Shemini Atzeres as supernatural addition

במדרש ע"פ ביום השמיני עצרת תהי' לכם.

In the Midrash on the verse: "On the eighth day there shall be an atzeres (assembly) for you." (Bamidbar 29:35)

The Sefas Emes opens with the Midrash on Shemini Atzeres.

יספת לגוי ה' נכבדת כו'.

"You have added to the nation, Hashem, You have been honored," etc. (Yeshayahu 26:15)

The verse speaks of an "addition" Hashem grants to His nation, which the Midrash links to Shemini Atzeres.

כי שמיני עצרת הוא הוספה כי הג' רגלים הם עמודי השנה אשר הם נקבעים ומוכרחים להיות בישראל.

For Shemini Atzeres is an addition, since the three regalim are the pillars of the year, which are fixed and must be observed by Bnei Yisrael.

The shalosh regalim are the necessary, fixed supports of the year, whereas Shemini Atzeres is something extra, beyond the obligatory framework.

כמ"ש שלש רגלים כו'.

As it is written, "three times (shalosh regalim) [you shall celebrate for Me in the year]," etc. (Shemos 23:14)

The Torah fixes three pilgrimage festivals as the established framework of the year.

ועליהם העולם עומד.

And upon them the world stands.

These three festivals are foundational pillars on which the world itself rests.

והם בחי' ג' אבות.

And they are the aspect of the three Avos.

The shalosh regalim correspond to Avraham, Yitzchak, and Yaakov — the foundational pillars of the nation.

ושמיני עצרת הוא תוספת בחי' דהמע"ה דלית לי' מגרמי' כלום.

And Shemini Atzeres is an addition, the aspect of Dovid HaMelech, "who has nothing of his own." (cf. Zohar)

Like Dovid, the "fourth leg" of the Heavenly Chariot who has nothing intrinsically his own, Shemini Atzeres adds nothing new of its own substance — it is pure receiving.

רק שהוא התאספות כל הג' רגלים כענין כל הנחלים הולכים אל הים.

Rather, it is the gathering-in of all three regalim, like the matter of "all the rivers flow to the sea." (Koheles 1:7)

Shemini Atzeres ("atzeres" from a root meaning to gather/hold in) draws together all the light of the three festivals, as all rivers empty into the one sea.

והוא בחי' שבת קודש שמתגלה בו אור שבעת הימים בחי' שמיני.

And it is the aspect of holy Shabbos, in which the light of the seven days is revealed — the aspect of the eighth.

Like Shabbos, which gathers and reveals the light of the preceding week, Shemini Atzeres, the "eighth," reveals the concentrated light of the seven days of Sukkos.

כי כל הארה שלמעלה מהטבע נקרא תוספות ובחי' זו מיוחד רק לבנ"י.

For every illumination that is above nature is called "addition" (tosefes), and this aspect is unique to Bnei Yisrael alone.

Anything beyond the natural order is a "tosefes" — like tosefes Shabbos — and this supernatural light belongs exclusively to Bnei Yisrael.

וסוכות הוא קיום הבריאה.

And Sukkos is the sustaining of creation.

Sukkos, with its offerings for the nations, maintains the natural order of creation.

ושמ"ע הוספה ממה שלמעלה.

And Shemini Atzeres is an addition from that which is above.

Shemini Atzeres draws down a higher, supernatural illumination beyond the maintenance of creation.

ואיתא כי הוא רגל בפ"ע ברכה לעצמו ויש בו כמה פירושים.

And it is taught that it is a festival unto itself, a blessing unto itself, and there are several explanations of this.

Chazal teach that Shemini Atzeres stands as its own regel with its own distinct blessing, understood in various ways.

והפשוט הוא כי כל רגל משאיר ברכה על כל השנה כמ"ש ברכת מועדיך.

And the simple explanation is that every festival leaves a blessing over the whole year, as it says, "the blessing of Your appointed times." (cf. liturgy)

Each regel deposits a blessing that radiates through the coming year.

ושמ"ע יש בו ברכה בפ"ע המיוחד רק לבנ"י כנ"ל:

And Shemini Atzeres has within it a blessing unto itself, unique to Bnei Yisrael alone, as above.

Beyond the blessings of the other festivals, Shemini Atzeres carries its own distinct blessing — the supernatural "addition" reserved for Bnei Yisrael alone.

Summary: The shalosh regalim are the fixed pillars of the year, corresponding to the three Avos and sustaining creation. Shemini Atzeres is a "tosefes" — an addition above nature, the aspect of Dovid HaMelech "who has nothing of his own" and of Shabbos — that gathers in and reveals the concentrated light of all the festivals, like rivers flowing to the sea. As a supernatural illumination, it is a festival and a blessing unto itself, belonging uniquely to Bnei Yisrael.