Genesis 2 records God's creation of the seventh-day Sabbath and hence, the institution of the weekly occasion. In this passage as well, neither the word moedim (appointed feasts) nor khodesh (new moon) appear even once:
By the seventh day God completed His work that He had done, and He rested on the seventh day from all His work that He had done. God blessed the seventh day and declared it holy, for on it He rested from His work of creation. (Genesis 2:2-3 [HCSB])
What is strikingly stressed in this passage is the cycle of the seventh day, not the arrival of a new moon. Other verses that stress the concept of “the seventh day” as a definitive element in the seventh-day Sabbath's timing include Exodus 23:12; 31:15, 17; 34:21; 35:2; and Deuteronomy 5:13-14.
Finally, khodesh and moedim are conspicuous by their absence in the Sabbath commandment itself—not even a hint:
Remember the Sabbath day, to keep it holy: You are to labor six days and do all your work, but the seventh day is a Sabbath to the Lord your God. You must not do any work—you, your son or daughter, your male or female slave, your livestock, or the foreigner who is within your gates. For the Lord made the heavens and the earth, the sea, and everything in them in six days; then He rested on the seventh day. Therefore the Lord blessed the Sabbath day and declared it holy. (Exodus 20:8-11 [HCSB])
In each of these pivotal passages concerning the weekly Sabbath, the word moedim is absent. Its absence shows that the weekly occasion is not an “appointed feast” and therefore not part and parcel with the annual occasions, which are defined by a separate cycle. In addition, in each of these same passages, the word khodesh is also absent, indicating that the new moon is not a factor in determining the coming of the seventh-day Sabbath.
In summary then, lunar Sabbatarians ignore the clear fact that God has instituted two discrete cycles and with them, two different methods of determining the fall of Sabbaths. Lunar Sabbatarians apply the method of counting the holy days—which at its core does involve the new moons—to determining the occurrences of the weekly Sabbaths. However, the Scriptures do not support using the same method for both cycles.
To reiterate: The new moon and the lunar month are irrelevant in determining which day the seventh-day Sabbath falls on.
The Lunar Sabbath or the Seventh-Day Sabbath: Which?