Leviticus 23:39

But on the fifteenth of the seventh month, at the time when you collect the produce of the ground, you shall solemnize a festival of the Lord seven days. On the first day, rest; and on the eighth day, rest.

Since the previous passage discusses self-affliction, Scripture now uses the word However to teach us that it is forbidden to fast on Sukkot, as it is written: “you shall rejoice” [Deuteronomy 16:14] and “you shall be only happy” [Deuteronomy 16:15].

when you gather the produce of the land fields as well as vineyards you will celebrate

This ‘ayin-‘ayin verb refers to the festival peace-offering.

on the first day is a day of rest The latter word is a predicate nominal; the connective “…there will be for you…” is implied (if the latter word were a predicate adjective, then the heh of the definite article would replace the preposition bet ).

WHEN YE HAVE GATHERED IN THE INCREASE OF THE LAND. “[This is to state] that this seventh month [in which the Festival of Tabernacles occurs] must be at the time of the harvest. From here we learn that they were commanded to intercalate the years [with an extra month], because if there would be no such intercalation, the seventh month [i.e., Tishri] would sometimes fall in the middle of the summer, or in the winter.” This is Rashi’s language. And the words of the Torath Kohanim are as follows: 15:6-7. “Intercalate the years so that you make the Festival of Tabernacles at the time of the ingathering of the fruits. I might think that this refers to the ingathering of all the fruits; Scripture therefore says, Thou shalt keep the feast of Tabernacles … after thou hast gathered in from thy threshing-floor and from thy wine-press — ‘from’ thy threshing-floor but not all thy threshing-floor, and ‘from’ thy wine-press, but not all thy wine-press. Now if I am to follow the expression after thou hast gathered in ‘from’ thy threshing-floor, I might think that even if only a little [of it has been gathered in, the Festival of Tabernacles may already be observed in that part of the year, and there is no need then for intercalating an extra month at the end of the preceding winter]; Scripture therefore says [here], when ye have gathered in the produce of the land. How can these be reconciled? [In the following manner]: Try to intercalate the year so that the Festival of Tabernacles occurs when most of the fruits have already been gathered in.” Now the Sages have already derived [the need for] intercalating the year from the verse Observe the month of ‘aviv’ (spring)., 16:1. This teaches that before it comes you are to watch whether that month will be capable of producing aviv (ripe ears), and if not, intercalate a year [by adding a month to the winter period] (Rashi ibid., on the basis of Sanhedrin 11 a). But there Scripture taught about [the intercalation of the year because of] the spring [i.e., so that the celebration of the exodus occurs in the month when there are ripe ears already, so that the sheaf of waving can be brought on the sixteenth of Nisan from the new barley], and here it teaches concerning the fruits of the trees [that most of them must be ripened at the time of the Festival of Weeks, so that they are ready to be brought as first-fruits to the Sanctuary, and that most of them are to …

אך בחמשה עשר יום לחודש השביעי, even though both New Year and the Day of Atonement are primarily designed to help the people achieve atonement for their sins and their being remembered favourably by G’d, Sukkot is for enjoyment and giving thanks to the Lord for having enabled them to fill their barns with good produce at the end of the harvest season.

אך בחמשה עשר יום, after the Torah had discussed the subject of the festivals in general terms, i.e. their common denominator being that these days are called מקראי קודש on which fire offerings on the altar are being offered on the altar in the presence of the Lord, the Torah continues 'אך בחמשה עשר יום וגו, by showing that the festival of Sukkot is different from all the other festivals: 1) the eighth day of that festival is called as we know from וביום השמיני שבתון, that the eighth day of that sequence of days is to be regarded as a kind of Sabbath. Such a concept does not exist as a special, day in the “week,” nor on the festival of matzot, neither in connection with months or years. In respect of all of these only the number seven has a connotation of holiness, not the number eight.
2) This is the only festival in which the Jew is required to change his home, move out of his regular home, as stated clearly in verse 42.
3) it requires that every Jew take four plants of specific categories and wave them in the 6 directions on earth. (compare verse 40)

אך בחמשה עשר יום, “but on the fifteenth day, etc.; the introductory word אך here is justified, as on Sukko,t when the harvests have all been brought in and stored, the degree of joy is much greater than on Pessach and Shavuot, the former being a festival when the word שמחה, joy, is not even mentioned, as no part of the year’s crops have as yet been harvested. On Sukkot we celebrate not only the material blessings the Lord has bestowed upon us but also the spiritual blessings, seeing that only four days before its beginning we have become relieved of the burdens of our sins. On this festival the expression שמחה is associated with these days no fewer than three times (including Deuteronomy 15,14). This joy is due to the harvests of our fields, orchards, and the forgiveness of our sins. This is why the Torah is able to urge us: והיית אך שמח, “you shall be joyous without any reservations.”