The Tur (או"ח סי' תיז) writes in the name of his brother, Rabbeinu Yehudah: just as the three great Yamim Tovim align with the three Avos - Pesach with Avraham, who baked matzos for his guests; Shavuos with Yitzchak, whose binding was accompanied by the very shofar that sounded at Mattan Torah; Sukkos with Yaakov, who built sukkos - so too the twelve months of the year correspond to the twelve Shevatim.
The Bach explains that the Yamim Tovim were given to us in the merit of our Avos, and the twelve Roshei Chodashim - in the merit of the Shevatim.
How are the Avos and the Shevatim connected to the calendar? The answer might lie in the fact that, unlike Shabbos, whose sanctity was fixed by Hashem at Creation, the sanctity of Rosh Chodesh depends upon Klal Yisrael. Through the mitzvah of Kiddush Hachodesh, it is the Yidden who determine when the new month begins, and consequently when the Yamim Tovim will be observed.
The extraordinary significance of this responsibility is highlighted by the Midrash. Commenting on the words "הַחֹדֶשׁ הַזֶּה לָכֶם", the Midrash describes a remarkable dialogue between the malachei hashareis and Hashem. The angels ask, "Master of the Universe, when will You establish the festivals?" Hashem replies, "I and you will agree with whatever Yisrael decide. The festivals are determined by their declaration, whether they proclaim the month at its proper time or not at its proper time."
Hashem then tells Klal Yisrael: "Until now, this authority rested in My hands, as it says, 'He made the moon for appointed times' (תהלים קד יט). But from now on, it is entrusted to you. If you say 'yes,' then yes; if you say 'no,' then no... Moreover, if you wish to intercalate the year, I join with your decision." (שמות רבה טו ב)
To understand the meaning of this statement, we have to know a little about the process of sanctifying the new month. As soon as someone saw the tiniest sliver of a new moon, they would run to the Sanhedrin, who needed two witnesses to testify that the moon was actually seen. They would then convene the court, declare the new month and send messengers across the land to tell everyone that the new month had begun on this certain day. They, in turn, would pass on the news and place torches on mountains and high spots to spread the news faster.
Our calendar determines on which day each Jewish holiday will occur. Each particular holiday brings with it a concrete spiritual reality from Above that is available for us to tap into on that specific day. Pesach, for instance, contains the opportunity to attain spiritual freedom; Rosh Hashanah is the time for judgment.
The determination of this calendar is placed squarely in human hands. Thus, if the moon were to appear, in fact, on a Monday, but no one actually saw it until Tuesday, the Sanhedrin would decide that the first of the month was on a Tuesday. As a result, Hashem, as it were, follows the decision of the court and acts accordingly, so that in the case of Rosh Hashana, He would push off His judgment of the entire world by one day!
Hashem is giving the Yidden an empowering message with this first commandment. Up until now, the Yidden have been slaves to the Egyptians. Their time was not their own. Now, says Hashem, you are becoming masters of your time. And not only of your own time, but of My time as well!
