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The holiday of Rosh Chodesh in scripture:
The commemoration of Rosh Chodesh as a joyful day is brought in scripture in the verse “Ubeyom Simchaschem Ubemoadeichem Ubiroshei Chodsheichem.” This verse lists the day of Rosh Chodesh together with Shabbos and Yom Tov, which gives implication to its holiday status. We likewise find that Yehonason discussed with David whether he would be present by the Rosh Chodesh feast taking place in the house of Shaul. Rashi explains that it was customary for Dovid to participate in the Holiday meals. From here we see that Rosh Chodesh was considered a Holiday. In various other areas of scripture, we likewise find reference to the Holiday of Rosh Chodesh. The above verses however do not prove that the Holiday of Rosh Chodesh has the Halachic status of a Moed, as do the other Holidays. The Talmud however concludes that Rosh Chodesh is considered a Moed, as the verse states “Vekara Alaiy Moed” and this verse is going on Rosh Chodesh Tamuz. For this reason, the sacrifices of Rosh Chodesh receive laws similar to the laws of the sacrifices of the other holidays, such as its ability to be offered even in impurity.
Is the festive celebration of Rosh Chodesh of Biblical or Rabbinical status?
Some Poskim rule the Holiday of Rosh Chodesh is of Biblical status, and it is hence Biblically forbidden to fast on that day. [Accordingly, one who eats on Rosh Chodesh is fulfilling a biblical preset ] Other Poskim, however, rule it is only of Rabbinical status [and hence there exists no Biblical prohibition of fasting or Biblical obligation to eat].
 Bamidbar 10:1-2, 10
 Shmuel 1 20:18
 See Melachim 2:4, 22-23; Divrei Hayamim 2:31; Moadim Behalacha [Zevin] p. 134
 Shavuos 10a; Pesachim 77; Taanis 29
 Eicha 1
 Mishneh Pesachim 76b
 See Michaber 418:4 and 570:1; M”A 418:1; Biur Halacha 418 “Rosh Chodesh Assur”; Kaf Hachaim 418:13
 Implication of Rambam, brought in Michaber and Poskim ibid regarding fasts
 Michaber ibid