The Jewish Encyclopedia says,
Those [appointed Festivals] connected with the moon: (a) Sabbath; (b) New Moon; and (c) the New Moon of the seventh month. Jewish Encyclopedia.com, the unedited full-text of the 1906 Jewish Encyclopedia, “Festivals,” Classification of Festivals, Emil Hirsch, Vol. 5, p. 376.
The moon was the beneficent… [herald] of the shepherds in the region and climate where ancient Israel had its ancestral home. Hence the many traces of lunar institutions in even the latest Israelitish cult and its phraseology… The Sabbath, as marking the end of the week, reveals its lunar origin; the phases of the moon having taught the shepherds, whose weal or woe depends so largely upon the benevolence or malevolence of the night season, to divide the period elapsing between two new moons into four equal groups (weeks), the last day of each… Indications are not wanting that at first the New Moon festival was not counted among the seven days of the week (see Week); but after… New Moon days… a new cycle of four weeks began… Later, the week and the Sabbath became fixed [according to the Babylonian/Roman continuous weekly cycle]; and this gradually resulted in taking away from the New Moon festival its popular importance. Jewish Encyclopedia.com, the unedited full-text of the 1906 Jewish Encyclopedia, “Festivals,” Pastoral Feasts, Emil Hirsch, Vol. 5, p. 376.
Under the reign of Constantius the persecutions of the Jews reached such a height that the computation of the (luni-solar) calendar (was) forbidden under pain of severe punishment. The Jewish Encyclopedia, “Calendar.”
At the end of four weeks an interval of one or two days [30th day and New Moon Day] … intervene before the new [lunar month and] week could begin. At an early date [359 AD], however, this intimate connection between the week and the moon must have been dissolved. Jewish Encyclopedia.com, unedited full-text of the 1906 Jewish Encyclopedia, “Week,” by Emil G. Hirsch, Vol. 12, p. 481.
A unit of time; the period between one new moon and another. According to the account of Creation in Genesis, it was decreed that the “lesser light” should “rule the night” and serve “for signs and for seasons” [mo’edim] (Gen. 1:14). The Psalmist also says, “He appointed the moon for seasons” [mo’edim] (Ps. 104:19).” Undoubtedly there was an occasional interpolation of an extra [automatic lunar] month to correct the lunar year to the solar cycle; and it is evident from the fact that the festivals named in given months—such as Passover, Pentecost, and Tabernacles—all had to do with crops…the highest antiquity. The relation of the months to the signs of the zodiac is a further evidence that the solar-lunar year was employed. Jewish Encyclopedia, “Month,” Cyrus Adler, Judah David Eisenstein, Vol. 8, p.671.
The history of the Jewish calendar may be divided into three periods—the Biblical, the Talmudic, and the post-Talmudic. The first rested purely on the observation of the sun and the moon, the second on observation and reckoning, the third entirely on reckoning. Jewish Encyclopedia.com, the unedited full-text of the 1906 Jewish Encyclopedia, “History of the Calendar,” by Joseph Jacobs, Cyrus Adler, Vol. 3, p. 498.
The Sabbath depending, in Israel’s nomadic period, upon the observation of the phases of the moon, it could not, accordingly be a fixed day [meaning a fixed planetary day of the modern Roman cycling week]. The Jewish Encyclopedia: A Descriptive Record of the History. Edited by Isidore Singer, Cyrus Adler, Volume 10, p. 590.
[When] dissociated from the moon, the Sabbath developed into a day of rest for the workers and animals on the farm… Traces of the old taboo [forbidden New Moon and lunar calendar model from creation] are, however, found. In Amos 8:5 it is the fear of… consequences [for not abstaining from work on the New Moon Day and Sabbath] that keeps the impatient merchants from plying their wicked trade. The Assyrian [Babylonian/Roman] calendar seems to disclose an effort to get rid of the movable [lunar] Sabbath in favor of the fixed [continuous weekly cycle]. Jewish Encyclopedia.com, Jewish Encyclopedia 1906, SABBATH, Emil G. Hirsch, Joseph Jacobs, Executive Committee of the Editorial Board, Julius H. Greenstone, Vol. 10, p. 591.
