Is the New Moon day a Sabbath?

The word "Sabbath" comes from the Hebrew word for "cease."  A good reference for this is Exodus 31:16,17 in the Hebrew.  We are to cease from our jobs, our occupation that we do on the other days of the week, and be refreshed in our spiritual life.  I like to refer to the Sabbath, from this point of view, as the "day of ceasing."

Some people say that the New Moon day is a Sabbath, because sacrifices were made on that day and David came to King Saul's table on the New Moon day.  Not every day of a festival / feast ("chag" #2282) is a Sabbath, "day of ceasing."  For example, the days during the Festival of Tabernacles other than the first day are not Sabbaths; yet sacrifices and offerings were made each of these days by the priests (Numbers 29:12-32).  A sacrifice being offered does not make that day a Sabbath. Indeed, daily sacrifices were required by Torah; and if one defines a Sabbath day as one that has a sacrifice required, then every day would be a day that required a set-apart assembly and a day that no one could go to work!

Although a sacrifice was made on the new moon (Ezek 46:6), the new moon day is not listed in Leviticus 23 with the "moed" # 4150 (appointed times), which includes the weekly Sabbath.  All "moed" require a set-apart assembly and ceasing from any gainful work.

The reference in Psalms 81:3 is to the Festival of Trumpets on the first of the seventh month, the only festival that falls on a new moon; it is called a solemn feast day in that verse, because it is Trumpets, not because it is a new moon.

I believe that in I Sam 20:5, David met with the King on the new moon by tradition, not as a required assembly of Yahweh.

Personally, we meet to look for the new moon and confirm the new month.  While we are there looking at the new moon, we offer the sacrifice of the praise of our lips (Hosea 14:2).