The prophet Isaiah declares: "Seek G-d when He can be found, call to Him when He is near." The Talmud explains: "This refers to the Ten Days of Repentance between Rosh Hashanah and Yom Kippur."
Torah is precise. Why does the Talmud speak of ten days "between" Rosh Hashanah and Yom Kippur, when in fact there are only seven?
Even while they share the general theme of repentance, Rosh Hashanah and Yom Kippur each contain a unique quality. Rosh Hashanah is a day of coronation of G-d as our King. In the process of recommitting ourselves as His subjects, we also repent "out of love" -- which is why the liturgy does not mention anything negative. Yom Kippur is a day which, on its own, brings atonement for sins; at the same time, it is also the culmination of the journey of repentance that began ten days earlier, on Rosh Hashanah.
On the one hand, they each have their own special quality; on the other, they share the overarching theme of the Ten Days of Repentance.
6 Tishrei, 5747 · October 9, 1986
From Living Torah Volume 105 Program 419