The Jewish calendar is reckoned according to both the solar and lunar cycles: the season of the festival is determined by the solar cycle while the day on which it begins is associated with the lunar cycle. Thus the proclamation of the new moon by the Sanhedrin during Temple times laid the groundwork for the monthly calendar reckoning. Roll your cursor over the different phases of the moon to learn their place in the various Hebrew months: The monthly ceremony of blessing the moon (qiddush levanah) generally takes place between the third and fifteenth day of each month, when the light of the moon is regarded as being at its strongest (link). Biblical sources for festival dates: Exodus 20:4; Deut. 4:19, 17:3-5 Hasidic tale of how a coat was sewn for the moon which keeps changing its size