[8] This follows the explanation of Pirkei De-Rabbi Eliezer 45, Tur 417, Perisha 417:1, and Darkhei Moshe 417:1 (quoting Or Zaru’a) explain the issue. R. Ĥayim Vital explains in Sha’ar Ha-kavanot 76b that women correspond to the sefira (kabbalistic "emanation") of malkhut (kingship) and the moon, both of which renew themselves, while men correspond to tiferet (beauty), which does not renew itself. (Furthermore, malkhut involves a decline, from which it can reach even higher than tiferet. This is alluded to in the verse, "A capable wife is a crown for her husband" [Mishlei 12:4].)

[9] Tur and Beit Yosef oĥ 417 explain that the main source for this custom is y. Ta’anit 1:6: "Those women who are accustomed not to work on Rosh Ĥodesh – it is a custom." According to Rabbeinu Yeruĥam, a woman who never followed such a custom need not take it on. However, bhl 417, s.v. "ve-hanashim," states that according to most Rishonim, all women must keep this custom, but they can fulfill their obligation by refraining from any minimal type of work. If, however, they have a more stringent custom that forbids additional types of work, their custom is binding. Indeed, some act more stringently, and I wrote that this is considered going above and beyond. Eshel Avraham (Buczacz) states that even those who go above and beyond should not treat Rosh Ĥodesh more stringently than they do Ĥol Ha-mo’ed. Therefore, they may wash clothes for the sake of Rosh Ĥodesh, because the reason for the prohibition on Ĥol Ha-mo’ed is only to ensure that people wash their clothes in anticipation of the holiday. Regarding washing machines: Sefer Rosh Ĥodesh 11:7 states that some are stringent, but that R. Shlomo Zalman Auerbach permits it, because it involves no effort.

ahs 417:10 states that a woman may work on Rosh Ĥodesh in order to make a living, and that this is the prevalent custom. Hilkhot Ĥagim 1:5 agrees. This can be derived from a kal va-ĥomer (a fortiori argument): If she is liable to lose her job, or if she needs that day’s wages desperately, she may work even on Ĥol Ha-mo’ed. Thus, it is all the more so on Rosh Ĥodesh, which is a lesser holiday. Some women go above and beyond and forgo working that day if they can do so easily. It seems to me that even women who go above and beyond are lenient when it comes to writing for purposes that are not related to work.

According to Shibolei Ha-leket, when Rosh Ĥodesh is two days long, the custom for women to refrain from working applies only on the second day, the first of the new month. Roke’aĥ maintains that it applies on both days. Mor U-ketzi’a maintains that the custom applies only during the day on Rosh Ĥodesh, not at night. It seems to me that women follow this custom at night as well. See mb 417:4, bhl (end of 417).

bhl 417, s.v. "minhag tov," states in the name of Baĥ that a husband may not demand that his wife work on Rosh Ĥodesh, but she may work if she desires. As stated above, most poskim agree that a woman should refrain from doing some form of work. Since it is a mitzva for a woman to refrain from working, even though it is not obligatory, it is clear that her husband cannot demand that she work on Rosh Ĥodesh, except for housework, like cooking.

Ĥida (Responsa Yosef Ometz §20) cites Rishonim who maintain that men had a custom as well to refrain from working on Rosh Ĥodesh. He explains that this custom developed because they would bow before God in the Holy Temple. Turei Even (on Tractate Megilla) claims that the custom was based on the musaf sacrifices that were offered in the Temple on Rosh Ĥodesh. Either way, most poskim believe that this custom is not binding (mb 417:2).