the witnesses to testify that they saw the new moon, the calculations were nevertheless more important.

4. The Rashba proves this from Gemara in Rosh Hashanah (20a) which states that if the month needed to 30 days long, but witnesses already saw the new moon on day 30, Beis Din "coerces" them (see Insights there) to remain quiet in order not to have to make the month a 29-day month. The Gemara there says that on occasion, even when the witnesses had not seen the moon they were told to say that they had seen it. The Rashba writes that the reason this policy was adopted was that Chazal knew, according to the calculations, when the new moon really would occur, and the witnesses were necessary only in order to fulifil the Mitzvah of sanctifying the moon by sight. The Rashba also cites Shmuel (Rosh Hashana 20b) who says that he was capable of fixing the calendar for all of Bavel based on his astronomical knowledge, without relying on witnessses.

5. The Kuzari (2:64) also relates how Chazal were expert in astronomy long before the fixed calendar alone was used. The Kuzari writes that there was a tradition received from the house of David ha'Melech concerning the amount of time between one month and the next, which has been passed on for thousands of years. The commentary Kol Yehudah on the Kuzari writes that through the influence of David ha'Melech, researchers from the sages of Yisrael were commissioned to study the calendar and they determined through their research and their competent instrumentation exactly when the "Molad" would occur.

6. We see that the months were arranged in advance so that Rosh Hashanah would not fall on Sunday, Wednesday, or Friday. Since the principle part of establishing the new month was done by the calendar and not by the witnesses, as the Rashba writes, we can now appreciate better how Chazal were able to organize the calendar in advance so that Rosh Hashanah would be on the desired day of the week.

Kol Tuv,

Dovid Bloom