The ancient middle eastern calendar was lunar. The moon changed at regular intervals, and therefore was the dominant fixture in the sky. The month began at the moment when, following the period of invisibility due to nearness of the sun, the lunar crescent appears again briefly on the western horizon just after sunset.
A ‘year’ referred to a season, not 364 days as our current calendar does. The 'new year' or Akitu, was at the spring and fall equinox. In addition to the seasonal cycle and the lunar cycle, the Mesopotamians were affected by a third cycle –the cycle between the equinoxes, a period when the sun and moon vied with each other for time in the sky.
The Babylonians divided the seasonal year into two periods, each beginning in the month of an equinox. The summer (emesh), the hot season, or the harvest season, began around March. The winter (enten) or the cold season began around September. The impact of the solstices, however, was also understood, though they did not define the year to the extent the equinoxes did. In the 1st millennium BC, Babylonia goddesses of the Ezisa and the Esagil temples exchanged placed on the 11th of the fourth month and on the 3rd of the tenth month (approximately the time of the solstices) as a remedy to increase the daylight in the winter or to lengthen the nights in the summer. The year was summarized by the weather patterns, in quarters, not halves: months 1-3: wind and bad weather; months 4-6: harvest and heat; months 7-9: wind and bad weather; months 10-12: cold.
Rainy season began around September, resulting in the sporadic flooding of the Tigris and Euphrates rivers from Nov through March. The main flooding occurred in April and May, the two rivers being swollen by the winter rains and snows in the mountains of Turkey. The winter months were a time of the brazier festival (kinanum), ceremonies presumably to combat the cold, and festivals of the storm-gods, such as Ninurta, hurling lightning, vanquishing the anzu-bird and the asakku-demon of the story mountains. After the winter rains subsided, the dry season set in, culminating with the very hot and dry months of July and August, when the parched and merciless steppe seemed to be a place of death and demons. These hot summer months were the time throughout Mesopotamia for the cult of the dead Dumuzi, who, as the embodiment of the power in the grain, had disappeared –the grain had already been harvested and the new seeds not yet sown.