The Rambam's Thirteenth Principle: The number of days a mitzvah is performed is irrelevant

Some mitzvos are only performed on a certain day or days. Biblically, sitting in a Succah is a mitzvah for seven days but it’s one mitzvah, not seven. A special sacrifice is offered on Rosh Chodesh, the start of the new month, but there are 12 months in a year. To offer the Rosh Chodesh offering is one mitzvah, not twelve. If someone were to suggest that it should be 12 mitzvos (one for Adar, one for Nisan, one for Shvat…), the obvious retort would be that the daily sacrifice isn’t 365 mitzvos! (Or 354 mitzvos, if we’re talking about the lunar year.)

So the musaf sacrifice for Rosh Chodesh is one mitzvah. The musaf sacrifice of Shabbos is one mitzvah. Similarly, the musaf of each holiday is one mitzvah, even though it may be offered for many days in a row. Likewise, the chagigah sacrifice brought on each of the three festivals is likewise one mitzvah. (The fact that the multiple days are not consecutive is irrelevant.) Similar to this, the obligation to travel to the Temple in Jerusalem for each of the three festivals is a single mitzvah.

As with other principles, the Rambam tells us that previous compilers erred in this matter. However, surprisingly, they erred by overcompensating. They counted the musaf offerings of Shabbos, Yom Tov and Rosh Chodesh as a single mitzvah, which they are not. Inconsistently, they counted the obligation to refrain from labor on each holiday as a separate mitzvah. The Rambam clarifies that just as the obligation to refrain from labor is a separate mitzvah for each festival, so too is each festival’s musaf offering.