Yom Teruah is September 24 at sundown until the 25th at sundown. Rabinically through the 26th.
Yom Kippur is October 3 at sundown and the eight day celebration of Sukkot begins October 8th.
Though Yom Teruah falls in the seventh month it is considered the new year spiritually, on the Hebrew calendar (it will be the year 5775), and is known as Rosh Hashanah--the head of the year.
Tell the people of Israel, "In the seventh month, the first of the month is to be for you a day of complete rest for remembering, a holy convocation announced with blasts on the shofar. Do not do any kind of ordinary work, and bring an offering made by fire to YHWH." -Vayikra 23:23-25
Where these feasts fall on the calendar used to seem a bit off to me. Last year I was so frustrated with the timing of the festivals and their no-work prohibitions because the garden was ripe with produce and if I wasn't working I needed to be preserving the harvest. I felt I didn't have time for extra days off, in addition to Shabbat. Finally, it occurred to me that might be exactly why YHWH positioned the feasts when he did. Because he knew we wouldn't make time to rest in the midst of the harvest. Surely he anticipated what a hectic time of year this is for an agriculturally driven society. He is taking care of us, making sure when get rest even when we don't look out for ourselves.
Slowing down for the feasts is a natural and lovely transition between seasons. It is a time to let go of the frantic pace of summer, refocus on YHWH and embrace this new, slower season.
Rest. Remembrance. Shofar. Offering.
Let's get ready for this new year! We are just two weeks away!