Klal Yisroel's existence crystalized with the revelation at Sinai, and indeed two yomim tovim speak of Sinai. Shavuos, the holiday that focuses on the giving of the Torah, places the events at Sinai as its focal point. But Rosh Hashana also carries an extraordinary focus on Sinai, and that is rather puzzling.
In the Mussaf shemoneh esrei of Rosh Hashana we introduce the Shofros - undoubtedly the central feature of Rosh Hashana - via the shofar of Sinai. This is quite surprising. For although there was the sound of a shofar at Sinai, the shofar seemed to play but a minor role in the Sinai revelation. [The Kaf Hachaim also says that that is the reason we blow at the bimah - to mirror Sinai.] If one were looking for an event to elaborate on in Shofros, one could have chosen the akeidah, where the ram and its horn, as well as the zechus of the akeidah, seem to play a major role.
The phrasing of that section of Shofros is that Hashem, "revealed Himself at Sinai to teach us Torah and mitzvos, and You let them hear the majesty of Your 'kol', and Your sacred words". There seem to be two communications here: the dibbur - sacred words - and the kol. One would venture to guess that these are two aspects of the revelation which express themselves in these two yomim tovim. But what are these aspects?
Let us first examine closely the concept of Malchiyos. At first glance Hashem's malchus is but a mere conceptual prerequisite, i.e. it is only because Hashem is boss that we are obligated to fulfill His dictates. Therefore, we first establish that Hashem is king, and as king He commands and judges us as to how well we have obeyed. But if we look at the bulk of the Malchiyos prayer, malchus is not a mere prerequisite; rather the prayer is all about establishing Hashem's malchus and realizing its fulfillment entirely.
One is therefore led to understand a much bigger picture of Hashem's malchus and His expectations of us. While there are detailed commands of what to do and what not to do, there is, more significantly, the sweeping vision of what it is that Hashem wants of the world. All the details of the various mitzvos come together to form a picture that integrates every element in creation. And that is malchus. Malchus is not so much the mere acknowledgement that Hashem is king; but more so that the world is His kingdom and it's meant to reflect in its entirety that vision that Hashem had for it when He created it. We, therefore, on the day of creation, start by expressing our yearning for the day that malchus will become totally revealed.
This grand vision was revealed to us at Sinai; for alongside the revelation of the particulars of Torah, Hashem revealed to us the big picture as well. When a person speaks, his dibbur-words define the specifics, but his voice-kol gives me the general sense of his emotions, etc. Hashem revealed to us at Sinai both the dibbur and the kol. The dibbur is the subject of Shavuos, and the kol is the focus of Rosh Hashana.
This adds another dimension to our cheshbon hanefesh on Rosh Hashana. It is not enough to merely ponder which details of the Torah am I following, and in which is my observance lacking. Perhaps, this is the point of Yom-Kippur, with its meticulously detailed vidui, based on the aleph-beis. And indeed, the passuk urges us, "k'chu imachem devarim v'shuvu el Hashem- bring your words with you and come back to Hashem."
But on Rosh Hashana we ask ourselves, is our vision of our life in consonance with Hashem's vision? Is our life's yearning to be btzelem Elokim; Adam as he was meant to be? Is our vision of the world, a world of "l'saken olam b'malchus Shakkai"?
Let us first make sure that our "kol" is the "kol of Yaakov", and only then can we pay attention to each and every dibbur.