Coronating G-d
The Gra has a relatively well-known thought on the difference between a melech (king) and a mosheil (ruler). Meluchah (kingship) is a major theme, if not the major theme of Rosh haShanah. Aside from the ubiquity of the word in our liturgy for Rosh haShanah and the 10 days of Teshuvah, we find another indication in the Amidah for Rosh haShanah's Mussaf.
Three blessings are inserted to the middle of that Amidah -- Malchios (statements about G-d being King), Zichronos (about His acting on His "Memory") and Shoferos (about shofar, about the glory and noise of divine intervention). Like every holiday and Shabbos, though, there also has to be a Birkhas haYom, a blessing about the day. For Rosh haShanah Mussaf, Malchios is fused with the Birkhas haYom, because kingship is the message of the day.
Before I add my 2 cents, here's the Gra's thought.
"Ki Lashem haMluchah uMosheil bagoyim..." (For G-d's in the Kingship, and He rules over nations...) Why is Hashem "only" a Mosheil to the other nations?
"Malchuscha malchus kol olamim, umemshalticha bichol dor vador." (Your kingship is a kingship for all eternity, and/but your rule is in every generation and generation. [Tehillim, said in "Ashrei"]) Why is meluchah "for all eternity", but memshalah (dominion) lasts only "generations"?
"Vihayah Hashem limelech al kol ha'aretz..." [should be familiar from Aleinu] (G-d will be King over all the land...) In the messianic age, after the "generations", Hashem will be Melech over the other nations as well.
What's the difference between memshalah and meluchah?
The Gra explains that a melech rules by acclamation of the people. A mosheil, however well intended, has to rule by imposing his (or His) will on them. Therefore, for now, Jews strive to make Hashem our king, but for other peoples Hashem must relate as mosheil. However, in the days of "veyei'asu kulam agudah achas la'asos ritzonicha..." ("and they will all make a single union to do Your will" -- High Holiday Amidah) Hashem will be "King over all the land".
So far the Gra, in painfully short summary.
This casts the point of Rosh haShanah into being about accepting Hashem as our Melech, thereby changing His relationship to us from one of Mosheil to that of Melech.
A Melech need not impose His will in the same way that a Mosheil does. A Melech, therefore, has the opportunity to act with kindness and mercy at times when a Mosheil could not. We therefore introduce High Holidays, the days of judgement, by declaring G-d's meluchah. By voluntarily accepting Him as king we obviate the need for G-d to direct us on the right path through trials and tribulations.
And when Moses asked "hareini na es kivodechah" (Show me Your Glory [Shemos]), Hashem's answer was the 13 terms describing the aspects of Divine Mercy. "Meloch al kol ha'olam kulo bichvodecha" (Be King over all the entire world in Your Glory [Siddur]) -- the Glory of Hashem's reign as King is His Mercy. And so His "throne" is Mercy, as we say in Selichos "Ke-l Melech yosheiv al kisei rachamim" (G-d, King, "sitting" on the throne of Mercy).
It's interesting to note that the man-Melech relationship is a subtheme in Purim as well. There is no over mention of G-d in the book of Esther. However, the Talmud tells us that each occurance of the word "melech" that appears in that book can be understood midrashically as a reference to G-d. When Esther approaches the king, which is apparantly Achashveirosh but has some parallel in her approaching the King as well, she opens her request with the word "Uvchein" ("therefore" or "with this"). Similarly as do a number of requests in the blessing of the day for the High Holidays (and therefore the Rosh Hashanah Mussaf berakhah about Divine Kingship).
Three blessings are inserted to the middle of that Amidah -- Malchios (statements about G-d being King), Zichronos (about His acting on His "Memory") and Shoferos (about shofar, about the glory and noise of divine intervention). Like every holiday and Shabbos, though, there also has to be a Birkhas haYom, a blessing about the day. For Rosh haShanah Mussaf, Malchios is fused with the Birkhas haYom, because kingship is the message of the day.
Before I add my 2 cents, here's the Gra's thought.
"Ki Lashem haMluchah uMosheil bagoyim..." (For G-d's in the Kingship, and He rules over nations...) Why is Hashem "only" a Mosheil to the other nations?
"Malchuscha malchus kol olamim, umemshalticha bichol dor vador." (Your kingship is a kingship for all eternity, and/but your rule is in every generation and generation. [Tehillim, said in "Ashrei"]) Why is meluchah "for all eternity", but memshalah (dominion) lasts only "generations"?
"Vihayah Hashem limelech al kol ha'aretz..." [should be familiar from Aleinu] (G-d will be King over all the land...) In the messianic age, after the "generations", Hashem will be Melech over the other nations as well.
What's the difference between memshalah and meluchah?
The Gra explains that a melech rules by acclamation of the people. A mosheil, however well intended, has to rule by imposing his (or His) will on them. Therefore, for now, Jews strive to make Hashem our king, but for other peoples Hashem must relate as mosheil. However, in the days of "veyei'asu kulam agudah achas la'asos ritzonicha..." ("and they will all make a single union to do Your will" -- High Holiday Amidah) Hashem will be "King over all the land".
So far the Gra, in painfully short summary.
This casts the point of Rosh haShanah into being about accepting Hashem as our Melech, thereby changing His relationship to us from one of Mosheil to that of Melech.
A Melech need not impose His will in the same way that a Mosheil does. A Melech, therefore, has the opportunity to act with kindness and mercy at times when a Mosheil could not. We therefore introduce High Holidays, the days of judgement, by declaring G-d's meluchah. By voluntarily accepting Him as king we obviate the need for G-d to direct us on the right path through trials and tribulations.
And when Moses asked "hareini na es kivodechah" (Show me Your Glory [Shemos]), Hashem's answer was the 13 terms describing the aspects of Divine Mercy. "Meloch al kol ha'olam kulo bichvodecha" (Be King over all the entire world in Your Glory [Siddur]) -- the Glory of Hashem's reign as King is His Mercy. And so His "throne" is Mercy, as we say in Selichos "Ke-l Melech yosheiv al kisei rachamim" (G-d, King, "sitting" on the throne of Mercy).
It's interesting to note that the man-Melech relationship is a subtheme in Purim as well. There is no over mention of G-d in the book of Esther. However, the Talmud tells us that each occurance of the word "melech" that appears in that book can be understood midrashically as a reference to G-d. When Esther approaches the king, which is apparantly Achashveirosh but has some parallel in her approaching the King as well, she opens her request with the word "Uvchein" ("therefore" or "with this"). Similarly as do a number of requests in the blessing of the day for the High Holidays (and therefore the Rosh Hashanah Mussaf berakhah about Divine Kingship).