Rosh Hashanah, Jewish new year

Hebrew calendar is a lunisolar calendar

Originally, the date of Rosh Hashanah was determined based on observation of the new moon ("molad"), and thus could fall on any day of the week. However, around the third century CE, the Hebrew calendar was fixed, such that the first day of Rosh Hashanah never falls out on Sunday, Wednesday, or Friday.

Rosh Hashanah occurs 163 days after the first day of Passover, and thus is usually (but not always) determined by the new moon closest to the autumnal equinox.

It also based on metonic cycle

Nisan is the first month of the ecclesiastical year and the seventh month (eighth, in leap year) of the civil year in the Hebrew calendar. ,

Tishrei is the first month of the civil year and the seventh month of the ecclesiastical year the Hebrew calendar and has 30 Days in it. Tishrei usually occurs in September – October on the civil calendar.

Lunisolar calendar:

The Chinese, Coligny and Hebrew lunisolar calendars track more or less the tropical year whereas the Buddhist and Hindu lunisolar calendars track the sidereal year. 

Therefore, the first three give an idea of the seasons whereas the last two give an idea of the position among the constellations of the full moon. The Tibetan calendar was influenced by the Buddhist calendar.

Calendar according to book of Enoch:

Season of the year. The four teḳufot are: 

(1) Teḳufat Nisan, the vernal equinox (March 21), when the sun is direct above the equator enters  Aries; (now is Pisces) this is the beginning of spring, or "'et hazera'" (seed-time), when day and night are equal;  Day ( northern hemisphere) is getting longer after vernal equinox 

(2) Teḳufat Tammuz, the summer solstice (June 21), when the sun enters Cancer; this is the summer season, or "'et ha-ḳaẓir" (harvest-time), when the day is the longest in the year;

 (3) Teḳufat Tishri, the autumnal equinox (Sept. 23), when the sun enters Libra, and autumn, or "'et ha-haẓir" (vintage-time),  when this Sun ia above equator begins, and when the day again equals the night; Days are getting shorter ( northern hemisphere) afterwards 

(4) Teḳufat Ṭebet, the winter solstice (Dec. 22), when the sun enters Capricornus; this is the beginning of winter, or "'et ha-ḥoref"(stripping-time), when the night is the longest during the year. Each teḳufah, according to Samuel Yarḥinai, marks the beginning of a period of 91 days and 7½ hours.

It will be noticed that the teḳufot fall from fourteen to eighteen days later than the true solar equinox or solstice; this, however, does not interfere with the calendar, which follows the figures of R. Ada.

IMHO, It's more meaningful to align Tekufot with position of Sun,  rather than beginning of seasons

Reference 

Observe the month of Aviv and celebrate the Passover of the LORD your God, because in the month of Aviv he brought you out of Egypt by night.

Deuteronomy 16:1

1 On the first day of the seventh month hold a sacred assembly and do no regular work. It is a day for you to sound the trumpets. 

2 As an aroma pleasing to the Lord, offer a burnt offering of one young bull, one ram and seven male lambs a year old, all without defect. 

3 With the bull offer a grain offering of three-tenths of an ephah of the finest flour mixed with olive oil; with the ram, two-tenths; 

4 and with each of the seven lambs, one-tenth. 

5 Include one male goat as a sin offeringto make atonement for you. 

6 These are in addition to the monthly and daily burnt offerings with their grain offerings and drink offerings as specified. They are food offerings presented to the Lord, a pleasing aroma.

Numbers 29:1-:6

wiki 

Akhlah

Lunisolar calendar wiki 

Chabad

Tekufah 

Tekufah in Dead sea scrolls , 2 , 364-day calendar, Qumran sect, Essene calendar

Enoch calendar , 2 book of Enoch

Tekufah is spring equinox?

Hillel II 

Online cal in JavaScript 

5761 A.M. Hebrew year id Gregorian year 1 Jan 2001