Albert Barnes Commentary Leviticus 23:34

"Speak unto the children of Israel, saying, On the fifteenth day of this seventh month is the feast of tabernacles for seven days unto Jehovah." — Leviticus 23:34 (ASV)

Seven days - Like the Passover, the Feast of Tabernacles commenced at the full moon, on the fifteenth day of the month, and lasted for seven days.

The week of the feast was followed by an eighth day, which strictly formed no part of it (Leviticus 23:36; Numbers 29:35; Nehemiah 8:18). This day was a holy convocation and appears to have been generally distinguished by the term translated “solemn assembly” (Deuteronomy 16:8; 2 Kings 10:20; Isaiah 1:13; Joel 1:14; Joel 2:15).

From its derivation, the original word appears strictly to denote a closing festival, and this rendering would apply most perfectly to the day after the week of the Feast of Tabernacles, as the conclusion of the series of yearly festivals.