Leviticus 23:8

but offer the oblation to the Name of the Lord seven days; in the seventh day of the feast shall be a holy convocation; you shall do no work of labour.

Scripture will give the details of the fire-offering in the parasha of Pinḥas [Numbers 28:19].

AND YE SHALL BRING AN OFFERING MADE BY FIRE UNTO THE ETERNAL SEVEN DAYS. Scripture is stating that all seven days [of Passover] should be a festival to bring an offering made by fire unto the Eternal, but not that they are all equally forbidden as far as doing work, like on the first and seventh days. He did not explain [here the precise nature of] the offering, since He is going to mention it in a special section dealing with all the offerings of the festivals, when it is His wish that they should be binding on the children of Israel, and as I have explained. And the interpretation of our Rabbis 10:5. is that [the intention of the verse here] is to state that we are to bring an offering under all circumstances, even if we do not have all the [required] Additional Offerings. This is a correct [explanation].

והקרבתם אשה לה' שבעת ימים, the offering of the mussaph offering for seven consecutive days is to remind us that the intervening days of this festival are not totally secular in nature, although only the first and seventh day have been accorded the title מקרא קודש. The whole matter of the mussaph, additional communal offerings, has not been gone into in detail here as this is a subject treated in Numbers when this legislation appears in detail in chapters 28-29. The reason why in connection with the New Year’s day the Torah does mention the offering of an אשה לה', is that this day already qualified for a mussaph offering, it being not only the first day of the new year but also the first day of the month of Tishrey. In Numbers 29,6 the Torah once more draws our attention to this fact, [presumably to tell us that New Year’s day does not replace the significance of the date of the new moon. Ed.] If you were to counter that אשה ה' is also mentioned in this chapter in connection with the day of Atonement, remember that what is referred to there are burnt offerings and sin offerings, both on behalf of the High Priest and the people but not by each individual member of the people as are sin offerings generally, not mussaph offerings which are mandatory communal offerings. The reason why the Torah listed the Sabbath and the festival of matzot in a single paragraph is that both were legislated prior to the giving of the Torah at Mount Sinai. Each of the other festivals has been accorded a paragraph of its own. The Torah commences its reference to the festival of weeks by speaking of the Omer, and the counting of the seven weeks from the Passover until that festival, seeing that the festival of weeks is also known as the harvest festival,חג הקציר and we thank the Lord for the שבועות חקות קציד, “who keeps for our benefit the weeks appointed for harvest” (Jeremiah 5,24). The principal reason for the festivals is to afford us an opportunity to express our gratitude in prayer and in deed. For instance, an example is the appointed time for the festival during spring when we pray to G’d giving thanks for His having given us our freedom at the time of the Exodus from Egypt. The Omer was an expression of gratitude for the barley harvest, the earliest opportunity to fulfill part of the bikkurim legislation, presenting the first of the ripened crop to G’d. This prayer also contains a request concerning the future. The counting of the 49 days between Passover and the festival of weeks reminds us of the need to offer such prayers on a daily basis. On the festival of Sukkot, the festival of ingathering, we thank the Lord for having enabled us to bring the year’s major harvest under our roofs.