When Rosh Chodesh is two days, it's on the 30th of the old month and the first of the new month. Rosh Hashana falls on the beginning of the new month of Tishrei. Why then is Rosh Hashana on Tishrei 1 and 2 instead of Elul 30 and Tishrei 1?
(I know there is no Elul 30; Elul always has 29 days. Yom Kippur is on Tishrei 10 which we count from the first day of Rosh Hashana, so we can't just call it Elul 30 and Tishrei 1 -- this affects all the other days that month.)
Rosh Hashana is the only yom tov that begins a month, and so I understand that halacha's treatment of it is different from the others: it's two days everywhere, including in Eretz Yisrael, and I've been told that the rabbis (in the talmud?) describe it as one long day. But none of that tells me why it's shifted a day from other months.