Hey :D
There is something with the new moon which is "Special" maybe other than the start of the month... and Trumpets - I am sure Ken knows more... as for the Shabbat? no - You count six days, and rest on the seventh - no moon linking was ever prescribed by Yah in the 7 day Sabbath cycle... any teaching of such has no basis and as far as I can see is false. You actually see a separation between Sabbaths and New Moon days anyway
But I have been meaning to investigate the new moon days and yes Ken should probably have something on that :)
Here are some out of context quotes with the "New moon" mentioned - notice is normally like "new moon nor Sabbath" "new moon and Sabbath" never the new moon Sabbath. and never commanded to count from the new moon other than to calculate feast days. Passover and the Trumpets for example. But this should give you some places to look up - obviously the translation is pretty pants being ESV...
1 Sam 20:18 Then Jonathan said to him, “Tomorrow is the new moon, and you will be missed, because your seat will be empty.
1 Sam 20:24 So David hid himself in the field. And when the new moon came, the king sat down to eat food.
1 Sam 20:27 But on the second day, the day after the new moon, David’s place was empty. And Saul said to Jonathan his son, “Why has not the son of Jesse come to the meal, either yesterday or today?”
2 Kings 4:23 And he said, “Why will you go to him today? It is neither new moon nor Sabbath.” She said, “All is well.”
1 Chron 23:31 and whenever burnt offerings were offered to the Lord on Sabbaths, new moons, and feast days, according to the number required of them, regularly before the Lord.
2 Chron 2:4 Behold, I am about to build a house for the name of the Lord my God and dedicate it to him for the burning of incense of sweet spices before him, and for the regular arrangement of the showbread, and for burnt offerings morning and evening, on the Sabbaths and the new moons and the appointed feasts of the Lord our God, as ordained forever for Israel.
2 Chron 8:13 as the duty of each day required, offering according to the commandment of Moses for the Sabbaths, the new moons, and the three annual feasts—the Feast of Unleavened Bread, the Feast of Weeks, and the Feast of Booths.
2 Chron 31:3 The contribution of the king from his own possessions was for the burnt offerings: the burnt offerings of morning and evening, and the burnt offerings for the Sabbaths, the new moons, and the appointed feasts, as it is written in the Law of the Lord.
Ezra 3:5 and after that the regular burnt offerings, the offerings at the new moon and at all the appointed feasts of the Lord, and the offerings of everyone who made a freewill offering to the Lord.
Neh 10:33 for the showbread, the regular grain offering, the regular burnt offering, the Sabbaths, the new moons, the appointed feasts, the holy things, and the sin offerings to make atonement for Israel, and for all the work of the house of our God.
Ps 81:3 Blow the trumpet at the new moon, at the full moon, on our feast day.
Isa 1:13 Bring no more vain offerings; incense is an abomination to me. New moon and Sabbath and the calling of convocations— I cannot endure iniquity and solemn assembly.
Isa 1:14 Your new moons and your appointed feasts my soul hates; they have become a burden to me; I am weary of bearing them.
Isa 47:13 You are wearied with your many counsels; let them stand forth and save you, those who divide the heavens, who gaze at the stars, who at the new moons make known what shall come upon you.
Isa 66:23 From new moon to new moon, and from Sabbath to Sabbath, all flesh shall come to worship before me, declares the Lord.
Ezek 45:17 It shall be the prince’s duty to furnish the burnt offerings, grain offerings, and drink offerings, at the feasts, the new moons, and the Sabbaths, all the
appointed feasts of the house of Israel: he shall provide the sin offerings, grain offerings, burnt offerings, and peace offerings, to make atonement on behalf of the house of Israel.
Ezek 46:1 “Thus says the Lord God: The gate of the inner court that faces east shall be shut on the six working days, but on the Sabbath day it shall be opened, and on the day of the new moon it shall be opened.
Ezek 46:3 The people of the land shall bow down at the entrance of that gate before the Lord on the Sabbaths and on the new moons.
Ezek 46:6 On the day of the new moon he shall offer a bull from the herd without blemish, and six lambs and a ram, which shall be without blemish.
Hos 2:11 And I will put an end to all her mirth, her feasts, her new moons, her Sabbaths, and all her appointed feasts.
Hos 5:7 They have dealt faithlessly with the Lord; for they have borne alien children. Now the new moon shall devour them with their fields.
Amos 8:5 saying, “When will the new moon be over, that we may sell grain? And the Sabbath, that we may offer wheat for sale, that we may make the ephah small and the shekel great and deal deceitfully with false balances,
Col 2:16 Therefore let no one pass judgment on you in questions of food and drink, or with regard to a festival or a new moon or a Sabbath.