Festivals Channeling Priestly Blessings
עוד רמז בג' רגלים שבהם יורד ן הברכות על כל השנה והם ג' ברכות שבברכת כהנים בחי' ג' אבות
There is a further hint within the Three Festivals, through which the blessings descend for the entire year, and these correspond to the three blessings of Birkas Kohanim, which are in the aspect of the three Avos.
The Three Festivals are channels through which blessing flows down for the whole year, and they parallel the three verses of the priestly blessing, which themselves correspond to the three Avos.
יברכך בחי' אברהם לכן כתיב וישמרך שצריך שמירה מפסולת דישמעאל
"May Hashem bless you" (Bamidbar 6:24) is the aspect of Avraham; therefore it is written "and guard you," for one requires protection from the dross of Yishmael.
The first verse aligns with Avraham, whose trait of kindness needs guarding so that no unworthy element, like that which issued from Yishmael, mixes in.
יאר בחי' יצחק וצריך חנינה כי הוא מדה"ד
"May Hashem cause His countenance to shine upon you" (Bamidbar 6:25) is the aspect of Yitzchak, and this requires "and be gracious to you," for he is the attribute of strict judgment.
The second verse, of Hashem's shining countenance, aligns with Yitzchak, who embodies strict judgment, which is why it must be tempered with the request for graciousness.
וי"ל נמי להיפוך יברכך בחי' יצחק ויאר בחי' אברהם
One may also say it in the reverse: "May Hashem bless you" is the aspect of Yitzchak, and "May Hashem cause His countenance to shine" is the aspect of Avraham.
Alternatively, the pairing can be flipped, so that the first verse reflects Yitzchak and the second reflects Avraham.
אכן ישא הוא בחי' יעקב והוא עצם הברכה
Indeed, "May Hashem lift up His countenance toward you" (Bamidbar 6:26) is the aspect of Yaakov, and this is the very essence of the blessing.
The third verse corresponds to Yaakov, the perfected middle path, and this is the true core of the blessing.
וכיון שנמסרו הרגלים לבנ"י הברכות בידם
And since the Festivals have been handed over to Bnei Yisrael, the blessings are in their hands.
Because the Festivals were entrusted to Bnei Yisrael, the power to draw down these blessings now rests with them.
ויתכן ג"כ לומר כי אהרן הוא שורש הברכות כדאיתא וישא אהרן את ידיו כו' מכאן זכה לברכת כהנים וכיון שנסתלק אהרן נולד ערעור על הברכות ורצה אותו הרשע לקללם והוצרך להיות אז התהפכות הקללה לברכה:
It is also fitting to say that Aharon is the root of the blessings, as it is brought down, "And Aharon lifted up his hands" (Vayikra 9:22) and so forth — from there he merited Birkas Kohanim; and since Aharon was taken away, a challenge arose over the blessings, and that wicked one wished to curse them, and it was necessary then for the curse to be transformed into a blessing.
Another approach is that Aharon is the source of all the blessings, having merited Birkas Kohanim when he raised his hands; once he passed away, the blessings were left vulnerable, which is why Bilaam sought to curse Bnei Yisrael and Hashem had to turn his intended curse into a blessing.
Summary: The Sfas Emes connects the Three Festivals, through which Hashem sends down blessing for the entire year, to the three verses of Birkas Kohanim, which in turn correspond to the three Avos. He maps each verse onto an Av: "May Hashem bless you" to Avraham, who needs guarding from the dross of Yishmael; "may His countenance shine" to Yitzchak, whose judgment needs the tempering of graciousness; and "may He lift His countenance" to Yaakov, which is the very essence of the blessing — while noting the first two pairings can also be reversed. Since the Festivals were handed over to Bnei Yisrael, the capacity to draw these blessings now lies in their hands. He further suggests that Aharon is the root of the blessings, having merited the priestly blessing when he lifted his hands, so that after his passing a challenge arose over the blessings, prompting Bilaam's attempt to curse Bnei Yisrael and Hashem's transformation of that curse into blessing.