On this basis, it is possible to explain the connection between bachodesh hashlishi, “in the third month” and bayom hazeh, “on this day”:וְזֶהוּ בַּחֹדֶשׁ הַשְּׁלִישִׁי גו' בַּיּוֹם הַזֶּה גו',
Even though the spiritual significance of bayom hazeh (interpreted in sec. 10 as referring to the revelation of G‑d’s Essence) is manifest every Rosh Chodesh,דַּהֲגַם שֶׁהָעִנְיָן דְּיוֹם הַזֶּה הוּא בְּכָל רֹאשׁ חֹדֶשׁ,
the fundamental dimension of bayom hazeh is manifest specifically on the (Rosh) Chodesh of the third month, the month of Sivan.עִקַּר הָעִנְיָן דְּיוֹם הַזֶּה הוּא בְּ(רֹאשׁ) חֹדֶשׁ הַשְּׁלִישִׁי.
The uniqueness of Sivan (as explained in the maamarim of the Tzemach Tzedek)1 can be understood as follows:וְהָעִנְיָן הוּא (כַּמְּבֹאָר בִּדְרוּשֵׁי הַצֶּמַח צֶדֶק),
The aspect of Rosh Chodesh of the first month of the year, Nissan, is identified with the moon, which represents the sefirah of Malchus.דְּחֹדֶשׁ הָרִאשׁוֹן הוּא בְּחִינַת סִיהֲרָא, מַלְכוּת.
Although on Rosh Chodesh Nissan there is also a union of the sun and the moon, as transpires on every Rosh Chodeshדַּהֲגַם שֶׁגַּם בְּרֹאשׁ חֹדֶשׁ נִיסָן יֵשׁ הַיִּחוּד דְּשִׁמְשָׁא וְסִיהֲרָא
(representative of Z’eir Anpin and Malchus respectively),(ז"א וּמַלְכוּת),
nevertheless, on Rosh Chodesh Nissan, the dominant aspect is Malchus.מִכָּל מָקוֹם, בְּרֹאשׁ חֹדֶשׁ נִיסָן, הָעִקָּר הוּא הַמַּלְכוּת.
The month of Iyar is referred to as ziv, “radiance,”2וְחֹדֶשׁ אִיָּר נִקְרָא זִיו,
alluding to the attribute of Yesod that shines within Malchus.3הוּא הַיְסוֹד שֶׁמֵּאִיר בְּמַלְכוּת.
The attribute of Yesod is referred to as ziv, “radiance,” for it is no more than a ray and a gleam.וְזֶה שֶׁהַיְסוֹד נִקְרָא זִיו הוּא לְפִי שֶׁהוּא זִיו וְהֶאָרָה בִּלְבָד.
In the third month, Sivan, Malchus receives influence from the attribute of Tiferes.וּבַחֹדֶשׁ הַשְּׁלִישִׁי מְקַבֶּלֶת הַמַּלְכוּת מִתִּפְאֶרֶת,
Tiferes embodies a revelation of G‑d’s name Havayah, which is His essential name.4דִּבְתִפְאֶרֶת הוּא הַגִּלּוּי דַּהֲוָיָ' שֶׁהוּא שֵׁם הָעֶצֶם.
Implied is that the revelation of the third month is not a mere radianceהַיְנוּ שֶׁהַגִּלּוּי דְּחֹדֶשׁ הַשְּׁלִישִׁי הוּא לֹא זִיו
(as is the revelation of the month of Iyar),(כְּהַגִּלּוּי דְּחֹדֶשׁ אִיָּר),
but rather a revelation of His Essence.אֶלָּא גִּלּוּי הָעֶצֶם.
Therefore, the fundamental spiritual significance of bayom hazeh is manifest on Rosh Chodesh Sivan, the third month.וְלָכֵן, עִקַּר הָעִנְיָן דְּיוֹם הַזֶּה הוּא בְּרֹאשׁ חֹדֶשׁ סִיוָן, בַּחֹדֶשׁ הַשְּׁלִישִׁי.
Through preparing to receive the Torah “in the third month, on this day,”וְעַל יְדֵי הַהֲכָנָה לְקַבָּלַת הַתּוֹרָה בַּחֹדֶשׁ הַשְּׁלִישִׁי בַּיּוֹם הַזֶּה
(Rosh Chodesh Sivan)(רֹאשׁ חֹדֶשׁ סִיוָן) –
both through the refinement of the emotional attributes of the animal soul (as alluded to by the term Sinai)הֵן בְּבֵרוּר הַמִּדּוֹת דְּנֶפֶשׁ הַבַּהֲמִית (סִינַי),
as well as through the Divine service of bittul (as alluded to by the term midbar, “desert”) of the G‑dly soul,וְהֵן בְּהַבִּטּוּל (מִדְבָּר) דְּנֶפֶשׁ הָאֱלֹקִית,
and, in particular, through joining together with all Jews “as one man, with one heart,”וּבִפְרָט בְּהָעִנְיָן דִּכְאִישׁ אֶחָד בְּלֵב אֶחָד
[for this (the love of one’s fellow Jew) is “the entire Torah; the remainder is merely commentary,”]5[שֶׁזּוֹ (אַהֲבַת יִשְׂרָאֵל) הִיא כָּל הַתּוֹרָה כֻּלָּהּ וְאִידָךְ פֵּרוּשָׁהּ הוּא] –
we merit to receive the Torah with joy and inner feeling,זוֹכִים לְקַבָּלַת הַתּוֹרָה בְּשִׂמְחָה וּבִפְנִימִיּוּת,
and extend its influence over the course of the entire year to come.וּמַמְשִׁיכִים זֶה עַל כָּל הַשָּׁנָה כֻּלָּהּ.

Summary

Although the spiritual significance of bayom hazeh (interpreted in sec. 10 as referring to the revelation of G‑d’s Essence) is manifest every Rosh Chodesh, the fundamental dimension of bayom hazeh is manifest specifically on Rosh Chodesh of the third month, Sivan, because it is characterized by a unique quality: In that month, Malchus receives influence from the attribute of Tiferes, which embodies a revelation of G‑d’s essential name Havayah. Thus, the revelation of the third month is not a mere radiance, but a revelation of G‑d’s very Essence.
Through preparing to receive the Torah “in the third month, on this day,” we merit to receive the Torah with joy and inner feeling, and extend its influence over the course of the entire year to come.