Why does the Shaliach Tzibbur start Shacharis on Shabbos from Shochein Ad, on Yom Tov from HaKeil, and on Rosh HaShana/Yom Kippur from HaMelech?
3also, according to nusach bnei Ashkenaz (German, not Eastern European), the sha"tz starts with a different section each yotiv (see Siddur Bnei Ashkenaz)– Charles KoppelmanJun 7, 2012 at 18:28
@CharlesKoppelman Dead link.– Double AA ♦Jul 10, 2015 at 3:17
Thanks for posting this question. It and its answers are going to go very well in Days of Awe - Mi Yodeya?.– Isaac Moses ♦Jul 20, 2015 at 4:41
The old Ashkenazi Minhag referenced above is HaEl on Shavuot, HaGadol on Sukkot/ShAtz and HaGibbor on Pesach. (See Tashbetz Kattan 245)– Double AA ♦Oct 28, 2016 at 6:04
Levush (Orach Chaim 488:1) says that we start with הא-ל בתעצומות on Yom Tov, because all of them are "in remembrance of the Exodus from Egypt," when Hashem displayed His mighty power. He also says (ibid. 584:1) that we start with המלך on Rosh Hashanah and Yom Kippur (and change the wording to המלך יושב, "the King is sitting"), because these are the times when He is sitting on His throne of judgement.
Not sure about Shochein Ad on Shabbos.
Rabbi Sir Jonathan Sacks, in his Siddur commentary, addresses this question along similar lines as the Levush quoted by Alex:
The Leader begins at different points on different holy days of the year. On Shabbat he begins with "He inhabits eternity," emphasizing creation; on Yom Tov, with "God - in Your absolute power," laying stress on God as He acts in history; on Rosh HaShana and Yom Kippur, with "The King - enthroned," evoking ideas of justice and judgement.
I know this question is many years old and I'm a bit late, but I was surprised that no one quoted the footnotes to the ArtScroll Siddur, which clearly give reasoning to this.
In many congregations it is customary to divide the Sabbath and Festival services among several chazzanim: one for Pesukei D'zimrah; another for Shacharis; and a third for Mussaf. On the Sabbath, the chazzan changes at שׁוֹכֵן עַד, He Who abides forever, because the Sabbath was the climax of creation, when God had all of creation, including man, to acknowledge and praise Him; on Festivals the chazzan of Shacharis begins הָאֵל בְּתַעֲצֻמוֹת, O God, in the Omnipotence, because the Festivals testify to the Exodus, when God revealed 'the omnipotence of His strength;' however, on Rosh HaShanah and Yom Kippur, when God is 'King sitting in judgment', the chazzan begins הַמֶלֶךְ, the King (Levush).
Why quote artscroll when Alex already quoted the Levush?– Double AA ♦Oct 25, 2017 at 17:48
@DoubleAA - Alex's answer doesn't include why we say שוכן עד on Shabbos. I just included the entire note though to make the whole thing cohesive.– ezraOct 25, 2017 at 18:01
If Alex didn't quote it I bet the Levush didn't say it which makes Artscroll misleading. Can anyone check what the Levush really said?– Double AA ♦Oct 25, 2017 at 18:04