Special Biblical Significance of Rosh Chodesh Sivan
Jewish Tradition says that "that very day" refers to Rosh Chodesh Sivan. About that day it is written, "And the People of Israel encamped there, opposite the Mountain." The verb written in Hebrew for "encamped" is "vayichan," a singular, rather than plural, form. This is to indicate that the acceptance of the Torah by the Jewish People was as if with a single mind, and a single heart. This was necessary because the Torah was like a marriage contract between G-d and Israel and, as such, there was no room for any hesitation or disloyalty between the parties.
In Divrei HaYamim (Chronicles II) (15:9-12), we find, regarding King Asa of Yehudah, "And he gathered all of Yehudah and Binyamin, and from those who lived with them, from Ephrayim and Menasheh and from Shimon, for they gathered unto him in multitudes, because they saw that the L-rd was with him. And they were gathered to Yerushalayim in the third month, of the fifteenth year of King Asa. And they sacrificed to the L-rd on that day, bringing from the booty, seven hundred cattle and seven thousand sheep. And they entered into the Covenant to seek the L-rd, the G-d of their fathers, with all their heart and all their soul."
And Jewish Tradition teaches us that this entry into a Covenant with G-d by the Jewish People, approximately six hundred years after the Covenant at Sinai, occurred on Rosh Chodesh Sivan.