Komentaryong Sumisipi para sa Levitico 8:33

Seven days... We separate the High Priest. Since all the service of Yom Kippur is not kosher except through him [Yuma 32a and many other places], as it says in regard to Yom Kippur (Vaikra chapter 16) "And the Cohen ,who will be anointed with oil, will atone." [note of the translator: from this verse we see that only the anointed Cohen, i.e. High Priest can perform atonement service of Yom Kippur]. And this separation is learned out for us from what is written in regard to seven days of the dedication [of the Mishkan] (ibid. chapter 8) "And from the entrance of the Tent of Meeting don't go away for seven days", and after this it is written (ibid.) "Just like was done on this day commanded Hashem to do to atone for you", and the sages expound: [the phrase] "to do" this is doings of the cow [red heifer], [and the phrase] "to atone for you" this is doings of the Yom Kippur. Thus, the Cohen that burns the cow [red heifer] and the Cohen serving on Yom Kippur, both require separation from their houses for seven days just like were required Aharon and his sons during the seven days of dedication [of the Mishkan]. [note of the translator: thus, from the proximity of the two verses, the verse that talks about the seven days of separation during the dedication of the Mishkan and the verse that was expounded to mean "just like was done on this day, commended Hashem to do for the procedure of the Red heifer and the Yom Kippur service", the sages learn that the Cohen that does the burning of the red heifer and the High priest that serves on Yom Kippur should be separated from their houses similar to the seven day separation of the days of dedication of the Mishkan.]

And it was on the eighth day. This is the eighth day of the inauguration. It appears from this that this day is also included among the inauguration days that preceded it, but this is not [correct], for the verse says For seven days shall your hands be filled (Leviticus 8:33). And although this day was an inauguration for the dedication of the altar, nevertheless, what does the initiation of Aaron and his sons have to do with the dedication of the altar?
Perhaps it is that since on this very day the Lord appeared to them, and not on the preceding days, therefore it needed to give a reason what made this day special among days — because this day was the eighth, and this is what gave it extra holiness. For every number seven is mundane and the number eight is sacred, according to the opinion of the Midrash (Yalkut Shimoni, Exodus 241:15) which says that all of Moses’s praise was with [the word] az [when/then], and from when I came to speak in Your name, then Moses sang, etc., because az [numerically equals eight, as alef = one, zayin = seven] refers to the One riding over the seven, meaning to establish the Holy One, blessed be He, over all seven planets and over all creations that were formed in the seven days of creation.
Therefore, the Lord appeared to them specifically on this day because it was the eighth, as this number is uniquely associated with Him, blessed be He. And this is the reason for a sacrifice not being acceptable except from the eighth day and onward, and this is the reason why circumcision on the eighth day overrides the Sabbath on the seventh, because the spiritual overrides the physical.

Seven days before the burning of the [red] cow they would separate the priest who was to burn the cow from his house to a chamber that was facing the north-eastern corner of the birah, and which was called the Stone Chamber. The idea of setting aside the priest who would burn the red cow seems to be derived from the setting aside of the high priest before the Yom Kippur worship (see Yoma 1:1). And both ideas are learned from the setting aside of Aaron and his sons for seven days before the original sanctification of the altar in Leviticus 8:33-34. Part of the reason that the priest had to leave his house was to prevent him from being with his wife and thereby becoming ritually defiled. There are two opinions as to what "Birah" is. One holds that this is another name for the Temple, while another holds that this is a tower that was on the Temple Mount. See also Pesahim 7:5.