Shemini Atzeres as crown of the festivals

ענין שמיני עצרת שהוא רגל בפני עצמו ומ"מ יש רק ג' רגלים.

The matter of Shemini Atzeres, which is a festival in its own right, and yet there are only three regalim.

The Sefas Emes raises the tension: Shemini Atzeres has the standing of an independent yom tov, yet the Torah counts only three pilgrimage festivals.

והענין הוא שהג' רגלים הם מתנות משמים.

The matter is that the three regalim are gifts from Heaven.

The three festivals are given to us from Above — pure gifts of Divine bounty.

וכשמקבלים הג' רגלים כראוי זוכין לשמ"ע.

And when one receives the three regalim properly, he merits Shemini Atzeres.

Shemini Atzeres is not a fourth gift but the reward earned by receiving the three festivals as one should — it flows from them.

וז"ש במד' פינחס עליך להוסיף לנו מועדות כו'.

And this is what the Midrash on [Parshas] Pinchas says: "It is upon You to add festivals for us..."

The Midrash hints that Shemini Atzeres is an "addition" — a bonus festival that comes as a result of our keeping the others.

וז"ש והיית אך שמח שהוא לרבות שמ"ע כי זה בא ממילא כשמקיימין הרגלים כראוי.

And this is the meaning of "and you shall be only joyful" (Devarim 16:15) — the word "only" (ach) comes to include Shemini Atzeres, for it comes of itself when one keeps the festivals properly.

The seemingly limiting word ach is expounded as an inclusion: the added joy of Shemini Atzeres arises automatically from a proper observance of the three regalim.

והוא כמו תוספות ברכה שמתפשט מהג' רגלים תוספות רגל בפני עצמו.

And it is like an added blessing that extends from the three regalim — an additional festival in its own right.

Shemini Atzeres is an overflow of berachah from the three festivals, so abundant that it crystallizes into a distinct yom tov of its own.

ואיתא במשנה שלשה כתרים הם כתר תורה כהונה ומלכות וכתר שם טוב עולה על גביהן.

And it is taught in the Mishnah: there are three crowns — the crown of Torah, of Kehunah, and of Malchus — and the crown of a good name (shem tov) rises above them all (Avos 4:13).

The Sefas Emes brings the parallel of the three crowns, over which a fourth — the crown of a good name — stands supreme.

והג' כתרים הם ג' מועדות ושמ"ע עולה על גביהם.

And the three crowns correspond to the three festivals, and Shemini Atzeres rises above them.

Just as the crown of a good name crowns the other three, Shemini Atzeres crowns the three regalim as their culmination.

והם הג' אבות ודוד המע"ה רגל ד' שבכסא:

And they correspond to the three Avos, with Dovid HaMelech, alav hashalom, as the fourth "leg" of the Throne.

The three festivals mirror the three Avos who are the legs of the Merkavah, and Shemini Atzeres corresponds to Dovid, the fourth leg of the Kisei HaKavod — the crowning completion.

Summary: Shemini Atzeres is a festival in its own right yet is not counted among the three regalim because it is not a separate gift but the reward and overflow that comes "of itself" from keeping the three festivals properly. Like the crown of a good name above the three crowns, and like Dovid as the fourth leg of the Throne beneath the three Avos, Shemini Atzeres is the crowning culmination of the three regalim.